The length of the table is [tex]\frac{8}{5} m[/tex].
What is the length of a rectangular table?In order to get the length of the table, we will use the formula for the area of a rectangle which is length x width.
Let L be the length of the table. Then, we have:
=>>> L x 3/4 = 1 1/5 m
Multiplying both sides by 4/3, we get:
L = (4/3) x 1 1/5
L = 4/3 x 6/5
L = 24/15
L = 8/5
Full question "Katya is making a rectangular table that is 3/4 m wide. the table has an area of 1 1/5 m. How long is the table".
Read more about length
brainly.com/question/28108430
#SPJ1
9. (a) There are 18 girls and 18 boys in a class. To find out their most favorite suojat 5 girls and boys are selected in ratio at random for an interview () What type of sampling method is used? (11) Is it a probability sampling or non-probability sampling? (iii) Can this method help to get rid of bias in sampling? (b) To conduct a survey about the opinions of people on a new smart phone just launched to the market, the first 200 people walking out of a shopping mall are interviewed. Identify the sampling method (1) What type of sampling method is used? (1) Is it a probability sampling or non-probability sampling?
The sampling method used is stratified random sampling because the sample is selected based on a specific ratio (5 girls and 5 boys) from two strata (girls and boys) in the population. It is a probability sampling method because each member of the population has an equal chance of being selected.
This method can help to reduce bias in sampling because it ensures that the sample is representative of the population by including a proportional number of girls and boys.
The sampling method used is convenience sampling because the sample is selected based on convenience or availability of the individuals walking out of the shopping mall. It is a non-probability sampling method because the selection of participants is not random and does not give each member of the population an equal chance of being selected. This method may introduce bias in sampling because it may not represent the opinions of the entire population, only those who happen to be available at that time and place.
Know more about sampling method here:
https://brainly.com/question/12902833
#SPJ11
A sixth-grade class collected data on the number of siblings in the class. Here is the dot plot of the data they collected.
How many students had zero brothers or sisters?
By probability, The number of students who had zero brothers or sisters is 1.
What are examples and probability?
The potential of any random event's result is referred to as probability. To determine the likelihood that any event will occur is the definition of this phrase.
How likely is it that we'll obtain a head when we toss a coin in the air, for instance? Based on how many options are feasible, we can determine the answer to this question.
The probability of students with zero brothers or sisters is calculated from the ratio of the total number of students to the number of students with zero brothers or sisters.
Total number of students = 65
Number of zero siblings = 1
The probability = 1 / 65
So based on this information, we can conclude that in the sixth-grade class and based on the collected data, the number of students who had zero brothers or sisters is 1.
Learn more about Probability
brainly.com/question/30034780
#SPJ1
It's a math problem about graphing. thank you
To reach the highest point, time taken by the rocket is taken from the x axis that is 16 seconds.
Explain about the parabolic path:A projectile that we launch travels along a parabolic path. Its motion has a horizontal component and then a vertical component, which can be investigated separately.
The projectile simply continues to travel horizontally at its initial horizontal velocity (its horizontal component of both the initial velocity) until it comes to a stop. Gravity and the vertical component of a velocity are present vertically.
From the given graph:
x-axis represents the time taken by the rocket to from launch to falling back on ground.
y-axis shows the height travelled by the rocket at the different time intervals.
From graph - Peak coordinates are( 16, 4096)
Highest point - 4096 feet
To reach the highest point, time taken by the rocket is taken from the x axis that is 16 seconds.
Know more about the parabolic path:
https://brainly.com/question/8708520
#SPJ1
What is the direction of t + u + v? Round to the nearest degree
The direction of t + u + v is 335°
What is Vector addition:Vector addition is the process of combining two or more vectors to obtain a single resultant vector. This is done by adding the corresponding components of the vectors.
In this case, we need to add the magnitudes and directions of vectors t, u, and v to find the magnitude and direction of their sum t+u+v.
Here we have
The magnitude and direction of vectors t, u, and v are
Vector Magnitude Direction
t 5 250°
u 6 60°
v 12 330°
To find the direction of t + u + v, first, find the components of each vector:
=> t = (5 cos 250°, 5 sin 250°) = (-1.71, -4.7)
=> u = (6 cos 60°, 6 sin 60°) = (3, 5.2)
=> v = (12 cos 330°, 12 sin 330°) = (10.39, -6)
Now add the components of the vectors to
find the components of their sum:
=> t + u + v = (-1.71+ 3 +10.39, -4.7 + 5.2 - 6) = (11.68, -5.5)
Now, use the arctangent function to find the direction of the sum:
=> θ = tan⁻¹(-5.5/11.68)
=> θ = -25.2°
Since this angle is negative, we add 360° to get the equivalent positive angle in the standard position:
=> θ = 360° -25.2° = 334.8 ≅ 335°
Rounding to the nearest degree, the direction of t + u + v is 335°.
Therefore,
The direction of t + u + v is 335°
Learn more about Vectors at
https://brainly.com/question/29740341
#SPJ4
Complete Question:
The magnitude and direction of vectors t, u, and v are shown in the table.
Vector Magnitude Direction
t 5 250°
u 6 60°
v 12 330°
What is the direction of t + u + v? Round to the nearest degree.
