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Zepler [3.9K]
3 years ago
9

Mr peterson will buy 80 feet of fencing. The pieces of fence come in whole numbers of feet. His enclosure will be a rectangle an

d have 4 sides. If he wants to enclose the least area, what should be the length, width, and area?
Mathematics
1 answer:
DIA [1.3K]3 years ago
5 0
The perimeter is:
 P = 2x + 2y = 80
 The area is:
 A = x * y
 The area as a function of a variable is:
 A (x) = x * (40-x)
 Rewriting we have:
 A (x) = 40x-x ^ 2
 We derive the function:
 A '(x) = 40-2x
 We equal zero and clear x:
 40-2x = 0
 2x = 40
 x = 40/2
 x = 20 feet
 The other dimension is:
 y = 40 - x
 y = 40 - 20
 y = 20 feet
 The area will be:
 A = x * y
 A = 20 * 20
 A = 400 feet ^ 2
 Answer:
 
The dimensions are:
 
x = 20 feet
 
y = 20 feet
 
The area is:
 
A = 400 feet ^ 2
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The average student loan debt for college graduates is $25,150.
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Using the normal distribution, it is found that:

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c) Low: $23,519.65, High: $26,580.35.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

\mu = 25150, \sigma = 12050.

Hence the distribution of X can be described as follows:

X \approx N(25150, 12050)

The probability that the college graduate has between $14,200 and $33,950 in student loan debt is the <u>p-value of Z when X = 33950 subtracted by the p-value of Z when X = 14200</u>, hence:

X = 33950:

Z = \frac{X - \mu}{\sigma}

Z = \frac{33950 - 25150}{12050}

Z = 0.73

Z = 0.73 has a p-value of 0.7673.

X = 14200:

Z = \frac{X - \mu}{\sigma}

Z = \frac{14200 - 25150}{12050}

Z = -0.91

Z = -0.91 has a p-value of 0.1814.

0.7673 - 0.1814 = 0.5859.

There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.

Considering the symmetry of the normal distribution, the middle 10% is between the 45th percentile(X when Z = -0.127) and the 55th percentile(X when Z = 0.127), hence:

Z = \frac{X - \mu}{\sigma}

-0.127 = \frac{X - 25150}{12050}

X - 25150 = -0.127(12050)

X = $23,519.65.

Z = \frac{X - \mu}{\sigma}

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X - 25150 = 0.127(12050)

X = $26,580.35.

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A gold mine has two​ elevators, one for equipment and another for the miners. The equipment elevator descends 77 feet per second
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Answer:

The position of the equipment elevator is 315 feet deep.

The position of the elevator of the miners is 208 feet deep.

At that time, the equipment elevator is deeper.

Step-by-step explanation:

Observation: Seems the numbers are doubled. 77 instead of 7; 1313 instead of 13; 2929 instead of 29; and 1616 instead of 16.

Hence, the question is:

A gold mine has two​ elevators, one for equipment and another for the miners. The equipment elevator descends 7 feet per second. The elevator for the miners descends 13 feet per second. One​ day, the equipment elevator begins to descend. After 29 ​seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 16 ​seconds? At that​ time, which elevator is​ deeper?

Step-by-step explanation:

From the question,

For the equipment elevator

Speed= 7 feet/second

For the elevator of the miners,

Speed= 13 feet/second

To determine the positions of each elevator relative to the surface, we will determine the distance each of the elevator descends.

From the formula

Speed= Distance / Time

Then,

Distance = Speed × Time

From the question,

The equipment elevator begins to descend and after 29 ​seconds, the elevator for the miners begins to descend. To determine the position of each elevator after another 16 ​seconds. That is, the equipment elevator descends for a total of (29+16) seconds and the elevator of the miners descends for 16 seconds.

For the equipment elevator

Speed= 7 feet/second

Time = 29 + 16 seconds = 45 seconds

From,  Distance = Speed × Time

∴ Distance = 7 feet/second × 45 seconds

Distance = 315 feet

Hence, the position of the equipment elevator is 315 feet deep.

For the elevator of the miners

Speed = 13 feet/second

Time = 16 seconds

Distance = Speed × Time

∴ Distance = 13 feet/second × 16 seconds

Distance = 208 feet

Hence, the position of the elevator of the miners is 208 feet deep.

At that time the equipment elevator is deeper.

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