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3 years ago

The distance, y, in miles, traveled by a car for a certain amount of time, x, in hours, is shown in the graph below:

Mathematics

1 answer:

Hoochie [10]3 years ago

4 0

Answer:

It travels for 1 h, then stops for 1 h, and finally travels again for 3 h.

Step-by-step explanation:

The sloped parts of the graph are where the car is moving.

For example, in the first hour the distance travelled changes from zero to 12 mi.

The horizontal part of the graph is where the car is stopped.

For example, between hours 1 and 2, the distance travelled stays the same at 12 mi.

The car travels for 1 h, then stops for 1 h, and finally travels again for 3 h.

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Sample Size for Proportion As a manufacturer of golf equipment, the Spalding Corporation wants to estimate the proportion of gol

Dima020 [189]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56$

And rounded up we have that n=2663

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$t_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.025$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume an estimated proportion of $\hat p =0.5$ since we don't have prior info provided. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56$

And rounded up we have that n=2663

6 0

3 years ago

A history exam features five questions. Three of the questions are multiple-choice with four options each. The other two questio

nadezda [96]

There are total 500 ways in which Caroline can answer the exam.

Step-by-step explanation:

Here, the total number of questions in the test = 5

The total number of multiple choice questions = 3

The total number of True/False question = 2

Let the numbers of the given question be 1,2 ,3,4, and 5.

Now, the total number of options available to answer question 1 = 5 options

Similarly, number of options available to answer question 2 = 5 options

The number of options available to answer question 3 = 5 options

The number of options available to answer question 4 = 2 options ( T or F)

The number of options available to answer question 5 = 2 options ( T or F)

So, here the total available options to answer all 5 questions

= The total option available for question ( 1 x 2 x 3 x 4 x 5)

= ( 5 ways x 5 ways x 5 ways x 2 ways x 2 ways)

= 500 ways

Hence, there are total 500 ways in which Caroline can answer the exam.

8 0

3 years ago

-4x – 2y=-12<br> 4x + 8y=-24<br> Solve each system by elimination

kirza4 [7]

Answer:

x = 6 and y = - 6

Step-by-step explanation:

- 4 x - 2 y = -12.......equ No 1

4 x + 8y = - 24.......equ No 2

Adding equ No 1 and equ No 2

6 y = - 36

∴ y = - 6

substitute y = - 6 in equ No 2

4 x + 8 y = -24

4 x + 8 ×( -6) = - 24

4 x - 48 = -24

4 x = -24 + 48

4 x = 24

∴ x = 6

x = 6 and y = - 6

7 0

3 years ago

Write an equation in slope intercept form for the cost at each store

Allushta [10]

Answer:

See attachment

Step-by-step explanation:

On attachment

7 0

3 years ago

Meg is a veterinarian. She found that 10 of the 59 dogs she saw this week were boxers. Steve is also a veterinarian. He found th

Finger [1]

Answer:

Meg:percent Steve:part

Step-by-step explanation:

I got it right

6 0

3 years ago