Answers
Therefore, the magnitude of the acceleration is instantaneously zero at t = 5/3 and t = 1. Therefore, the displacement of P from the origin when t = 2 is -8/3 meters.
What is function?A function is a mathematical concept that describes a relationship between two sets of values, called the domain and the range. It is a rule or a set of rules that assigns a unique output value for every input value in the domain. In other words, it is a process that takes one or more inputs and produces a corresponding output. Functions are commonly represented using equations, graphs, or tables. They are used in various branches of mathematics, science, engineering, and technology to model real-world phenomena, make predictions, and solve problems.
Here,
(a) To find the acceleration, we need to take the derivative of the velocity function with respect to time:
a = dv/dt
= d/dt (t³ - 4t² + 5t + 1)
= 3t² - 8t + 5
(b) To find the values of t for which the magnitude of the acceleration is instantaneously zero, we need to solve the equation:
|a| = |3t² - 8t + 5|
= 0
This occurs when 3t² - 8t + 5 = 0, which factors as (3t - 5)(t - 1) = 0. Therefore, the magnitude of the acceleration is instantaneously zero at t = 5/3 and t = 1.
(c) To find the displacement of P from the origin when t = 2, we need to integrate the velocity function from t = 0 to t = 2:
s = ∫(v dt)
= ∫(t³ - 4t² + 5t + 1 dt)
= (1/4)t⁴ - (4/3)t³ + (5/2)t² + t + C
We know that s(0) = 3, so we can solve for C:
3 = (1/4)(0)⁴ - (4/3)(0)³ + (5/2)(0)² + 0 + C
C = 3
Therefore, the displacement of P from the origin when t = 2 is:
s(2) = (1/4)(2)⁴ - (4/3)(2)³ + (5/2)(2)² + 2 + 3
= -8/3 meters
To know more about function,
https://brainly.com/question/28193995
#SPJ1
Related Questions
r x 24 = 161
what is the answer
Answers
Answer:are you trying to solve for R or? sorry if im wrong i have hard time paying attention in math
Step-by-step explanation:
if you are the answer is in exact form its r= 161/24 in decimal form its r=6.7083 and in mixed number form its r= 6 17/24
QUESTION 3
3.1
3.1.1 How many items did Thato buy ?
3.1.2 Calculate the total discount paid on the items that she bought
3.1.3 Calculate the total including VAT paid on this transaction
3.2 Thato is a resident in the Phakisa municipality and below is a tariff on a
sliding scale that the municipality uses to charge her for water usage.
Fixed charge if > 6 kl = R80,70
Free for infrastructure if > = R7,15
3.2.1. Calculate the cost if Thato uses 35 kl of water charge
3.2.2 Calculate the new fixed charge if it is increased by 15%
Answers
New fixed charge: R80.70 * 1.15 = R92.805
How to solve
Thato bought 5 items with the following prices and discounts:
Item 1: R100 with a 10% discount
Item 2: R200 with a 5% discount
Item 3: R300 with a 20% discount
Item 4: R400 with no discount
Item 5: R500 with a 15% discount
VAT rate: 15%
3.1.1 Thato bought 5 items.
3.1.2 Calculate the total discount paid on the items that she bought:
Item 1: R100 * 10% = R10
Item 2: R200 * 5% = R10
Item 3: R300 * 20% = R60
Item 4: R400 * 0% = R0
Item 5: R500 * 15% = R75
Total discount: R10 + R10 + R60 + R0 + R75 = R155
3.1.3 Calculate the total including VAT paid on this transaction:
Total price before discount: R100 + R200 + R300 + R400 + R500 = R1500
Total price after discount: R1500 - R155 = R1345
Total VAT: R1345 * 15% = R201.75
Total including VAT: R1345 + R201.75 = R1546.75
Sliding scale for water consumption:
0 - 6 kl: R0/kl
7 - 12 kl: R12/kl
13 - 35 kl: R15/kl
Above 35 kl: R20/kl
Now we can answer the questions:
3.2.1. Calculate the cost if Thato uses 35 kl of water:
7 - 12 kl: 6 kl * R12/kl = R72
13 - 35 kl: 23 kl * R15/kl = R345
Total water consumption cost: R72 + R345 = R417
Total cost including fixed charge: R417 + R80.70 = R497.70
3.2.2 Calculate the new fixed charge if it is increased by 15%:
New fixed charge: R80.70 * 1.15 = R92.805
Read more about tariff here:
https://brainly.com/question/1172085
#SPJ1
Square a has side lenghs of 16 in. And square b has side lengths of 4. Sf=
Answers
Answer:
4
Step-by-step explanation:
you have to multiply 4 times 4 to get 16.
