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3 years ago

Each marble bag sold by Yolanda's Marble Company contains 8 orange marbles for every 5 yellow marbles.

Mathematics

1 answer:

Stells [14]3 years ago

7 0

Answer:

64.

Step-by-step explanation:

By proportion to number of orange marbles = (40 / 5) * 8

= 320 / 5

= 64 .

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(5x^2 - 2x^3 + x) - (6x^3 - 8x^2 - x)

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Answer:

-8x^3+13x^2+2x

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Collette wanted to know if there was a difference in favorite food types among students at her large high school. She took a ran

AleksandrR [38]

Answer:

(29-23)²/23 + (16-23)²/23 + (19-23)²/23 + (28-23)²/23

Step-by-step explanation:

Given :

n(American) = 29

n(Chinese) = 16

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n(Italian) = 28

Expected value = (29 + 16 + 19 + 28) / 4

Where, 4 = sample size

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χ² = (Observed value - Expected value)² / expected value

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3 years ago

What is the value of X

erica [24]

Answer:

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What is the quotient when 4x3 + 2x + 7 is divided by x + 3?

Arte-miy333 [17]

Answer:

The quotient of this division is $(4x^2 -12x + 38)$ . The remainder here would be $-26$ .

Step-by-step explanation:

The numerator $4x^3 + 2x + 7$ is a polynomial about $x$ with degree $3$ .

The divisor $x + 3$ is a polynomial, also about $x$ , but with degree $1$ .

By the division algorithm, the quotient should be of degree $3 - 1 = 2$ , while the remainder shall be of degree $1 - 1 = 0$ (i.e., the remainder would be a constant.) Let the quotient be $a\,x^2 + b\, x + c$ with coefficients $a$ , $b$ , and $c$ .

$4x^3 + 2x + 7 = \left(a\,x^2 + b\, x + c\right)(x + 3)$ .

Start by finding the first coefficient of the quotient.

The degree-three term on the left-hand side is $4 x^3$ . On the right-hand side, that would be $a\, x^3$ . Hence $a = 4$ .

Now, given that $a = 4$ , rewrite the right-hand side:

$\begin{aligned}&\left(4\,x^2 + b\, x + c\right)(x + 3) \cr =& \left(4x^2 + (b\, x + c)\right)(x + 3) \cr =& 4x^2(x + 3) + (bx + c)(x + 3) \cr =& 4x^3 + 12x^2 + (bx + c)(x + 3)\end{aligned}$ .

Hence:

$4x^3 + 2x + 7 = 4x^3 + 12x^2 + (b\,x + c)(x + 3)$

Subtract $\left(4x^3 + 12x^2\right$ from both sides of the equation:

$-12x^2 + 2x + 7 = (b\,x + c)(x + 3)$ .

The term with a degree of two on the left-hand side has coefficient $(-12)$ . Since the only term on the right hand side with degree two would have coefficient $b$ , $b = -12$ .

Again, rewrite the right-hand side:

$\begin{aligned}&\left(-12 x + c\right)(x + 3) \cr =& \left(-12 x+ c\right)(x + 3) \cr =& (-12x)(x + 3) + c(x + 3) \cr =& -12x^2 -36x + (bx + c)(x + 3)\end{aligned}$ .