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2 years ago

Darius wants to create a large mural to cover part of his wall. He drew a sketch of his design to

Mathematics

1 answer:

LiRa [457]2 years ago

5 0

Model mural::

L*W = 0.3 sq. ft

--------------

Actual mural::

(5L)(5W) = 25*LW = 25*0.3 = 7.5 sq ft.

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A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimat

Vedmedyk [2.9K]

Using the z-distribution, we have that:

a) A sample of 601 is needed.

b) A sample of 93 is needed.

c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.

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

In which z is the z-score that has a p-value of $\frac{1+\alpha}{2}$ .

The margin of error is:

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

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 $z = 1.96$ .

For this problem, we consider that we want it to be within 4%.

Item a:

The sample size is <u>n for which M = 0.04.</u>

There is no estimate, hence $\pi = 0.5$

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

$0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2$

$n = 600.25$

Rounding up:

A sample of 601 is needed.

Item b:

The estimate is $\pi = 0.96$ , hence:

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

$0.04 = 1.96\sqrt{\frac{0.96(0.04)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.96(0.04)}$

$\sqrt{n} = \frac{1.96\sqrt{0.96(0.04)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.96(0.04)}}{0.04}\right)^2$

$n = 92.2$

Rounding up:

A sample of 93 is needed.

Item c:

The closer the estimate is to $\pi = 0.5$ , the larger the sample size needed, hence, the correct option is A.

For more on the z-distribution, you can check brainly.com/question/25404151

8 0

2 years ago

(PLEASE HELP) The histogram shows the number of hours that 25 college students spent studying for their final exams. Which state

Semmy [17]

The statement on the bottom left is correct. (6 students studied for 20 to 24 hours)

6 0

3 years ago

Read 2 more answers

Please help

OlgaM077 [116]

First, we're going to see the candies per minute that machine C packs.
150 / 2 = 75

Now that we know that machine C packs 75 candies per minute, we're going to multiply the candies machine C makes by 11 minutes.
75 x 11 = 825

We're now gonna do the same with machine D.
130 x 11 = 1430

Then we're going to find the difference between machine C and machine D, we do this because the question basically asks how much more candies can machine D pack than machine C.
1430 - 825 = 605 candies.

This is how we find our final answer.

Our answer would be D) 605.

Hope this helps!~

4 0

3 years ago

Simplify 3c^2 + 5c^2 - c^2

yKpoI14uk [10]

Since they’re all like terms u can just add/subtract them
3+5-1=7
7c^2 is the answer

6 0

3 years ago

Read 2 more answers

Someone please help me !!!

alexandr1967 [171]

Because this triangle is a right traingle and has one angel that is 45 degrees, the third angle must be 45 degrees to because 90+45+45=180. With that, km must be the same length as lm. we know lm is 5 so km is 5 too. No we can plug this into the Pythagorean Theorem too get

5^2+5^2=c^2

25+25=c^2

50=c^2

√50=√c^2

√25*2=c

5√2=c

Thats your answer to the length of lk.

3 0

3 years ago