Solve the equation by completing the square. 0 = 4x2 − 72x
1 answer:
Answer:
B
Step-by-step explanation:
Given
4x² - 72x = 0 ← factor out 4 from each term
4(x² - 18x) = 0
To complete the square
add/subtract (half the coefficient of the x- term)² to x² - 18x
4(x² + 2(- 9)x + 81 - 81) = 0
4(x - 9)² - 4(81) = 0
4(x - 9)² - 324 = 0 ( add 324 to both sides )
4(x - 9)² = 324 ( divide both sides by 4 )
(x - 9)² = 81 ( take the square root of both sides )
x - 9 = ± = ± 9 ( add 9 to both sides )
x = 9 ± 9
Then
x = 9 - 9 = 0
x = 9 + 9 = 18
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We (reject) the null hypothesis. That means that we (found) evidence to support the alternative.
Step-by-step explanation:
We have the following info given:
represent the sampel mean for the age of customers
represent the population standard deviation
represent the sample size selected
We want to test if the mean age of her customers is over 35 so then the system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis
The statistic for this case is given by:
And replacing the data given we got:
We can calculate the p value since we are conducting a right tailed test like this:
Since the p value is lower than the significance level given of 0.05 we have enough evidence to reject the null hypothesis on this case. And the best conclusion for this case is:
We (reject) the null hypothesis. That means that we (found) evidence to support the alternative.