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seraphim [82]
3 years ago
14

The volume of a rectangular prism with a square base is 180 in3. Its height is 5 in. Find the length of the edge of the square b

ase.
Mathematics
1 answer:
amid [387]3 years ago
4 0

Answer:

l = 6 inches

Step-by-step explanation:

We have,

The volume of a rectangular prism with a square base is 180\ in^3.

Height of the prism is  5 in

It is required to find the length of the edge of the square base. Let it is l.

The formula of the volume of the rectangular prism is given by :

V=l\times b\times h

A is area of base of prism

It has a square base, l =b

V=l^2\times h\\\\l=\sqrt{\dfrac{V}{h}} \\\\l=\sqrt{\dfrac{180}{5}} \\\\l=6\ in

So, the length of the  edge of the square base is 6 inches.                  

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Among a group of 100 people, 68 can speak English, 45 can speak French, 42 can speak Spanish. 27 can speak both English and Fren
Nat2105 [25]

Answer:

Step-by-step explanation:

Given

No of People who can speak English is n(E)=68

No of People who can speak French is n(F)=45

No of People who can speak Spanish is n(S)=42

No of People who can speak both English and French n\left ( E\cap F\right )=27

No of People who can speak both English and Spanish n\left ( E\cap S\right )=25

No of People who can speak both French and Spanish n\left ( F\cap S\right )=16

No of people who can speak all languages is n\left ( E\cap F\cap S\right )=9

no of People who can Speak at least one Language is

n\left ( E\cup F\cup S\right )=n\left ( E\right )+n\left ( F\right )+n\left ( S\right )-n\left ( E\cap F\right )-n\left ( E\cap S\right )-n\left ( F\cap S\right )+n\left ( E\cap F\cap S\right )

n\left ( E\cup F\cup S\right )=68+45+42-27-25-16+9=96

Probability that Randomly selected can speak at least 1 of these languages

P=\frac{96}{100}=0.96

8 0
3 years ago
Two opposite sides of a square with length x are increased by 3 units each and the other two opposite sides are decreased by 3 u
SCORPION-xisa [38]
All four sides of the original square have length s.

Adding 3 to s results in s+3, the length of the resulting rectangle.
Subtracting 3 from s results in s-3, the width of the rectangle.

The area of the rectangle is (s+3)(s-3) = s^2 - 9 = 27,  

and therefore s^2 = 36, and s = 6 square units.
5 0
3 years ago
What is the solution to the system of equations?use the linear combination method
galina1969 [7]
The 2 equations are 
-2x + y = -17 ---1)
3x + y = 23 ---2)
we need to have the same coefficient for one of the variables.
Already y variable has the coefficient of 1 for both equations so we can use the equations  as it is. 
2) - 1) subtract 1) from 2)
3x-(-2x) + y -y = 23-(-17)
5x = 40
x = 8
substituting x = 8 in the 2nd equation 
3*8 + y = 23
24 + y = 23
y = -1

solution - (8,-1)

3 0
3 years ago
Which of the following equations has infinitely many solutions?
Valentin [98]

Answer:

B

Step-by-step explanation:

If you look at A and you subtract 3x by 4x you get x and you subtract 3 from -7 and you get -10. But if you look at B you do the stuff in the parentheses first and you get 4x+12x+28=16x+28 and they're the same so it's B.

7 0
3 years ago
Write a linear inequality to represent the information given. shanley would like to give $5 gift cards and $4 teddy bears as par
aliya0001 [1]
Given that S<span>hanley would like to give $5 gift cards and $4 teddy bears as party favors and that Shanley has $128 to spend on party favors.

The inequality to find the number of </span><span>gift cards x and teddy bears y Shanley could purchase</span> is given by

5x+4y\leq128

One solution to the inequality is that Shanley can buy 12 gift cards and 15 teddy bears.
5 0
3 years ago
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