circle A has an area of 254.469 square units. What is the circumference of circle A? Round your answer to the nearest hundredth,
2 answers:
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First of all, we have to observe this triangles separated by the height. These small and big triangles are similar according to the Angle-Angle-Angle principle.
a. We can find all of these length using the cosine of the angle, Pythagoras theorem and the principle of the similarity of triangles.
b. According to the cosine of the angle we can write that, cosθ = 12/a = 5/13 and from here a = 31.2. After finding that using Pythagoras theorem, we can write that . According to the similarity of the triangles, we can write that 31.2/d = 28.8/12 and d = 13. Applying Pythagoras theorem we find that c = 5.
c. We already gave the answer for this question in part b
Answer:
1) test is one tail hypothesis test.
2) 110 sampled customers must have favored Coke.
3) at 5% significance, We cannot conclude that the proportion of customers who prefer Coca-Cola exceeds 50%.
4) at 1% significance level, the conclusion would not change.
Step-by-step explanation:
1) Let p be the proportion of customers who prefer Coke to other brands
: p=0.50
: p>0.50
Since the alternative hypothesis claims p <em>more than</em> 0.50, this test is one tail hypothesis test.
2) Out of a random sample of 200 consumers, 55% favored Coca-Cola over other brands. Thus 200 × 0.55 = 110 sampled customers must have favored Coke.
3) at 5% significance level, p-value =0.07761 >0.05, therefore we fail to reject the null hypothesis. We cannot conclude that the proportion of customers who prefer Coca-Cola exceeds 50%.
4) at 1% significance level, p-value =0.07761 >0.01, thus the conclusion does not change