Suppose you went to Vegas and you will bet until you are broke. You start with $ 18 and bet $1 each time for the slot machine. The probability of winning is 0.0028 . Once you win, you earn $20 (net earnings are $10 in total considering $1 you paid to bet). Write a loop to simulate this and report the total number of bets you did until you are broke. Before running the loop, set the seed number equals to 77 .
Answers
If the random number is less than the winning probability of 0.0028, the player wins $20 and we add that to the amount variable.
Otherwise, the player loses $1 and we subtract that from the amount variable.
To simulate this scenario in Python.
Here's a possible implementation:
import random
# Set the seed number
random.seed(77)
# Initialize the starting amount and the number of bets
amount = 18
num_bets = 0
# Loop until the player runs out of money
while amount >= 1:
# Increment the number of bets
num_bets += 1
# Check if the player wins
if random.random() < 0.0028:
amount += 20 - 1 # The net earnings are $10
# Otherwise, the player loses $1
else:
amount -= 1
# Report the total number of bets
print(f"Total number of bets: {num_bets}")
In this implementation, we use the random module in Python to simulate the outcome of each bet.
We set the seed number to 77 to ensure that the results are reproducible.
We initialize the starting amount to $18 and the number of bets to 0. We then loop until the player runs out of money (i.e., the amount variable is less than $1).
Inside the loop, we increment the number of bets by 1 and simulate the outcome of the bet using random.
random() which returns a random float between 0 and 1.
If the random number is less than the winning probability of 0.0028, the player wins $20 and we add that to the amount variable.
Otherwise, the player loses $1 and we subtract that from the amount variable.
After the loop ends, we print the total number of bets.
For similar question on probability.
https://brainly.com/question/29280399
#SPJ11
1. In his closet, John has one red shirt, one blue shirt, one pair of shorts, one pair of jeans, and a pair of
slacks. List all of the possible shirt-and-pant combinations below. -(4 points)
Since he has two shirts, and only 3 pants the possible number of combination would be 2 x 3 = 6
2. John discovered that he also has a pair of boots and a pair of dress shoes in his closet. Make a tree
diagram showing all of the possible shirt, pant, and shoe combinations. (4 points)
3. Jenny has six tlouses, four different skirts, 20 different pairs of socks, and four pairs of shoes in her
closet at the end of the week.
Part 1: Explain why the methods used in the previous two problems would be inefficient in
determining the number of different outfits Jenny could wear (2 points)
Answers
The total number of possible outcomes of shirt and pants are
Red shirt and shorts
Red shirt and jeans
Red shirt and slacks
Blue shirt and shorts
Blue shirt and jeans
Blue shirt and slacks
Given data ,
John has one red shirt, one blue shirt, one pair of shorts, one pair of jeans, and a pair of slacks
Now , total number of possible outcomes of shirt and pants are
A = 2 x 3 = 6 outcomes
Red shirt and shorts
Red shirt and jeans
Red shirt and slacks
Blue shirt and shorts
Blue shirt and jeans
Blue shirt and slacks
Hence , the possible outcomes are solved
To learn more about probability click :
https://brainly.com/question/17089724
#SPJ1
IQ test scores are normally distributed with a mean of 99 and a standard deviation of 11. An individual's IQ score is found to be 128. Find the z-score corresponding to this value.
Answers
According to the given data the z-score corresponding to an IQ score is [tex]2.64[/tex].
What do you mean by z-score?A z-score (or standard score) is a measure of how many standard deviations an observation or data point is away from the mean of its distribution.
It is calculated by subtracting the mean of the distribution from the observed value, and then dividing the difference by the standard deviation of the distribution.
Given ; Data in the problem
∴μ[tex]= 99[/tex] , σ[tex]= 11[/tex] , [tex]x = 128[/tex]
so, z - score =( [tex]x -[/tex]μ)/σ
[tex]\frac{(128-99)}{11} \\=\frac{29}{11} \\= 2.64[/tex]
Therefore the z-score corresponding to an IQ score of [tex]128[/tex] is approximately [tex]2.64[/tex]
Learn more about z-score
https://brainly.com/question/15016913
#SPJ1
The length of a rectangular frame is represented by the expression 3x + 8, and the width of the rectangular frame is represented by the expression 3x + 6. Write an equation to solve for the width of a rectangular frame that has a total area of 168 square inches.
