In a given hypothesis test, the null hypothesis can be rejected at the 0.10 and the 0.05 level of significance, but cannot be rejected at the 0.01 level. The most accurate statement about the p- value for this test is: A. p-value = 0.01 B. 0.01 < p-value < 0.05 C. 0.05 value < 0.10 D. p-value = 0.10 If we do not reject the null hypothesis, we conclude that: A. there is enough statistical evidence to infer that the alternative hypothesis is true B. there is not enough statistical evidence to infer that the alternative hypothesis is true C. there is enough statistical evidence to infer that the null hypothesis is true D. the test is statistically insignificant at whatever level of significance the tested

Answers

Answer 1

Option B is the correct answer: "There is not enough statistical evidence to infer that the alternative hypothesis is true.".

What is a p-value?

The p-value is the probability that the difference between the observed test statistics and the null distribution is due to chance. If the p-value is less than or equal to the significance level, the null hypothesis is rejected. The following are the correct statements regarding the p-value for this test:

The p-value is greater than or equal to 0.10The most accurate statement is that the p-value is 0.10.

The null hypothesis is rejected at the 0.10 and 0.05 significance levels but cannot be rejected at the 0.01 level.

As a result, the p-value must be greater than 0.01. Therefore, option D is correct.

If we do not reject the null hypothesis, what do we conclude? If we do not reject the null hypothesis, it means that there isn't enough statistical evidence to infer that the alternative hypothesis is true.

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Related Questions

Scroll down to Page 18.

Answers

Step-by-step explanation:

sometimes i just wanna kill my self for pOiNtS

A. 3 (x + 2) = 18

B. x + 2 = 6

1) How can we get Equation B from Equation A?

Choose 1 answer:

(Choice A) Add/subtract the same quantity to/from both sides

(Choice B) Add/subtract a quantity to/from only one side

(Choice C) Multiply/divide both sides by the same non-zero constant

(Choice D) Multiply/divide only one side by a non-zero constant

Answers

Answer:

c

Step-by-step explanation:

2 A marathon race is 42 195 m in length. The world record in 2016 was
2 hours, 2 minutes and 57 seconds held by Dennis Kimetto of Kenya.
a How many seconds in total did Kimetto take to complete the race?
b Calculate his average speed in m/s for the race, giving your answer to
2 decimal places.
c What average speed would the runner need to maintain to complete
the marathon in under two hours?

Answers

Answer:

A. 7377 s

B. 5.72 m/s

C. 5.86 m/s

Step-by-step explanation:

A. Determination of the time in second.

Time (t) = 2 hours, 2 minutes and 57 seconds

We'll begin by converting 2 hours to seconds. This can be obtained as follow:

1 hour = 3600 s

Therefore,

2 hour = 2 hours × 3600 s / 1 hour

2 hours = 7200 s

Next, we shall convert 2 mins to seconds. This can be obtained as follow:

1 min = 60 s

Therefore,

2 mins = 2 mins × 60 s / 1 min

2 mins = 120 s

Finally, we shall determine the total time in second. This can be obtained as follow:

2 hours, 2 minutes and 57 seconds = 7200 s + 120 s + 57 s

= 7377 s

Therefore, the total time in second is 7377 s

B. Determination of the average speed.

Total distance = 42195 m

Total time = 7377 s

Average speed =?

Average speed = Total distance / total time

Average speed = 42195 / 7377

Average speed = 5.72 m/s

Therefore, the average speed is 5.72 m/s

C. Determination of the average speed.

We'll begin by converting 2 hours to seconds. This can be obtained as follow:

1 hour = 3600 s

Therefore,

2 hour = 2 hours × 3600 s / 1 hour

2 hours = 7200 s

Finally, we shall determine the average speed. This can be obtained as follow:

Total distance = 42195 m

Total time = 7200 s

Average speed =?

Average speed = Total distance / total time

Average speed = 42195 / 7200

Average speed = 5.86 m/s

Therefore, the average speed is 5.86 m/s.

