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3 years ago

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

Read 2 more answers

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