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3 years ago

Solve each system by substitution

Mathematics

1 answer:

Thepotemich [5.8K]3 years ago

4 0

Step-by-step explanation:

{9x+3y=-36

y=-3x-21

9x-9x-36=-36

y=-3x-21

x=0

y=-21

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Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n 2 if heads comes up

Artyom0805 [142]

Answer:

In the long run, ou expect to lose $4 per game

Step-by-step explanation:

Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n^2 if heads comes up first on the nth toss.

Assuming X be the toss on which the first head appears.

then the geometric distribution of X is:

X $\sim$ geom(p = 1/2)

the probability function P can be computed as:

$P (X = n) = p(1-p)^{n-1}$

where

n = 1,2,3 ...

If I agree to pay you $n^2 if heads comes up first on the nth toss.

this implies that , you need to be paid $\sum \limits ^{n}_{i=1} n^2 P(X=n)$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = E(X^2)$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =Var (X) + [E(X)]^2$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p}{p^2}+(\dfrac{1}{p})^2$ ∵ X $\sim$ geom(p = 1/2)

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p}{p^2}+\dfrac{1}{p^2}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p+1}{p^2}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{2-p}{p^2}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{2-\dfrac{1}{2}}{(\dfrac{1}{2})^2}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ \dfrac{4-1}{2} }{{\dfrac{1}{4}}}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ \dfrac{3}{2} }{{\dfrac{1}{4}}}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ 1.5}{{0.25}}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =6$

Given that during the game play, You pay me $10 , the calculated expected loss = $10 - $6

= $4

∴

In the long run, you expect to lose $4 per game

3 0

3 years ago

Five less than the product of -2 and a number is -13

deff fn [24]

Answer:

-2 -5 + 13 = x

Step-by-step explanation:

x would be the product

and i dont know if i got this correct o.O

I tried is all imma say

8 0

3 years ago

What is the volume of a hemisphere with a radius of 29 m, rounded to the nearest tenth of a cubic meter?

salantis [7]

Answer:

19.4 cubic meter

Step-by-step explanation

Round your answer to the nearest tenth of a cubic centimeter.

4 0

3 years ago

CONVERT TO SCIENTIFIC NOTATION:

Otrada [13]

1)1.082*10^9
2)1.496*10^8
3)2.2794*10^8
4)7.784*10^5
5)1.4236*10^9
6)2.867*10^9
7)4.4884*10^9
Hope it helped!

6 0

3 years ago

What is the slope of the line containing (6, -7) and (5, -9)?<br> A) 1<br> B) -2.<br> C) 2<br> D) 16

zloy xaker [14]

Answer: C

Step-by-step explanation:

y2-y1/x2-x1

-9+7/5-6 = 2

7 0

3 years ago