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telo118 [61]
3 years ago
13

^DEF and ^RSQ are shown in the diagram below

Mathematics
1 answer:
lakkis [162]3 years ago
6 0

Answer:

53.3 degrees

Step-by-step explanation:

∆DEF and ∆RSQ are similar. We know this, because the ratio of their corresponding sides are equal. That is:

DE corresponds to RS

EF corresponds to SQ

DF corresponds to RQ.

Also <D corresponds to <R, <E corresponds to <S, and <F corresponds to <Q.

The ratio of their corresponding sides = DE/RS = 6/3 = 2

EG/SQ = 8/4 = 2

DF/RQ = 4/2 = 2.

Since the ratio of their corresponding sides are equal, it means ∆DEF and ∆RSQ are similar.

Therefore, their corresponding angles would be equal.

Thus, m<Q = m<F

Let's find angle F

m<F = 180 - (98 + 28.7)

m<F = 53.3°

Since <F corresponds to <Q, therefore,

m<Q = 53.3°

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If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can say that the population mean is not singificantly higher than 425.  

Step-by-step explanation:

Data given and notation  

\bar X=433.75 represent the mean height for the sample  

\sigma=\sqrt{2500}=50 represent the population standard deviation for the sample  

n=100 sample size  

\mu_o =425 represent the value that we want to test

\alpha=0.01 represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean height actually is higher than the mean height for men in 1960, the system of hypothesis would be:  

Null hypothesis:\mu \leq 425  

Alternative hypothesis:\mu > 425  

Since we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

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P-value

Since is a one right tail test the p value would be:  

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Conclusion  

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