Write an equation in slope-intercept form of the line that passes through (−5, 19) and (5, 13)

A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. The number of subjects needed to estima

Ludmilka [50]

Answer:

$n=(\frac{1.64(14.7)}{3})^2 =64.57 \approx 65$

So the answer for this case would be n=65 rounded up to the nearest integer

And the sample size would decrease by 160-65=95 subjects

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

ME represent the margin of error

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

2) Solution to the problem

Since the new Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Assuming that the deviation is known we can express the margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =\pm 3 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

Replacing into formula (b) we got:

$n=(\frac{1.64(14.7)}{3})^2 =64.57 \approx 65$

So the answer for this case would be n=65 rounded up to the nearest integer

And the sample size would decrease by 160-65=95 subjects

8 0

3 years ago

Find the area of each figure

Anon25 [30]

Area of trapezoid = a + b/2 * h
a = 20, b = 9, h = 21/-16
20+9/2 * (21-16) = 29/2 * 5 = 72.5
The area of the trapezoid = 72.5 in^2

Area of the rectangle = l * w
l = 16, w = 20
16 * 20 = 320
The area of the rectangle: 320 in^2

7 0

3 years ago

PLEASE HELP ME WITH THIS

Vedmedyk [2.9K]

Let's start with the drawing. (See the drawing at the bottom of this answer.)

Draw a vertical segment.
At the bottom endpoint, draw a horizontal segment to the right.
The angle at the bottom left is a right angle.
So far this should look like an "L" shape.
The vertical segment is the wall, and the horizontal segment is the ground.

Now draw a segment that connects the right endpoint of the horizontal segment and the top endpoint of the vertical segment. Now you have a right triangle. The diagonal segment represents the ladder. The diagonal segment is the hypotenuse. Label the diagonal segment, the hypotenuse, 12 ft.
Label the vertical segment, the wall, 11.8 ft.

The angle at the bottom right is A. It is the angle the ladder makes with the ground. This angle cannot be greater than 75 degrees.

Now we use trigonometry to find the measure of angle A.

For this right triangle, and its angle A, you have a hypotenuse that measures 12 ft, and an opposite leg that measures 11.8 ft.
We need to find angle A.
The trig ratio that relates the opposite leg and the hypotenuse is the sine.

$\sin A = \dfrac{opp}{hyp}$

$\sin A = \dfrac{11.8}{12}$

$\sin A = 0.98333$

Since the sine of angle A equals 0.98333, we use the inverse sine function to find the measure of angle A.

$A = \sin^{-1} 0.98333$

$A = 79.5^\circ$

Answer:
The angle the ladder makes with the ground is 79.5 degrees which is greater than 75 degrees, so the ladder it will be unsafe in this position.

           |\
     | \
     |    \
       |    \
opp = |    \ hyp = 12
= 11.8 |    \
     |       \
     |_______\ A

3 0

3 years ago

liubo4ka [24]

Answer:D 4 units

Enjoy

4 0

2 years ago

Emery bought 3 cans of beans that had a total weight of 2.4 pounds. If each can of beans weighed the same amount, which model co

andreev551 [17]

Answer:

y=0.8x
See Explanation for others

Step-by-step explanation:

The 3 cans of beans had a total weight of 2.4 Pounds

Therefore:

1 can of beans = (2.4 ÷ 3) =0.8 Pounds

The following applies from the options.

y=0.8x where y is the weight and x is the number of cans.
A 2-column table with 3 rows. Column 1 is labeled number of cans with entries 5, 15, 20. Column 2 is labeled total weight (in pounds) with entries 4, 12, 16.

Using y=0.8x

When x=5, y=0.8 X 5=4

When x=15, y=0.8 X 15=12

When x=20, y=0.8 X 20=16

$\left|\begin{array}{c|c}\text{Number of Cans,x}&\text{Total Weight (in Pounds),y}\\-------&--------\\5&4\\15&12\\20&16\end{array}\right|$

On a coordinate plane, the x-axis is labeled number of cans and the y-axis is labeled total weight (in pounds. A line goes through points (5, 4) and (15, 12). This can be clearly seen from the table above as (5,4) and (15,12) are points on the line.

8 0

2 years ago

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