Find the critical value t for the confidence level c= 0.98 and sample size n=7.

Mathematics

1 answer:

kenny6666 [7]3 years ago

8 0

Answer:

The critical value is T = 3.143.

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 7 - 1 = 6

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.98}{2} = 0.99$ . So we have T = 3.143.

The critical value is T = 3.143.

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‼️GEOMETRY‼️

ella [17]

Answer:

A.) 1018 square inches

Step-by-step explanation:

The largest sphere will have a diameter equaling the length of the cube (see picture).

If the side length of the cube is 18 inches, the diameter of the sphere is also 18 inches. Use the surface area formula for a circle:

$SA=4\pi r^2$

For this formula, we need the radius of the sphere. Divide the diameter by 2:

$\frac{18}{2}=9$

The radius is 9 inches. Plug this into the equation:

$SA=4\pi *9^2$

Simplify the equation:

$SA=4\pi *81\\\\SA=324\pi \\\\SA=1017.87$

Round the result to the nearest whole number:

$1017.87$ → $1018$

The surface area is 1,018 inches².

:Done

Picture:

In a 2D version, we can clearly see that if the circle fits snuggly inside of the square, the diameter of a sphere is the same as the length of a side of the cube.