Answer: First option.
Step-by-step explanation:
Given the following equation provided in the exercise:
You can follow the steps indicated below in order to find the solution of this equation:
1. Cubing both sides of the equation, you get:
2. Finally you must subtract 8 from both sides of the equation:
You can notice that this solution matches with the first option.
Answer:
1. M=108
2. μ=110
3. In the explanation.
4. Test statistic t = -1.05
5. P-value = 0.1597
Step-by-step explanation:
The question is incomplete: to solve this problem, we need the sample information: size, mean and standard deviation.
We will assume a sample size of 10 matches, a sample mean of 108 points and a sample standard deviation of 6 points.
1. The mean points is the sample points and has a value of 108 points.
2. The null hypothesis is H0: μ=110, meaning that the mean score is not significantly less from 110 points.
3. This is a hypothesis test for the population mean.
The claim is that the mean score is significantly less than 110.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=10.
The sample mean is M=108.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.
The estimated standard error of the mean is computed using the formula:
4. Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
5. This test is a left-tailed test, with 9 degrees of freedom and t=-1.05, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.1597) 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 mean score is significantly less than 110.
Answer:
<h2>A rotation -90° around point I.</h2><h2>A translation upwards 2 units.</h2><h2>Step-by-step explanation:</h2>The given figures are attached.
We have to find two transformations that help to show that both polygon are congruent.
First transformation would be a rotation -90° around point I.
Second transformation would be a translation upwards 2 units.
Applying these transformation, we would have both polygons at the same position, that will show the congruence between them.
Answer:
Step-by-step explanation:
The explanation of given question is described below:
Here, the test of hypothesis states that
The test statistic is
= 2.1
According to the given data α = 0.05,
So, the major value is
(refer to the standard normal table) .
Finally
Answer:
Largest possible length is <em>21 inches</em>.
Step-by-step explanation:
Given:
Total material available = 60 inches
Length to be 3 more than twice of width.
To find:
Largest possible length = ?
Solution:
As it is rectangular shaped frame.
Let length = inches and
Width = inches
As per given condition:
..... (1)
Total frame available = 60 inches.
i.e. it will be the perimeter of the rectangle.
Formula for perimeter of rectangle is given as:
Putting the given values and conditions as per equation (1):
Putting in equation (1):
So, the answer is:
Largest possible length is <em>21 inches</em>.