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Greeley [361]
2 years ago
8

A sphere of radius 7 in. Is placed inside a rectangular prism with length 15 in., width 18 in., and height 20 in. What is the vo

lume of the prism not occupied by the sphere?
Mathematics
1 answer:
iragen [17]2 years ago
5 0

Answer:

3964 in³

Step-by-step explanation:

volume of sphere:  V = 4/3 πr³

v₁ = 4/3 x 3.14 x 7³ = 1436

volume of prism: v = Bh     B = 15 x 18 = 270    h = 20

v₂ = 270 x 20 = 5400

v₂ - v₁ = 5400 - 1436 = 3964 in³

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Suppose you take the small prism and stack it on top of the larger prism. What will be the volume of the composite figure?
Degger [83]
Find the volume of the first figure, then find the volume of the second figure, then add them together.
V=lwh
V(1)=(15)(12)(6)
= 1,080in^3
V(2)=(12)(6)(6)
= 432in^3
--------------------------------------------
1,080+432= 1,512 in^3
--------------------------------------------
Your answer should be 1,512
3 0
2 years ago
Brianna’s lacrosse coach suggested that she practices yoga to improve her flexibility. “Yoga-ta try this” yoga studio has two me
alexdok [17]
B20.00+10.00=100.00
Now the opposite of addiction is subtraction so you subtract 20.00 from 10.00 , the key is to find out what “b” is.


B20.00+10.00=100.00
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Use this way to help you and continue from there ☺️
5 0
2 years ago
What are the possible values of x if (4x – 5)2 = 49? check all that apply. -4/5 -1/2 3 5 7
dexar [7]
4 x - 5 = - 7
4 x = - 2
x = -\frac{1}{2}
or 
4 x - 5 = 7
4 x = 12
x = 3
Answer B) and C)

9 0
2 years ago
Read 2 more answers
Triangle XYZ is translated by the rule (x + 1, y â 1) and then dilated by a scale factor of 4 centered at the origin. Which stat
marysya [2.9K]

Answer:  Y and Y'' are congruent after the translation, but not after the dilation.

Step-by-step explanation:

We know that we generally prefer rigid transformations if want to create congruent images.

There are three basic kinds of rigid transformations:  

1) rotation 2) reflection 3) translation

So, they all create congruent images.

But a dilation does not create congruent images because it creates an image of similar same shape as the original but not the same size.

Given : Triangle XYZ is translated and then dilated by a scale factor of 4 centered at the origin.

Then, the correct option is "Y and Y'' are congruent after the translation, but not after the dilation."

5 0
2 years ago
Meteorologists look for weather trends across US states in the same geographical region. Kentucky and Illinois share a border. T
olya-2409 [2.1K]

The average annual temperatures (°F) from 1991 to 2000 for Kentucky were 57.5, 55.1, 52.2, 55.6, 55.6, 54.4, 54.5, 58.3, 57.3, and 55.7.

We have to evaluate the measures of center.

Firstly, we will calculate the mean.

Mean = (Sum of all the observations)/ (Total number of observations)

Mean =  \frac{57.5+55.1+52.2+55.6+55.6+54.4+54.5+58.3+57.3+55.7}{10}

= \frac{556.2}{10}

= 55.62

Now, we will calculate mode.

Mode is a statistical term that refers to the most frequently occurring number found in a set of numbers.

Consider the data 57.5, 55.1, 52.2, 55.6, 55.6, 54.4, 54.5, 58.3, 57.3, and 55.7.

Mode = 55.6

Now, we will calculate the median.

Firstly, we will arrange in the ascending order.

52.2, 54.4, 54.4,55.1 ,55.6, 55.6, 55.7, 57.3, 57.5, 58.3

Since there are 10 terms.

Median = \frac{n}{2}th observation

Median = 5th observation.

Since, the 5th observation is 55.6.

Therefore, the median is 55.6

5 0
2 years ago
Read 2 more answers
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