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Shalnov [3]
3 years ago
7

A large university accepts 60% of the students who apply. Of the students the university accepts, 25% actually enroll. If 10,000

students apply, how many actually enroll?​
Mathematics
1 answer:
Alja [10]3 years ago
6 0

Answer:

1500 students

Step-by-step explanation:

To do this you must figure how many people the university accepts by times the no. of students applying by the percentage that are accepted

10,000 X 60% = 6000 students

You then figure out the number of students that actually enrols by doing

no. of students accepted X 25%

6000 X 25% = 1500 students

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Which of the following segments is tangent to the circle?
MrRissso [65]
2) DE

Best luck with your studying
3 0
3 years ago
A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N. A new batch of yarn was made, usin
AlexFokin [52]

Answer:

The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction of normal variables:

When we subtract two normal variables, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N.

This means that \mu_1 = 6.1, s_1 = \frac{0.7}{\sqrt{125}} = 0.0626

In a sample of 75 pieces of yarn from the new batch, the mean breaking strength was 5.8 N and the standard deviation was 1.0 N.

This means that \mu_2 = 5.8, s_2 = \frac{1}{\sqrt{75}} = 0.1155

Distribution of the difference:

\mu = \mu_1 - \mu_2 = 6.1 - 5.8 = 0.3

s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0626^2+0.1155^2} = 0.1314

Confidence interval:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.9}{2} = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.05 = 0.95, so Z = 1.645.

Now, find the margin of error M as such

M = zs

M = 1.645*0.1314 = 0.22

The lower end of the interval is the sample mean subtracted by M. So it is 0.3 - 0.22 = 0.08N

The upper end of the interval is the sample mean added to M. So it is 0.3 + 0.22 = 0.52N

The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).

3 0
3 years ago
Use the definition of the derivative to differentiate v=4/2 pie r^3
nata0808 [166]

I suspect 4/2 should actually be 4/3, since 4/2 = 2, while 4/3 would make V the volume of a sphere with radius r. But I'll stick with what's given:

\displaystyle \frac{dV}{dr} = \lim_{h\to0} \frac{2\pi(r+h)^3-2\pi r^3}{h}

\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{(r^3+3r^2h+3rh^2+h^3)- r^3}{h}

\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{3r^2h+3rh^2+h^3}{h}

\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} (3r^2+3rh+h^2)

\displaystyle \frac{dV}{dr} = 2\pi \cdot 3r^2 = \boxed{6\pi r^2}

In Mathematica, you can check this result via

D[4/2*Pi*r^3, r]

3 0
2 years ago
Please help!! 15 Points!!!!
Ray Of Light [21]

Answer:

I think it is ether A are B

3 0
3 years ago
Read 2 more answers
State the domain and range<br> {(2,4), (3,7), (4,9), (6,11)}
mihalych1998 [28]

Answer:

Domain= 2,3,4,6

Range=4,7,9,11

or

Domain [2,6]

Range [4,11]

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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