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3 years ago

In a class of 24 students, 25 percent of them failed a test. How many students failed a test

Mathematics

2 answers:

scZoUnD [109]3 years ago

8 0

25 is 1/4 and 1/4 of 24 is 6 ( that is the easy way)

Tcecarenko [31]3 years ago

4 0

X/24 = 25/100
100x = 600
100x/100 = 600/100
x = 6
6 students failed the test

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A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained i

Scorpion4ik [409]

Answer:

a) We need a sample size of at least 3109.

b) We need a sample size of at least 4145.

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 of $1-\alpha$ , we have the following confidence interval of proportions.

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

In which

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

The margin of error is:

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

99% confidence level

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

(a) he uses a previous estimate of 25%?

we need a sample of size at least n.

n is found when $M = 0.02, \pi = 0.25$ . So

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

$0.02 = 2.575\sqrt{\frac{0.25*0.75}{n}}$

$0.02\sqrt{n} = 2.575\sqrt{0.25*0.75}$

$\sqrt{n} = \frac{2.575\sqrt{0.25*0.75}}{0.02}$

$(\sqrt{n})^{2} = (\frac{2.575\sqrt{0.25*0.75}}{0.02})^{2}$

$n = 3108.1$

We need a sample size of at least 3109.

(b) he does not use any prior estimates?

When we do not use any prior estimate, we use $\pi = 0.5$

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

$0.02 = 2.575\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 2.575\sqrt{0.5*0.5}$

$\sqrt{n} = \frac{2.575\sqrt{0.5*0.5}}{0.02}$

$(\sqrt{n})^{2} = (\frac{2.575\sqrt{0.5*0.5}}{0.02})^{2}$

$n = 4144.1$

Rounding up

We need a sample size of at least 4145.

8 0

3 years ago

Multi step equations plz help me with the problems in the picture

Natali [406]

6. 5
8. 3
10. 3
12. -5
14. 11
16. 27
18. 21

I don't garentee this is correct but I'm pretty sure.

6 0

3 years ago

Read 2 more answers

A farmer builds a fence to enclose a rectangular pasture.He uses 160 feet of fence. Find the total area if the pasture is 50 fee

Sergeeva-Olga [200]

2L +2W=160
100+ 2W=160
subtract 100 from each side
2W=60
divide by two each side
W=30
use the formula L×W=Area or 50×30 which equals 150 the are of the pasture is 150 feet²

3 0

3 years ago

Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary. Hint: Use the Pythagorean T

Paul [167]

The distance between two points on the plane is given by the formula below

$\begin{gathered} A=(x_1,y_1),B=(x_2,y_2) \\ \Rightarrow d(A,B)=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2} \end{gathered}$

Therefore, in our case,

$A=(-1,-3),B=(5,2)$

Thus,

$\begin{gathered} \Rightarrow d(A,B)=\sqrt[]{(-1-5)^2+(-3-2)^2}=\sqrt[]{6^2+5^2}=\sqrt[]{36+25}=\sqrt[]{61} \\ \Rightarrow d(A,B)=\sqrt[]{61} \end{gathered}$

Therefore, the answer is sqrt(61)

In general,