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3 years ago

What is the least common denominator of the rational expressions below? 1/x^2 - 4/3x^2+15x

Mathematics

2 answers:

mylen [45]3 years ago

7 0

Answer:3x^2(x+5)

Step-by-step explanation: A P E X

vladimir1956 [14]3 years ago

5 0

Answer:

The LCD is 3x²

The other two denominators can be factors of 3x²

Step-by-step explanation:

To get the equivalent fractions, divide the original denominator into the LCD, then multiply the original numerator by the quotient.

For the first term: 1/x²

3x² ÷ x² = 3 3×1=3 The equivalent is 3/3x²

Second term: Leave it as it is.

For the third term: 15x

The implied denominator is 1

3x² ÷ 1 = 3x² 3x² × 15 = 135x²

The equivalent is 135x²/3x²

To check the validity, substitute a value for x and calculate the numbers.

For example let x = 3

The original expression becomes

1/3² + 4/3(3²) - 15(3)

1/9 + 4/27 - 45

With the LCD it is

3/27 + 4/27 - 1215/27

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Step-by-step explanation:

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3 years ago

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An individual who has automobile insurance from a certain company is randomly selected. Let y be the number of moving violations

Hoochie [10]

Answer:

a) $E(Y)= \sum_{i=1}^n Y_i P(Y_i)$

And replacing we got:

$E(Y) = 0*0.45 +1*0.2 +2*0.3 +3*0.05= 0.95$

b) $E(80Y^2) =80[ 0^2*0.45 +1^2*0.2 +2^2*0.3 +3^2*0.05]= 148$

Step-by-step explanation:

Previous concepts

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".

The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).

And the standard deviation of a random variable X is just the square root of the variance.

Solution to the problem

Part a

We have the following distribution function:

Y 0 1 2 3

P(Y) 0.45 0.2 0.3 0.05

And we can calculate the expected value with the following formula:

$E(Y)= \sum_{i=1}^n Y_i P(Y_i)$

And replacing we got:

$E(Y) = 0*0.45 +1*0.2 +2*0.3 +3*0.05= 0.95$

Part b

For this case the new expected value would be given by:

$E(80Y^2)= \sum_{i=1}^n 80Y^2_i P(Y_i)$

And replacing we got

$E(80Y^2) =80[ 0^2*0.45 +1^2*0.2 +2^2*0.3 +3^2*0.05]= 148$

5 0

3 years ago

the least common denominator for the sum 3/8 + 512 is 24 name another common denominator that you could use

bogdanovich [222]

You could also use 48 because 8 and 12 divide into it.

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3 years ago