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abruzzese [7]
3 years ago
11

In a certain city, 30 percent of the people are conservatives, 50 percent are liberals, and 20 percent are independents. records

show that in a particular election, 65 percent of the conservatives voted, 82 percent of the liberals voted, and 50 percent of the independents voted. if a person in the city is selected at random and it is learned that she did not vote in the last election, what is the probability that she is a liberal?
Mathematics
1 answer:
nignag [31]3 years ago
6 0
If the person did not vote it can be:
30/100 (30%) people in the city are conservatives, and only 65/100 voted - so 45/100 did not voted.

Liberals are 50% of the city population (1/2), and 82/100 of them voted, so 100/100-82/100=8/100 did not voted!

So let’s make 2 probability events:
1) A person did not voted
2) a person is liberal

Probability that the person is a liberal: 1/2
Person didn’t voted and it’s a liberal:
1/2*8/100= 8/200=4/100 [*]

[*] To count the probability of two probability events you need to multiply them.
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The diagonal of a TV set is 13 inches long. It’s length is 7 inches more than the height. Find the dimensions of the TV set.
alukav5142 [94]

Answer: The length is 12 inches while the height is 5 inches

Step-by-step explanation: It the Television has a diagonal of 13 inches, and a height of H inches, then the length would be (H + 7) inches. It’s length is 7 inches more than the height. At this point we can draw up a right angled triangle with the hypotenuse as 13 (diagonal side) and the other two sides as H and (H + 7)

Then we can apply the Pythagoras theorem which states that

AC^2 = AB^2 + BC^2

(Where AC is the hypotenuse and AB and BC are the two other sides)

Hence,

13^2 = H^2 + (H + 7)^2

169 = H^2 + (H^2 + 14H + 49)

169 = 2H^2 + 14H + 49

By collecting like terms we now have

169 - 49 = 2H^2 + 14H

120 = 2H^2 + 14H

By re-arranging all terms on one side of the equation, we arrive at

2H^2 + 14H - 120 = 0

Divide all sides by 2

H^2 + 7H - 60 = 0

To solve the quadratic equation, we now factorize and we have,

H^2 + 12H - 5H - 60 = 0

(H + 12) (H - 5) = 0

Therefore

Either H + 12 = 0 OR

H - 5 = 0

Hence, Either H = -12 or H = 5

The dimension can not be a negative value so we shall take h equals 5.

Having calculated the height of the television as 5 inches, the length which was given as H + 7 can now be calculated as

Length = H + 7

Length = 5 + 7

Length = 12

Therefore, the length of the Television is 12 inches and the height is 5 inches

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Step-by-step explanation:

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