Given csc A= 37/12 and that angle A is in Quadrant I, find the exact value of sec A in
1 answer:
Answer:
Step-by-step explanation:
Below is the pic of how this would be set up in order to determine what it is you are looking for. The angle is set in QI, and since csc A is the reciprocal of sin, the ratio is hypotenuse over side opposite. Solve for the missing side using Pythagorean's Theorem:
and
1369 = 144 + b² and
1225 = b² so
b = 35
The sec ratio is the reciprocal of cos, so if cos is adjacent over hypotenuse, the sec is hypotenuse over adjacent, which is 37/35
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Answer:
b. The null and alternative hypothesis are:
c. Student's t distribution, as it is a two-sample test for the difference between means.
d. Test statistic t = 5.42.
P-value = 0
e. They appear to be significantly different, as the sample data gives strong evidence that the difference is greater than 0.
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that the mean life spans in the county is significantly different for whites and nonwhites.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample 1 (white), of size n1=124 has a mean of 45.3 and a standard deviation of 12.7.
The sample 2 (non-white), of size n2=82 has a mean of 34.1 and a standard deviation of 15.6.
The difference between sample means is Md=11.2.
The estimated standard error of the difference between means is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this test are:
df=n_1+n_2-2=124+82-2=204
This test is a two-tailed test, with 204 degrees of freedom and t=5.42, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.0000002) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the mean life spans in the county is significantly different for whites and nonwhites.