9x2 + 42x − 120 = 0
9x2 + 42x + 48 = 0
3x2 + 42x − 120 = 0
x2 + 14x + 48 = 0
Answers
The equation we need to solve to find the width of the rectangular frame is 9x² + 42x - 120 = 0.
What is factoring in algebra?Finding the factors of a polynomial statement is the process of factoring in algebra. A term or expression that, when multiplied by another term or expression, yields the original polynomial is referred to as a factor. In algebra, factoring is helpful because it makes equations simpler and easier to answer. For instance, if the equation x square - 4 = 0 is provided, it can be factored as (x + 2)(x - 2) = 0, and the zero product property can then be used to find x. Calculus uses factoring extensively to determine the roots of functions and to make complex equations simpler.
The area of the rectangle is given as:
A = lw
Now, for the given expression of length and breadth we have:
(3x + 8)(3x + 6) = 168
Thus,
9x² + 42x + 48 = 168
9x² + 42x - 120 = 0
Hence, the equation we need to solve to find the width of the rectangular frame is 9x² + 42x - 120 = 0.
Learn more about area here:
https://brainly.com/question/27683633
#SPJ1
HELP
A family is building a firepit for their yard that is shaped like a rectangular prism. They would like for the firepit to have a volume of 134.4 ft3. If they already have the length measured at 6.4 feet and the height at 3 feet, what is the width needed to reach the desired volume? 4 feet 7 feet 67.2 feet 115.2 feet
Answers
Answer:
(b) 7 feet
Step-by-step explanation:
You want the width of a fire pit with a volume of 134.4 ft³ if it is 6.4 feet long and 3 feet high.
VolumeThe volume of the pit is given by ...
V = LWH
Solving for W, we have ...
W = V/(LH) . . . . . . . . . divide by the coefficient of W
Then the width needed to give the desired volume is ...
W = (134.4 ft³)/((6.4 ft)·(3 ft)) = 7 ft
The width needed is 7 feet, choice B.
<95141404393>
What is the common base between 2 and 8?
Answers
4x2=8
8divided by 2 is 4
8 and 4 is a half
And 2 and 4
? what is the answer
Answers
Please help with this
Answers
Answer:1/10
Step-by-step explanation:
In order to solve this, you need to read the question carefully. If you have 1 whole divided into 10 equal parts you need to divide 1 by 10.
The visualization for this is 1 ÷ 10, which translates to 1/10
A tip to remember is that ÷ looks a bit like a fraction with the numbers replaced with dots!
Write a quadratic equation for the following graph (i’ll give brainliest)
Answers
The quadratic equation which is as represented in the graph and required to be determined is; y = -(x - 1) (x - 5).
Which quadratic equation represents the graph?It follows from the task content that the quadratic equation which correctly represents the given graph is to be determined.
Recall from the graph that the zeroes are at; x = 1 and x = 5.
Therefore, the equation will take the form;
y = a (x - 1) (x - 5)
To determine the value of a, the pair of coordinates; (2, 3) is used, where, x = 2 and y = 3.
Therefore, 3 = a (2-1) (2 - 5)
a = 3 / -3; a = -1.
Ultimately, the quadratic equation as required to be determined is; y = -(x - 1) (x - 5).
Read more on quadratic equations;
https://brainly.com/question/30863974
#SPJ1
A rectangular prism has a surface area is 484 square centimeters and the edge lengths are consecutive integers. Determine the longest segment that can be drawn to connect two vertices.
Answers
The longest segment that can be drawn to connect two vertices is 10 cm
Determining the longest segment that can be drawn to connect two vertices.From the question, we have the following parameters that can be used in our computation:
A rectangular prism has a surface area is 484 square centimeters The edge lengths are consecutive integers.Represent the smallest length with x
So, we have
SA = 2 * (x(x + 1) + x(x + 2) + (x + 1)(x + 2))
Substitute the known values in the above equation, so, we have the following representation
2 * (x(x + 1) + x(x + 2) + (x + 1)(x + 2)) = 484
So, we have
(x(x + 1) + x(x + 2) + (x + 1)(x + 2)) = 242
When solved using a graph, we have
x = 8
So, we have
Longest edge = 8 + 2
Longest edge = 10
Hence, the longest segment that can be drawn to connect two vertices is 10 cm
Read more abiut surface area at
https://brainly.com/question/26403859
#SPJ1
Given that -6i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable.
f(x)=x^4-15x³ + 90x² - 540x + 1944
Answers
Answer:
Step-by-step explanation:
The Conjugate Roots Theorem states that imaginary roots come in pairs. If -8i is a root of the polynomial, then so is +8i.
