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kati45 [8]
3 years ago
14

A large university accepts 70​% of the students who apply. Of the students the university​ accepts, 45​% actually enroll. If 30

comma 000 students​ apply, how many actually​ enroll?
Mathematics
1 answer:
uysha [10]3 years ago
4 0

Answer: the number of students that actually enroll is 9450

Step-by-step explanation:

The large university accepts 70​% of the students who apply. If 30 comma 000 students​ apply, it means that the total number of students that applied is 30000 and the number of students accepted would be 70/100 × 30000 = 21000

Of the students that the university​ accepts, 45​% actually enroll. This means that the number of students that enrolled would be

45/100 × 21000 = 0.45×21000

= 9450

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The brand name of Mrs. Fields (cookies) has a 90% recognition rate. If Mrs. fields herself wants to verify that rate by beginnin
Schach [20]

Answer:

0.3874 = 38.74% probability that exactly 9 of the 10 consumers recognize her brand name.

0.6126 = 61.26% probability that the number who recognize her brand name is not nine.

Step-by-step explanation:

For each consumer, there are only two possible outcomes. Either they recognize the name, or they do not. The probability of a customer recognizing the name is independent of anu other customer. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

The brand name of Mrs. Fields (cookies) has a 90% recognition rate.

This means that p = 0.9.

Sample of 10

This means that n = 10

Find the probability that exactly 9 of the 10 consumers recognize her brand name.

This is P(X = 9). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 9) = C_{10,9}.(0.9)^{9}.(0.1)^{1} = 0.3874

0.3874 = 38.74% probability that exactly 9 of the 10 consumers recognize her brand name.

Also, find the probability that the number who recognize her brand name is not nine.

1(100%) subtracted by those who recognize. So

1 - 0.3874 = 0.6126

0.6126 = 61.26% probability that the number who recognize her brand name is not nine.

4 0
3 years ago
What is the slope of the line passing through the points (0,4) and (-8, -1)?​
telo118 [61]

Answer: The top left one is -3, 6     bottom right is -6, 3

Step-by-step explanation:

3 0
2 years ago
Find the equation of the line perpendicular to y =<br> 3x + 6 and containing the point (-9,-5).
neonofarm [45]

The equation of the line perpendicular to y =  3x + 6 and containing the point (-9,-5) is y = \frac{-1}{3}x - 8

<em><u>Solution:</u></em>

Given that line perpendicular to y =  3x + 6 and containing the point (-9, -5)

We have to find the equation of line

<em><u>The slope intercept form is given as:</u></em>

y = mx + c  ------ eqn 1

Where "m" is the slope of line and "c" is the y - intercept

<em><u>Let us first find the slope of line</u></em>

The given equation of line is y = 3x + 6

On comparing the given equation of line y = 3x + 6 with eqn 1, we get,

m = 3

Thus the slope of given equation of line is 3

We know that <em>product of slopes of given line and slope of line perpendicular to given line is equal to -1</em>

Slope of given line \times slope of line perpendicular to given line = -1

3 \times \text{ slope of line perpendicular to given line }= -1

\text{ slope of line perpendicular to given line } = \frac{-1}{3}

Let us now find the equation of line with slope m = \frac{-1}{3} and containing the point (-9, -5)

Substitute m = \frac{-1}{3} and (x, y) = (-9, -5) in eqn 1

-5 = \frac{-1}{3}(-9) + c\\\\-5 = 3 + c\\\\c = -8

<em><u>Thus the required equation of line is:</u></em>

Substitute m = \frac{-1}{3} and c = -8 in eqn 1

y = \frac{-1}{3}x - 8

Thus the required equation of line perpendicular to given line is found

6 0
3 years ago
Jon Ericson bought a home with a 11.5% adjustable rate mortgage for 20 years. He paid $10.67 monthly per thousand on his origina
Eva8 [605]

You are told to ignore the amount of principal paid, so you are apparently to assume the loan amount was for $50 thousand.

a) The old monthly payment was $10.67×50 = $533.50

b) The new monthly payment is $11.72×50 = $586.00

c) The increase in monthly payment is figured in the usual way:

... (new/old -1)×100% = (1.0984-1)×100% = 9.84%

_____

In reality, about 3% of the loan will have been paid at the end of 2 years. Thus, the original loan amount may have been near $51,500. This problem is telling you to ignore the difference.

3 0
3 years ago
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Can some help me with my homework it’s number 5. 6. 7. 8. And 9.
BaLLatris [955]

Answers:

5. 296

6. 479

7. 801

8. 920

9. $281

Step-by-step explanation:

For 5-8, you add the 2 numbers. Line up the numbers by their place value.

For 9, it says she starts with $233. She worked for 6 hours today. She makes $8 for every hour. First, you have to find how much she made today. 6 hrs times $8 for every hr is $48. In total, she has $281 because we added the amount she starts with, and the amount she earned today.

4 0
3 years ago
Read 2 more answers
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