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pogonyaev
3 years ago
14

A vending machine operator has determined that the number of candy bars sold per week by a certain machine is a random variable

with mean 125 and standard deviation 7. His profit on each bar sold is $0.25, and it costs him $2.00 per day to maintain the machine and rent the space for it. What is the mean for Y
Mathematics
1 answer:
docker41 [41]3 years ago
6 0

Answer:

The answer is below

Step-by-step explanation:

Let Y represent the profit per day, and x represent the number of bar sold per day. Hence:

Y = 0.25x - 2

a) The mean is given as:

\mu_y=E(Y)=E(0.25X-2) = 0.25E(X)-2\\\\But\ E(X)=mean\ of\ machine=125. Hence:\\\\E(Y)=0.25(125)-2=29.25\\\\E(Y)=\$29.25

b) The standard deviation of y is:

\sigma_y=var(0.25X-2)\\\\\sigma_y=0.25\sigma(X)\\\\but\ \sigma_X=7,hence:\\\\\sigma_y=0.25(7)=1.75\\\\\sigma_y=\$1.75

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Suppose that, on a 3,000-mile New York to Los Angeles flight, United Continental, American, and Southwest flew a total of 270 em
allsm [11]

Answer:

The number of empty seats each of these three airlines carried on its flight are as follows:

United Continental = 150 empty seats

American = 50 empty seats

Southwest = 70 empty seats

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf for the complete question.

The explanation of the answers is now provided as follows:

Let U, A and W represents number of empty seats of United Continental, American, and Southwest respectively. Therefore, we have:

U + A + W = 270 ………………………. (1)

Since United Continental had three times as many empty seats as American, this implies that:

U = 3A ………………………………… (2)

Substituting U = 3A into equation (1), we have:

3A +A + W = 270

4A + W = 270

W = 270 - 4A ………………………….. (3)

For the cost, we have:

3,000[((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100)] = $114,990

((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100) = $114,990 / 3,000

((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100) = 38.33

0.447A + 0.146A + 0124W = 38.33

0.593A + 0.124W = 38.33 ………………… (4)

Substituting W = 270 - 4A from equation (3) into (4) and solve for A, we have:

0.593A + 0.124(270 - 4A) = 38.33

0.593A + 33.48 - 0.496A = 38.33

0.593A - 0.496A = 38.33 - 33.48

0.097A = 4.84

A = 4.84 / 0.097

A = 49.8969072164948

Rounding to a whole number, we have:

A = 50

Substituting A = 50 into each of equations (2) and (3), we have:

U = 3 * 50 = 150

W = 270 - (4 * 50) = 70

Therefore, the number of empty seats each of these three airlines carried on its flight are as follows:

United Continental = 150 empty seats

American = 50 empty seats

Southwest = 70 empty seats

Download pdf
6 0
2 years ago
2. The water level in a reservoir is now 52 meters. Which equation can be used to find the initial depth, d, if this is the wate
Maru [420]

Answer:

1.23d = 52

Explanation:

If 52 meters is the water level after a 23% increase, then we can say that the initial depth d added to the 23% of d is equal to 52 meters. So:

d + 23%d = 52 meters

Since 23% is equivalent to 0.23, we get:

d + 0.23d = 52

Finally, adding the like terms, we get:

(1 + 0.23)d = 52

1.23d = 52

So, the equation is:

1.23d = 52

8 0
11 months ago
Jean drove 64 miles per hour for a total of 448 miles on a trip. She used the equation below to calculate the time, t, it would
Alexandra [31]

Answer:

Step-by-step explanation:

since there is no given formula I'm guessing that's what we want to find?

use the dist. = rate * time   formula for this kind of problem

or  d = r*t     ( this looks like the word  "dirt" to me so I call this the dirt formula partly b/c it's dirt simple, and it's generally about moving across some give dist. of dirt  :P )  

so Jean's rate is 64 MPH

her total distance is 448 miles  

rearrange the  d = rt  formula so that you are solving for the thing you don't know.. yet....   t (time)  for this case

soooo...

d/r = t

plug in number

448 / 64 = t

7 = t  (in hours)

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3 years ago
Candace wants to find the height of a local lighthouse. Since she knows something about similar triangles, she decides to stand
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In short, let x be the height of the Light House
2.5/36 = 1.5/X

===> X= (36 x 1.5)/2.5 = 21.6 meters
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3 years ago
What height on the wall will a 15 foot ladder reach if its plaxed 3.5 feet from the base of a wall
quester [9]
I would be happy to help with this question!
you would need to use the pythagorean theorem inputting 3.5 for a and 15 for c. after this you will need to solve for b and you should get the answer of 14.6feet
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