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Marat540 [252]
2 years ago
15

A rectangle and a square have the same area. The length of the rectangle is seventy feet more than two times its width. The leng

th of a side of the square is thirty feet. What equation would help you solve for the dimensions of the rectangle? What are the dimensions of the rectangle?
Mathematics
1 answer:
Zanzabum2 years ago
8 0

Using the side of the square find the area:

Area = 30^2 = 900 square feet.

The rectangles area is the same, 900 square feet.

Let the width = X

The length would be 2X + 70

Area = length x width

X * 2x+ 70 = 900

This expands to 2x^2 * 70x = 900

Use the quadratic formula to solve for x:

-70 +/- sqrt(70^2-4*2(-900))/2*2

X = 10

Width = x = 10 feet

Length = 2x + 70 = 90 feet

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3 years ago
Of 150 adults selected randomly from one town, 30 of them smoke. Construct a 99% confidence interval for the true percentage of
anyanavicka [17]

Answer:

The 99% confidence interval for the true percentage of all adults in the town that smoke is (0.1159, 0.2841).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence interval 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

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For this problem, we have that:

Of 150 adults selected randomly from one town, 30 of them smoke. This means that n = 150, p = \frac{30}{150} = 0.2

99% confidence interval

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The lower limit of this interval is:

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The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.20 + 2.575\sqrt{\frac{0.20*0.80}{150}}{119}} = 0.2841

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<span>0.55 and 0.65 </span>

In general, the uncertainty in a single measurement from a single instrument is half the least precise decimal given for the instrument.
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so we take 0.1 /2 = 0.05, and divide by the measurement

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