The rectangular prism and rectangular pyramid below have the same volume. Determine the value of x, the length of the prism.

ANSWER

[tex]x[/tex]= 9 [tex]in[/tex]

EXPLANATION

The volume of a rectangular prism is given by the formula,

[tex]V[/tex]= [tex]l[/tex] x [tex]b[/tex] x [tex]h[/tex]

We substitute the dimensions to obtain,

[tex]V[/tex]= 6 x 3 x 12 [tex]in^{3}[/tex]

The volume of the rectangular pyramid is,

[tex]V[/tex]= [tex]\frac{1}{3}[/tex] x 6 x 12 x [tex]x[/tex] [tex]in^{3}[/tex]

Equating the two values gives,

[tex]\frac{1}{3}[/tex] x 6 x 12 x [tex]x[/tex] = 6 x 3 x 12

We divide through by 6×12 to get,

[tex]\frac{x}{3}[/tex] = 3

We solve for x to obtain,

[tex]x[/tex] = 3 x 3

[tex]x[/tex] = 9 [tex]in[/tex]

Hope this helps! Happy Monday!

What will happen? (Newton's 1st Law Egg Drop)

i forgot to put the picture so- but pls help me don't just put something random

HURRY PLEASE

Solve the equation. 4x − 2 = 8x + 10 Use algebra tiles to assist you.

x = -3

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QUICKKK

please give correct answer ! :)

plsss help me i also dont understand this

Please answer all the questions in the pictures attached today. If you steal my points, you will be reported ASAP!! Thank you! :)

The lines s and t intersect at point R.
What is the value of y?

Enter your answer in the box.

y =

Lines t and s intersect at point R. Obtuse vertical angles measure seventy-nine plus y degrees and four y minus eight degrees.

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Lake City uses a cone-shaped building to store the salt they spread on their roads during winter. Each storage building has a radius of 39 feet and a height of 48 feet.

Using 3.14 for , approximately how much salt can each storage building hold?
A. 76,415.04 cubic feet

B. 229,245.12 cubic feet

C. 5,878.08 cubic feet

D. 94,049.28 cubic feet

Answer this question please and thank you

I dont understand this loll

Find the distance between C and D
C:(4, -5) D:(-3, -5)

A jar contains 1,000 marbles. Omar is entering a contest to guess the number of any one color of marbles in the jar. He is allowed to take four random samples of 200 marbles, and his results are shown in the table.

Sample Blue/Green/Red/White
1. 82 42 36 40
2. 70 51 49 30
3. 58 66 45 31
4. 65 62 38 35
Which statements are true? Choose all that apply. (There are three correct answers).
A.There are probably more white marbles than green marbles in the jar.
B. There are likely more blue marbles in the jar than any other color.
C.The ratio of the number of red marbles in the jar to the number of green marbles in the jar is most likely greater than the ratio of the number of white marbles in the jar to the number of blue marbles in the jar.
D. The number of green marbles in the jar is approximately 21% to 33% of the marbles in the jar.
E.The total number of red marbles in the jar is approximately 168.

In a wildlife preserve, a random sample of the population of 150 raccoons was caught and weighed. The results, given in pounds, were 17, 19, 19, 24, 25, 27, 30, 31, 31, and 32. Jean made the qualitative statement, "The average weight of the raccoon population is 26 pounds." Is her statement reasonable? Complete the explanation.

Jean's statement (is/is not) reasonable because the median value of the data is _________ pounds.

Kelly drew the angle shown,
which value is closest to measurement of Kelly's angle?

leven purple marbles, seven orange marbles and two pink marbles are in a bag. What is the probability of selecting a purple marble, not replacing it, and then selecting an orange marble?

Question 4 options:

19%


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Solve for zzz: -0.25z = -1.25−0.25z=−1.25minus, 0, point, 25, z, equals, minus, 1, point, 25 z =\,z=z, equals

NEED HELP ASAP
Alan used the expression StartFraction 5 over 9 EndFraction (F minus 32), where F is a temperature in degrees Fahrenheit, to convert a temperature from Fahrenheit to Celsius. He evaluated the expression as shown below and found that 45 degrees Fahrenheit was equivalent to –7 degrees Celsius.

StartFraction 5 over 9 EndFraction (F minus 32) = StartFraction 5 over 9 (45 minus 32) = 25 minus 32 = negative 7

What error did Alan make?
He substituted 45 for F instead of –7 and should have found the answer to be Negative 21 and two-thirds degrees Celsius.
He did not combine within the parentheses first before multiplying and should have found the answer to be 7 and StartFraction 2 over 9 EndFraction degrees Celsius.
He multiplied 45 by the fraction incorrectly and should have found the answer to be 49 degrees Celsius.
He divided 5F by 9 before subtracting 32 and should have found the answer to be 21 and StartFraction 4 over 9 EndFraction degrees Celsius.

does anyone know this?

I really need help!! Which box doesn't belong??

he owner of a produce stand is selling bunches of grapes, priced by the pound. She rounded each measurement to the nearest \dfrac{1}{8} 8 1 ​ start fraction, 1, divided by, 8, end fraction of a pound.

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Don't use a bot have actual proof please.

pls answer quickly
Rewrite without absolute value for the given condition: y=|10-x|, if x <10

WILL GIVE BRAINLIEST



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y = 3x + 4

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HURRY I need help Three corporations each own land. Corporation A owns 3.2 × 105 acres, corporation B owns 4 × 104 acres, and corporation C owns 4.3 × 105 acres. Which corporation owns the most land? How many times greater is corporation A’s land than corporation B’s land?
A.
Corporation A owns the most land. Corporation A owns 8 times more land than corporation B.
B.
Corporation B owns the most land. Corporation A owns 4 times more land than corporation B.
C.
Corporation C owns the most land. Corporation A owns 8 times more land than corporation B.
D.
Corporation C owns the most land. Corporation A owns 80 times more land than corporation B.
E.
Corporation A owns the most land. Corporation A owns 40 times more land than corporation B.

You randomly choose one of the tiles. Without replacing the first tile, you randomly choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth.

Simplify write without the absoulute value.

|x-(-12)|, if x<-12

Answer this question please and thank you

Are my answers correct??