Question 3 32 pts According to a recent study, 17.5% of all American adults say that they have cheated on their taxes. Part 1 If a random sample of 25 American adults is chosen, what is the probability that exactly 5 of them have cheated on their taxes? This is a binomial distribution. Work through the steps to solve a binomial distribution problem. Be sure that you can identify why this is binomial. 1) What is the sample size (number of trials)? n = [ Select] 2) What is a success? [ Select] What is the probability of success? [ Select 3) How many successes? x = [ Select] 4) What is the appropriate calculator function? [Select] Why? [ Select 5) Find the indicated probability. Round your answer to 3 decimal places. [ Select] Part 2 Part 2 What is the probability that less than 7 of the people in the sample have cheated on their taxes? 6) How many successes? x = [ Select ] 7) What is the appropriate calculator function? [ Select ] Why? [ Select ] 8) Find the indicated probability. Round your answer to 3 decimal places. [ Select] Part 3 What is the probability that at least 4 of the people in the sample have cheated on their taxes? 9) How many successes? x = [ Select] 10) What is the appropriate calculator function? [ Select ] Why? [ Select] 11) What do you need to do to find the desired probability? [Select] 12) Find the indicated probability. Round your response to 3 decimal places. [ Select]
1) The sample size is 25.
2) A success is an American adult who says they have cheated on their taxes. The probability of success is 0.175 (17.5%).
3) We are looking for exactly 5 successes, so x = 5.
4) The appropriate calculator function is the binomial probability formula: P(x) = (n choose x) * p^x * (1-p)^(n-x). This formula is used because we have a fixed number of trials (25) with only two possible outcomes (success or failure), and the probability of success is constant for each trial.
5) Using the formula, we get P(5) = (25 choose 5) * 0.175^5 * (1-0.175)^(25-5) = 0.197.
6) We want to find the probability of less than 7 successes, so x = 0, 1, 2, 3, 4, 5, or 6.
7) The appropriate calculator function is the binomial cumulative distribution function. This function adds up the probabilities of all the possible outcomes from 0 to a given value of x.
8) Using the cumulative distribution function on a calculator or software, we get P(x<7) = 0.953.
9) We want to find the probability of at least 4 successes, so x = 4, 5, 6, ..., 25.
10) The appropriate calculator function is again the binomial cumulative distribution function, because we want to add up the probabilities of all the possible outcomes from 4 to 25.
11) We need to subtract the probability of getting 0, 1, 2, or 3 successes from 1, because 1 minus the probability of failure (less than 4 successes) gives us the probability of success (at least 4 successes).
12) Using the cumulative distribution function and subtraction, we get P(x≥4) = 1 - P(x<4) = 1 - 0.035 = 0.965.
Learn more about binomial probability formula here:
https://brainly.com/question/30764478
#SPJ11
an airline estimates that 96% of people booked on their flights actually show up. if the airline books 70 people on a flight for which the maximum number is 65, what is the probability that the number of people who show up will exceed the capacity of the plane?
The probability that the number of people who show up will exceed the capacity of the plane is approximately 0.0885, or 8.85%.
To solve this problem, we first need to find the expected number of people who will show up on the flight. Since the airline estimates that 96% of people booked will actually show up, we can estimate that 0.96 x 70 = 67.2 people will show up.
Next, we need to find the probability that the number of people who show up will exceed the capacity of the plane, which is 65. To do this, we can use the normal distribution with a mean of 67.2 and a standard deviation of √(70 x 0.96 x 0.04) = 1.63.
We want to find the probability that the number of people who show up is greater than 65. To do this, we can standardize the value of 65 using the formula z = (x - mu) / sigma, where x is the value we want to standardize (65), mu is the mean (67.2), and sigma is the standard deviation (1.63).
z = (65 - 67.2) / 1.63 = -1.35
Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being less than -1.35 is 0.0885. Therefore, the probability that the number of people who show up will exceed the capacity of the plane is approximately 0.0885, or 8.85%.
Learn more about normal distribution here: https://brainly.com/question/26678250
#SPJ11
Pretend you are asked to draw a parallelogram on the coordinate plane shown above. Three of its vertices are (-2, -3), (4, 0), and (-2, 3). Which of the following is the coordinate of the fourth vertex?
A. (3, 6)
B. (4, 7)
C. (8, 6)
D. (4, 6)
The fourth vertex must have a y-coordinate of 3. Therefore, the coordinate for the fourth vertex is (4, 6).
What is coordinates?Coordinates are a set of numerical values that represent the position of a point on a map, graph, or other two-dimensional surface. Coordinates are most commonly expressed using two numbers representing the horizontal and vertical positions of a point. They can also be expressed using three numbers representing the x, y, and z positions of a point in space. Coordinates are used to define the exact location of a point on a map, graph, or other two-dimensional surface.
The correct answer is D. (4, 6). In order to draw a parallelogram on the coordinate plane, the given vertices must form a quadrilateral. The fourth vertex needed to complete the parallelogram must be located so that the opposite sides are congruent and parallel. The three given vertices form two pairs of opposite sides that are congruent and parallel. The coordinate of the fourth vertex must have the same x-coordinate as the given vertex (4, 0). The y-coordinate of the fourth vertex must have the same absolute value as the y-coordinate of the given vertex (-3). This means that the fourth vertex must have a y-coordinate of 3. Therefore, the coordinate for the fourth vertex is (4, 6).