1. Find volume, show work round to 2 decimal places

*cylinder*

1. Find volume, show work round to 2 decimal places*cylinder*

Answers

in this case since it's a cylinder always have to do is multiply the two given measurements dancing that she gets all you need to do is run it off to the nearest two decimal places when you say to the nearest two decimal places while trying to say they are two numbers after the coma

Solve the pair of simultaneous equation 4x+6y=21 and 7x-3y=3

Answers

Answer:

X=1.5,y=2.5

Step-by-step explanation:

By elimination method

U have to make either x or y values equal and then eliminate it

The y values have a common value 12

By multiplying 6×2 and 3×4

2(4x+6y)=(21)2

4(7x-3y)=(3)4

8x+12y=42

+

28x-12y=12

36x=54

X=54/36=1.5

Substitute x with 1.5

Y=2.5

The solution to the simultaneous equation is x = 3/2 and y = 5/2.

What is a system of equations?

A system having more than two equations is known as a system of equations

The given pair of equations is:

4x + 6y = 21       (1)

7x - 3y = 3          (2)

Multiply equation (2) by 2 and add into equation (1):

4x + 6y + 14x -6y = 21 + 6

18x = 27

x = 27/18

x = 3/2

Substitute x = 3/2 into equation (1):

4(3/2) + 6y = 21

6 + 6y = 21

6y = 15

y = 15/6

y = 5/2

Hence, the solution to the simultaneous equation is x = 3/2 and y = 5/2.

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A car company claimed that it improved the gas mileage of a particular model of car between 2011 and 2012. A consumer advocacy group obtains a random sample of 16 cars from 2011 and finds the average number of miles driven on exactly 25 gallons of gas in laboratory conditions is 574. 4 miles, with a standard deviation of 43. 1 miles. The consumer advocacy group also obtains a random sample of 24 cars from 2012 and finds the average number of miles driven on exactly 25 gallons of gas in laboratory

conditions is 604. 6 miles, with a standard deviation of 27. 8 miles. The 99% confidence interval for the difference in mean miles driven on 25 gallons of gas (2012 model – 2011 model) is (–3. 95, 64. 35).


Does this confidence interval support the company’s assertion that their gas mileage has increased?


a)Yes, we are 99% confident that the true mean difference in miles driven per 25 gallons is 30. 2 miles.


b)Yes, the fact that most of the values in the confidence interval are positive means that the true mean number of miles driven on 25 gallons is higher in 2012.


c)Yes, the 2012 sample mean of 604. 4 miles per 25 gallons is 30. 2 more miles than the 2011 sample mean of 574. 4, which is an increase of 1. 208 miles per gallon.


d)No, the confidence interval contains 0, so we are 99% confident that the true mean increase in number of miles driven on 25 gallons is 0.


e)No, the confidence interval contains 0, so 0 is a plausible value for the true mean increase in number of miles driven on 25 gallons. An increase of 0 would indicate the gas mileage has not increased

Answers

Using the interpretation of the confidence interval, it is found that the correct option is:

e) No, the confidence interval contains 0, so 0 is a plausible value for the true mean increase in number of miles driven on 25 gallons. An increase of 0 would indicate the gas mileage has not increased.

What is the interpretation of a x% confidence interval?

It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.

In this question, the 99% confidence interval for the increase is of (-3.95, 64.35). It contains 0 and negative values, hence those are plausible values, and this is not enough evidence that the mean has increased, hence option e is correct.

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Which of the following could be an example of a function with a domain
(-∞0,00) and a range (-∞,4)? Check all that apply.
A. V = -(0.25)* - 4
-
□ B. V = − (0.25)*+4
c. V = (3)* +4
□ D. V = − (3)* — 4
-

Which of the following could be an example of a function with a domain(-0,00) and a range (-,4)? Check

Answers

The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4

A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.

From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.

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Which expression is equal to 4x (30 + 7)?

A (4 + 30) × (4.+7)
B. (4 + 30) × (30 + 7)
C (4x30) + (4x7)
D. (4x 30) + (30 27)

Answers

Answer:

I believe the answer is c

Answer and show work plz hurry i will give brainiest PLEASE HURRY TIMED QUESTIONS

Answer and show work plz hurry i will give brainiest PLEASE HURRY TIMED QUESTIONS
Answer and show work plz hurry i will give brainiest PLEASE HURRY TIMED QUESTIONS
Answer and show work plz hurry i will give brainiest PLEASE HURRY TIMED QUESTIONS
Answer and show work plz hurry i will give brainiest PLEASE HURRY TIMED QUESTIONS
Answer and show work plz hurry i will give brainiest PLEASE HURRY TIMED QUESTIONS

Answers

Answer:

14. b

12. b.

