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3 years ago

How do you solve a two step equation

Mathematics

1 answer:

Schach [20]3 years ago

8 0

Isolate the variable, and see what kind of equation it is. if it's adding, let's say, then add one number to itself. this cancels it out, so it's taken care of. next, add that same number to the second one, and take the result. you should be able to subtract that from the answer i believe, it's been a while since I've done these so it might not be spot on

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We would like to create a confidence interval.

Vlada [557]

Answer:

c.A 90% confidence level and a sample size of 300 subjects.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level $1-\alpha$ , we have the confidence interval with a margin of error of:

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

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

In this problem

The proportions are the same for all the options, so we are going to write our margins of error as functions of $\sqrt{\pi(1-\pi)}$

a.A 99% confidence level and a sample size of 50 subjects.

$n = 50$

99% confidence interval

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The margin of error is

$M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{2.575}{\sqrt{50}}\sqrt{\pi(1-\pi)} = 0.3642\sqrt{\pi(1-\pi)}$

b.A 90% confidence level and a sample size of 50 subjects.

$n = 50$

90% confidence interval

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The margin of error is

$M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{1.645}{\sqrt{50}}\sqrt{\pi(1-\pi)} = 0.2623\sqrt{\pi(1-\pi)}$

c.A 90% confidence level and a sample size of 300 subjects.

$n = 300$

90% confidence interval

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The margin of error is

$M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{1.645}{\sqrt{300}}\sqrt{\pi(1-\pi)} = 0.0950\sqrt{\pi(1-\pi)}$

This produces smallest margin of error.

d.A 99% confidence level and a sample size of 300 subjects.

$n = 300$

99% confidence interval

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The margin of error is

$M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{2.575}{\sqrt{300}}\sqrt{\pi(1-\pi)} = 0.1487\sqrt{\pi(1-\pi)}$

6 0

4 years ago

If three angles of a triangle are in the ratio 3:7:10, show that triangle is right –

Galina-37 [17]

3+7+10=20

180/20=9

3x10=90

3 0

4 years ago

Read 2 more answers

Prove the divisibility of the following numbers: 45^10·5^40 by 25^20

beks73 [17]

For this case we have the following expressions:

$45^{10} * 5^ {40}$ and $25^{20}$

Let:

$45^{10} * 5^ {40}$ (Integer m)

$25^{20}$ (Integer n)

By definition, an integer m is divisible by an integer n if the remainder of the division is 0. That is, there is an integer p such that: $m = n * p$

Rewriting the expression we have:

$25^{20} = 5^{2 * (20)} = 5^{ 40}$

So:

$\frac {45^{10} * 5^{ 40}} {5^{40}} =$

We cancel similar terms:

$45^{10}$

We check:

$45^{10} * 5^{ 40} = 5^{ 40} * 45^{ 10}$

Answer:

If they are divisible

6 0

3 years ago

I need some help I’m so bad at geometry

11111nata11111 [884]

Answer:

Triangle BDA

Step-by-step explanation:

Since triangle BDA seems to share congruent sides with triangle ACB they seem to be congruent

7 0

3 years ago

Write an inequality that compares-6, 3, and 5

olga_2 [115]

Is that 6 or negative 6? I'll do both situations, as I can't tell (sorry!)

With negative 6:

-6 < 3 < 5

With positive 6:

3 < 5 < 6

8 0

3 years ago