We call the part or the remaining number in a percent problem the?
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By solving a quadratic equation, we will see that the width of the walkway is 3ft.
<h3>How to get the width of the walkway?</h3>Remember that for a rectangle of length L and width W, the area is:
A = W*L
Now, we know that for our garden we have:
W = 8ft
L = 12ft
If we add a walkway of width x around the garden, then the new measures are:
W' = 8ft + 2x
L' = 12ft + 2x
So the area is:
A' = ( 8ft + 2x)*( 12ft + 2x)
And we know that it is equal to 192 ft^2, then:
192 ft^2 = ( 8ft + 2x)*( 12ft + 2x)
Now we can solve this for x.
192ft^2 = 96ft^2 + 4x^2 + 20ft*x
0 = 96ft^2 - 192ft^2 + 20ft*x + 4x^2
0 = -96ft^2 + 20ft*x + 4x^2
This is a quadratic equation, and the solutions are given by the Bhaskara's formula:
We only take the positive solution, so we get:
x = (-20ft + 44ft)/8 = 3ft
So the width of the walkway is 3ft.
If you want to learn more about quadratic equations, you can read:
Using the t-distribution, it is found that since the <u>test statistic is greater than the critical value</u> for the right-tailed test, it is found that there is enough evidence to conclude that the students' claim that they work more than 19 hours is correct.
At the null hypothesis, it is <u>tested if they spend on average 19 hours a week working</u>, that is:
At the alternative hypothesis, it is <u>tested if they spend more than 19 hours a week working</u>, that is:
We have the <u>standard deviation for the sample</u>, hence, the <em>t-distribution</em> is used.
The test statistic is given by:
The parameters are:
is the sample mean.
is the value tested at the null hypothesis.
- s is the standard deviation of the sample.
- n is the sample size.
Searching the problem on the internet, it is found that the values of the <em>parameters </em>are:
Hence, the value of the <em>test statistic</em> is:
The critical value for a <u>right-tailed test</u>, as we are testing if the mean is greater than a value, with a <u>significance level of 0.05</u> and 25 - 1 = <u>24 df</u> is of
Since the <u>test statistic is greater than the critical value</u> for the right-tailed test, it is found that there is enough evidence to conclude that the students' claim that they work more than 19 hours is correct.
To learn more about the t-distribution, you can take a look at brainly.com/question/13873630