If Sarah is 24 years younger than her mother and if the sum of their ages is 68, how old is Sarah?
2 answers:
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Answer with step-by-step explanation:
The way the question is worded, this actually shouldn't be correct. The correct answer should be .
Because the trapezoids are similar, we can find the ratio of their perimeters by actually just finding the ratio of their sides.
Why?
By definition, the corresponding sides of a polygon are in a constant proportion. The perimeter is simply the sum of all sides of the polygon. Since we're just adding the sides, the proportion will still be maintained.
Therefore, we'll just need to ratio of their corresponding sides. The only two corresponding sides that are marked are and
.
The ratio of is
.
The reason why it ideally should be and not
is because the question states
, which mentions
first, so our answer should follow this respective order. I believe you were marked right anyways because the specific order is not specified, but generally, you want to give your answer respectively by default.
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.