In the diagram given below, lines I1 and l2 are parallel and t is a transversal. Find the value of x.
2 answers:
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Answer:
We can assume that the statistic is
So the p value obtained was a very high value and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of interest is not different from 3/5
Step-by-step explanation:
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 3/5 or not.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Calculate the statistic
We can assume that the statistic is
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
So the p value obtained was a very high value and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of interest is not different from 3/5
The first thing to do is to sort the given data from smallest to largest. Doing so leads to this ordered list:
{13, 15, 15, 17, 18, 18, 20, 21, 21, 23, 26, 27, 28, 30, 32, 33, 37, 40}
From this list, we can see which values are between 10 and 19 (inclusive). Those values are {13, 15, 15, 17, 18, 18} which represents 6 values. So the first bar (for the "10-19" group) is going to be 6 units high.
The next group, in the "20-29" group, is this set of values {20, 21, 21, 23, 26, 27, 28} which is 7 items this time. The second bar is 7 units high.
The "30-39" bar will be 4 units high because there are 4 items in the set {30, 32, 33, 37}
There is only one person who is between 40 and 49, and that person is 40 years old. So the "40-49" group has a bar that has height of 1.
The final histogram and frequency chart is shown in the attached image. The frequency chart is optional, but it helps supplement the histogram in my opinion.
{13, 15, 15, 17, 18, 18, 20, 21, 21, 23, 26, 27, 28, 30, 32, 33, 37, 40}
From this list, we can see which values are between 10 and 19 (inclusive). Those values are {13, 15, 15, 17, 18, 18} which represents 6 values. So the first bar (for the "10-19" group) is going to be 6 units high.
The next group, in the "20-29" group, is this set of values {20, 21, 21, 23, 26, 27, 28} which is 7 items this time. The second bar is 7 units high.
The "30-39" bar will be 4 units high because there are 4 items in the set {30, 32, 33, 37}
There is only one person who is between 40 and 49, and that person is 40 years old. So the "40-49" group has a bar that has height of 1.
The final histogram and frequency chart is shown in the attached image. The frequency chart is optional, but it helps supplement the histogram in my opinion.
Answer:
(x - 4)(x + 4)(x - 1)(x + 1)
Step-by-step explanation:
Given
- 17x² + 16
Use the substitution u = x², then
u² - 17u + 16
Consider the factors of the constant term (+ 16) which sum to give the coefficient of the u- term (- 17)
The factors are - 16 and - 1, then
u² - 17u + 16
= (u - 16)(u - 1) ← replace u by x²
= (x² - 16)(x² - 1) ← both factors are difference of squares
= (x - 4)(x + 4)(x - 1)(x + 1)