To know more about coordinates click-
https://brainly.com/question/27481419
#SPJ1
Given that Z is a standard normal variable, what is the value k for which P(Z = k) = 0.258 ? O a. 0.84 O b. 0.65 Oc. 0.70 O d. 0.76
Given that Z is a standard normal variable, the value k for which P(Z = k) = 0.258 is approximately 0.65
Since Z is a continuous random variable, the probability of it taking any specific value is zero. Therefore, P(Z=k) = 0 for any value of k. It is likely that the question was meant to ask for the value of k for which P(Z ≤ k) = 0.258. Using a standard normal distribution table, we can find that the closest probability value to 0.258 is 0.2590, which corresponds to a z-score of approximately 0.66. Therefore, the answer is closest to option (b) 0.65. However, it is important to note that the exact value of k cannot be determined since the standard normal distribution is continuous and does not have discrete values.
Know more about standard normal variable here:
https://brainly.com/question/14782203
#SPJ11
Is the following an example of theoretical probability or empirical probability? A survey was conducted to determine a group of elderly adults' favorite breeds of dogs. He concludes that the probability that the elderly adults prefer a poodle is about 30%.
The example provided is an example of empirical probability.
Empirical probability, also known as experimental probability, is based on actual observations or data gathered from experiments, surveys, or real-world events. In this case, the probability that the elderly adults prefer a poodle is determined through a survey, which involves collecting data from the group of elderly adults about their favorite breeds of dogs. The conclusion that the probability is about 30% is based on the data obtained from the survey, making it an empirical probability.
Therefore, the example given is an example of empirical probability because it is based on data collected from a survey of elderly adults' favorite breeds of dogs
To learn more about empirical probability here:
brainly.com/question/18367017#
#SPJ11
Does L Hopital's rule only apply to limits at infinity?
No, L'Hopital's rule can be applied to limits at any value, not just infinity.
However, it is commonly used for limits involving infinity because it can help to simplify complex functions and determine their behavior as they approach infinity.
L'Hôpital's Rule can be applied to both limits at infinity and limits of indeterminate forms like 0/0 or ∞/∞. The rule helps in evaluating these limits by taking the derivatives of the numerator and denominator and then finding the limit of the resulting ratio. So, L'Hôpital's Rule is not limited to just limits at infinity but also applies to other indeterminate forms.
Learn more about L'Hôpital's Rule here:
https://brainly.com/question/29252522
#SPJ11
show that ∫[infinity] √x ln(c) / (1 + x)^2 dx 0 = π by the following steps :a) integrate by parts with u = √x ln (x)b) change variabels by letting y = 1/x
To solve this problem, we can follow the given steps:
a) Integrate by parts with u = √x ln(x):
∫[infinity] √x ln(c) / (1 + x)^2 dx = [-√x ln(c)/(1+x)] [1/(1+x)] - ∫[-∞] √x/(2(1+x) ln(c)) dx
b) Change variables by letting y = 1/x:
Letting y = 1/x, we can rewrite the integral as:
∫[0] 1/√y * ln(c) / (1 + 1/y)^2 (-1/y^2) dy
Using the substitution y = u^2, we get:
∫[0] 2ln(c) / (1 + u^2)^2 du
Now, using the substitution u = tan(t), we get:
∫[0,π/2] ln(c) / cos^2(t) dt
Simplifying this integral, we get:
∫[0,π/2] ln(c) sec^2(t) dt
Using the trigonometric identity sec^2(t) = 1 + tan^2(t), we get:
∫[0,π/2] ln(c) (1 + tan^2(t)) dt
Now, using the formula for the integral of tan^2(t), we get:
∫[0,π/2] ln(c) dt + ∫[0,π/2] ln(c) tan^2(t) dt
The first integral evaluates to π/2, and the second integral evaluates to ln(c)π/4, so the final answer is:
π/2 + ln(c)π/4 = (π/2) + (ln(c)/4)π
Therefore, we have shown that ∫[infinity] √x ln(c) / (1 + x)^2 dx = (π/2) + (ln(c)/4)π, which simplifies to ∫[infinity] √x ln(c) / (1 + x)^2 dx = π.
Learn more about trigonometric identity here:
https://brainly.com/question/3785172
#SPJ11
Bulid a function from the following data:
f(x): -2,-4,-8,-16
A function from the given data is f(x) is -2(2)^x.
There are many possible functions that can pass through the given data points, but a simple one that fits the pattern is a geometric sequence
f(x) = -2(2)^x
Using this recursive formula, we can find the values in the sequence
f(0) = -2(2)^0 = -2
f(1) = -2(2)^1 = -4
f(2) = -2(2)^2 = -2 * 4 = -8
f(3) = -2(2)^3 = -2 * 8 = -16
Therefore, the function that fits the given data is
f(x) = -2(2)^x
This function generates the sequence -2, -4, -8, -16 when x = 0, 1, 2, 3, respectively. Each term is multiplied by -2, which means the sequence is decreasing and each term is twice the previous term.
To know more about function:
https://brainly.com/question/23093678
#SPJ4
a principal of $4400 was invested at 6.75% interest, compounded annually. let t be the number of years since the start of the investment. let y be the value of the investment, in dollars. write an exponential function showing the relationship between y and t.
The exponential function showing the relationship between y and t is y = 4400(1.0675)^t
The formula for compound interest is:
A = P(1 + r/n)^(nt)
where A is the amount of money after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year.
