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3 years ago

A hollow sphere sits snugly in a foam cube so that the sphere touches each side of the cube. Find the volume of the foam.

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

5 0

Answer:

V-foam = 4r³( 2 - ----- )

Step-by-step explanation:

Let the radius of the sphere be r. Then the volume of the sphere is

V = (4/3)(π)(r³).

Next, recognize that the side length of the cube is 2r, and that the volume of the cube is thus

V = (2r)³, or 8r³.

Then the volume of the foam is equal to the volume of the cube less the volume of the sphere:

V-foam = 8r³ - (4/3)(π)(r³). This could be factored into

V-foam = 4r³( 2 - ----- )

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Find ten rational numbers between -1 by 5 and 1 by 2

uysha [10]

Answer:

Step-by-step explanation:

First both the rational numbers should have same denominators. So, find least common denominator

Least common denominator is 10

$\frac{-1}{5}=\frac{-1*2}{5*2}=\frac{-2}{10}\\\\\\\frac{1}{2}=\frac{1*5}{2*5}=\frac{5}{10}\\\\\\$

Now multiply the numerator and denominators of the both the numbers by 10.

$\frac{-2*10}{10*10}= \frac{-20}{100} \ and \ \frac{5*10}{10*10}=\frac{50}{100}\\\\\\Now\ 10 \ rational \ numbers \ between\frac{-20}{10} \ and \ \frac{50}{100} \ is \\\\\\\frac{-19}{100},\frac{-18}{100},\frac{-17}{100},\frac{-16}{100}.\frac{-15}{100},\frac{-14}{100},\frac{-13}{100},\frac{-12}{100},\frac{-11}{100};\frac{-10}{100}$

8 0

2 years ago

PLZZZZ HELPPPPPPPPP!!!! a survey asks teachers and students whether they would like the new school mascot to be a Viking or a Pa

VARVARA [1.3K]

Answer:

Step-by-step explanation:

Two events A and B are called independent, when

$P(B|A)=P(B),$

where $P(B|A)$ is the probability that B occurs given that A has already occurred.

A = randomly selected person is a student

B = randomly selected person prefer "Vikings"

B|A = randomly selected student prefer "Vikings"

Probabilities:

$P(A)=\dfrac{100}{125}=\dfrac{4}{5}=0.8\\ \\P(B|A)=\dfrac{80}{85}=\dfrac{16}{17}\approx 0.94$

Since

$0.80\neq 0.94$

we can state that events are not independent.

8 0

2 years ago

Read 2 more answers

Which equation, when solved, results in a different value of x than the other three?

kicyunya [14]

I would have to say -7(1/8)x-4/3=20.

The first and the second one both result in
-23 5/7

The last one results in -24 8/21

but the third one is -22 3/8.

So your answer is either the third of the last one. I assumed the third because, it is lower than all others and the first two are closer to 24 than they are to 22. It’s your choice on how to judge it.

5 0

2 years ago

SOMEONE PLEASE HELP ME

goldfiish [28.3K]

Answer:

First break up 72 into

36 x 2 x -1

Then take the square root of 36

6 square root 2 x -1

Finally make square root -1 = i

6i square root 2 is your answer

Step-by-step explanation: