We have 24 possible permutations because there are four choices for the first place, three choices for the second place (as two people have already won first and second place), and two choices for the third place (as three people have already won first, second, and third place).
Where else would the sample size be?For the 100 m race with Mark Chase and Beatrice, the sample space of all the possible ways in which the three runners can win first, second, and third place is:
{M-C-B, M-B-C, C-M-B, C-B-M, B-M-C, B-C-M}
where M stands for Mark, C stands for Chase, and B stands for Beatrice. We have six possible permutations because there are three choices for the first place, two choices for the second place (as one person has already won first place), and one choice left for the third place.
If there were four runners and three positions to be won, the sample space would be:
{A-B-C-D, A-B-D-C, A-C-B-D, A-C-D-B, A-D-B-C, A-D-C-B, B-A-C-D, B-A-D-C, B-C-A-D, B-C-D-A, B-D-A-C, B-D-C-A, C-A-B-D, C-A-D-B, C-B-A-D, C-B-D-A, C-D-A-B, C-D-B-A, D-A-B-C, D-A-C-B, D-B-A-C, D-B-C-A, D-C-A-B, D-C-B-A}
where A, B, C, and D represent the four runners. We have 24 possible permutations because there are four choices for the first place, three choices for the second place (as two people have already won first and second place), and two choices for the third place (as three people have already won first, second, and third place).
Note that in both cases, we assume that all runners are equally skilled and have an equal chance of winning each position. In reality, there may be differences in skill levels, which would affect the probabilities of each possible outcome.
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What is the value of x to the nearest tenth?
In a triangle, the acute angle is 28 degrees and the obtuse angle is 126 degrees. The adjacent side of 28-degree angle is 8.2 and the opposite side is x.
The value of the side x is 4. 36
How to determine the valueTo determine the value, we need to know that there are six different trigonometric identities. They are;
tangentcotangentcosecantsecantsinecosineFrom the information given, we have that;
the acute angle is 28 degrees and the obtuse angle is 126 degrees. The adjacent side of 28-degree angle is 8.2 and the opposite side is x.
Opposite side = x
Adjacent side = 8.2
Now, using the tangent identity;
tan 28 = x/8.2
multiply the values
x = 0. 5317(8.2)
multiply
x = 4. 36
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Y-4=-3x+6 in standard form with explanation.
Answer:
Y + 3x = 10
Step-by-step explanation:
You need to know that Standard Form is: Ax + By = C
Y-4=-3x+6 Add 3x to both sides
Y - 4 + 3x = 6 Add 4 to both sides
Y + 3x = 10
I’ll give all 30 points for just the back of this, maybe show some work
The Savings budget is $150 per month
Utility budget is $225,000
Auto budget is $823 per month
How to calculate the valueSaving behavior, they want to save 15% of their income, so their savings budget would be:
a. Savings budget = 15% of $1,000 = $150 per month
b. Tri-County Supply budgets 5% of the previous year's total revenue for utilities, so their utility budget would be:
Utility budget = 5% of $4,500,000 = $225,000
c. Mr. Jones needs to increase his auto budget to 15% of his monthly income, which is $5,488 per month. So his monthly auto budget would be:
Auto budget = 15% of $5,488 ≈ $823 per month
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There are 6 mcdonalds and 2 chic fil as. How many fast food restaurants are there in total?
Answer:
8
Step-by-step explanation:
6 + 2 = 8
Answer:8
Step-by-step explanation: 6 +2 =8
For the right triangles below, find the exact values of the side lengths c and h. If necessary, write your answers in simplified radical form.
the value of the side c is √3 and h is 7.
What is Trigonometric Functions?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used in various fields such as engineering, physics, and navigation. The six fundamental trigonometric functions are sine, cosine, tangent, secant, cosecant, and cotangent. These functions are based on the ratios of the sides of a right-angled triangle. By using trigonometric formulas and identities, we can calculate the values of these functions for the perpendicular side, hypotenuse, and base of a right triangle.
tan(60)= 3/c
c = 3/tan(60)
c = 3/√3
c = √3
for 2nd
tan(45)= h/7
h = 7*1
h=7
Hence the value of the side c is √3 and h is 7.
