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Burka [1]
1 year ago
8

A​ cone-shaped paper water cup has a height of 12 cm and a radius of 6 cm. If the cup is filled with water to one-third its​ hei

ght, what portion of the volume of the cup is filled with​ water?
Mathematics
1 answer:
solniwko [45]1 year ago
8 0
Answer is 150.72 cu.cm.
Let’s find the total cone volume first
Cone volume formula is 1/3 pi r^2 height
We know r = 6
We know height is 12
We will use 3.24 for pi
So
(1/3) (3.14) (6^2) (12) = 452.16
Now we want to find 1/3 of the volume so divide that by 3
Amount of water is 150.72 cu.cm.
Problem solved
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A​ half-century ago, the mean height of women in a particular country in their 20s was 64.7 inches. Assume that the heights of​
Ainat [17]

Answer:

99.5% of all samples of 21 of​ today's women in their 20's have mean heights of at least 65.86 ​inches.

Step-by-step explanation:

We are given that a half-century ago, the mean height of women in a particular country in their 20's was 64.7 inches. Assume that the heights of​ today's women in their 20's are approximately normally distributed with a standard deviation of 2.07 inches.

Also, a samples of 21 of​ today's women in their 20's have been taken.

<u><em /></u>

<u><em>Let </em></u>\bar X<u><em> = sample mean heights</em></u>

The z-score probability distribution for sample mean is given by;

                          Z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \mu = population mean height of women = 64.7 inches

            \sigma = standard deviation = 2.07 inches

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the sample of 21 of​ today's women in their 20's have mean heights of at least 65.86 ​inches is given by = P(\bar X \geq 65.86 inches)

  P(\bar X \geq 65.86 inches) = P( \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } } \geq \frac{65.86-64.7}{\frac{2.07}{\sqrt{21} } } ) = P(Z \geq -2.57) = P(Z \leq 2.57)

                                                                        = <u>0.99492  or  99.5%</u>

<em>The above probability is calculated by looking at the value of x = 2.57 in the z table which has an area of 0.99492.</em>

<em />

Therefore, 99.5% of all samples of 21 of​ today's women in their 20's have mean heights of at least 65.86 ​inches.

3 0
3 years ago
Use substitution to solve the system of equations.
dusya [7]

Answer:

A

Step-by-step explanation:

1/2(2/3y) - 1/3y = 5

1/3y - 1/3y = 5

0 ≠ 5

No Solutions

These are linear equations and, when graphed, are parallel

7 0
2 years ago
45 points!<br><br> x+1(8+5)+y2-3(x3+y-4)=36-4+x7-y-1<br> pls i need help now!
Nadya [2.5K]
The answer is X=-2/5
3 0
2 years ago
How many centimeter squares would be wrapped around this rectangular prism?
denis23 [38]
You haven't told us whether the rectangular prism is the size of a pack of gum or more like the size of a cruise ship.

Whatever size it is, here's the number of centimeter squares you need to cover the whole outside of it:

(2 x length x width) + (2 x length x height) + (2 x width x height)

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4 0
3 years ago
What is the expanded and word form for 101.06
Dvinal [7]
Word form: one hundred one and six hundredths.

expanded form: 100+1+0.06
5 0
3 years ago
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