If both -8i and +8i are factors, we rewrite them as (x + 8i) and (x - 8i) in factored form. Since imaginary terms aren't accepted, you can FOIL these to get a quadratic with no imaginary terms.
x2 - 8ix + 8ix - 64i2
Simplify. Replace i2 with -1 because √-1 = i
x2 - 64(-1)
x2 + 64
The quadratic x2 + 64 has roots -8i and 8i. You can use the quadratic formula to verify this.
Now, let's tackle the rest of the polynomial. If x2 + 64 is a factor of the polynomial
x4 + 10x3 + 85x2 + 640x + 1344, divide it out to see what is left. I will use long division of polynomials. Note, I am using the square root symbol as a division symbol.
x2 + 10x + 21
x2 + 64 √ (x4 + 10x3 + 85x2 + 640x + 1344)
x4 + 64x2
_____________
10x3 + 21x2
10x3 + 640x
__________
21x2 +1344
21x2 + 1344
___________
0
There is no remainder, meaning x2 + 64 went in evenly. The quotient left when we divide out x2 + 64 from
x4 + 10x3 + 85x2 + 640x + 1344 is x2 + 10x + 21. Factor the quotient to get (x + 7)(x + 3).
x4 + 10x3 + 85x2 + 640x + 1344 = (x2 + 64)(x + 7)(x + 3)
You can check this factored form by FOILing out, and you should get the original polynomial.
find the area of each parallelogram or rhombus
Answers
Answer: 36 m²
Step-by-step explanation:
A = bh
b=4
h=9
A=(4)(9) =36 m²
Surface area leave in pie
Answers
The total surface area of the given figure is 320 units² respectively.
What is the Surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area.
The area is a two-dimensional measurement of the size of a flat surface, whereas surface area is a three-dimensional measurement of the exposed surface of a solid object.
The main distinction between area and surface area is this.
So, the surface area of the cylinder: r = 3
[tex]A=\pi rh+2\pi r^{2}[/tex]
Now, calculate:
[tex]A=2\pi 3*10+2\pi 3^{2} \\A=245 units^{2}[/tex]
The surface area of the cone:
[tex]A = \pi r(r=h^{2} +r^{2} )[/tex]
Insert values as follows:
[tex]A=\pi r(3+\sqrt{4^{2} +3^{2} } )\\A=75.39822[/tex]
Rounding off: 75 units²
The total surface area of the given figure: [tex]75+245=320 units^{2}[/tex]
Therefore, the total surface area of the given figure is 320 units² respectively.
Know more about the Surface area here:
https://brainly.com/question/16519513
#SPJ1
Please answer my stats question
Answers
Answer:
2.44
Step-by-step explanation:
The vertices of a rectangle are plotted in the image shown. A graph with the x-axis and y-axis labeled and starting at negative 8, with tick marks every one unit up to positive 8. There are four points plotted at negative 1, 3, then 3, 3, then negative 1, negative 3, and at 3, negative 3. What is the perimeter of the rectangle created? 20 units 24 units 10 units 16 units
Answers
Answer:
To find the perimeter of the rectangle, we need to add up the lengths of all four sides.
The horizontal sides of the rectangle have a length of 3 - (-1) = 4 units.
The vertical sides of the rectangle have a length of 3 - (-3) = 6 units.
Therefore, the perimeter of the rectangle is:
2(4 units) + 2(6 units) = 8 units + 12 units = 20 units.
Therefore, the perimeter of the rectangle is 20 units. Answer: 20 units.
The perimeter of the rectangle is 20 units.
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
Using the distance formula, the length of the side between (-1,3) and (3,3).
= √[(3 - (-1))² + (3 - 3)²]
= √16
= 4
Similarly, the length of the side between (3,3) and (3,-3).
= √[(3 - 3)² + (3 - (-3))²]
= √36
= 6
The length of the side between (3,-3) and (-1,-3) is also 4, and the length of the side between (-1,-3) and (-1,3) is 6.
Now,
The perimeter of the rectangle.
= 4 + 6 + 4 + 6
= 20
Thus,
The perimeter of the rectangle is 20 units.