13. a.

11. c.

10. I'm not sure (I have not learned this)

3. b.

4. a.

a news poll which estimated that 82% of all voters believe global warming exists had a margin of error of /- 3%. suppose an environmental group planning a follow-up survey on this issue wants to determine a 95% confidence interval with a margin of error of no more than 2%. how large a sample do they need? (for estimate of p use 0.82)

Answers

The needed sample size is 1419. Sample Size is defined as the number of observations in the study.

In the question we have ,

estimate value of all voters who believe global warming ( p) = 82% = 0.82

margin of error (M.E) = 2% = 0.02

confidence of interval is calculated by estimate point value and add or subtract margin of error .

here,we have the value of confidence of interval is 95% = 0.95

Margin of error formula is

M.E = Z × √(p(1-p)/n)

where, p --> is estimated value

n---> sample size , which we required

Z ----> is z-value for observation

for the confidence of interval level 95% , the Z-value is 1.96 exist.

put all value in above formula we get,

0.02 = 1.96 × sqrt( ( 0.82)(1-0.82)/n)

=> 0.02 = 1.96× √(0.82×0.18/n)

= 0.02/1.96 = √0.1476/n => 0.000104= 0.1476/n

=> n = 1419

So, sample size is large and it is 1419.

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find slope (4, -3) (7,10)

Answers

Answer:

The answer is 4 1/3

Step-by-step explanation:

\(m=\frac{10-(-3)}{7-4} =\frac{13}{3} =(simplify)= 4\frac{1}{3}\)

What is the distance between the two points?

What is the distance between the two points?

Answers

7.8 or 8.5 the other ones are ridiculous

Please solve for X and find the measure of A.

Please solve for X and find the measure of A.

Answers

Answer:

x = 18°

m∠A = 110°

Step-by-step explanation:

Hello!

Angle A and Angle B are supplementary. Supplementary means they add up to 180°.

Step 1: Solve for x

We can add the two angles together and make it equal to 180° because they are supplementary.

Angle A + Angle B = 180°5x + 20° + 9x - 92° = 180°14x - 72° = 180°14x = 252°x = 18°

x = 18°

Step 2: Solve for Angle A

Now that we know the value of x, we can plug it in for the equation of Angle A and solve for the measure of Angle A

Angle A = 5x + 20°Angle A = 5(18°) + 20°Angle A = 90° + 20°Angle A = 110°

Angle A = 110°

-Chetan K

Solve the system of equations using the elimination method 2x + 9y = -40

Answers

Wait like find the variables number ?

Please HELP ME Shanti brought 5-46 pounds of shrimp to the seaweed boil. james brought 4-12 pounds of crawfish. Roberto brought 6-58 pounds of crab.How many pounds of seaweed were at the boil?5TH GRADE

Answers

The total weight of seafood at the boil is 16 15/24 pounds.

Hence the correct option is C.

To find the total weight of seafood at the boil, we need to add up the weights of shrimp, crawfish, and crab.

First, we can convert the mixed numbers to improper fractions for easier calculations

Shrimp: 5 4/6 pounds = 5 × 6/6 + 4/6 = 30/6 + 4/6 = 34/6 pounds

Crawfish: 4 1/2 pounds = 4 × 2/2 + 1/2 = 8/2 + 1/2 = 9/2 pounds

Crab: 6 5/8 pounds = 6 × 8/8 + 5/8 = 48/8 + 5/8 = 53/8 pounds

Now we can add these fractions

34/6 + 9/2 + 53/8

We need a common denominator to add these fractions, which is the least common multiple of 6, 2, and 8, which is 24. So we can convert each fraction to have a denominator of 24

(34/6) × (4/4) = 136/24

(9/2) × (12/12) = 108/24

(53/8) × (3/3) = 159/24

Now we can add these fractions

136/24 + 108/24 + 159/24 = 403/24

This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1

403/24 = 16 15/24

Therefore, the total weight of seafood at the boil is 16 15/24 pounds.

Hence the correct option is C.

