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larisa [96]
3 years ago
9

The admissions office of a private university released the following data for the preceding academic year: From a pool of 3900 m

ale applicants, 30% were accepted by the university, and 30% of these subsequently enrolled. Additionally, from a pool of 3600 female applicants, 35% were accepted by the university, and 30% of these subsequently enrolled. What is the probability of each of the following?
a. A male applicant will be accepted by and subsequently will enroll in the university?
b. A student who applies for admissions will be accepted by the university?
c. A student who applies for admission will be accepted by the university and subsequently will enroll?
Mathematics
1 answer:
Finger [1]3 years ago
7 0

Answer:

a. 0.09 or 9%

b. 0.324 or 32.4%

c. 0.0972 or 9.72%

Step-by-step explanation:

Male applicants = 3900

Female applicants = 3600

Total applicants = 7,500

Proportion of male applicants (m) = 0.52

Proportion of female applicants (f) = 0.48

a. The probability that a random male applicant is accepted and enrolls is given by the probability of a male student being accepted multiplied by the probability of a male student enrolling:

P(a) = 0.30*0.30=0.09=9\%

b. The probability that a random student is accepted is given by the probability of a male applicant being accepted added to the probability of a female applicant being accepted

P(b) = m*0.30+f*0.35\\P(b) = 0.52*0.30+0.48*0.35\\P(b) = 0.324=32.4\%

c. The probability that a random student is accepted and enrolls is given by the probability of a male applicant being accepted and enrolling added to the probability of a female applicant being accepted and enrolling

P(b) = m*0.30*0.30+f*0.35*0.30\\P(b) = 0.52*0.30*0.30+0.48*0.35*0.30\\P(b) = 0.0972=9.72\%

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Determine if the situation is a percent INCREASE or DECREASE
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Step-by-step explanation:

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3 years ago
What is the slope of the line which passes through (4, 7) and (2, 3)? (5 points)
Basile [38]

Answer:

slope = 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (4, 7)

m = \frac{7-3}{4-2} = \frac{4}{2} = 2

3 0
2 years ago
Find the range of y = -3x + 7 for the domain {-8, -6, -3, -2, 2}
svetlana [45]
The domain is the set of x-values of a function. The range is the set of y-values of a function.

You are told that the domain, or x-values, are -8, -6, -3, -2, and 2. To find the range, you just need to plug in each of the x-values into the function <span>y = -3x + 7 and find the value of y.
1) When x = -8:
</span><span>y = -3x + 7
y = -3(-8) + 7
y = 24 + 7
y = 31

2) When x = -6
</span>y = -3x + 7
y = -3(-6) + 7
y = 18 + 7
y = 25

3) When x = -3
y = -3x + 7
y = -3(-3) + 7
y = 9 + 7
y = 16

4) When x = -2
y = -3x + 7
y = -3(-2) + 7
y = 6 + 7
y = 13

5) When y = 2
y = -3x + 7
y = -3(2) + 7
y = -6 + 7
y = 1

The range is {31, 25, 16, 13, 1}.

-------

Answer: 
{31, 25, 16, 13, 1}
5 0
3 years ago
A least squares regression line was calculated to relate the length​ (cm) of newborn boys to their weight in kg. The relationshi
maks197457 [2]

Answer:

58.6% of the variation in length (in cm) of new born boys and their weight (in kg) is explained by the line of best fit.

Step-by-step explanation:

Given the following :

R² value = 58.6% comparing the length (cm) of new born boys to their weight (kg)

The R² value is called the Coefficient of determination. It is obtained by taking the square of the correlation Coefficient (R). The value gives the proportion of Variation between the independent and dependent variables which is explained by regression line. In the scenario above, the R² value means that 58.6% of the variation in length in centimeter of new born boys and their weight (in kg) is explained by the line of best fit. While (100% - 58.6% = 41.4%) is due to other factors.

8 0
3 years ago
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