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3 years ago

8

Suppose that the functions g and h are defined for all real numbers as follows:

1 answer:

Zinaida [17]3 years ago

6 0

(h+g)(x) = 3x + 5 + 6x = 9x + 5Answer

(h - g)(x) = 6x - (3x + 5) = 3x- 5 Answer

(h*g)(x) = 6x(3x + 5) = 18x^2 + 30x

(h*g)(2) = 18(4) + 30(2) = 72 + 60 = 132 Answer

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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

4 years ago

A 3pack of boxes of juice costs 1.09. A 12 pack of boxes cost 4.49. A case of 24 boxes costs 8.78. Which is the best buy?Explain

Leona [35]

1.09÷3= .3633 each
4.49÷12= .37416 each
8.78÷24= .3658 each

so the first one

5 0

4 years ago

Subtract the given function and indicate the domain of the difference

maxonik [38]

Answer:

The domain is $x\in (-\infty,\infty).$

Step-by-step explanation:

Given functions $f(x)=x^2+3x+1$ and $g(x)=2x^2-4x-1$

Subtract these two functions:

$f(x)-g(x)\\ \\=(x^2+3x+1)-(2x^2-4x-1)\\ \\=x^2+3x+1-2x^2+4x+1\\ \\=(x^2-2x^2)+(3x+4x)+(1+1)\\ \\=-x^2+7x+2$

Plot these difference on the coordinate plane (see attached diagram). This function is defined for all vlues of x, so the domain is $x\in (-\infty,\infty).$

6 0

4 years ago

HELP HELP ME WITH THIS PLSSS!!!!

givi [52]

Answer:

B, C, D, A, E

Step-by-step explanation:

hope it helps

4 0

3 years ago

Read 2 more answers

A binomial event has n = 60 trials. The probability of success for each trial is 0.20. Let x be the number of successes of the e

OLga [1]

Answer:

12 and 3.0984

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$\mu_{x} = np$

The standard deviation of the binomial distribution is:

$\sigma_{x} = \sqrt{np(1-p)}$

In this problem, we have that:

$n = 60, p = 0.2$

So

$\mu_{x} = np = 60*0.2 = 12$

$\sigma_{x} = \sqrt{np(1-p)} = \sqrt{60*0.8*0.2} = 3.0984$

So the correct answer is:

12 and 3.0984

4 0

3 years ago