Hi! I just need somebody to explain how this is done.
1 answer:
Answer:
Exact form: x =
Rounded to the Nearest Tenth: x = 12.9
Step-by-step explanation:
<em>In the right-angled triangle, we can use the trigonometry functions to find the length of a side or a measure of an angle</em>
In the given figure
∵ ∠C is the right angle
∴ ΔACB is a right triangle
∵ m∠B = 57°
∵ AC = 10.8
∵ AC is the opposite side of ∠B
∵ AB is opposite to the right angle
∴ AB is the hypotenuse
∵ AB = x
→ We can use the function sine to find x
∵ sin∠B =
∴ sin∠B =
→ Substitute the values of ∠B, AC, and AB in the rule of sine above
∴ sin(57°) =
→ By using cross multiplication
∵ x × sin(57°) = 10.8
→ Divide both sides by sin(57°)
∴ x =
∴ x = 12.87752356
→ Round your answer to the nearest tenth
∴ x = 12.9
Exact form: x =
Rounded to the Nearest Tenth: x = 12.9
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Answer:
a. The test statistic for this hypothesis would be z=1.71
b. Critical value at α = 0.10: z=1.282
c. Reject H0, the television network should not keep its current lineup.
d. H0: p ≤ 0.50; HA: p > 0.50
Step-by-step explanation:
We have to performa an hypothesis test on a proportion.
The claim is that the proportion of viewers that prefer the new show is bigger than 50% (meaning that most viewers prefer the new show).
The null hypothesis will state that both shows have the same proportion.
Then, the null and alternative hypothesis are:
The sample proportion is p=0.53
The standard error of the proportion is:
Then, the z-statistic can be calculated as:
The critical value for a right tailed test at a significance level of 0.10 is zc=1.282. This value can be looked up in a standard normal distribution table.
As the statistic is bigger than the critical value, it lies in the rejection region. The null hypothesis is rejected. There is evidence to support the claim that the proportion of viewers which support the new show is larger than 0.50.