How does Cavalieri's Principle justify the statement
2 answers:
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To solve a system of inequalities we graph both of them.
The inequality representing their combined pay would be
. This is because Jane makes 12.50/hr, Jack makes 10.00/hr, and they want to make at least, so greater than or equal to, $750 combined.
The inequality representing their combined hours working would be
, since they do not want their combined hours to be over 65. In both of these inequalities, <em>x</em> represents the number of hours Jane works and <em>y</em> represent the number of hours Jack works.
To graph these, we solve both of them for <em>y</em>:
The attached screenshot shows what the graph looks like. Going to the point where they intersect, we see that the shaded region that satisfies both inequalities begins when Jane works 40 hours and Jack works 25.
The inequality representing their combined pay would be
The inequality representing their combined hours working would be
To graph these, we solve both of them for <em>y</em>:
The attached screenshot shows what the graph looks like. Going to the point where they intersect, we see that the shaded region that satisfies both inequalities begins when Jane works 40 hours and Jack works 25.
Using the z-distribution, we have that:
- The mean hip measurement for the random sample of 15 pairs of women's size 16 jeans is of 44.1 inches.
- The <u>margin of error</u> is of 0.8 in.
- The interpretation is: Mallorie is 99% sure that the mean hip measurement of size 16 jeans is between 43.3 in and 44.9 in.
The first step to solve this question, before building the confidence interval, is finding the sample mean, which is the <u>sum of all observations divided by the number of observations</u>. Hence:
The margin of error of a z-confidence interval is given by:
In which:
- z is the critical value.
is the population standard deviation.
- n is the sample size.
We have to find the critical value, which is z with a p-value of , in which
is the confidence level.
In this problem, , thus, z with a p-value of
, which means that it is z = 2.575.
Then, the margin of error is:
The <u>margin of error</u> is of 0.8 in.
The interval is:
The interpretation is:
Mallorie is 99% sure that the mean hip measurement of size 16 jeans is between 43.3 in and 44.9 in.
A similar problem is given at brainly.com/question/25300297