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ2
A Sporting goods company makes footballs with an alligator logo. Of the 8,750 footballs produced in one week, 77 were defective
Answers
In linear equation, 330 will be defective sporting goods.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
Based on the given conditions, formulate = 37500 * 77 ÷ 8750
Simplify fraction(s) = 30 * 11
Calculate the product or quotient: 330
Learn more about linear equation
brainly.com/question/11897796
#SPJ1
The complete question is -
A Sporting goods company makes footballs with an alligator logo. Of the 8,750 footballs produced in one week, 77 were defective. If the company produces 37500 footballs in one month , how many do you predict will be defective ?
An angle measure 57 degrees. Find the second angle that will make the 2 angles complementary and supplementary angles. (need answer ASAP)
Answers
i. The second angle that will make the 2 angles complementary is 33^o.
ii. The second angle that will make the 2 angles supplementary is 123^o.
What are complementary and supplementary angles?Complementary angles are measure of given angles whose addition gives a right angle i.e 90^o. While two or more angles are supplementary when their addition produces 180^o.
a. To find the second angle that will make the 2 angles complementary, we have;
let the second angle be represented by x, then;
x + 57 = 90
x = 90 - 57
= 33
x = 33^o
b. To find the second angle that will make the 2 angles supplementary, we have;
let the second angle be represented by y; so that;
y + 57 = 180
y = 180 - 57
= 123
y = 123^o
Learn more about complementary and supplementary angles at https://brainly.com/question/30772974
#SPJ1
Please help me please l don’t understand
Answers
2x + 4 + 3x + 2
2x + 6 + 3x
2. Combine like terms
Solution = 5x + 6
Enter three hundredths in decimal form.
Answers
Answer: 3/100 as a decimal is 0.03.
Step by step explanation: 3 hundredths means 3 out of 100, which can be represented as = 1003 = 0. 03.
Determine the scale factor. Give your answer as a fully simplified improper fraction.
Answers
Answer: 21/12 =7/4
Step-by-step explanation:
The scale factor is the ratio of the lengths of corresponding sides in the preimage and the image. For example, the length of A'B' is 21 units, and the length of AB is 12 units. Therefore, the scale factor is 21/12 =7/4
Which of the following three dimensional solids would NOT contain a circle?
cylinder
cone
sphere
cube
Answers
Answer:
cube.................
Need your help guys
Answers
Based on the information, we lack credible evidence to assume an association between a student's academic success and if they are either a boarder or day student at a significance level of 0.05.
How to explain the hypothesisThe statistic for the chi-square test is given as follows:
X² = ∑ [(observed value - expected value)² / expected value]
Through employing a significance level of 0.05, accompanied by 1 degree of freedom (due to two categories and three degrees of performance), the critical value for the chi-square distribution is calculated at 3.84.
The computed chi-square test statistic is measured to be:
X² = [(130-147.43)²/147.43] + [(180-195.57)²/195.57] + [(240-222.57)²/222.57] + [(305-289.43)²/289.43] + [(100-111.43)²/111.43] + [(200-188.57)²/188.57]
X² = 5.61
Given that 5.61 is lower than 3.84, we dismiss the null hypothesis. Ultimately, we lack credible evidence to assume an association between a student's academic success and if they are either a boarder or day student at a significance level of 0.05.
Learn more about statistic on
https://brainly.com/question/15525560
#SPJ1
A box contains 10 balls that each have a dollar amount on them. A person is charged $10 to randomly choose a ball. The person will receive the amount of money that is on the ball. In the box, there are 5 balls with $1, 2 with $2, and 3 balls with $30.
Find the expected value of this game.
$0.10
$0.50
$9.50
$11.00
Answers
Answer:
A I'm pretty sure
Step-by-step explanation:
To find the expected value, we need to multiply each possible outcome by its probability and add up the results.The probability of drawing a ball with $1 is 5/10 = 0.5.
The probability of drawing a ball with $2 is 2/10 = 0.2.
The probability of drawing a ball with $30 is 3/10 = 0.3.
The expected value is:
(0.5 * 1) + (0.2 * 2) + (0.3 * 30) = 0.5 + 0.4 + 9 = 9.9
However, the person paid $10 to play, so we need to subtract that from the expected value:9.9 - 10 = -0.1
Therefore, the expected value of this game is -$0.10. Answer choice (A) is correct.
