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wolverine [178]
3 years ago
15

Rounded to the nearest tenth, what is the perimeter of rectangle ABCD? rectangle ABCD with diagonal AC, labeled as measuring 20

centimeters, angle BAC measuring 30 degrees, angle BCA measuring 60 degrees, angle DCA measuring 30 degrees, and angle DAC measuring 60 degrees A. 48.3 cm B. 54.6 cm C. 60.0 cm D. 173.2 cm

Mathematics
1 answer:
Mumz [18]3 years ago
4 0

Answer:

54.6 cm : B

Step-by-step explanation:

Mathematically the area of a rectangle is 2( l + b)

So in practical terms we only need the measure of two sides as we have 2 equal sides for a rectangle.

We can see that we have two right angles on each sides

Now to find b, we can use trigonometric ratios

For each of the rectangles, the diagonal represents the hypotenuse

Mathematically;

sin 30 = b/20

From triangle ABC

b = 20 sin 30 = 20 * 0.5 = 10 cm

Now, to get l

Mathematically;

Sin 60 = l/20

l = 20 sin 60 = 17.32 cm

So the perimeter is;

2(10 + 17.32)

2(27.32) = 54.64 cm which is 54.6 to the nearest tenth

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Using the z-distribution, it is found that the 95% confidence interval for the proportion of sales that occured in December is (0.1648, 0.2948).

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

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In this problem, we have a 95% confidence level, hence\alpha = 0.95, z is the value of Z that has a p-value of \frac{1+0.95}{2} = 0.975, so the critical value is z = 1.96.

The sample size and the estimate are given by:

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\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2298 - 1.96\sqrt{\frac{0.2298(0.7702)}{161}} = 0.1648

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The 95% confidence interval for the proportion of sales that occured in December is (0.1648, 0.2948).

More can be learned about the z-distribution at brainly.com/question/25890103

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