The given question is incomplete and the complete question is '' Shanti brought 5 4/6 pounds of shrimp to the seafood boil. James brought 4 1/2 pounds of crawfish. Roberto brought 6 5/8 pounds of crab. How many pounds of seafood were at the boil? 15 10/24 pounds 15 10/12 pounds 16 15/24 pounds 7 6 19/24 pounds''.

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The price of a computer is marked down from $550 to $484 for a sale. The
following week, the computer is marked down again by the same percent as
during the week before. How much lower than the original price is the price after
the second markdown?
A $425.92
C
$124.08
B $132.00
D
$58.08

Answers

Answer:

A) $425.92

Step-by-step explanation:

The new price percentage with relation to the previous can be determined by dividing \(p = \frac{484}{550}\). Once we calculate p, we can multiply it by 484, which is equivalent to applying the same discount, thus \(\frac{484}{550}484=425.92\)

jeremiah lives in new york city and takes a taxi almost everywhere he goes. in order to calculate the price of his taxi ride, jeremiah came up with the equation p

Answers

Jeremiah has come up with an equation, p, to calculate the price of his taxi ride in New York City. The equation p represents the total cost of the taxi ride and includes variables such as the base fare, distance traveled, and any additional fees or surcharges. The specific values and coefficients of these variables in the equation determine the final price of the taxi ride.

The equation p that Jeremiah has developed is likely a mathematical representation of the pricing structure for taxi rides in New York City. It takes into account various factors that contribute to the overall cost of the ride. These factors may include a base fare, which is the initial cost incurred upon entering the taxi, a per-mile or per-minute charge for the distance or time traveled, and any additional fees or surcharges that may apply.

The equation p can be customized based on the specific pricing regulations and rates set by the taxi service or the local transportation authority. By plugging in the appropriate values for the variables in the equation, Jeremiah can calculate the total cost of his taxi ride.

It's important to note that the exact form of the equation p will depend on the specific pricing structure and regulations in New York City. Variables such as the base fare, distance traveled, and additional fees can vary across different taxi services and jurisdictions. Therefore, Jeremiah's equation p provides a personalized way for him to estimate and calculate the price of his taxi rides.

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Jeremiah lives in New York City and takes a taxi almost everywhere he goes. In order to calculate the price of his taxi ride, Jeremiah came up with the equation P = 1. 80 x 7+2. 50, where x is the number of miles or partial miles traveled in the taxi. Explain the meaning of the constant 2. 50 as it relates to the situation.

What is the surface area of this composite figure?

What is the surface area of this composite figure?

Answers

Answer:

Step-by-step explanation:

HELP PLEASE ASAP

Proportions/ percents workout 16

HELP PLEASE ASAPProportions/ percents workout 16

Answers

#1

91% of 600.91(60)54.6

#2

12.5% of 600.125(60)7.5

#3

125% of 601.25(60)75

#4

40% of 600.4(60)24
Percents

Solution:

Problem 1.

= 0.91 (60)= 54.6

Problem 2.

= 0.12(60)= 7.5

Problem 3.

= 0.12.5(60)= 75

Problem 4.

= 0.40(60)= 24

If xy = 13 and both x and y are positive integers, then what is the sum of x + y?.

Answers

The sum of x + y is always equal to 14.

What is positive integers?

Positive integers are the numbers that we use to count: 1, 2, 3, 4, and so on. A collection of positive integers excludes numbers with a fractional element that is not equal to zero and negative numbers.

Since x and y are positive integers, we can find the possible values of x and y by finding the factors of 13. The positive integer factors of 13 are 1 and 13. Therefore, the possible pairs of x and y are (1, 13) and (13, 1).

The sum of the two values for x and y in each pair is 14.

So, The sum of x + y is always equal to 14.

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can someone helpp with this

can someone helpp with this

Answers

Here is my answer, hope to help you
can someone helpp with this

Determine whether y=2x^3 represents an exponential function.

Answers

Answer:

This is not an exponential function.

Step-by-step explanation:

x would have to be the exponent for it to be an exponential function.

Quantitative Problem 1t You deposit \( \$ 2,300 \) into an account that pays \( 6 \% \) per year. Your plan is to withdraw this amount at the end of 5 years to use for a down payment on a new car. How

Answers

You will be able to withdraw approximately $3,076.32 at the end of 5 years.

To calculate the amount you will be able to withdraw at the end of 5 years, we can use the future value formula for compound interest.

