Answer:
41
Step-by-step explanation:
So basically you need to use the pythagorean thrm. Essentially, the diagonal and the width and length create a triangle, the diagonal being the hypothenuse. So the formula goes as . the variable "a" being the length and the variable "b" being the width. So plug it in and there you have your answer!
Given:
Carrie has 180 ft of the fencing and wishes the fence to be 4times as long as it is wide.
To Find:
The area in square feet that the fencing encloses.
Answer:
The fence encloses 3600 sq ft.
Step-by-step explanation:
Let x denote the length of the dog run and y denote the width of the dog run.
Given that the garage wall serves as one side of the dog run, we are left with 3 other sides to instal the fence.
Carrie has 180ft of fencing with her, so the sum of the lengths of the 3 sides has to be equal to 180. We can represent this in the form of an equation as
We are also given that Carrie wishes the fence to be 4 times as long as it is wide.
So,
Replacing this value into the first equation, we have
Therefore,
Thus, the length of the dog run is 120ft and the width is 30ft.
The area enclosed will be equal to the length multiplied with the width. So,
The fence encloses 3600 sq ft.
Step-by-step explanation:
Hey there!
Please see your required answer in picture.
<u>Hope</u><u> it</u><u> helps</u><u>!</u>
Answer:
a) One-tailed t-test about a mean.
b) The null hypothesis would be that there is no significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.
While the alternative hypothesis is that there is significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.
Mathematically,
The null hypothesis is represented as
H₀: μ ≤ 40 yards
The alternative hypothesis is given as
Hₐ: μ > 40 yards
c) p-value = 0.00621
d) The graph is presented in the attached image. The p-value obtained is less than the significance level at which the test was performed, hence, we accept the alternative hypothesis and say that there is significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.
Step-by-step explanation:
a) This test checks if the adjusted grip leads to more distance than before on the ball throws.
So, it is a one tailed test (testing only in one direction), a t-test about a mean.
b) For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
Since this question aims to test if adjusting the grip leads to more distance on the ball thrown.
The null hypothesis would be that there is no significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball. That is, The adjusted grip leads to a distance lesser than or equal to the previous distance on the thrown ball.
While the alternative hypothesis is that there is significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.
Mathematically,
The null hypothesis is represented as
H₀: μ ≤ 40 yards
The alternative hypothesis is given as
Hₐ: μ > 40 yards
c) To do this test, we will use the z-distribution because there is information on the population standard deviation.
So, we compute the test statistic
z = (x - μ₀)/σ
x = 45 yards
μ₀ = 40 yards
σ = standard deviation = 2 yards
z = (45 - 40)/2 = 2.50
The p-value for a one-tailed test for z-test statistic of 2.50 is 0.00621
d) The sketch of the graph is presented in the attached image.
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.00621
0.00621 < 0.05
Hence,
p-value < significance level
This means that we reject the null hypothesis & accept the alternative hypothesis and say that there is enough evidence to conclude that the adjusted grip leads to more distance on the thrown ball.
Hope this Helps!!!