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What is the equation in slope intercept form of the line that passes through the point (-13,-2)and (26,25)
Answer:
y =27/39x + 7
Step-by-step explanation:
Step 1: Calculating Slope (m).
m = y2-y1/x2-x1
m = (25)-(-2)/(26)-(-13)
m = 25+2/26+13
m = 27/39
m = 0.692
Now putting value of m in equation (i)
y = 0.692x + b -----(ii)
Step 2: Calculating Y-intercept (b).
Lets choose the first point, (-13,-2) for calculating y-intercept:
y = mx + b
-2 = 0.692(-13) + b
-2 = -9.00 + b
7 = b
b = 7
Now putting value of b in equation (ii)
y = 0.692x + 7
Stanley Marks had the following petty cash transactions in April of the current year. Apr 2 Write a $300 check to establish a petty cash fund.
To sum up, Stanley Marks had a starting balance of $300 to establish the petty cash fund. During the month of April, he paid out a total of $160 and replenished the petty cash fund with $400.
What is amount?Amount is a term used to refer to the size or quantity of something. It can refer to a physical quantity, such as the amount of water in a container, or to a more abstract concept, such as the amount of money owed. Amounts can be measured in physical units, such as liters or kilograms, or in monetary units, such as dollars or euros. Amounts can also be expressed in terms of other units, such as the number of hours worked or the number of miles driven.
Apr 6 Paid $40 to a supplier for office supplies
Apr 10 Paid $60 to a delivery person
Apr 15 Paid $25 to a vendor
Apr 20 Paid $15 to a cab driver
Apr 25 Paid $20 to a repair person
Apr 30 Paid $400 to replenish the petty cash fund
At the end of April, Stanley Marks had to reconcile the petty cash fund. In order to do so, he had to calculate the total amount of money that he had paid out during the month and the total amount of money that he had replenished the petty cash fund with. Stanley Marks needed to make sure that the total amount of money paid out matched the total amount of money replenished, so that he could properly balance the petty cash fund.
Stanley Marks reconciled the petty cash fund by totaling the amount of money that had been paid out during the month of April. He totaled the amounts of $40, $60, $25, $15, and $20, which amounted to $160. He then totaled the amount of money that had been replenished in the petty cash fund, which was $400. The total amount of money that was paid out was equal to the total amount of money that was replenished, so the petty cash fund was properly balanced.
Stanley Marks had a starting balance of $300, which was the amount of money he wrote a check for to establish the petty cash fund. He then had a total of $160 that he paid out during April. Finally, he had a total of $400 that he replenished the petty cash fund with. This brought the total balance of the petty cash fund to $340, which was $40 more than the starting balance of $300. This is the amount of money that Stanley Marks had at the end of April.
To sum up, Stanley Marks had a starting balance of $300 to establish the petty cash fund. During the month of April, he paid out a total of $160 and replenished the petty cash fund with $400. This brought the total balance of the petty cash fund to $340 at the end of April. By properly reconciling the petty cash fund, Stanley Marks was able to ensure that the total amount of money paid out matched the total amount of money replenished. This is how Stanley Marks was able to properly balance the petty cash fund.
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i dont under stand 0=
Answer:
b = 90°
Step-by-step explanation:
There are three angles indicated in this image: 244°, 23°, and m∠b and the sum of these three angles is equal to 360° because they make full angle.
So to find the measure of m∠b, we need to add all given angles:
244° + 23° + m∠b = 360°
Add like terms.267° + m∠b = 360°
Subtract 267° from both sides to isolate b.m∠b = 93°
What is the quotient of 2 and 1 over 3 divided by 3 over 5
let's firstly convert the mixed fraction to improper fraction and then divide.
[tex]\stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{3}\div \cfrac{3}{5}\implies \cfrac{7}{3}\cdot \cfrac{5}{3}\implies \cfrac{35}{9}\implies {\Large \begin{array}{llll} 3\frac{8}{9} \end{array}}[/tex]
the width of a block of wood with rectangular cross-section is x cm. it's height is two- thirds its width and length is 4 times its height what is its volume in cm3?
Answer:
The height of the block is two-thirds of its width, so we have h = (2/3)x.
The length of the block is 4 times its height, so we have l = 4h = 4(2/3)x = (8/3)x.
The volume of the block is given by V = lwh, so substituting the values we have:
V = (8/3)x * x * (2/3)x = (16/81)x³
Therefore, the volume of the block is (16/81)x³ cubic cm.