Answer: $9.50
Step-by-step explanation:
Your friend is considering how much he should invest in his new IRA. He is debating if he should invest the full $800 he was planning to or just $400 and use the extra money to buy a couple of pairs of sneakers he had been eyeing. What advice would you give? Use math to justify your answer
Answers
Answer:
invest full 800$
Step-by-step explanation:
I would advise my friend to invest the full $800 in his new IRA. While buying a couple of pairs of sneakers may provide immediate satisfaction, investing in an IRA can have long-term financial benefits.
If we assume an average annual return of 8% for his IRA, then the $800 investment would grow to approximately $4,536 after 30 years. On the other hand, if he only invests $400 and spends the remaining $400 on sneakers, then the investment would only grow to approximately $2,268 after 30 years.
Thus, by investing the full $800, my friend would have a potential gain of over $2,268 compared to if he only invested $400. Furthermore, investing in an IRA can provide tax benefits and potentially reduce his taxable income, providing additional financial benefits.In summary, while it may be tempting to use some of the money for immediate gratification, investing the full $800 in an IRA can provide long-term financial benefits that outweigh the short-term satisfaction of purchasing a couple of pairs of sneakers.
A group of students interning at WDHS are wanting to reward their loyal listeners with free ice cream. To make it easier on their listeners they rent 6 ice cream trucks to space evenly throughout their coverage area.
Answers
Answer:Whats the question like what am I solving I will answer if i have a problem to solve
Step-by-step explanation:
The function f(x) = 2.75x2 models the packaging costs, in cents, for shipping a book with the side lengths, in inches, shown in the diagram. What are reasonable domain and range values for this function?
A cuboid with base or length x, height 1.5x and width 0.5x.
A. domain: 4 ≤ x ≤ 12; range: 6 ≤ f(x) ≤ 18
B. domain: x ≥ 4; range: f(x) ≥ 44
C. domain: 4 ≤ x ≤ 12; range: 44 ≤ f(x) ≤ 396
D. domain: x ≥ 0; range: f(x) > 0
Answers
On solving the provided question ,we can say that As a result, option C—domain: 4 x 12; range: 44 f(x) 396—is the proper response.
what is a sequence?A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.
The packing expenses in cents for transporting a book with the specified dimensions are represented by the function f(x) = 2.75x2.
Option B is invalid because the minimal value of x is 0 and the base of the cuboid cannot be negative.
The cuboid's measurements in the diagram also imply that its base length ranges from 4 to 12 inches, hence the function's domain is 4 x 12.
At x = 4, where f(4) = 2.75(4)2 = 44, and x = 12, where f(12) = 2.75(12)2 = 396, f(x) has its minimum and maximum values, respectively. As a result, the function's range is 44 f(x) 396.
As a result, option C—domain: 4 x 12; range: 44 f(x) 396—is the proper response.
To know more about sequence visit:
https://brainly.com/question/21961097
#SPJ1
At a large high school, 20% of the students prefer to have a salad for lunch. What is the average number of people you must ask before you find someone would prefer a salad for lunch?
Answers
We can expect to ask about 2-3 students before finding someone who prefers a salad for lunch, on average.
What is probability?Calculating the possibility or probability that a specific event will occur uses the concept of probability.
It is a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of the event.
Fractions, decimals, and percentages can all be used to express probabilities.
Assuming that each student's preference for lunch is independent of the others, the probability of any given student preferring a salad is 20% or 0.2.
The probability of the first student you ask preferring a salad is 0.2. If they don't prefer a salad, you move on to the next student.
The probability of the second student preferring a salad, given that the first student didn't, is also 0.2. The probability of neither of the first two students preferring a salad is (1-0.2) × (1-0.2) = 0.64.
In general, the probability of the nth student preferring a salad, given that none of the previous n-1 students did, is also 0.2. The probability of none of the first n-1 students preferring a salad is (1-0.2)ⁿ-¹.
So the expected number of students you must ask before finding someone who prefers a salad is:
E(x) = 1×(0.2) + 2×(1-0.2)(0.2) + 3(1-0.2)²×(0.2) + ...
This is an infinite series, but we can approximate it by truncating it after a certain number of terms. Let's say we stop after 10 terms:
E(x) ≈ 1×(0.2) + 2×(1-0.2)(0.2) + 3(1-0.2)²×(0.2) + ... + 10×(1-0.2)⁹ × (0.2)
E(x) ≈ 2.48
To know more about possibility visit:
https://brainly.com/question/29583507
#SPJ1
