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3 years ago

20 POINTS PLEASE HELP

Mathematics

1 answer:

aleksley [76]3 years ago

8 0

Answer:

Step-by-step explanation:

Exponents of the same base add

A. 2^4 • 2^3 = 212

2^7 = 128 ≠ 212

B. 3^3 • 3^6 > 3^8

3^9 > 3^8

C. 4^2 • 4^2 > 4^4

4^4 = 4^4

D. 5^5 • 5^2 = 5^10

5^7 ≠ 5^10

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A cylinder with a height of 12 cm has a volume of 1728 pi cm^ 3 What is the diameter of the cylinder?

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Answer:

Step-by-step explanation:

let r be radius of the cylinder.

volume of cylinder=πr²h

1728π=πr²×12

r²=1728 π/12π=144

r=√144=12

diameter=2r=2×12=24 cm

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According to Nielsen Media Research. of all the U.S. households that owned at least one television set, 83% had two or more sets

Rudik [331]

Answer:

The proportion of U.S. households that owned two or more televisions is 83%.

Step-by-step explanation:

To determine whether the proportions of U.S. households that owned two or more televisions is less than 83% or not let us perform a hypothesis test for single proportion.

Assumptions:

The sample size (n) selected by the local cable company is 300 which is quite large. Then according to the Central limit theorem the sampling distribution of sample proportion follows a normal distribution with mean p and standard deviation $\sqrt{\frac{p(1-p)}{n} }$ .

Since the sampling distribution of sample proportions follows a normal distribution use the z-test for one proportion to perform the test.

The hypothesis is:

$H_{0}$ : The proportion of U.S. households that owned two or more televisions is 83%, i.e. $p=0.83$

$H_{1}$ :The proportion of U.S. households that owned two or more televisions is less than 83%, i.e. $p< 0.83$

Decision Rule:

At the level of significance α = 0.05 the critical region for a one-tailed z-test is:

$\\ Z\leq -1.645\\$

**Use the z table for the critical values.

So, if $\\ Z\leq -1.645\\$ the null hypothesis will be rejected.

Test statistic value:

$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$

Here $\hat{p}$ is the sample proportion.

Compute the value of $\hat{p}$ as follows:

$\hat{p}=\frac{X}{n} \\=\frac{240}{300}\\ =0.80$

Now compute the value of the test statistic as follows:

$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\\=\frac{0.80-0.83}{\sqrt{\frac{0.83*(1-0.83)}{300} } } \\=-1.383$

The test statistic is -1.383 which is more than -1.645.

Thus, the test statistic lies in the acceptance region.

Hence we fail to reject the null hypothesis.

Conclusion:

At 0.05 level of significance we fail to reject the null hypothesis stating that the proportion of U.S. households that owned two or more televisions is 83%.

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3 years ago

3. JK Rowling and R.L. Stine are both reading the Hunger Games. J.K. reads 35

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Answer:

Part A:

For J.K. Rowling: 17.5pages/hour

For R.L. Stine: 15pages/hour

Part B:

J.K. Rowling will finish the book first.

Step-by-step explanation:

Part A:

The rate of change in this case represents how much changes a variable in a specific period of time. The variable is the amount of pages.

You have to calculate the amount of pages that J.K. Rowling and R.L. Stine read in one hour.

For J.K. Rowling, 35 pages every 2 hours can be written as:

If you divide 35/2 you can obtain the amount of pages in one hour:

17.5pages/hour (17.5 pages per hour)

For R.L. Stine, 45 pages every 3 hours can be written as:

If you divide 45/3 you can obtain the amount of pages in one hour:

15pages/hour (15 pages per hour)

Part B:

In order to calculate who will finish the hunger games first, you have to calculate the amount of time needed to finish the book.

For J.K. Rowling:

You have to multiply 355 pages by (because in one hour she reads 17.5 pages) to obtain the amount of hours

For R.L. Stine:

You have to multiply 355 pages by (because in one hour he reads 15 pages) to obtain the amount of hours

So, J.K. Rowling will finish the book first because she needs less time than R.L. Stine.

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Step-by-step explanation:

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