The width of a rectangle is 10 feet shorter than its length. The area of the rectangle is 60 square feet. Find the length and width. Round your answer to the nearest tenth of a foot.


Answer 1


  length: 14.2 ft; width 4.2 ft.

Step-by-step explanation:

Let x represent the length of the rectangle in feet. Then x-10 represents the width, and the area is ...

  area = length×width

  60 = x(x -10) . . . . . substitute the expressions for area, length, width

  60 = x² -10x

  85 = x² -10x +25 . . . . add (10/2)² to complete the square

  85 = (x -5)² . . . . . . . . . rewrite as a square

  √85 = x -5 . . . . . . . . . take the square root. Only the positive root is useful for this problem

  x = 5 + √85 ≈ 14.2

  x-10 = 4.2

The length and width of the rectangle are 14.2 ft and 4.2 ft.

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I=$720, P=$1000, r=9%Find the amount of the time.

Can someone please help me –4x ≤ 36



x > -9

Step-by-step explanation:

–4x ≤ 36

Divide by -4, remembering to flip the inequality

-4x/-4 > 36/-4

x > -9

Which of the following equations represents the graph shown? ​




Step-by-step explanation:



m= slope


b = y-intercept

What sample size would be required to estimate the true proportion of American female business executives who prefer the title "Ms.," with an error of ±0.025 and 98 percent confidence? (Enter your answer as a whole number (no decimals). Use a z-value taken to three decimal places in your calculations.) Sample size




And rounded up we have that n=2165

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".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

p represent the real population proportion of interest

\hat p represent the estimated proportion for the sample

n is the sample size required (variable of interest)

z represent the critical value for the margin of error

The population proportion have the following distribution  

p \sim N(p,\sqrt{(\hat p(1-\hat p))/(n)})  

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 98% of confidence, our significance level would be given by \alpha=1-0.98=0.02 and \alpha/2 =0.01. And the critical value would be given by:  

z_(\alpha/2)=-2.326, z_(1-\alpha/2)=2.326

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

ME=z_(\alpha/2)\sqrt{(\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:  


We can assume that the estimated proportion is 0.5 since we don't have other info provided to assume a different value. And replacing into equation (b) the values from part a we got:  


And rounded up we have that n=2165

The mortgage department of a large bank is interested in the nature of loans of first-time borrowers. This information will be used to tailor their marketing strategy. They believe that 40% of first-time borrowers take out smaller loans than other borrowers. They perform a hypothesis test to determine if the percentage is the same or different from 40%. They sample 100 first-time borrowers and find 53 of these loans are smaller than the other borrowers. For the hypothesis test, they choose a 5% level of significance. What would be the null and alternative hypotheses



Step-by-step explanation:

The null hypothesis is the statement or claim that is believed or assumed to be true. In this case, the null hypothesis is "They believe that 40% of first-time borrowers take out smaller loans than other borrowers". Since we are dealing with proportion, we will denote it with p. The null hypothesis would be

p = 0.4

The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected. The alternative hypothesis is "They perform a hypothesis test to determine if the percentage is the same or different from 40%". It would be written as

p ≠ 0.4

The base of a triangle is 3 inches more than 2 times the height.If the area is 7 square inches, find the base and the height. ​


Answer: 6 inches

Step-by-step explanation:

Hope this helped

Segment addition.........



The answer is 2

Step-by-step explanation:

because if you can add the 9 and the 4 you will get  13 and you subtract 13 from 11 and you get 2.I hope that helps