Customers of a phone company can choose between two service plans for long distance calls. The first plan has an $18 monthly fee and charges an additional $0.15 for each minute of calls. The second plan has a $12 monthly fee and charges an additional $0.20 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
Let's call the number of minutes of calls "x".
For the first plan, the cost will be:
Cost = $18 + $0.15x
For the second plan, the cost will be:
Cost = $12 + $0.20x
To find the point at which the costs of the two plans are equal, we can set the two equations equal to each other and solve for x:
$18 + $0.15x = $12 + $0.20x
Subtracting $12 from both sides, we get:
$6 + $0.15x = $0.20x
Subtracting $0.15x from both sides, we get:
$6 = $0.05x
Dividing both sides by $0.05, we get:
x = 120
Therefore, if a customer makes more than 120 minutes of calls per month, the first plan with the $18 monthly fee and $0.15 per minute charge will be more cost-effective. If a customer makes less than 120 minutes of calls per month, the second plan with the $12 monthly fee and $0.20 per minute charge will be more cost-effective.
Answer:
120 minutes
Step-by-step explanation:
Let x be the number of minutes of calls made in a month.
For the first plan, the monthly cost is $18 + $0.15x.
For the second plan, the monthly cost is $12 + $0.20x.
To find the point where the costs are equal, we need to solve the equation:
18 + 0.15x = 12 + 0.20x
Subtracting 0.15x from both sides gives:
18 = 12 + 0.05x
Subtracting 12 from both sides gives:
6 = 0.05xDividing both sides by 0.05 gives:
x = 120
Therefore, the costs of the two plans will be equal for 120 minutes of calls.
Find the volume of the following regular pentagonal prism, if the apothem is 6.9 cm and the height of the prism is 8 cm. Round your final answer to the nearest tenth if necessary.
The volume of the following regular pentagonal prism rounded to the nearest tenth is: 1384.1 cm³.
How to calculate the volume of a pentagonal prismTo calculate the volume of a pentagonal prism, we should apply the formula:
V = 5/2 × apothem × base × height
In the given question, the height is 8 cm and the apothem is 6.9 cm. This apothem can be applied in solving for side length as follows:
2 × 6.9cm × tan 36°
= 10.03
Next, we find the area of the Pentagon as follows:
5/2 × 10.03 × 6.9 cm
= 173.02
The volume now equals:
173.02 × 10.03
= 1384.1 cm³.
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7x -8(10x-20)+(90x-10)
Help please!
angle A and angle B are vertical angles. If m angle A=(5x+63)^ and m angle B=(x+37)^ . then what is the value of x?
Answer:
Vertical Angles are congruent, therefore,
m∠A = m∠B(5x+63)° = (x+37)°4x = -26x = -13/2Rosa needs a $4,500 loan in order to buy a car. Which loan option would allow her to pay the least amount of interest?
Regarding resolving the given issue, we have Consulting a financial advisor or credit counsellor may also be beneficial.
what is expression ?It is possible to multiply, divide, add, or subtract in mathematics. The following is how an expression is put together: Number, expression, and mathematical operator The components of a mathematical expression (such as addition, subtraction, multiplication or division, etc.) include numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and an arithmetic operation between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as does the variable m in the expression 4m + 5.
Rosa has a variety of loan alternatives, and the one with the lowest interest rate will rely on a number of elements, including her credit score, her income, and the loan's length. However, she would generally be able to pay the least amount of interest with a secured loan with a lower interest rate.
A loan that is secured by property, such a car or a house, is known as a secured loan. Rosa may want to think about a secured auto loan in this situation, where the vehicle itself acts as security for the loan. The lender is assuming less risk because the loan is secured, therefore they can charge a lower interest rate.
Rosa may also take into account an unsecured personal loan from a bank or credit union if she has strong credit. Personal loans are frequently provided with set interest rates and terms, which can make budgeting for them simpler. They do, however, often have higher interest rates than secured loans since they are unsecured.
Rosa should shop about and evaluate offers from several lenders to locate the best loan choice for her, taking into account things like interest rates, costs, loan periods, and repayment alternatives. Consulting a financial advisor or credit counsellor may also be beneficial.
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I need some help please.
Where the above conditions are given, the IQR for X is from 156 acres to 192 acres.