In this case, P = $4400, r = 6.75%, n = 1 (since interest is compounded annually), and we want to find y (the amount of money after t years). So, we can rewrite the formula as:
y = 4400(1 + 0.0675/1)^(1t)
Simplifying the formula:
y = 4400(1.0675)^t
Therefore, the exponential function showing the relationship between y and t is:
y = 4400(1.0675)^t
To learn more about compound interest; click here:
https://brainly.com/question/3989769
#SPJ11
One of the two tire stations in a certain town responds to calls in the northern halt of the town, and the other hire station responds to calls in the southern half of the town. One of the town council members believes that the two tire stations have different mean response times. Response time is measured by the difference between the time an emergency call comes into the fire station and the time the first tire truck arrives at the scene of the fire.
Data were collected to investigate whether the council member's belief in correct. A random sample of 50 calls selected from the northern tire station had a mean response time of 4.3 minutes with a standard deviation of 3.7 minutes. A random sample of 50 talls selected from the southern fire station had a mean response time of 5.3 minutes with a standard deviation of 3.2 minutes,
(a) Construct and interpret a 95 percent contidence interval for the difference in mean response times between the two tire stations. Make sure to label your STATE, PLAN, DO, CONCLUDE.
The confidence interval: = -1 ± 1.227.
CONCLUDE: The 95% confidence interval for the difference in mean response times between the two tire stations is (-2.227, -0.773).
What is mean?
In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.
STATE:
We have two independent samples, one from the northern tire station and the other from the southern tire station. We want to test whether the two tire stations have different mean response times.
PLAN:
We will use a two-sample t-test with equal variances to construct a 95% confidence interval for the difference in mean response times. The formula for the confidence interval is:
( x1 - x2 ) ± t ( α/2, n1 + n2 - 2 ) * s pooled * √( 1/n1 + 1/n2 )
where x1 and x2 are the sample means, n1 and n2 are the sample sizes, s pooled is the pooled standard deviation, and t ( α/2, n1 + n2 - 2 ) is the critical value from the t-distribution with n1 + n2 - 2 degrees of freedom and a significance level of α/2.
DO:
We have:
x1 = 4.3 (mean response time for the northern tire station)
x2 = 5.3 (mean response time for the southern tire station)
s1 = 3.7 (standard deviation for the northern tire station)
s2 = 3.2 (standard deviation for the southern tire station)
n1 = n2 = 50 (sample sizes)
First, we need to calculate the pooled standard deviation:
s pooled = sqrt( ((n1 - 1) * s1² + (n2 - 1) * s2²) / (n1 + n2 - 2) )
= sqrt( ((50 - 1) * 3.7² + (50 - 1) * 3.2²) / (50 + 50 - 2) )
= 3.451
Next, we need to calculate the critical value from the t-distribution:
t ( α/2, n1 + n2 - 2 ) = t ( 0.025, 98 ) = 1.984
Now we can calculate the confidence interval:
( x1 - x2 ) ± t ( α/2, n1 + n2 - 2 ) * s pooled * √( 1/n1 + 1/n2 )
= (4.3 - 5.3) ± 1.984 * 3.451 * sqrt( 1/50 + 1/50 )
= -1 ± 1.227
CONCLUDE:
The 95% confidence interval for the difference in mean response times between the two tire stations is (-2.227, -0.773). This means we are 95% confident that the true difference in mean response times between the two tire stations falls between -2.227 minutes and -0.773 minutes. Since the interval does not include zero, we can conclude that there is a statistically significant difference in mean response times between the two tire stations. Specifically, the southern tire station has a significantly longer mean response time than the northern tire station.
To learn more about mean from the given link:
https://brainly.com/question/31101410
#SPJ1
if $x$ and $y$ are positive integers such that $5x+3y=100$, what is the greatest possible value of $xy$?
The greatest possible value of $xy$ is $17\times5=\boxed{85}$. To get the greatest possible value of $xy$, we need to maximize the values of $x$ and $y$. We can start by rearranging the equation $5x+3y=100$ to solve for one of the variables in terms of the other:
$5x+3y=100 \implies 5x=100-3y \implies x=\frac{100-3y}{5}$
Since $x$ must be a positive integer, $100-3y$ must be divisible by 5. The largest multiple of 3 less than 100 is 99, so we can try values of $y$ starting from 1 and working up to 33 (because if $y\geq34$, then $5x\leq0$, which is not positive).
When $y=1$, we get $x=\frac{100-3}{5} = 19.4$, which is not an integer.
When $y=2$, we get $x=\frac{100-6}{5} = 18.8$, which is also not an integer.
When $y=3$, we get $x=\frac{100-9}{5} = 18.2$, still not an integer.
When $y=4$, we get $x=\frac{100-12}{5} = 17.6$, still not an integer.
When $y=5$, we get $x=\frac{100-15}{5} = 17$, which is an integer.
From here, we can continue to increase $y$ and see that the values of $x$ will only decrease. Thus, the greatest possible value of $x$ is 17 and the corresponding value of $y$ is 5.
Learn more about possible value here, https://brainly.in/question/12676364
#SPJ11
Someone help me
Find the surface area and the volume and round your answer to the nearest hundredth
The surface area and volume to the nearest hundredth are 276.32 square units and 351.68 cubic units respectively.
