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oee [108]
3 years ago
12

The length of a rectangle is 13 centimeters less than three times its width. Its area is 56 square centimeters. Find the dimensi

ons of the rectangle. Use the​ formula, area=length*width.
Mathematics
2 answers:
tatuchka [14]3 years ago
4 0

Answer:

Area = length  x width

Area = (3width - 13) x width

Area = 3 width^2 -13width

56 = 3width^2 -13 width

Width = 7

Length = (3 *7) -13 = 8

Step-by-step explanation:

Katyanochek1 [597]3 years ago
4 0

Answer:

The dimensions of the rectangle are 8 by 7 centimeters.

Step-by-step explanation:

The length of a rectangle is 13 centimeters less than three times its width. In other words:

\ell = 3w-13

Given that the area of the rectangle is 56 square centimeters, we want to determine its dimensions.

Recall that the area of a rectangle is given by:

A = w \ell

Substitute in known values and equations:

(56)=w(3w-13)

Solve for <em>w</em>. Distribute:

3w^2-13w=56

Isolate the equation:

3w^2-13w-56=0

Factor. We want to find two numbers that multiply to 3(-56) = -168 and that add to -13.

-21 and 8 suffice. Hence:

3w^2 - 21w + 8w - 56 = 0 \\ \\ 3w(w-7) + 8(w-7) = 0 \\ \\ (3w+8)(w-7) = 0

Zero Product Property:

3w+8=0\text{ or } w-7=0

Solve for each case:

\displaystyle w = -\frac{8}{3} \text{ or } w=7

Since the width cannot be negative, we can ignore the first solution.

Therefore, the width of the rectangle is seven centimeters.

Thus, the length will be:

\ell = 3(7) - 13 = 8

Thus, the dimensions of the rectangle are 8 by 7 centimeters.

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The manager of a paint supply store wants to estimate the actual amount of paint contained in 1​-gallon cans purchased from a na
lorasvet [3.4K]

Answer:

a. 95​% confidence interval estimate for the population mean amount of paint included in a​ 1-gallon can is 0.998±0.0055

b.  <u>No,</u> because a​ 1-gallon paint can containing exactly​ 1-gallon of paint lies <u>within</u> the 95​% confidence interval.

c. Yes.  The population amount of paint per can is assumed normally distributed, because confidence interval calculations assume normal distribution of the parameter.

d. 90% confidence interval is 0.998±0.0046. ​The answer in b. didn't change; 1-gallon paint can containing exactly​ 1-gallon of paint lies <u>within</u> the 90​% confidence interval. The manager <u>doesn't have</u> a right to complain to the manufacturer.

Step-by-step explanation:

Confidence Interval can be calculated using M±ME where

M is the sample mean amount of paint per 1​-gallon can (0.998 gallon)

ME is the margin of error from the mean

And margin of error (ME) can be calculated using the equation

ME=\frac{z*s}{\sqrt{N} } where

  • z is the corresponding statistic in the 95% confidence level (1.96)
  • s is the sample standard deviation (0.02 gallon)
  • N is the sample size (50)

Then ME=\frac{1.96*0.02}{\sqrt{50} }≈0.0055

95% confidence interval is 0.998±0.0055

90% confidence interval can be calculated similary, only z statistic is 1.64.

ME=\frac{1.64*0.02}{\sqrt{50} }  ≈0.0046

90% confidence interval is 0.998±0.0046

8 0
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Find the selling price. Where necessary, round to the nearest cent. Regular price:$14.99. Percent of discount:15%
RSB [31]

Answer:

the price is approximately $12.75

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

This is the correct simplified form of ( g + h ) ( p + q − r )

Hope this helped!

7 0
2 years ago
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(2,57) and (6,57)

When you solve for change between the y and x, you get (57-57)/(6-2
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agasfer [191]

Answer:

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Step-by-step explanation:

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8 0
3 years ago
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