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klemol [59]
3 years ago
14

John is curious about the type of music his classmates enjoy and decides to survey 125 of his classmates. In his survey, 63 stud

ents enjoy both hip hop and pop music, 13 enjoy only pop music, and a total of 90 enjoy hip hop. How many of his classmates do not enjoy hip hop or pop?

Mathematics
1 answer:
goldfiish [28.3K]3 years ago
3 0

Answer:

Total 22 students do not enjoy hip hop or pop.

Step-by-step explanation:

It is given that total number of students is 125.

A : Total number of students, who enjoy hip hop

B : Total number of students, who enjoy pop

A∩B : Total number of students, who enjoy both hip hop and pop music.

From the given information it is clear that

A=90

A\cap B=63

A'\cap B=13

A'\cap=B-A\cap B

13=B-63

B=76

Total number of students, who enjoy at least one of the music.

A\cupB=A+B-A\cap B

A\cupB=90+76-63

A\cupB=103

Total number of students, who do not enjoy any music.

125-A\cupB=125-103=22

Therefore total 22 students do not enjoy hip hop or pop.

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A motorcyclist traveled a distance of 120 miles in 2 hours. Traveling at the same speed, how far would this motorcyclist travel
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Step-by-step explanation:

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Read 2 more answers
A student solves the following equation and
Phoenix [80]

Answer:

Since the equation is undefined for -2

Therefore, NO SOLUTION for the given equation.

Step-by-step explanation:

Considering the expression

\frac{3}{a+2}-6\cdot \frac{a}{-4+a^2}=\frac{1}{a-2}

\frac{3}{a+2}-\frac{6a}{-4+a^2}=\frac{1}{a-2}

\mathrm{Find\:Least\:Common\:Multiplier\:of\:}a+2,\:-4+a^2,\:a-2:\quad \left(a+2\right)\left(a-2\right)

\mathrm{Multiply\:by\:LCM=}\left(a+2\right)\left(a-2\right)

\frac{3}{a+2}\left(a+2\right)\left(a-2\right)-\frac{6a}{-4+a^2}\left(a+2\right)\left(a-2\right)=\frac{1}{a-2}\left(a+2\right)\left(a-2\right)

as

  • \frac{3}{a+2}\left(a+2\right)\left(a-2\right):\quad 3\left(a-2\right)
  • -\frac{6a}{-4+a^2}\left(a+2\right)\left(a-2\right):\quad -6a
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so equation becomes

3\left(a-2\right)-6a=a+2  

-3a-6=a+2

-3a-6+6=a+2+6

-4a=8

\mathrm{Divide\:both\:sides\:by\:}-4

\frac{-4a}{-4}=\frac{8}{-4}

a=-2

\mathrm{Verify\:Solutions}

\mathrm{Take\:the\:denominator\left(s\right)\:of\:}\frac{3}{a+2}-6\frac{a}{-4+a^2}-\frac{1}{a-2}\mathrm{\:and\:compare\:to\:zero}

\mathrm{Solve\:}\:a+2=0:\quad a=-2

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\mathrm{Solve\:}\:a-2=0:\quad a=2

So the following points are undefined

a=-2,\:a=2

Since the equation is undefined for -2

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4 0
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Use the distributive property to write an expression that is equivalent to 9(c+5).
shepuryov [24]

Answer:

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Step-by-step explanation:

The distributive property also known as distributive law of multiplication and division.

In the given expression, distributive law of multiplication is applied where we can multiply first before addition.

Given

9(c+5)

Using distributive property

9(c+5)

= (9 × c) + (9 × 5)

= 9c + 45

9(c+5) = 9c + 45

3 0
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