Look at the pictures and solve. WILL GIVE BRAINIEST

Mathematics

1 answer:

Reika [66]3 years ago

3 0

Answer:

1. y = 4x - 4

2. y = x + 2

3. y = -2x - 4

4. y = -x + 2

Step-by-step explanation:

Slope-intercept form is y = mx+b. As we know, m is the slope and b is the y-intercept. We need to find the slope and y-intercept and put them in the equation. Slope is rise over run, so we just count up then over until we get to an intersection. For the y-intercept, we look where the line crosses the y-axis.

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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

Please help, when you give me the answer please can you put the number of the question so I know

ZanzabumX [31]

Didn't answer all because I got lazy and I think you should try and do the rest yourself. Did this in 5 mins, try putting more effort into your homework. This is basic mathematics.