Answer:
49π in²
Step-by-step explanation:
Step 1: Find the radius.
Step 2: Apply area of circle formula.
Step 3: Simplify.
Since we're finding the area in terms of pi, we don't have to multiply 121 by pi, so the answer is 49π in².
In order to answer this question, the figure in the first picture will be helpful to understand what a right triangle is. Here, a right angle refers to .
However, if we want to solve the problem we have to know certain things before:
In the second figure is shown a general right triangle with its three sides and another given angle, we will name it :
So, going back to the triangle of our question (first figure):
Now, if we want to find the length of each side of a right triangle, we have to use the <u>Pythagorean Theorem</u> and T<u>rigonometric Functions:</u>
Pythagorean Theorem
(1)
Trigonometric Functions (here are shown three of them):
Sine: (2)
Cosine: (3)
Tangent: (4)
In this case the function that works for this problem is cosine (3), let’s apply it here:
(5)
And we will use the Pythagorean Theorem to find the hypotenuse, as well:
(6)
(7)
Substitute (7) in (5):
Then clear BC, which is the side we want:
Finally is approximately 13 cm
Answer:
1. There is not enough evidence to support the claim that men who were distance runners lived, on average, five years longer than those who were not distance runners.
2. The test statistic is t.
Step-by-step explanation:
<em>The question is incomplete:</em>
The test statistic is t, as this is a t-test for the difference of means.
The claim is that men who were distance runners lived, on average, five years longer than those who were not distance runners.
Then, the null and alternative hypothesis are:
H_0: \mu_1-\mu_2=5\\\\H_a:\mu_1-\mu_2> 5
The significance level is 0.05.
The sample 1, of size n1=50 has a mean of 84.2 and a standard deviation of 10.2.
The sample 1, of size n1=30 has a mean of 79.2 and a standard deviation of 6.8.
The difference between sample means is Md=5.
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:
This test is a right-tailed test, with 78 degrees of freedom and t=0, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.5) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that men who were distance runners lived, on average, five years longer than those who were not distance runners.