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fiasKO [112]
3 years ago
14

The number of home runs scored by a certain team in one baseball game is a random variable with the distribution x 0 1 2 P(x) 0.

4 0.4 0.2 The team plays 2 games. The number of home runs scored in one game is independent of the number of home runs in the other game. Let Y be the total number of home runs. Find E(Y ) and Var(Y ).
Mathematics
1 answer:
DanielleElmas [232]3 years ago
5 0

Answer: E(Y) = 1.6 and Var(Y)=1.12

Step-by-step explanation:

Since we have given that

X       0        1       2

P(X)   0.4   0.4    0.2

Here, number of games = 2

So, Y=X_1+X_2

Since X_1\ and\ X_2 are independent variables.

so, E[Y]=2E[X]\\\\Var[Y]=2Var[X]

So, we get that

E(X)=0.4\times 0+0.4\times 1+0.2\times 2=0.8\\\\and Var[x]=E[x^2]-(E[x])^2\\\\E[x^2]=0\times 0.4+1\times 0.4+4\times 0.2=1.2\\\\So, Var[x]=1.2-(0.8)^2\\\\Var[x]=1.2-0.64=0.56

So, E[y]=2×0.8=1.6

and Var[y]=2×0.56=1.12

Hence, E(Y) = 1.6 and Var(Y)=1.12

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lyudmila [28]

(\stackrel{x_1}{\frac{5}{6}}~,~\stackrel{y_1}{0})~\hspace{10em} \stackrel{slope}{m}\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{-3}(x-\stackrel{x_1}{\frac{5}{6}})

8 0
2 years ago
Heather measured a swimming pool and made a scale drawing. In real life, the pool is 45 meters long. It is 65 millimeters long i
oksano4ka [1.4K]
Greetings!

"<span>Heather measured a swimming pool and made a scale drawing. In real life, the pool is 45 meters long. It is 65 millimeters long in the drawing. What scale did Heather use for the drawing?"...

65mm=</span>45m<span>
Reduce to Simpliest Form.
</span>65/5=<span>45/5
13mm=9m

As a Representative Fraction (scale), it would look like: (in regards to mm)
13:9000

Hope this helps.
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4 0
3 years ago
Aubrey claims that if the dimensions of the parallelogram shown are doubled, then the area of the larger parallelogram will be 4
Ostrovityanka [42]

Answer:

Aubrey is correct because the area of the new parallelogram is 12 (6) = 72 square inches. The original area is 18 square inches. Since 4 (18) = 72, the new parallelogram has 4 times the area of the original.

Step-by-step explanation:

A parallelogram with a base of 6 inches and height of 3 inches. A side has a length of 5 inches.

Aubrey is correct because the area of the new parallelogram is 12 (6) = 72 square inches. The original area is 18 square inches. Since 4 (18) = 72, the new parallelogram has 4 times the area of the original.

Aubrey is correct because the area of the new parallelogram is 10 (7) = 70 square inches. The original area is 18 square inches. Since 4 (18) = 72, it is about 4 times larger than the original.

Aubrey is incorrect because if one doubles each dimension, then the area will automatically be doubled as well. The original area is 18 square inches so the new parallelogram will have an area of 2 (18) = 36, or two times more than the original.

Aubrey is incorrect because if one doubles each dimension, then the area will automatically be doubled as well. The original area is 30 square inches so the new parallelogram will have an area of 2 (30) = 60, or 2 times more than the original.

Workings

Area of a parallelogram=base×height

Original parallelogram

Base=6 inches

Height=3 inches

Area=base×height

=6×3

=18 square inches

New parallelogram with doubled dimensions

Base=6 inches doubled=12 inches

Height=3 inches doubled=6 inches

Area=base×height

=12×6

=72 square inches

New area=4 times original area

New area=4×18

New area=72 square inches

5 0
3 years ago
Mrs. Hall records the heights of 50 students in a spreadsheet. The mean height is 68 inches. After looking at the data again, sh
defon
67.33. You would first find the total height of people. So 50 would be multiplied by 68, giving you the answer of 3,400. After, you would subtract 82 and 86, giving you 3,232. To get the final answer you would divide the value by 48, since two of them are removed, giving you 67.33.
7 0
3 years ago
Read 2 more answers
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Black_prince [1.1K]

Answer:

One solution

Step-by-step explanation:

We know there is only one solution because the lines do not have the same slope, nor are they the exact same line.

So we know they must have just one solution.

Best of luck

6 0
2 years ago
Read 2 more answers
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