What is the explanation for the above response?To find the interquartile range (IQR), we need to first find the first and third quartiles of the sample.
Given:
Sample size (n) = 38
Sample mean (μ) = 174
Sample standard deviation (σ) = 55
We know that the first quartile (Q1) is the 25th percentile and the third quartile (Q3) is the 75th percentile.
Using the standard normal distribution table, we can find the z-scores for Q1 and Q3:
z-score for Q1 = invNorm(0.25) = -0.6745
z-score for Q3 = invNorm(0.75) = 0.6745
Now, we can use the following formulas to find Q1 and Q3:
Q1 = μ + z-score for Q1 * (σ / sqrt(n))
Q3 = μ + z-score for Q3 * (σ / sqrt(n))
Substituting the given values, we get:
Q1 = 174 - 0.6745 * (55 / sqrt(38)) ≈ 155.52
Q3 = 174 + 0.6745 * (55 / sqrt(38)) ≈ 192.48
Therefore, the IQR for X is from 156 acres to 192 acres.
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A rectangular garden is to be constructed using a rock wall as one side of the garden and wire fencing for the other three sides. Given that there are 30 meters of fencing available, determine the dimensions that would create the garden of maximum area. What is the maximum possible area?
The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters
What is measurement?
Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.
Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.
Since we have 30 meters of fencing available, the total length of wire fencing used is:
L + 2W = 30 - W
Simplifying this equation, we get:
L = 30 - 3W
The area of the garden is:
A = LW
Substituting the expression for L from the previous equation, we get:
A = W(30 - 3W)
Expanding the expression, we get:
A = 30W - 3W²
To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:
dA/dW = 30 - 6W = 0
Solving for W, we get:
W = 5
Substituting this value back into the expression for L, we get:
L = 15
Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:
A = 5(15) = 75 square meters
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Find the equation of a line passing through the point (-3, -7) that is perpendicular to the line 5x-3y=10. Show detailed steps.
To find the equation of a line passing through a given point that is perpendicular to a given line, we need to follow these steps:
Find the slope of the given line by rearranging the equation into slope-intercept form y = mx + b, where m is the slope.
Find the slope of a line perpendicular to the given line by taking the negative reciprocal of the slope found in step 1.
Use the point-slope form y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope found in step 2, to write the equation of the perpendicular line.
Step 1: Find the slope of the given line 5x - 3y = 10
We can rearrange the equation into slope-intercept form by solving for y:
5x - 3y = 10
-3y = -5x + 10
y = (5/3)x - (10/3)
The slope of this line is 5/3.
Step 2: Find the slope of a line perpendicular to the given line
The slope of a line perpendicular to the given line is the negative reciprocal of 5/3:
m_perp = -3/5
Step 3: Use the point-slope form to write the equation of the perpendicular line passing through (-3, -7).
We plug in the values we found for the slope and the given point into the point-slope form:
y - y1 = m_perp(x - x1)
y - (-7) = (-3/5)(x - (-3))
Simplifying this equation, we get:
y + 7 = (-3/5)x - 9/5
Now we can rearrange this equation into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept:
y = (-3/5)x - 44/5
Therefore, the equation of the line passing through the point (-3, -7) and perpendicular to the line 5x - 3y = 10 is y = (-3/5)x - 44/5.
On January 9 , 2015 , Jakes’s truck had 89,176 miles on it . one year later, it had 103,688 . How many miles did he drive during that 1 year ?
Answer:
Step-by-step explanation:
just subtract 89,176 minus 103,688 answer is 14,512
A big set of data can be messy, even when it's arranged in neat columns and rows. However, when data is displayed as a bar graph or histogram patterns emerge that reveal new information.
1. Imagine a real-world scenario and a possible corresponding data distribution that is either skewed left, skewed right, normally distributed, or some other shape.
-Create a sketch of the data distribution that represents the scenario.
-Post a description of your chosen real-world scenario with a data set. As others reply, respond with the sketch you drew and an explanation of why it looks like that.\
*it would probably be helpful if you did this on paper if possible, thank you!*
Upon answering the query The distribution to the right would be expressions skewed as a result, as seen in the sketch.
what is expression ?It is possible to multiply, divide, add, or subtract in mathematics. The following is how an expression is put together: Number, expression, and mathematical operator The components of a mathematical expression (such as addition, subtraction, multiplication or division, etc.) include numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and an arithmetic operation between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as does the variable m in the expression 4m + 5.
