Mathematics, 23.04.2020 02:09 rb3910

A campus radio station surveyed 500 students to determine the types of music they like. The survey revealed that 198 like rock, 152 like country, and 113 like jazz. Moreover, 21 like rock and country, 22 like rock and jazz, 16 like country and jazz, and 5 like all three types of music. What is the probability that a radomly selected student likes jazz or country but not rock?

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Answer from: palmekar000

The probability that a randomly selected student likes jazz or country but not rock is 0.422.

Step-by-step explanation:

The information provided is:

Total number of students selected, N = 500.

The number of students who like rock, n (R) = 198.

The number of students who like country, n (C) = 152.

The number of students who like jazz, n (J) = 113.

The number of students who like rock and country, n (R ∩ C) = 21.

The number of students who like rock and Jazz, n (R ∩ J) = 22.

The number of students who like country and jazz, n (C ∩ J) = 16.

The number of students who like all three, n (R ∩ C ∩ J) = 5.

Consider the Venn diagram below.

Compute the probability that a randomly selected student likes jazz or country but not rock as follows:

P (J ∪ C ∪ not R) = P (Only J) + P (Only C) + P (Only J ∩ C)

$=\frac{80}{500}+\frac{120}{500}+\frac{11}{500}\\=\frac{211}{500}\\=0.422$

Thus, the probability that a randomly selected student likes jazz or country but not rock is 0.422.

A campus radio station surveyed 500 students to determine the types of music they like. The survey r

Answer from: Quest

none of the above.

for one of the equations to be used in the process, there has to be a $2x^2$ term in the equation since $2x$ squared is $2x^2$ .

since there is only a $x^2$ term in the first equation, we cannot derive a $2x+4$ from completing the square.

solving with completing the square

$x^2=-4x+3$

$x^2+4x=3$

$x^2+4x+4=7$

$(x+2)^2=7$

$x+2=+-\sqrt{7}$

$x=2+-\sqrt{7}$

Answer from: Quest

c. x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

$\frac{little}{big} =\frac{side mn}{side ab}=\frac{side on}{side cb}$ .

$\frac{0.96}{1.2}=\frac{x}{3}$

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

$0.96(3)=1.2(x)\\2.88=1.2x\\\frac{2.88}{1.2}=\frac{1.2x}{1.2} \\2.4=x$

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