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Fynjy0 [20]
3 years ago
9

A family plans to have the hardwood floors in their square dining room re-finished, and new baseboards installed. The cost of re

-finishing the hardwood floors is $2.25 per square foot and the cost of purchasing and installing the new baseboards $14.5 per linear foot. If the family paid $1773, you have to find out dimensions of the room.
Mathematics
1 answer:
Alexus [3.1K]3 years ago
7 0

Answer:

Dimension of room = 18 foot x 18 foot

Step-by-step explanation:

Let the square room is of side a foot,

The cost of re-finishing the hardwood floors is $2.25 per square foot and the cost of purchasing and installing the new baseboards $14.5 per linear foot

Total cost is  $1773.

Cost for re-finishing the hardwood floors = Area x 2.25

Area = a²

Cost for re-finishing the hardwood floors = 2.25 a²

Cost of purchasing and installing the new baseboards = Perimeter x 14.5

Perimeter = 4a

Cost of purchasing and installing the new baseboards = 4a x 14.5 = 58 a

Total cost = Cost for re-finishing the hardwood floors + Cost of purchasing and installing the new baseboards

1773 = 2.25 a² + 58a

2.25 a² + 58a - 1773 = 0

a = 18 or a = -43.77(not possible)

Dimension of room = 18 foot x 18 foot

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Answer:

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And rounded up we have that n=2663

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

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Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

t_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.025 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

We can assume an estimated proportion of \hat p =0.5 since we don't have prior info provided. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56  

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Step-by-step explanation:

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