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Salsk061 [2.6K]

3 years ago

7

Lori needs more than 250 signatures to run for the position of class president for her middle school. She already has 75 signatu

res and believes that she can get 25 more signatures each day. She wants to figure out how many days, d, she should collect the signatures she needs. Which inequality and solution for d correctly represent Lori’s situation?

1 answer:

olga55 [171]3 years ago

7 0

Answer:

75 + 25d > 250

d > 7

Step-by-step explanation:

Number of signatures needed : > 250

Amount of signatures ready = 75

Exoected number of signatures per day = 25

Number of days, d, needed signatures will be collected ;

Number of ready signatures + (expected number of signatures per day * number of days) > number of signatures needed

Mathematically,

75 + 25d > 250

25d > 250 - 75

25d > 175

d > 175 / 25

d > 7

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Using the z-distribution, as we are working with a proportion, it is found that 1016 constituents are required.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

The margin of error is given by:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.

The estimate is of $\pi = 0.61$ , while the margin of error is of M = 0.03, hence solving for n we find the minimum sample size.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.96\sqrt{\frac{0.61(0.39)}{n}}$

$0.03\sqrt{n} = 1.96\sqrt{0.61(0.39)}$

$\sqrt{n} = \frac{1.96\sqrt{0.61(0.39)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.61(0.39)}}{0.03}\right)^2$

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More can be learned about the z-distribution at brainly.com/question/25890103

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1 year ago

If the length of each side of an equilateral triangle were increased by 50 percent, what would be the percent increase in the ar

Shkiper50 [21]

Answer:

<u><em>The area increase by 225%</em></u>

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

<em><u>attachment of a triangle</u></em>

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<em><u>A= $\frac{a*h}{2}$ </u></em>

<em><u> $h^{2} +(\frac{a}{2})^{2}$ = $a^{2}$ </u></em>

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<em><u>replacing in the A equation:</u></em>

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