The formula for calculating the future value (FV) of a present value (PV) invested at an annual interest rate (r) for a certain number of years (t) is:

\(FV = PV * (1 + r)^t\)

Given:

PV = $2,300

r = 6% = 0.06 (decimal representation)

t = 5 years

Substituting these values into the formula, we get:

FV = $2,300 * \((1 + 0.06)^5\)

Calculating the expression inside the parentheses:

\((1 + 0.06)^5 = 1.338225\)

Multiplying the present value by this factor:

FV = $2,300 * 1.338225

FV ≈ $3,076.32

Therefore, you will be able to withdraw approximately $3,076.32 at the end of 5 years.

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You deposit $2,300 into an account that pays 6% per year. Your plan is to withdraw this amount at the end of 5 years to use for a down payment on a new car. How much will you be able to withdraw at the end of 5 years? Do not round intermediate calculations. Round your answer to the nearest cent

I got the first part but i dont onow how to get the other ones

I got the first part but i dont onow how to get the other ones

Answers

The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

m < CAB = 32º.m < FDE = 32º.

How to obtain the value of x?


We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

m < CAB = 7(5) - 3 = 35 - 3 = 32º.m < FDE = 5(5) + 7 = 32º.

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Consider the function g(x)=−(x−1)^3−2. Which ordered pair lies on the inverse of the function?
(62,−3)
(−4, 123)
(3, 1)
(3,−6)

Answers

The ordered pair lie on the inverse of the function is (62,−3).

Option A is the correct answer.

What is a function?

function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -(x - 1)³ - 2

The inverse of f(x).

y = -(x - 1)³ - 2

interchange x and y and solve for y.

x = -(y - 1)3 - 2

(y - 1)³ = -2 - x

(y - 1)³ = -(2 + x)

Cuberoot on both sides.

y - 1 = ∛-(2 + x)

y = ∛-(2 + x) + 1

Now,

Substitute in the inverse of g(x).

(62, -3) = (x, y)

(−4, 123) = (x, y)

(3, 1) = (x, y)

(3,−6) = (x, y)

So,

y = ∛-(2 + x) + 1

y = ∛-(2 + 62) + 1

∛-1 = -1

y = -1∛64 + 1

y = -1 x 4 + 1

y = -4 + 1

y = -3

So,

(62, -3) ______(1)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 - 4) + 1

∛-1 = -1

y = ∛(-2 + 4) + 1

y = ∛2 + 1

y =  1.26 + 1

y = 2.26

So,

(-4, 2.26) _______(2)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) _______(3)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) ______(4)

Thus,

From (1), (2), (3), (4) we see that,

(62, -3) is the solution to the inverse of g(x).

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Aircraft A has 126 more seats than aircraft B. If their total number of seats is 440 ​, find the number of seats for each aircraft.

Answers

Answer:

Aircraft A = 283 seats

Aircraft B = 157 seats

Step-by-step explanation:

Aircraft A = B + 126

Aircraft B

A + B= 440

B + 126 + B= 440

Collect the like terms

B+B+126= 440

2B+126= 440

2B= 440-126

2B= 314

B= 157

Substitute 157 for B in equation 1

A= B+126

A= 157+126

A= 283

Hence Aircraft A has 283 seats and Aircraft B has 157 seats

Find an equation for the line with slope m = -6/7 and which goes through the point (14, 4).​

Answers

Answer:

A line with a slope of – that passes through the point (–14, 4)

Step-by-step explanation:

The equation of a line is typically written as y= mx+b where m is the slope and b is the y- intercept.

Four different linear functions are represented below.Part A: Which function has the graph with a y-intercept closest to 0? Part B: which function has the graph with the greatest y-intercept?Part C: which functions have graphs with slopes less than 4? Check all that apply

Four different linear functions are represented below.Part A: Which function has the graph with a y-intercept
Four different linear functions are represented below.Part A: Which function has the graph with a y-intercept

Answers

We have here four linear functions, and we have to compare the slopes of them as well as their y-intercept. For this, it is important to remember the general equation for the line in the slope-intercept form:

\(y=mx+b\)

Where

• m is the slope of the line

,

• b is the y-intercept of the line (0, b)

The y-intercept is the point where the line passes through the y-axis, and at this point, we have that x = 0.

