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a_sh-v [17]
3 years ago
15

Salaries differ greatly between faculty members at public universities in the United States. Full professors (who have tenure an

d do research) earn an average of $125,572 per year with a standard deviation of $18,328. Associate professors (who are working towards tenure and do research) earn an average of $90,101 per year with a standard deviation of $12,741. Lecturers (whose primary responsibility is teaching and do not earn tenure) earn an average of $59,707 per year with a standard deviation of $7,386. Assume all three populations are normally distributed.
a. What is the probability that a randomly selected full professor makes less than $100,000 per year?

Mathematics
1 answer:
fiasKO [112]3 years ago
8 0

We standardize the $100,000 as a z score of

z = (100,000 - 125572)/18328 = -1.395

That's 1.4 standard deviations below the mean.   We look up the area of the standard normal from -infinity to -1.40 standard deviations and find

P(salary < $100,00) = 0.08076 = 8%

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Four different digits from 1 to 9 are required to open a safe.
masha68 [24]

Answer:  5942

<u>Step-by-step explanation:</u>

Clue 4 states exactly two of the digits = 1, 4, or 9

Clue 1 leaves us with the following combinations:

1, 9, 2, 8

1, 9, 3, 7    eliminate by clue 5

4, 9, 2, 5

1, 4, 7, 8

Clue 5 directs us to the following order for 1,9,2,8

2 __ __ 1     --> 2981 or 2891   eliminate by clue 2

9 __ __ 8    --> 9128 or 9218   eliminate by clue 6

9 __ __ 2    --> 9182 or 9812   eliminate by clue 6

Clue 5 directs us to the following order for 4,9,2,5

5 __ __ 2     --> 5492 or 5942   eliminate 5492 by clue 2

9 __ __ 2    --> 9452 or 9542   eliminate by clue 3

Clue 5 directs us to the following order for 1,4,7,8

4 __ __ 1    --> 4781 or 4871    eliminate by clue 2

The only combination not eliminated is 5-9-4-2, which satisfies all six clues.

1) 5 + 9 + 4 + 2 = 20

2) 5 > 4

3) 9 - 2 > 5

4) 4 & 9 but not 1 are included

5) 5 + 2 = 7, which is a prime number

6) 2 <  5, 9, 4

5 0
3 years ago
{29, 29, 29, 28, 28, 27}
Tatiana [17]
A is the answer hope this helps
4 0
3 years ago
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HELP PLZ ILL MAKE YOU BRAINLEIST
klemol [59]

Answer:

depends on the force acting on the two objects. For the gravitational force the formula is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m / s2 at the surface of the earth) and h is the height in meters.

Step-by-step explanation:

7 0
3 years ago
"If x is not &gt; 0, then x^2 is not &gt; 10" is the: -
Elanso [62]
<span>If </span><span /><span><span><span><span><span><span>x</span><span>≠</span><span><span><span>0</span></span></span></span><span /></span></span><span /></span><span>x≠0</span></span><span>, then </span><span /><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>x</span><span /></span><span><span>2</span><span /></span></span></span></span><span /></span><span><span><span><span>−</span><span /></span><span><span>−</span><span /></span></span><span /></span><span><span><span>√</span></span><span /></span></span></span><span /></span><span><span>x</span><span /></span><span><span /><span /></span></span></span><span>=</span></span><span /></span></span><span /></span><span>x2x=</span></span>
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3 years ago
F(x)=x^2+8x-10 find f(a)+5
Papessa [141]

Answer:

We conclude that:

f(a) + 5 = a² + 8a - 5

Step-by-step explanation:

Given

The function is given by

f(x) = x²+8x-10

To determine

f(a)+5

In order to determine f(a)+5, first, we need to determine f(a).

Now substitute x = a in the function f(x) = x²+8x-10

f(a) = (a)² + 8(a) - 10

f(a) = a² + 8a - 10

Thus,

f(a) + 5 = (a² + 8a - 10) + 5

f(a) + 5 = a² + 8a - 5

Therefore, we conclude that:

f(a) + 5 = a² + 8a - 5

4 0
2 years ago
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