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2 years ago

José plotted points on a coordinate plane to represent the vertices of a rectangle. The first

Mathematics

1 answer:

Tema [17]2 years ago

3 0

Jose's rectangle must have equal and parallel opposite sides

The coordinates of the other points could be C(7,5) and D(7,1)

<h3>How to determine the other points?</h3>

The coordinates are given as;

A = (2,5).

B = (2,1).

To form a rectangle, each of the remaining points must have the same y-coordinates as points A and B.

So, we have:

C = (x,5)

D = (x,1)

Also, the remaining points must have the same x-coordinates.

i.e.

Cx = Dx

From the list of options, we have:

C(7,5) and D(7,1)

Hence, the coordinates of the other points could be C(7,5) and D(7,1)

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2 years ago

A data set includes 103 body temperatures of healthy adult humans having a mean of 98.1 F and a standard deviation of 0.56 F. Co

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The 99% confidence interval estimate of the mean body temperature of all healthy humans is (97.955F, 98.245F).

98.6F is above the upper end of the interval, which means that the sample suggests that the mean body temperature could be lower than 98.6F.

Step-by-step explanation:

The first step is finding the confidence interval

The sample size is 103.

The first step to solve this problem is finding how many degrees of freedom there are, that is, the sample size subtracted by 1. So

$df = 103-1 = 102$

Then, we need to subtract one by the confidence level $\alpha$ and divide by 2. So:

$\frac{1-0.99}{2} = \frac{0.01}{2} = 0.005$

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 102 and 0.005 in the t-distribution table, we have $T = 2.63$ .

Now, we need to find the standard deviation of the sample. That is:

$s = \frac{0.56}{\sqrt{103}} = 0.055$

Now, we multiply T and s

$M = T*s = 2.63*0.055 = 0.145$

For the lower end of the interval, we subtract the mean by M. So 98.1 - 0.145 = 97.955F.

For the upper end of the interval, we add the mean to M. So 98.1 + 0.145 = 98.245F.

The 99% confidence interval estimate of the mean body temperature of all healthy humans is (97.955F, 98.245F).

98.6F is above the upper end of the interval, which means that the sample suggests that the mean body temperature could be lower than 98.6F.

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