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Diano4ka-milaya [45]
3 years ago
7

Molly wants her rectangular rooftop garden plot to have an area of 21 square feet. If she makes the width 5 feet, what must be t

he length? is this an example of direct variation or inverse variation?
A)105 ft; direct
B)4.2 ft;direct
C)4.2 ft; inverse
D)105 ft;inverse
Mathematics
2 answers:
Over [174]3 years ago
3 0
Area = length x width
21 = length x 5
length = 21/5 = 4.2

The length is inversely proportional to the width because as the length increases the width reduces and vice-versa

Citrus2011 [14]3 years ago
3 0

Answer:

Option C.

Step-by-step explanation:

Molly wants her rectangular rooftop garden to have the area = 21 feet²

Width of the rectangular garden is = 5 feet

Let the length of the garden = l feet

Since we know the formula of "area of the garden = Length × width"

Length = \frac{\text{Area of the garden}}{\text{Width}}

This formula represents length of the garden ∝ \frac{1}{\text{Width}}

Length of the garden is inversely proportional to the width of the garden.

(Length increases with the decrease in width)

Now we plug in the values in the formula.

l = \frac{21}{5}

 = 4.2 feet

Option C. is the answer.

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(a) PRIVATE COLLEGES

Sample mean is $42.5 thousand

Sample standard deviation is $6.65 thousand

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Sample mean is $22.3 thousand

Sample standard deviation is $4.34 thousand

(b) Point estimate is $20.2 thousand. The mean annual cost to attend private colleges ($42.5 thousand) is more than the mean annual cost to attend public colleges ($22.3 thousand)

(c) 95% confidence interval of the difference between the mean annual cost of attending private and public colleges is $19.2 thousand to $21.2 thousand

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(a) PRIVATE COLLEGES

Sample mean = Total cost ÷ number of colleges = (51.8+42.2+45+34.3+44+29.6+46.8+36.8+51.5+43) ÷ 10 = 425 ÷ 10 = $42.5 thousand

Sample standard deviation = sqrt[summation (cost - sample mean)^2 ÷ number of colleges] = sqrt([(51.8-42.5)^2 + (42.2-42.5)^2 + (45-42.5)^2 + (34.3-42.5)^2 + (44-42.5)^2 + (29.6-42.5)^2 + (36.8-42.5)^2 + (51.5-42.5)^2 + (43-42.5)^2] ÷ 10) = sqrt (44.24) = $6.65 thousand

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Sample mean = (20.3+22+28.2+15.6+24.1+28.5+22.8+25.8+18.5+25.6+14.4+21.8) ÷ 12 = 267.6 ÷ 12 = $22.3 thousand

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(b) Point estimate = mean annual cost of attending private colleges - mean annual cost of attending public colleges = $42.5 thousand - $22.3 thousand = $20.2 thousand.

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95% confidence interval is $19.2 thousand to $21.2 thousand

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