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inna [77]
2 years ago
13

A teacher assigns 10 questions for homework and wants to randomly pick 3 questions to be graded. He writes the numbers 1–10 on e

qually sized slips of paper and places them in a bag. He shakes the bag and selects 3 slips of paper. Is the sample of 3 questions a simple random sample? Yes, because the paper slips were equally sized. Yes, because the paper slips were equally sized and the bag was shaken. No, because there are only 10 questions. No, because the questions were selected using a bag.
Mathematics
1 answer:
Ivenika [448]2 years ago
6 0

Answer:

B:yes because the paper slips were equally size and the bag was shaken

Step-by-step explanation:

Taking the test

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Find the area of the region which is inside the polar curve r=5sin(θ) but outside r=4. Round your answer to four decimal places
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The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be 3.75 square units.

<h3>What is an area bounded by the curve?</h3>

When the two curves intersect then they bound the region is known as the area bounded by the curve.

The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be

Then the intersection point will be given as

\rm 5 \sin \theta  = 4\\\\\theta = 0.927 , 2.214

Then by the integration, we have

\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214}[ (5 \sin \theta)^2 - 4^2] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [25\sin ^2 \theta - 16] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [ \dfrac{25}{2}(1 - \cos 2\theta ) - 16] d\theta \\

\rightarrow \dfrac{1}{2} [\dfrac{25 \theta }{5} - \dfrac{25 \cos 2\theta }{2} - 16\theta]_{0.927}^{2.214} \\\\\\\rightarrow \dfrac{1}{2} [\dfrac{25(2.214 - 0.927) }{5} - \dfrac{25 (\cos 2\times 2.214 - \cos 2\times 0.927) }{2} - 16(2.214 - 0.927]\\

On solving, we have

\rightarrow \dfrac{1}{2} \times 7.499\\\\\rightarrow 3.75

Thus, the area of the region is 3.75 square units.

More about the area bounded by the curve link is given below.

brainly.com/question/24563834

#SPJ4

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