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3 years ago

Which line is parallel to y=-4x+3?

Mathematics

2 answers:

Oxana [17]3 years ago

6 0

Answer:

Step-by-step explanation:

x = 0

y = -4 (0) + 3

y = 3

(0,3) is a solution.

x-axis is parallel

wolverine [178]3 years ago

3 0

I think yes it is parallel

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Derek and Mia place two green marbles and one yellow marble in a bag. Somebody picks a marble out of the bag without looking and

cluponka [151]

Answer:

Thus, the expected value of points for Derek and Mia are $\dfrac{-1}{9}$ and $\dfrac{1}{9}$ respectively.

Step-by-step explanation:

Number of green marbles = 2 and Number of Yellow marbles = 1

Then, total number of marbles = 2+1 = 3

A person selects two marbles one after another after replacing them.

So, the probabilities of selecting different combinations of colors are,

$1.\ P(GG)=P(G)\times P(G)\\\\P(GG)=\dfrac{2}{3}\times \dfrac{2}{3}\\\\P(GG)=\dfrac{4}{9}$

$2.\ P(GY)=P(G)\times P(Y)\\\\P(GY)=\dfrac{2}{3}\times \dfrac{1}{3}\\\\P(GY)=\dfrac{2}{9}$

$3.\ P(YG)=P(Y)\times P(G)\\\\P(YG)=\dfrac{1}{3}\times \dfrac{2}{3}\\\\P(YG)=\dfrac{2}{9}$

$4.\ P(YY)=P(Y)\times P(Y)\\\\P(YY)=\dfrac{1}{3}\times \dfrac{1}{3}\\\\P(YY)=\dfrac{1}{9}$

Now, we have that,

If two marbles are of same color, then Mia gains 1 point and Derek loses 1 point.

If two marbles are of different color, then Derek gains 1 point and Mia loses 1 point.

<h3>Also, the expected value of a random variable X is $E(X)=\sum_{i=1}^{n} x_i\times P(x_i)$ .</h3>

Then, the expected value of points for Derek is,

$E(D)= (-1)\times \dfrac{4}{9}+1\times \dfrac{2}{9}+1\times \dfrac{2}{9}+(-1)\times \dfrac{1}{9}\\\\E(D)= \dfrac{-5}{9}+\dfrac{4}{9}\\\\E(D)=\dfrac{-1}{9}$

And the expected value of points for Mia is,

$E(M)= 1\times \dfrac{4}{9}+(-1)\times \dfrac{2}{9}+(-1)\times \dfrac{2}{9}+1\times \dfrac{1}{9}\\\\E(M)= \dfrac{5}{9}-\dfrac{4}{9}\\\\E(M)=\dfrac{1}{9}$ .

Thus, the expected value of points for Derek and Mia are $\dfrac{-1}{9}$ and $\dfrac{1}{9}$ respectively.

8 0

3 years ago

Read 2 more answers

Danielle and Drew are sightseeing for the day. Between the two of them they take 77 pictures. Danielle takes 17 more than twice

Alex Ar [27]

Let's break this down:
Total Pictures = 77
Drew's Pictures = X (An unknown amount)
Danielle's Pictures = 17 + 2X (2 times the amount of Drew plus 17)

So, let's put the pieces together, the problem should look like this:
Total Pictures = Drew's Pictures + Danielle's Pictures

So let's put in what we know:
77 = X + (17 + 2X)

1st step is to get X to one side:
77 = X + 17 + 2X
-17 - 17
=> 60 = X + 2X
=> 60 = 3X

Now that X is on one side, the 2nd step is to get X to be alone:
60/3 = 3X/3 (We have to divide to each side because the answer is equal)
20 = X

So, now that we know what X equals, let's go back to what we broke down:
Drew's Pictures = X (An unknown amount)
Danielle's Pictures = 17 + 2X (2 times the amount of Drew plus 17)

*Remember that X = 20*
So the amount of Drew's Pictures (since the amount is equal to X) is 20.

Danielle had 17 + 2X pictures which means:
17 + 2(20)
17 + 40
57

So Danielle took 57 pictures

7 0

3 years ago

Which rectangle will have the largest area?

olga nikolaevna [1]

Answer:

l = 6 cm, w = 7 cm

Step-by-step explanation:

3 0

3 years ago

1. In the file MajorSalary.xlsx, data have been collected from 111 College of Business graduates on their monthly starting salar

lara31 [8.8K]

Solution :

a.The table below shows the different distribution of the students in differnt majors :

Subjects No. of graduates

Accounting 28

Finance 21

Management 24

Info System 16

Marketing 22

Therefore, "accounting" have the maximum number of graduates.

b. The average monthly salaries of the graduates from some of the different majors are :

Subjects Average salary Overall salary

Finance 699 77595

Accounting 1014 112560

Info Sys 577 64000

Marketing 663 73590

Management 688 76320

Therefore, the "Accounting" group have the highest average salary.

c. The "info System" has the lowest overall salary.

2.b. The data showing is more or less the linear relationship between the "Annual Expenses" and the "Weekly usage", therefore initially, we fit the linear regression equation of the form.

$AE = a+b \times(WU)$

The ordinary least square estimates are $$\hat{a} = 10.528 \text{ and} \ \hat{b} = 0.9534$

So, $AE = 10.528+0.9534 \times(WU)$

c. The amount of the variation the estimated model explains for the entire variation is given by the measure of

$R^2 = \frac{\text{variance of fitted observation}}{\text{variance in original data}}$

= 0.856

It shows the linear regression that explains the good amount of entire variability of the annual expenses. It also supports the assumption of the "Linear Model".

a. The Scatter plot is attached below.

3 0

3 years ago

Sarah scored 68 out of 80 in a test.Write her score as a simplified fraction

attashe74 [19]

$\frac{68}{80} \\ \\ \frac{(4)17}{(4)20} \\ \\ \boxed{ \frac{17}{20}}$

5 0

3 years ago