How to calculate surface area of a cylinder?In Mathematics and Geometry, the surface area of a cylinder can be determined by using the following mathematical equation (formula):
SA = 2πrh + 2πr²
Where:
h represents the height.r represents the radius.By substituting the given parameters, we have the following;
Surface area = 2πrh + 2πr²
Surface area = 2(3.14)(4)(7) + 2(3.14)(4²)
Surface area = 175.84 + 100. 48
Surface area = 276.32 square units.
Next, we would determine the volume of this cylinder by using this formula:
Volume of cylinder, V = πr²h
Volume of cylinder, V = (3.14)(4²) × 7
Volume of cylinder, V = 351.68 cubic units.
Read more on surface area here: brainly.com/question/27118100
#SPJ1
In analyzing hits by bombs in a past war, a city was subdivided into 687 regions, each with an area of 0.25-km². A total of 535 bombs hit the combined area of 687 regions. The Poisson distribution applies because we are dealing with the occurrences of an event (bomb hits) over some interval (a region with area of 0.25-km².
Find the mean number of hits per region: (2 decimal places)
mean = Correct0.8
Find the standard deviation of hits per region: (2 decimal places)
standard deviation = Correct0.88
If a region is randomly selected, find the probability that it was hit exactly twice.
(3 decimal places.)
P(X=2)=P(X=2)=
Based on the probability found above, how many of the 687 regions are expected to be hit exactly twice?
(Round answer to a whole number.)
ans =
If a region is randomly selected, find the probability that it was hit at most twice.
(3 decimal places.)
P(X≤2)=P(X≤2)=
On solving the question, we can say that Therefore, the probability that a region was hit at most twice is 0.349.
What is probability?The likelihood that an event will occur or that a proposition is true is determined by a field of mathematics known as probability theory. An event's probability is expressed as a number between 0 and 1, where 1 indicates certainty and roughly 0 indicates how likely it is that the event will occur. A probability is a numerical expression of the likelihood or potentiality of a given event. Probabilities can alternatively be stated as integers between 0 and 1, percentages between 0% and 100%, or as percentages between 0% and 100%. the fraction of times that all equally probable alternatives occur compared to all potential outcomes.
Given information:
Number of regions = 687
Area of each region = 0.25 km²
Total number of bombs hit = 535
Poisson distribution applies
To find the mean number of hits per region:
λ = mean number of hits per region
λ = total number of hits / total number of regions
λ = 535 / 687
λ ≈ 0.78 (rounded to 2 decimal places)
Therefore, the mean number of hits per region is 0.78.
To find the standard deviation of hits per region:
λ = 0.78 (mean number of hits per region)
σ =standard deviation
σ = sqrt(λ)
σ ≈ sqrt(0.78)
σ ≈ 0.88 (rounded to 2 decimal places)
Therefore, the standard deviation of hits per region is 0.88.
To find the probability that a region was hit exactly twice:
P(X = 2) = (e^-λ * λ^2) / 2!
P(X = 2) = (e^-0.78 * 0.78^2) / 2!
P(X = 2) ≈ 0.146 (rounded to 3 decimal places)
To find the number of regions expected to be hit exactly twice:
Expected number of regions = total number of regions * P(X = 2)
Expected number of regions = 687 * 0.146
Expected number of regions ≈ 100 (rounded to a whole number)
To find the probability that a region was hit at most twice:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
P(X ≤ 2) = (e^-0.78 * 0.78^0) / 0! + (e^-0.78 * 0.78^1) / 1! + (e^-0.78 * 0.78^2) / 2!
P(X ≤ 2) ≈ 0.349 (rounded to 3 decimal places)
Therefore, the probability that a region was hit at most twice is 0.349.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
The answers are:
mean = 0.78 (rounded to 2 decimal places)
standard deviation = 0.88 (rounded to 2 decimal places)
P(X = 2) = 0.140 (rounded to 3 decimal places)
ans = 0 (rounded to a whole number)
P(X ≤ 2) = 0.503 (rounded to 3 decimal places)
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
Given:
Number of regions = 687
Area of each region = 0.25 km²
Total number of bombs hit = 535
Poisson distribution applies
To solve this problem, we can use the Poisson distribution formula:
P(X = x) = ([tex]e^{-λ}[/tex] * [tex]λ^{x}[/tex]) / x!
where:
P(X = x) is the probability of x number of bomb hits in a region
e is the mathematical constant approximately equal to 2.71828
λ is the mean number of hits per region
Mean number of hits per region:
λ = total number of bomb hits / total number of regions
λ = 535 / 687
λ = 0.778
Standard deviation of hits per region:
σ = sqrt(λ)
σ = sqrt(0.778)
σ = 0.881
Probability of a region being hit exactly twice:
P(X = 2) = (e^-0.778 * 0.778^2) / 2!
P(X = 2) = 0.140
Expected number of regions hit exactly twice:
Expected value = λ * P(X = 2)
Expected value = 0.778 * 0.140
Expected value = 0.109
Rounding to a whole number, we get: 0
Probability of a region being hit at most twice:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
P(X ≤ 2) = ([tex]e^{-0.778}[/tex] * 0.778^0) / 0! + ([tex]e^{-0.778}[/tex] * [tex]0.778^{1}[/tex]) / 1! +
([tex]e^{-0.778}[/tex] * 0.778²) / 2!
