A park has a walking path in the shape of a rectangle. The side by a lake is 180 meters. The walking path also has a 200-meters
long diagonal that takes walkers to a basketball court. How long is the side adjacent to the side by the lake?
3 answers:
The park side length by the lake as given 180 meters.The walking path is in the shape of a rectangle with diagonal 200 square meters. Angles of a rectangle are 90 degrees.We have a right triangle with diagonal as the hypotenuse ,one of the leg as 180 meters and we need to find the adjacent side of the side by the lake that is the other leg
Pythagorean Theorem states: that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Or , Where a,b are the legs of the triangle and c is the hypotenuse.
Substituting the values of c and a we have:
Or
Subtracting 32400 both sides ,
Or b= 87.17.= 87 m.
The side adjacent to the side by the lake is 87m.
Option A is the right answer.
The park side length by the lake as given 180 meters.The walking path is in the shape of a rectangle with diagonal 200 square meters. Angles of a rectangle are 90 degrees.We have a right triangle with diagonal as the hypotenuse ,one of the leg as 180 meters and we need to find the adjacent side of the side by the lake that is the other leg
Pythagorean Theorem states: that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Or , Where a,b are the legs of the triangle and c is the hypotenuse.
Substituting the values of c and a we have:
Or
Subtracting 32400 both sides ,
Or b= 87.17.= 87 m.
The side adjacent to the side by the lake is 87m.
Option A is the right answer.
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Answer:
No, the sample evidence is not statistically significant (P-value = 0.125).
To reject the null hypothesis, the P-value has to be smaller than the significance level, so the significance level to reject the null hypothesis has to be 0.125 or higher.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average weekly grocery bill per five-person family in San Antonio is significantly different from the national average.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=50.
The sample mean is M=133.474.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=11.193.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a two-tailed test, with 49 degrees of freedom and t=1.563, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.125) 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 the average weekly grocery bill per five-person family in San Antonio is significantly different from the national average.