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andrew11 [14]
3 years ago
8

In one year three awards (research, teaching, and service) will be given to a class of 25 graduate students in a specific depart

ment. If each student can receive at most one award, how many possible selections are there?
Mathematics
1 answer:
Murrr4er [49]3 years ago
3 0

Answer:

Step-by-step explanation:

25C3 × 3! = 13800

Alternately,

25×24×23 = 13800

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For the right triangles below, find the exact values of the side lengths b and d.
Ivanshal [37]

Answer:

Step-by-step explanation:

The question lacks the required diagram. Find the diagram attached below;

According to the first triangle, taking 30° as the reference angle, the opposite side of the triangle will be 5 and the adjacent will be the unknown side "b"

According to SOH, CAH, TOA;

tanθ = opposite/adjacent (using TOA)

Given;

θ = 30°, opposite = 5 and adjacent = b

tan30° = 5/b

b = 5/tan30°

b = 5/(1/√3)

b = 5*√3/1

b = 5√3

According to the 45° triangle, the opposite side of the triangle will be d and the hypotenuse will be 7

Using SOH;

sinθ = opposite/hypotenuse

Given;

θ = 45°, opposite = d and adjacent = 7

sin45° = d/7

d = 7sin45°

d = 7(1/√2)

d = 7/√2

Rationalize 7/√2

= 7/√2*√2/√2

=7√2/2

Hence the value of d is 7√2/2

7 0
3 years ago
Researchers measured the percent body fat and the preferred amount of salt (percent weight/volume) for several children. Here ar
Anon25 [30]

Answer: b) τ = 0.3

Step-by-step explanation:

Given the data :

Amount of salt (x)____% body fat(y)

0.2 _______________20

0.3 _______________30

0.4 _______________22

0.5 _______________30

0.7 _______________38

0.9 _______________23

1.1 ________________30

The correlation Coefficient as obtained from the online pearson correlation Coefficient calculator is 0.3281 = 0.3 (to one decimal place) which implies that a weak positive correlation or relationship exists between the preferred amount of salt taken to the percentage body weight of an individual. This is because the value is positive and closer to 0 than 1. The closer the weaker the degree of correlation. With positive values implying a positive relationship (that is an increase in variable A leads to a corresponding increase in B and vice-versa).

4 0
3 years ago
The volume of a rectangular prism is 57 cubic inches. What is the volume of a
BARSIC [14]

Answer:I'd sayb

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Beth said that g(x)=f(x)=x²-12 is a horizontal translation of f(x)=x² . Find and fix the errors and write the correct equation f
gtnhenbr [62]

Answer:

Step-by-step explanation:

it is a vertical translation.

for horizontal translation

f(x)=(x-12)²

8 0
3 years ago
Tim and Tom are trying to earn money to buy a new game system over a 3-month period. Tim saved $45.34 each month. If they need a
Readme [11.4K]
45.34 X 3= 136.02
212.52 - 136.02= 76.50
76.50/3= 25.50

the answer is $25.50
8 0
3 years ago
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