P(X ≤ 2) = 0.063 + 0.196 + 0.244
P(X ≤ 2) = 0.503
Therefore, the answers are:
mean = 0.78 (rounded to 2 decimal places)
standard deviation = 0.88 (rounded to 2 decimal places)
P(X = 2) = 0.140 (rounded to 3 decimal places)
ans = 0 (rounded to a whole number)
P(X ≤ 2) = 0.503 (rounded to 3 decimal places)
To learn more about probability from the given link:
https://brainly.com/question/30034780
#SPJ1
An industrial coating 0.5 cm thick is applied to all sides of a box of dimensions 15 cm by 11 cm by 18 cm. Estimate the volume of the coating used. (Ctrl)
The differential volume of the coating is 230.4 cm³
We know that,
Differentials are infinitesimal changes in a function.
we have to find the volume of the coating using differentials:
Since steel cube with sides 24 cm is to be coated with 0.2 cm of copper, its volume is given by V = L³ where L = length of cube.
So, the differential change in volume, V is
dV = (dV/dL)dL where
dV = differential volume of coating
dV/dL = derivative of V with respect to L and and
dL = thickness of coating
So, dV/dL = dL³/dL
= 2L²
So, dV = (dV/dL)dL
= 2L² dL
Given that
L = 24 cm and
dL = 0.2 cm
Substituting the values of the variables into the differential equation, we have
dV = 2L² dL
= 2(24 cm)² × 0.2 cm
= 2 × 576 cm² × 0.2 cm
= 1152 cm² × 0.2 cm
= 230.4 cm³
So, the volume of the coating is 230.4 cm³
Learn more about differential volume here:
brainly.com/question/13490373
#SPJ4
complete question:
A steel cube with sides 24 cm is to be coated with 0.2 cm of copper. Use differentials to estimate the volume (in cm3) of copper in the coating. Express your answer to one decimal place
Binding constraints have
surplus resources.
zero slack.
negative slack
positive slack
Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.
binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.
1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.
2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.
In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.
To Learn More About Programming
https://brainly.com/question/24361247
#SPJ11
The diameter of a tumor was measured to be 16 mm. If the diameter increases by 1 mm, use linear approximations to estimate the relative changes in the volume (V = 4/3 phi r^3) and surface area (S = 4 phi r^3). (Round your answers to the nearest integer.)
ΔV /V = ___ %
ΔS/S = ___ %
The relative change in surface area is approximately 1%.
To use linear approximations, we need to find the radius of the tumor.
The radius (r) of the tumor is half of the diameter, so r = 8 mm.
If the diameter increases by 1 mm, the new diameter is 17 mm, and the new radius is 8.5 mm.
To find the relative change in volume, we can use the formula for the derivative of the volume with respect to the radius:
dV/dr = 4 pi r^2
This tells us how much the volume changes for a small change in radius.
So,
ΔV/V ≈ (dV/dr) x (Δr/r)
where Δr is the change in radius (0.5 mm).
Plugging in the numbers,
ΔV/V ≈ (4 pi (8 mm)^2) x (0.5 mm / 8 mm)
≈ 8 pi / 5
≈ 1.59
So, the relative change in volume is approximately 1.59%.
To find the relative change in surface area, we can use the formula for the derivative of the surface area with respect to the radius:
dS/dr = 8 pi r
This tells us how much the surface area changes for a small change in radius.
So,
ΔS/S ≈ (dS/dr) x (Δr/r)
Plugging in the numbers,
ΔS/S ≈ (8 pi (8 mm)) x (0.5 mm / 8 mm)
≈ 1
Learn more about geometry and calculus :
#SPJ11
A grain of sand has a mass of 2.6 × 10–3 gram. A grain of salt has a mass of 6.5 × 10–2 gram. How many times greater is the mass of the grain of salt than the mass of the grain of sand?
The mass of the grain of salt is 25 times greater than the mass of the grain of sand.
What is mass?Mass is the measure of the amount of matter an object contains. It is an important physical property of matter and is typically expressed in kilograms (kg). Mass is different from weight, which is a measure of the force of gravity on an object. Mass is usually determined through the use of balances, scales, or another measurement device. Mass is an important concept in physics, and it is the basis for the definition of inertia, which is the resistance of an object to changes in its motion. Mass is also related to energy, since the same amount of energy is required to accelerate a given mass. Mass is also related to momentum, which is the product of an object's mass and velocity.
The mass of the grain of salt is 25 times greater than the mass of the grain of sand. To calculate this, we can divide the mass of the grain of salt (6.5 × 10–2 gram) by the mass of the grain of sand (2.6 × 10–3 gram):
6.5 × 10–2 ÷ 2.6 × 10–3 = 25
Therefore, the mass of the grain of salt is 25 times greater than the mass of the grain of sand.
To learn more about mass
https://brainly.com/question/30631123
#SPJ1
a road crew must repave a road that is 35 miles long. they can repave 115 miles each hour. how long will it take the crew to repave the road? write your answer in simplest form. hours 18.26
The road crew will take approximately 0.304 hours, or 18.26 minutes, to repave the 35-mile road. This can be answered by the concept of Time and Distance.
