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2 years ago

Which expression is equivalent to the expression shown ? 2 (x + 5) +3 (x2 - 5x +13)

1 answer:

3 0

$\text{Use the distributive property:}\\\\a(b+c)=ab+ac$

$2(x+5)+3(x^2-5x+13)=(2)(x)+(2)(5)+(3)(x^2)-(3)(5x)+(3)(13)\\\\=2x+10+3x^2-15x+39=3x^2-13x+49$

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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

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Lorine drew the model below to represent the equation 16 + 28 = ___ ´ (4 + 7).

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Answer:

Step-by-step explanation:

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Hey:) can you please help me posted picture of question

oee [108]

Answer:
x² + 10x + 25

Explanation:
Before we begin, remember the following:
(a + b)(a + b) = (a + b)² = a² + 2ab + b²

Now, for the given we have:
(x + 5)(x + 5)
We can note that the two brackets are identical.
Therefore, we can apply the above rule as follows:
(x + 5)(x + 5) = (x + 5)²
= (x)² + 2(x)(5) + (5)²
= x² + 10x + 25

Hope this helps :)

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Answer:

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Step-by-step explanation:

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1,800 hrs? im not sure tbh

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