The monthly sales income of a corporation in the real world.
Right-skewed distribution of data.
With a lengthy tail to the right and the majority of the data on the graph's left side, a distribution is said to be skewed right. When it comes to a company's sales income, it's typical for the most of the sales to be modest, with a few high-earning months (such as those brought on by a holiday sale, the debut of a new product, etc.) creating a long tail to the right. The distribution to the right would be skewed as a result, as seen in the sketch.
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HELP
Draw any length line segment that will fit in the space shown. The line segment can go in any direction, but it must be straight. Draw another line segment of any length that is parallel to the first one. Connect the ends of each line segment with line segments to make a closed four-sided figure. What does your shape look like? Can you classify it?
Note that the shape with with two parallel sides is called an irregular parallelogram. See the attached image.
What is an irregular parallelogram?The polygon is an irregular quadrilateral because two sides are parallel lines and the other two sides are not.
Irregular polygons have infinitely many sides because their lengths are not equal. Shapes such as parallelograms, trapeziums, and quadrilaterals are irregular polygons because their neighboring sides and angles are not equal.
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Help solve this problem
The equivalent expression to the given expression; - √-7 as required to be written in terms of i is; -i√7.
What is the equivalent expression?It follows from the task content that the equivalent expression to the given; -√-7 is to be determined.
Since the given expression is; - √-7; we have;
- (√-1 × √7) where √-1 = i, so that we have;
= -i√7.
Ultimately, the expression in terms of i is; -i√7.
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give the statement missing for number 3 and the reason missing for number 5 in the column proof below.
Answer:
3 = equal
5 = equal
Step-by-step explanation:
3. both angles are alternate angles
5. both triangles are equal
Need help will give brainliest and 5 stars! :)
Answer: -4
Step-by-step explanation:
50 Points! Multiple choice algebra question. Photo attached. Thank you!
The equation for the vertical asymptote of f(x) = (x - 1)/(x - 2) is given as follows:
D) x = 2.
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.The function for this problem is given as follows:
f(x) = (x - 1)/(x - 2)
The vertical asymptote is the zero of the denominator, hence it is obtained as follows:
x - 2 = 0
x = 2.
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A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand A aspirin how many docs use brand A aspein
What is 16 g as a fraction of 2 kg?
Answer:
Step-by-step explanation:
8
_9
k
OR 8/k 9
The ages (in years) and heights (in inches) of all pitchers for a baseball team are listed Find the coefficient of variation for each of the two data sets. Then compare the results
Heights:
73, 77, 74, 76, 79, 78, 79, 70, 72, 71, 79, 79
Ages:
23, 28,28, 27, 27, 29, 26, 28, 30, 37, 36,33
CVheights= %
228 in base three is
228 in base 10 to base three is determined as 22110₃.
What is 228 in base 10 to base 3?
Converting a number from one base to another involves representing the same value in a different positional numeral system.
To convert the number 228 from base 10 to base 3, we can follow these steps:
3 | 228
= 76 R 0 (so the remainder here 0)
= 25 R 1 (the remainder here 1)
= 8 R 1 (the remainder here 1)
= 2 R 2 (the remainder here 2)
= 0 R 2 (the remainder here 2)
write the remainders from bottom to top = 22110₃
228 in base 10 to base 3 = 22110₃
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How many liters each of a 35% acid solution and a 70% acid solution must be used to produce 70 liters of a 55% acid solution
We need 30 liters of the 35% acid solution and 40 liters of the 70% acid solution.
What is the volume of each solution?The volume of each solution is calculated as follows;
Let x be the number of liters of the 35% acid solution
Let y be the number of liters of the 70% acid solution
x + y = 70 ----- (1)
0.35x + 0.70y = 0.55(70) ----- (2)
The equation is simplified as;
0.35x + 0.70y = 38.5
from (1) x = 70 - y
Substitute x = 70 - y into equation 2:
0.35(70 - y) + 0.70y = 38.5
24.5 - 0.35y + 0.70y = 38.5
0.35y = 14
y = 40
Substitute y = 40 into equation 1 to solve for x:
x + 40 = 70
x = 30
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