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3 years ago

The data shows the distances, in miles, run by runners in a track club.

Mathematics

1 answer:

Novay_Z [31]3 years ago

4 0

Answer:

Refer to image

Step-by-step explanation:

To create a histogram of the given data set, we first must check for the frequency of each value.

6, 3, 8, 8, 6, 6, 8, 2, 5, 2, 5, 10, 3, 5

2 - 2

3 - 2

5 - 3

6 - 3

8 - 3

10 - 1

Now that we have the frequencies of each, we need to add them to each range.

0 - 2 : 2

3 - 5 : 5

6 - 8 : 6

9 - 11 : 1

Refer to the image for the histogram.

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Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,

kompoz [17]

If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is

$V_{flask}=V_{sphere}+V_{cylinder}.$

Use following formulas to determine volumes of sphere and cylinder:

$V_{sphere}=\dfrac{4}{3}\pi R^3,\\ \\V_{cylinder}=\pi r^2h,$

wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.

Then

$V_{sphere}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi \left(\dfrac{4.5}{2}\right)^3=\dfrac{4}{3}\pi \left(\dfrac{9}{4}\right)^3=\dfrac{243\pi}{16}\approx 47.71;$
$V_{cylinder}=\pi r^2h=\pi \cdot \left(\dfrac{1}{2}\right)^2\cdot 3=\dfrac{3\pi}{4}\approx 2.36;$
$V_{flask}=V_{sphere}+V_{cylinder}\approx 47.71+2.36=50.07.$

Answer 1: correct choice is C.

If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So

R'=2R, r'=2r, h'=2h.

Write the new fask volume:

$V_{\text{new flask}}=V_{\text{new sphere}}+V_{\text{new cylinder}}=\dfrac{4}{3}\pi R'^3+\pi r'^2h'=\dfrac{4}{3}\pi (2R)^3+\pi (2r)^2\cdot 2h=\dfrac{4}{3}\pi 8R^3+\pi \cdot 4r^2\cdot 2h=8\left(\dfrac{4}{3}\pi R^3+\pi r^2h\right)=8V_{flask}.$

Then

$\dfrac{V_{\text{new flask}}}{V_{\text{flask}}} =\dfrac{8}{1}=8.$

Answer 2: correct choice is D.

8 0

4 years ago

Read 2 more answers

Solve the linear system using substitution <br><br> y - 5 = x<br> 4x - y = 4

Agata [3.3K]

Step-by-step explanation:

X=y-5

Now,

4x-y=4

4(y-5)-y=4

4y-20-y=4

3y=24

Y=8

Substituting the value of y

8-5=x

X=3

3 0

3 years ago

Does anyone know what to do it’s OK if you can only do one

prisoha [69]

Answer:

the picture isnt big enough

3 0

3 years ago

Find all numbers for which the rational expression is undefined

Dafna1 [17]

Answer:

{-3, 8}

Step-by-step explanation:

This rational expression is undefined wherever the denominator is 0.

Thus, our task is to determine the roots of x² - 5x - 24:

This expression factors as follows: (x - 8)(x + 3) = 0

Setting x - 8 = 0 and solving for x yields x = 8.

Similarly, x + 3 = 0 yields x = -3.

This rational expression is undefined for {-3, 8}.

8 0

3 years ago

How many quarts are equal to 8 cups

exis [7]

Answer:8 Cups:2 cups

8 0

4 years ago