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3 years ago

A sweater was originally 55$ it is now marked down to 65% of its original price how much is the sweater now

Mathematics

1 answer:

damaskus [11]3 years ago

7 0

The sweater is now $19.25

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Let X be a continuous random variable with density functionf(x)={1−|x|0 for −1

BlackZzzverrR [31]

Answer:

$f_Y (y) =\frac{d}{dy} = 2 \frac{1}{2 |\sqrt{y}|} -1 = \frac{1}{|\sqrt{y}|} -1,0 \leq Y\leq 1$

Step-by-step explanation:

For this case we want to find the density function for $Y=X^2$

And we have the following density function for the random variable X:

$f(X) = 1- |X|,-1 \leq X \leq 1$

So we can do this replacing $Y=X^2$

$F_Y (Y \leq y) = P(X^2 \leq y)$

If we apply square root on both sides we got:

$P(-\sqrt{y} \leq X \leq \sqrt{y}) = \int_{-\sqrt{y}}^0 1+t dt +\int_{0}^{\sqrt{y}} 1-t dt$

And if we integrate we got this:

$F_Y (y) = [t+ \frac{t^2}{2}] \Big|_{-\sqrt{y}}^0+ [t -\frac{t^2}{2}] \Big|_{0}^{\sqrt{y}}$

And replacing we got:

$F_Y (y) = [0 -(-\sqrt{y} +\frac{y}{2})] + [\sqrt{y} -\frac{y}{2}]$

$F_Y (y) = 2 |\sqrt{y}| -y$

And if we want to find the density function we just need to derivate the pdf like this:

$f_Y (y) =\frac{d}{dy} = 2 \frac{1}{2 |\sqrt{y}|} -1 = \frac{1}{|\sqrt{y}|} -1,0 \leq Y\leq 1$

3 0

4 years ago

The value of coin A is twice the value of coin B. Together, the total value of the two coins is $30.00 What is the value of each

Vesna [10]

Answer: Coin A is $20, coin B is $10

Explanation:

A + B = $30

B = $10

$10 x 2 = $20

A = $20

$20 + $10 = $30

6 0

3 years ago

Which statement best describes the slope of the line?

Anton [14]

Answer:A

Step-by-step explanation:

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3 years ago

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Find the product of (x − 7)2 and explain how it demonstrates the closure property of multiplication.

Ksivusya [100]

Answer:

Step-by-step explanation:

(x-7)^2=(x-7)(x-7)=x^2-7x-7x+49=x^2-14x+49

3 0

3 years ago

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How many different strings can be formed by rearranging the letters in the word DCDCD?

Natali [406]

<h2>Answer:</h2>

The different strings which can be formed by rearranging the letters in the word DCDCD are:

<h2>Step-by-step explanation:</h2>

We are asked to find the different number of arrangements that may be me made in the word:

DCDCD

There are a total of 5 words such that D is repeated 3 times and C is repeated two times.

Hence, the total number of ways of arrangement is given by:

$=\dfrac{5!}{3!\times 2!}\\\\=\dfrac{5\times 4\times 3!}{3!\times 2!}\\\\=\dfrac{5\times 4}{2!}\\\\=\dfrac{5\times 4}{2}\\\\=10$

Hence, the total number of ways are: 10

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3 years ago