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3 years ago

8

For what values of a and b is the line 3x y=b tangent to the curve y=ax3 when x=3?

1 answer:

Sav [38]3 years ago

6 0

Hello : here is a solution

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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

Simplify the expression -(2m+3)+5m

astra-53 [7]

Answer:

$3m-3$

Step-by-step explanation:

So we have the expression:

$-(2m+3)+5m\\$

Distribute the negative:

$=-2m-3+5m$

Combine like terms:

$=3m-3$

And we're done!

5 0

3 years ago

Read 2 more answers

Is the following exponential graph increasing or decreasing? If it is, what exponent problem is it? Explain.

Akimi4 [234]

It is increasing and the exponential problem should be 5e^x-8

3 0

3 years ago

HALPPPPP :(((((((((((

SVEN [57.7K]

Answer: 5

Explanation: 12(3) - 3(1/3)/4(3)-5

= 36-1/12-5

= 35/7

= 5

3 0

2 years ago

Trong những năm 2005, sản xuất đường ở Mỹ : 11,4 tỷ pao; tiêu dùng 17,8 tỷ pao; giá cả ở Mỹ 22 xu/pao; giá cả thế giới 8,5 xu/pa

ira [324]

xin lỗi nhưng không ai có thể hiểu bạn ở đây vì họ chỉ nói tiếng anh ở đây

5 0

2 years ago