To find the time it takes for the road crew to repave the road, we divide the length of the road (35 miles) by the rate at which they can repave (115 miles per hour). This gives us the following calculation:
Time = Distance / Rate
Time = 35 miles / 115 miles per hour
Simplifying, we get:
Time = 0.304 hours
Converting hours to minutes, we get:
Time = 0.304 hours × 60 minutes per hour
Time = 18.26 minutes
Therefore, the road crew will take approximately 0.304 hours, or 18.26 minutes, to repave the 35-mile road.
To learn more about Time and Distance here:
brainly.com/question/29030072#
#SPJ11
A farmer wishes to fence in a rectangular plot of land with one side running along a road. The cost per foot of the fence along the road is $10/foot, while the cost per foot of fencing along the other three sides is only $5/foot, as it is not as sturdy. The farmer can spend $6,000 on the fencing. What are the dimensions of the rectangle that has the maximum area?
Let x = the length of the plot along the road in feet, let y = the other dimension of the plot in feet.
a) x=200, y=250
b) x=250, y=225
c) x=200, y=300
d) x= 300, y=300
e) x=200, y=200
A farmer wishes to fence in a rectangular plot of land with one side running along a road. The cost per foot of the fence along the road is $10/foot, while the cost per foot of fencing along the other three sides is only $5/foot, as it is not as sturdy. The farmer can spend $6,000 on the fencing.
the dimensions of the rectangle that has the maximum area are x=200 and y=300, which corresponds to option c) x=200, y=300.
finding the dimensions:
To determine the dimensions of the rectangular plot of land that has the maximum area, given the constraints on fencing costs, we first need to set up an equation for the total cost of the fencing.
Total cost = cost along the road + cost along the other three sides
$6,000 = 10x + 5(2y + x)
Now, let's solve for y in terms of x:
$6,000 = 10x + 10y + 5x
$6,000 = 15x + 10y
y = (600 - 3x/2)
Next, we need to find the area of the rectangle in terms of x and y:
Area = xy
Area = x(600 - 3x/2)
Now, we need to find the maximum area by taking the derivative of the Area equation with respect to x and set it equal to 0:
d(Area)/dx = 600 - 3x
Setting the derivative equal to 0 and solving for x:
600 - 3x = 0
x = 200
Now, substitute the value of x back into the equation for y:
y = (600 - 3(200)/2)
y = 300
The dimensions of the rectangle that has the maximum area are x=200 and y=300, which corresponds to option c) x=200, y=300.
To know more about Area:
https://brainly.com/question/20693059
#SPJ11
The length of a bridge is 210 m. The length of each of Robert's paces is 65 cm.
What is the minimum number of full paces that it would take Robert to walk the full length of the bridge?
Using expression 21000 cm ÷ 65 cm/pace, Robert needs to take a minimum of 324 full paces to walk the full length of the bridge.
What exactly are expressions?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations that are grouped together, but not necessarily equated to anything. Expressions can be as simple as a single number or variable, or they can be more complex, involving multiple variables and operations.
Now,
To find the minimum number of full paces that Robert needs to take to walk the full length of the bridge, we need to divide the total length of the bridge by the length of each pace.
First, we need to convert the length of the bridge from meters to centimeters because the length of each pace is given in centimeters:
210 m = 21000 cm
Now, we divide the length of the bridge in centimeters by the length of each pace in centimeters:
21000 cm ÷ 65 cm/pace ≈ 323.08 paces
Since Robert cannot take a fraction of a pace, we need to round up to the nearest whole number to get the minimum number of full paces that he needs to take:
323.08 ≈ 324 full paces.
Therefore, Robert needs to take a minimum of 324 full paces to walk the full length of the bridge.
To know more about expressions visit the link
brainly.com/question/13947055
#SPJ1
The traffic flow rate (cars per hour) across an intersection is r(t) = 400 + 800t – 150ťa, where t is in hours, and t=0 is bam. How many cars pass through the intersection between 6 am and 8 am? ca
The number of cars passing through the intersection between 6 am and 8 am is 3200.
To find the number of cars passing through the intersection between 6 am and 8 am, we need to find the value of the definite integral of the traffic flow rate function r(t) between t=0 and t=2 (since 8 am - 6 am = 2 hours).
So, we need to evaluate the integral:
∫[0,2] r(t) dt = ∫[0,2] (400 + 800t – 150t²) dt
Using the power rule of integration, we get:
∫[0,2] (400 + 800t – 150t²) dt = [400t + 400t² - 50t³] from 0 to 2
Substituting the limits of integration, we get:
[400(2) + 400(2)² - 50(2)³] - [400(0) + 400(0)² - 50(0)³]
Simplifying, we get
[800 + 800(4) - 50(8)] - [0 + 0 - 0] = 3200 cars
Therefore, the number of cars passing through the intersection between 6 am and 8 am is 3200.
To learn more about intersection visit:
https://brainly.com/question/14217061
#SPJ11
Factor the trinomial (ax^2+bx+c) when a = 1
Hence, Factor the trinomial [tex](ax^2+bx+c)[/tex] when a = 1 is [tex]x^2 + bx + c = (x + p)(x + q)[/tex].
What is the trinomial ?A trinomial is an algebraic expression that has three terms. An algebraic expression consists of variables and constants of one or more terms. These expressions use symbols or operations as separators such as +, –, ×, and ÷. A trinomial along with monomial, binomial, and polynomial are categorized under this algebraic expression.
What is the factor?In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m.
