Help! If a sphere has a radius of 8mm, what is its volume? (Show work)

1 answer:

7 0

The formula for the volume of a sphere is V = (4/3) * π * r³. Knowing this, we can plug in the radius:

$V = \frac{4}{3} \pi *8^{3} \\ V = \frac{4}{3} \pi*512 \\ V = 2144.66$

The sphere's volume is approximately 2144.66 mm^3.

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In a random sample of 18 families, the average weekly food expense was $95.60 with a sample standard deviation of $22.50. Determ

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Answer:

t-distribution should be used to construct a confidence interval.

Step-by-step explanation:

We are given that a random sample of 18 families, the average weekly food expense was $95.60 with a sample standard deviation of $22.50.

We have to determine whether a normal distribution (Z values) or a t- distribution should be used or whether neither of these can be used to construct a confidence interval.

Since in this question we are provided with;

Sample average weekly food expense, $\bar X$ = $95.60

Sample standard deviation, s = $22.50

Sample of families, n = 18

The distribution that we will use here to construct a confidence interval will be t-distribution because in the question we don't know anything about population standard deviation $(\sigma)$ .

Normal distribution is used when we know population standard deviation $(\sigma)$ .

So, the pivotal quantity for confidence interval that will be used is One-sample t-test statistics;

P.Q. = $\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

Therefore, t-distribution should be used to construct a confidence interval.

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the length of a soccer pitch is 20 m less than twice its width. the area of the pitch is 6000m^2. find its dimensions.

Setler79 [48]

X=width of a coccer pitch
2x-20=length of a soccer pitch
Area (rectangule)=length x width
We suggest this equation:
x(2x-20)=6000
2x²-20x=6000
2x²-20x-6000=0
x²-10x-3000=0
We solve this quadratic equation:

x=[10⁺₋√(100-4*1*-3000)]/2=[10⁺₋√(100+12000)]/2=
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we have two solutions:
x₁=(10-110)/2=-50, invalid solution.
x₂=(10+110)/2=60

x=60
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Solution: the length is 100 m, and the width is 60 m.

To check:
Area=100 m*60 m=6000 m²
The twice of width is =2(60 m)=120 m,
20 m less than twice its width is: 120 m-20 m=100 m=the length.

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