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Leokris [45]
3 years ago
12

Taylor tried to solve an equation step by step:

Mathematics
2 answers:
Leya [2.2K]3 years ago
3 0
His mistake was on step 1
Sedbober [7]3 years ago
3 0

Answer:

Step one

Step-by-step explanation:

Thats what it says on Khan Academy

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Samantha sends her son, Barry, to a preschool center on certain days. The cost of preschool is $45 per day along with a fixed mo
Travka [436]

Answer: Option D

D. 880 = 45d + 70; 18\ days

Step-by-step explanation:

We know that the cost of preschool is $ 45 per day plus a monthly fee of $ 70.

We also know that a total of $ 880 was paid last month

To write an equation that represents this situation, let us call "d" the number of days that Barry attends school

So the cost was:

45d + 70 = 880

Now we solve the equation for the variable d

45d= 880-70

d= \frac{810}{45}

d= 18\ days

Therefore answer is the option D

8 0
3 years ago
Can somebody help me... plsssss
NeX [460]
X > -8
The line would be on -8 going to the left, the circle would not be shaded
7 0
3 years ago
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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
you buy a package of 6 rolls of paper towels for $5.74 and another package of 12 rolls for $16.97 at this linear rate, how much
Keith_Richards [23]

Answer:

23.24 i think

Step-by-step explanation:


3 0
3 years ago
Ming needs 1/2 pint of red paint for an art project. He has 6 jars that have the following amounts of red paint in them. He want
Alex17521 [72]

Answer:

Step-by-step explanation:

GIvn that Ming needs 1/2 pint of red paint for an art project

The 6 jars he has, have the following red paint in them

A. 2/3 pint

B.1/4 pint

C.4/6 pint

D.3/4 pint

E. 3/8 pint

F.2/6 pint

Since he want 1/2 pint he can use only jar B two times

First pour jar B contents equal to 1/4 pint to a new empty jar.

Now he can pour from A 1/4 pint to B, and then again use that

So altogether he gets 1/2 pint of red paint.

7 0
3 years ago
Read 2 more answers
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