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2 years ago

7

For your sports equipment store, you purchase a case containing 24 canisters of tennis balls for $60. You in turn charge $4 for

each canister. How much is the price of each case of tennis balls marked up?

1 answer:

balandron [24]2 years ago

8 0

4*24/60= $1.6 for each canister

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In JKL and PQR, if JK = PQ, congruent to PQR.<br><br> True or False

Kaylis [27]

Answer:

True

Step-by-step explanation:

Two shapes are congruent if when turning, flipping or sliding one shape it can become another.

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2 years ago

Make a dot plot of the following set of numbers: 2, 1, 2, 0, 0 , 2, 1, 6, 1, 1, 0. Which number is the peak of the data set?

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A. 1
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2 years ago

Graph the solution to the inequality 2x-3y<18

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$2x-3y\dfrac{2}{3}x-6\\\\y=\dfrac{2}{3}x-6-\text{It's a linear function}\\\\for\ x=0\to y=\dfrac{2}{3}(0)-6=0-6=-6\to(0;\ -6)\\\\for\ x=6\to y=\dfrac{2}{3}(6)-6=2(2)-6=4-6=-2\to(6;\ -2)$

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2 years ago

Consider the following time series data. Week 1 2 3 4 5 6 Value 18 12 15 10 18 14 Using the naive method (most recent value) as

fenix001 [56]

Answer:

(a) MAE = 5.20

(b) MSE = 10

(c) MAPE = 38.60%

(d) Forecast for week 7 = 14

Step-by-step explanation:

Note: See the attached excel for the calculations of the Error, Error^2, and Error %.

(a) mean absolute error

MAE = Total of absolute value of error / Number of observations considered = |Error| / 5 = 26 / 5 = 5.20

(b) mean squared error

MSE = Total of Error^2 / Number of observations considered = Error^2 / 5 = 150 / 5 = 10

(c) mean absolute percentage error (Round your answer to two decimal places.)

MAPE = Total of Error % / Number of observations considered = Error % / 5 = 193.02 / 5 = 38.60%

(d) What is the forecast for week 7?

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Forecast for week 7 = 14

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2 years ago

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:

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

Subtract $-12x^2 -36x$ from both sides of the equation:

$38x + 7 = c(x + 3)$ .

By the same logic, $c = 38$ .

Hence the quotient would be $(4x^2 - 12x + 38)$ .

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2 years ago