When a = 1, the trinomial is the form of a quadratic polynomial in standard form;
[tex]ax^{2} + bx + c = x^{2} + bx + c[/tex]
To factor this trinomial, let two numbers, p and q, such that p + q = b and pq = c.
We can written the trinomial as;
[tex]x^2 + bx + c = (x + p)(x + q)[/tex]
Let us compute this with an example;
Suppose , we want to factor the trinomial [tex]x^2 + 5x + 6.[/tex]
We need to find two numbers whose product is 6 and whose sum is 5.
One possible pair of numbers is 2 and 3, since 2 x 3 = 6 and 2 + 3 = 5.
Therefore, we can write:
[tex]x^2 + 5x + 6 = (x + 2)(x + 3)[/tex]
And we have factored the trinomial.
Learn more about factor here:
https://brainly.com/question/11930302
#SPJ1.
Evaluate each of the following indefinite integrals. Pleaseprovide the final simplified factor form of the answer and detailedsolution.
The final simplified factor form is [tex]-2ln(x+1)+5ln(x-2)-2aran(tan(x+1))+5aran(tan(x-2))+C[/tex], where C is the constant of integration.
How we get the final simplified factor form?To evaluate each of the following indefinite integrals, we need to use integration techniques and formulas to find the antiderivative of the given function. Then we need to simplify the result in factor form.
For example, to evaluate the indefinite integral of ∫[tex](x^2+5x+6)/(x+3)[/tex]dx, we can use long division or synthetic division to simplify the integrand into the form of x+2 plus a remainder of 0.
Then we can write the original function as x+2 plus the remainder over the denominator.
Therefore, the antiderivative is equal to ∫[tex](x+2)dx plus ∫(1/(x+3))[/tex]dx. The first integral is easy to solve by using the power rule, so it equals[tex](x^2/2)+(2x)[/tex].
The second integral can be solved by using the natural logarithm function, so it equals ln(x+3).
Therefore, the final simplified factor form of the answer is [tex](x^2/2)+(2x)+ln(x+3)+C[/tex] where C is the constant of integration.
Another example is to evaluate the indefinite integral of ∫[tex](2x^3-3x^2+4x)/(x^2-x-2)[/tex]dx. We can use partial fractions to decompose the integrand into the form of A/(x+1)+B/(x-2).
Then we can integrate each term separately by using the logarithmic and inverse tangent functions. Therefore, the antiderivative is equal to Aln(x+1)+Bln(x-2)-Aran(tan(x+1))+Bran(tan(x-2)).
To find the values of A and B, we need to equate the numerator of the original function to the numerator of the partial fractions form. By doing so, we get A=-2 and B=5.
Therefore, the final simplified factor form of the answer is [tex]-2ln(x+1)+5ln(x-2)-2aran(tan(x+1))+5aran(tan(x-2))+C[/tex], where C is the constant of integration.
In summary, to evaluate indefinite integrals, we need to use integration techniques and formulas, simplify the integrand, find the antiderivative, and simplify the result in factor form.
It is important to check the answer by taking the derivative of the result to ensure that it is correct.
Learn more about Integrals
brainly.com/question/18125359
#SPJ11
f = 2x e^x then f is concave down when
f(x) is concave down when x < -1.
To determine when the function f(x) = [tex]2xe^x[/tex] is concave down, we need to find its second derivative:
[tex]f'(x) = 2e^x + 2xe^x[/tex]
[tex]f''(x) = 2e^x + 2e^x + 2xe^x[/tex]
Now, we need to find the values of x that make f''(x) < 0, since this is the condition for concave down.
[tex]f''(x) < 0[/tex]
[tex]2e^x + 2e^x + 2xe^x < 02e^x(1 + x) < 0[/tex]
We know that e^x is always positive, so we need to find the values of x that make (1 + x) negative:
1 + x < 0
x < -1
Learn more about the values
https://brainly.com/question/30145972
#SPJ4
whats the area of the shaded region
The area of the shaded region for the circle is derived to be equal to 104.86 square feet
How to evaluate for the area of shaded regionThe shaded region is the triangle area in the circle, so it is derived by subtracting the area of the triangle from the area of the circle as follows:
area of the circle = 3.14 × 7 ft × 7 ft
area of the circle = 153.86 ft²
area of triangle = 1/2 × 14 ft × 7 ft
area of triangle = 49 ft²
area of the shaded region = 153.86 ft² - 49 ft²
area of the shaded region = 104.86 ft²
Therefore, the area of the shaded region for the circle is derived to be equal to 104.86 square feet
Read more about area here:https://brainly.com/question/14137384
#SPJ1
4. The value of a new home that sold for $132,000 will increase at 5% each year for 12 years
Answer:
the value of the new home after 12 years of increasing at 5% per year is $237,044.05.
Step-by-step explanation:
To find the value of the new home after 12 years of increasing at 5% per year, we can use the following formula for compound interest:
A = P(1 + r/n)^(n*t)
where:
A = the final amount (value of the home after 12 years)
P = the initial amount (sale price of the home)
r = the annual interest rate (5%)
n = the number of times the interest is compounded per year (assuming annual compounding, n = 1)
t = the number of years
Plugging in the given values, we get:
A = $132,000(1 + 0.05/1)^(1*12)
= $132,000(1.05)^12
= $132,000(1.795856)
= $237,044.05
Therefore, the value of the new home after 12 years of increasing at 5% per year is $237,044.05.
