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Reptile [31]
3 years ago
14

A carton of paper is priced at $27.00 now. If the papergoes on sale for 25% off the current price, what will be the sale price o

f the carton?
Mathematics
1 answer:
Alenkinab [10]3 years ago
3 0
Divide the 27 by 4 and that will give you 6.75. Subract the 6.75 from the 27 and theres your answer (20.25) so the sale price is $20.25
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Select all that could be x
kari74 [83]

Answer:

4 (a.)

Step-by-step explanation:

The x line has to be under 7 and 6 is too close to 7, therefore 4 is the answer

8 0
3 years ago
The joint probability density function of X and Y is given by fX,Y (x, y) = ( 6 7 x 2 + xy 2 if 0 < x < 1, 0 < y < 2
fredd [130]

I'm going to assume the joint density function is

f_{X,Y}(x,y)=\begin{cases}\frac67(x^2+\frac{xy}2\right)&\text{for }0

a. In order for f_{X,Y} to be a proper probability density function, the integral over its support must be 1.

\displaystyle\int_0^2\int_0^1\frac67\left(x^2+\frac{xy}2\right)\,\mathrm dx\,\mathrm dy=\frac67\int_0^2\left(\frac13+\frac y4\right)\,\mathrm dy=1



b. You get the marginal density f_X by integrating the joint density over all possible values of Y:

f_X(x)=\displaystyle\int_0^2f_{X,Y}(x,y)\,\mathrm dy=\boxed{\begin{cases}\frac67(2x^2+x)&\text{for }0

c. We have

P(X>Y)=\displaystyle\int_0^1\int_0^xf_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx=\int_0^1\frac{15}{14}x^3\,\mathrm dx=\boxed{\frac{15}{56}}

d. We have

\displaystyle P\left(X

and by definition of conditional probability,

P\left(Y>\dfrac12\mid X\frac12\text{ and }X

\displaystyle=\dfrac{28}5\int_{1/2}^2\int_0^{1/2}f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\boxed{\frac{69}{80}}

e. We can find the expectation of X using the marginal distribution found earlier.

E[X]=\displaystyle\int_0^1xf_X(x)\,\mathrm dx=\frac67\int_0^1(2x^2+x)\,\mathrm dx=\boxed{\frac57}

f. This part is cut off, but if you're supposed to find the expectation of Y, there are several ways to do so.

  • Compute the marginal density of Y, then directly compute the expected value.

f_Y(y)=\displaystyle\int_0^1f_{X,Y}(x,y)\,\mathrm dx=\begin{cases}\frac1{14}(4+3y)&\text{for }0

\implies E[Y]=\displaystyle\int_0^2yf_Y(y)\,\mathrm dy=\frac87

  • Compute the conditional density of Y given X=x, then use the law of total expectation.

f_{Y\mid X}(y\mid x)=\dfrac{f_{X,Y}(x,y)}{f_X(x)}=\begin{cases}\frac{2x+y}{4x+2}&\text{for }0

The law of total expectation says

E[Y]=E[E[Y\mid X]]

We have

E[Y\mid X=x]=\displaystyle\int_0^2yf_{Y\mid X}(y\mid x)\,\mathrm dy=\frac{6x+4}{6x+3}=1+\frac1{6x+3}

\implies E[Y\mid X]=1+\dfrac1{6X+3}

This random variable is undefined only when X=-\frac12 which is outside the support of f_X, so we have

E[Y]=E\left[1+\dfrac1{6X+3}\right]=\displaystyle\int_0^1\left(1+\frac1{6x+3}\right)f_X(x)\,\mathrm dx=\frac87

5 0
3 years ago
The 10 participants in an experiment had the following reaction times ( in milliseconds ) : 778,783,784,786,790,804,807,810,819,
Nata [24]

Answer:

Mean. It includes all data points.

Step-by-step explanation:

-We first need to calculate the mean, median and mode then compare our values:

#Mean:

\bar x=\frac{1}{n}\sum{x_i}\\\\=\frac{1}{10}\sum{778+783+784+786+790+804+807+810+819+823}\\\\=\frac{1}{10}\times \\\\=798.40

#The median is the middlemost data point in a lsit data:

778,783,784,786,790,804,807,810,819,823

-Since our data points is an even number, the median number is calculated as:

median=\frac{1}2}\sum{5^{th}+6^{th}}\\\\=0.5[790+804]\\\\=797.00

#Mode is the data point with the highest frequency:

-Since there's no number appearing more than once, our set has no mode.

#Since our data set has no outliers and is not a skewed distribution, the mean will be the best measure as it includes all data points

8 0
3 years ago
Solve for f. <br> -f +2+4f =8 -3f
Hitman42 [59]

Answer:

f=1

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
If the fourth of 5 consecutive numebrs is 15, what is their sum?
Tju [1.3M]

BRAINLIEST PLEASEEEEEEEEEEEEE

Answer:

70

Step-by-step explanation:

You know the fourth number in this pattern is 15, and that they are all consecutive. With this information you know that the fifth number will be 16, and by counting backwards from 15 you can figure out all of the numbers are 12, 13, 14, 15, and 16. Now, to find the sum of these numbers you must add them together.

This is what it could look like: 12+13+14+15+16

Now to find the answer you need to calculate what the addition would equal, which is 70.

8 0
3 years ago
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