Finding the slopes and the y-intercept for the four functionsFunction 1

We have in this case that the function passes through the points:

• (0, 5), (1, 1)

We can find the equation of this line using the two-point form of the line equation:

\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

Using the points above, we can label them as follows:

• (0, 5) ---> x1 = 0, y1 = 5

,

• (1, 1) ---> x2 = 1, y2 = 1

Then we have:

\(\begin{gathered} y-5_{}=\frac{1_{}-5}{1-0_{}}(x-0_{}) \\ y-5=-\frac{4}{1}x \\ y-5=-4x \\ y=-4x+5 \end{gathered}\)

Therefore, the slope for this line is m = -4, and the y-intercept is (0, 5).

Function 2

For Function 2 we need to do the same procedure as before. We have to select two points of the function to find its equation:

We can select the following points: (0, 1), (1, 6).

Then we can proceed as we did in the previous part:

• (0, 1) ---> x1 = 0, y1 = 1

,

• (1, 6) ---> x2 = 1, y2 = 6

\(\begin{gathered} y-1_{}=\frac{6_{}-1_{}}{1-0_{}}(x-0) \\ y-1=5x \\ y=5x+1 \end{gathered}\)

Therefore, the slope in Function 2 is 5, m = 5, and the y-intercept is (0, 1).

Function 3

We can see that Function 3 has already its line equation in slope-intercept form:

\(y=-x-2\)

Then the slope for Function 3 is m = -1, and its y-intercept is (0, -2).

Function

From the question, we have:

A parking garage has 230 cars in it when it opens at 8 ( = 0). On the interval 0 ≤ ≤ 10, cars enter the parking garage at the rate ′ () = 58 cos(0.1635 − 0.642) cars per hour and cars leave the parking garage at the rate ′ () = 65 sin(0.281) + 7.1 cars per hour (a) How many cars enter the parking garage over the interval = 0 to = 10 hours? (b) Find ′′(5). Using correct units, explaining the meaning of this value in context of the problem. (c) Find the number of cars in the parking garage at time = 10. Show the work that leads to your answer.

Answers

Therefore, (a) ∫58cos(0.1635t - 0.642)dt from 0 to 10 gives approximately 822.6 cars, (b) ′′(5) = -65cos(0.281) which is approximately -62.4 cars per hour per hour, (c) Approximately 559 cars in the garage at t = 10.


(a) To find the number of cars entering the parking garage over the interval 0 ≤ t ≤ 10, we need to integrate the rate of cars entering the garage with respect to time. ∫58cos(0.1635t - 0.642)dt from 0 to 10 gives approximately 822.6 cars.
(b) To find ′′(5), we need to differentiate the rate of cars leaving the garage with respect to time twice. ′′(t) = -65cos(0.281) and ′′(5) = -65cos(0.281) which is approximately -62.4 cars per hour per hour. This value represents the rate of change of the rate of cars leaving the garage at t = 5.
(c) To find the number of cars in the parking garage at time t = 10, we need to subtract the total number of cars leaving the garage from the total number of cars entering the garage from t = 0 to t = 10. This gives approximately 559 cars in the garage at t = 10.


Therefore, (a) ∫58cos(0.1635t - 0.642)dt from 0 to 10 gives approximately 822.6 cars, (b) ′′(5) = -65cos(0.281) which is approximately -62.4 cars per hour per hour, (c) Approximately 559 cars in the garage at t = 10.

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Find the equation of the line that models.....
Suppose the initial cost to make T-Shirts is $50. Each
T-Shirt costs $6.00 to make.
a) Write an equation to model this situation.
b) How much will it cost to make 10 T-Shirts.
c) Suppose you collected $200. How many T-shirts
can you have made for the club.

Answers

Answer:

a) T= 6s +50

b) $110

c) 25 T-shirts

Step-by-step explanation:

Let $T be the total cost to make T-shirts and s be the number of shirts.

a) T= 6s +50

b) T= 6s +50

When s= 10,

T= 6(10) +50

T= 60 +50

T= 110

It will cost $110 to make 10 T-shirts.

c) T= 6s +50

When T= 200,

200= 6s +50

6s= 200 -50 (-50 on both sides)

6s= 150

s= 150 ÷6 (÷6 on both sides)

s= 25

25 T-shirts have been made for the club.

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