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1 year ago

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Dustin and melanie are playing a game where they roll 2 standard 6-sided number cubes and find the sum of their outcomes. each p

layer gets a chance to guess the correct sum, and the player who guesses the correct sum wins the game. dustin decides to guess a sum of 6. melanie decides to guess a sum of 7. which player made the better decision?

1 answer:

spayn [35]1 year ago

6 0

Answer: Melanie is the correct answer (hopefully)

Step-by-step explanation:

7 is a better decision because its higher than 6 which gets a better chance of winning (sorry for being bad at explaining)

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62/8 <br> With a remainder

patriot [66]

Answer:

7 and 6/8

Step-by-step explanation:

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3 years ago

Read 2 more answers

Florence has $400 in a savings account. The interest rate is 5% per year and is not

Sati [7]

Answer:

$20

Step-by-step explanation:

I = 400(.05)(1)

I = 20

3 0

3 years ago

Harold uses the binomial theorem to expand the binomial (3x^5 - 1/9y^3)^4

riadik2000 [5.3K]

<h3><em>The complete question:</em></h3>

<u><em> </em></u><u>Harold uses the binomial theorem to expand the binomial </u> $(3x^5 -\dfrac{1}{9}y^3)^4$ <u />

<u>(a) What is the sum in summation notation that he uses to express the expansion? </u>

<u>(b) Write the simplified terms of the expansion.</u>

Answer:

(a). $(3x^5 -\dfrac{1}{9}y^3)^4=$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}( -\dfrac{1}{9}y^3)^k $$$

(b). $(3x^5 -\dfrac{1}{9}y^3)^4=81x^{20}-12x^{15}y^3+\dfrac{2x^{10}y^6}{3}-\dfrac{4x^5y^9}{243}+\frac{y^{12}}{6561}$

Step-by-step explanation:

(a).

The binomial theorem says

$(x+y)^n=$$\sum_{k=0}^{n} \binom{n}{k}x^{n-k}y^k $$$

For our binomial this gives

$\boxed{(3x^5 -\dfrac{1}{9}y^3)^4=$$\sum_{k=0}^{n} \binom{4}{k}x^{4-k}y^k $$}$

(b).

We simplify the terms of the expansion and get:

$$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}y^k $$= \binom{4}{0}(3x^5)^{4-0}(-\dfrac{1}{9}y^3 )^0+\binom{4}{1}(3x^5)^{4-1}(-\dfrac{1}{9}y^3 )^1+\\\\\binom{4}{2}(3x^5)^{4-2}(-\dfrac{1}{9}y^3 )^2+\binom{4}{3}(3x^5)^{4-3}(-\dfrac{1}{9}y^3 )^3+\binom{4}{4}(3x^5)^{4-4}(-\dfrac{1}{9}y^3 )^4$

$$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}(-\frac{1}{9}y^3 )^k $$= (3x^5)^{4}+4(3x^5)^{3}(-\frac{1}{9}y^3 )+6(3x^5)^{2}(-\frac{1}{9}y^3 )^2+\\\\4(3x^5)(-\frac{1}{9}y^3 )^3+(-\frac{1}{9}y^3 )^4$

$\boxed{(3x^5 -\dfrac{1}{9}y^3)^4=81x^{20}-12x^{15}y^3+\dfrac{2x^{10}y^6}{3}-\dfrac{4x^5y^9}{243}+\frac{y^{12}}{6561} }$

3 0

3 years ago

What is the surface area of the cube below? 9 9 9

Natali5045456 [20]

Answer:

$A_s=486\ units^2$

Step-by-step explanation:

Remember that the sides of a cube always have the same length.

In this case the length of the sides L is:

$L = 9$ .

The cubes have 6 faces. Then the surface area of the cube is equal to the area of its 6 faces.

Since all sides of the cube have the same measure, then the area of each face is:

$A = L ^ 2$

Then the area of the 6 faces is:

$A_s = 6L ^ 2$

$A_s = 6 * (9 ^ 2)$

$A_s=486\ units^2$

3 0

3 years ago

Solve the system of inequalities: a) .4x−1≤0 <br> 2.3x≥4.6

OleMash [197]

Answer:

(a) $x \leq 2.5$

(b) $x \geq 2$

Step-by-step explanation:

Solving (a):

$0.4x - 1 \leq 0$

Add 1 to both sides

$0.4x - 1 + 1\leq 0 + 1$

$0.4x \leq 1$

Solve for x

$x \leq 1/0.4$

$x \leq 2.5$

Solving (b):

$2.3x \geq 4.6$

Solve for x

$x \geq 4.6/2.3$

$x \geq 2$

4 0

3 years ago