In triangle ABC, ∠A and ∠B are complementary, where cos A = 0.24. What is the measure, to the nearest degree of, ∠B?
1 answer:
Answer:
Step-by-step explanation:
we know that
In this problem, if angle A and angle B are complementary, then triangle ABC is a right triangle
If two angles are complementary, then their sum is equal to 90 degrees and the cofunction identities state that the sine of one equals the cosine of the other and vice versa
so
sin(A)=cos(B)
cos(A)=sin(B)
we have
therefore
Find the measure of angle B
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Answer:
Option c: Fail to reject the null hypothesis at α = 0.10
Step-by-step explanation:
We are given;
Population mean; μ = 70
population standard deviation; σ = 17.32
Sample mean; x¯ = 72.43
Sample size; n = 35
Thus;
Null hypothesis; H0: μ = 70
Alternative hypothesis; Ha: μ > 70
Z-score formula is;
z = (x¯ - μ)/(σ/√n)
z = (72.43 - 70)/(17.32/√35)
z = 2.43/2.9276
z = 0.83
From online p-value from z-score calculator attached, using z = 0.83; significance level = 0.05 and one tailed hypothesis, we have;
P-value ≈ 0.2033
It's more than the significance value, so we will fail to reject the null hypothesis at α = 0.05
Similarly, From online p-value from z-score calculator attached, using z = 0.83; significance level = 0.01 and one tailed hypothesis, we have;
P-value ≈ 0.2033
It's more than the significance value, so we will fail to reject the null hypothesis at α = 0.01
Similarly, From online p-value from z-score calculator attached, using z = 0.83; significance level = 0.10 and one tailed hypothesis, we have;
P-value ≈ 0.2033
It's more than the significance value, so we will fail to reject the null hypothesis at α = 0.10
From the 3 significance values, the correct option is option c. fail to reject the null hypothesis at α = 0.10
