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dexar [7]
3 years ago
8

I need some help with these math problems

Mathematics
1 answer:
photoshop1234 [79]3 years ago
3 0

a. Number of more pictures they could take = 43 pictures (approx.)

b. The inequality can be given as 1 ≤ pictures taken ≤ 43

c. The inequality 1 ≤ pictures taken ≤ 43 represents that the pictures taken are equal to or greater than 1 to less than or equal to 43 (The inequality consists of 1 to 43 pictures)

<u>Step-by-step explanation</u>:

a. <u>Given</u>,

The total memory capacity = 65536 KB

The memory for 1 picture = 760 KB

The number of pictures already taken = 43 pictures

The memory used for 43 pictures = 760 * 43 = 32680 KB

The remaining memory space = total memory - used memory

                                                  = 65536 - 32680 = 32856 KB

Number of more pictures they could take = remaining space / space per picture

= 32856 KB / 760 KB = 43.231 ≈ 43 pictures.

b. <u>Given</u>,

Number of pictures taken during school = 19 pictures.

Number of pictures taken after school = 24 pictures.

The inequality can be given as 1 ≤ pictures taken ≤ 43

c. <u>Inequality</u> :

<em>"An inequality is a relation that compares a set of values between two numbers and it does not equals to a particular number alone".</em>

Here, the inequality 1 ≤ pictures taken ≤ 43 represents that the pictures taken are equal to or greater than 1 to less than or equal to 43 (The inequality consists of 1 to 43 pictures)

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Ten years ago 53% of American families owned stocks or stock funds. Sample data collected by the Investment Company Institute in
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Answer:

a) The null and alternative hypothesis are:

H_0: \pi=0.53\\\\H_a:\pi

b) If 300 families were sampled, for a significance level of 5%, there is enough evidence to support the claim that a smaller proportion of American families own stocks or stock funds this year than 10 years ago (P-value = 0.001).

 

Step-by-step explanation:

The claim that we want to have evidence to support is that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.

The hypothesis for this test should state:

- For the null hypothesis, that the population proportion is not significantly different from 53%.

H_0:\pi=0.53

- For the alternative hypothesis, that the population proportion is significantly less than 53%.

H_a: \pi

If 300 families are sampled, we can perform a hypothesis test for a proportion.

The claim is that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.

Then, the null and alternative hypothesis are:

H_0: \pi=0.53\\\\H_a:\pi

The significance level is 0.05.

The sample has a size n=300.

The sample proportion is p=0.44.

The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.53*0.47}{300}}\\\\\\ \sigma_p=\sqrt{0.00083}=0.029

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z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.44-0.53+0.5/300}{0.029}=\dfrac{-0.088}{0.029}=-3.065

This test is a left-tailed test, so the P-value for this test is calculated as:

\text{P-value}=P(z

As the P-value (0.001) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.

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