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1 year ago

What is the quotient of (x cubed 3 x squared minus 4 x minus 12) divided by (x squared 5 x 6)?

Mathematics

1 answer:

liubo4ka [24]1 year ago

4 0

The quotient of $x^{3}+3x^{2} -4x-12$ divided by $x^{2} +5x+6$ is (x-2_.

Given the polynomial $x^{3}+3x^{2} -4x-12$ and $x^{2} +5x+6$ and the first expression or polynomial is divided by second.

Quotient is a number that is obtained by dividing two numbers. It can be of two numbers or two expressions. Remainder is a number or an expression left after division of two numbers.

To find the quotient of $x^{3}+3x^{2} -4x-12$ divided by , we have to divide the expression first.

We know that ,

Divident=Divisor*Quotient+remainder

$x^{3}+3x^{2} -4x-12$ = $x^{2} +5x-6$ *(x-2)-12

If we carefully watch the above equation and compares with the above formula then we can easily find that the value of quotient is (x-2).

Hence the quotient of $x^{3}+3x^{2} -4x-12$ divided by $x^{2} +5x-6$ is (x-2).

Learnmore about quotient at brainly.com/question/673545

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Question is incomplete as the given expressions are incomplete as they should be like this:

$x^{3}+3x^{2} -4x-12$ and $x^{2} +5x-6$ .

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The diagram represents a 12cm by 4cm what is the area?

olga_2 [115]

Well, to calculate the area, we would simply do length times width and we would get our area.
Area = Length * Width
Area = 12cm * 4cm
Area = 48cm squared.
So, in conclusion, the area is 48 cm squared.

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2 years ago

A discount store bought two dozen cameras for $14 each.

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Answer:

72.24

Step-by-step explanation:

Price for each camera = 14

Number of camera = 2dozen = 12 x 2 = 24

Total cp = 24 x 14 = 336

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Price for each camera= 10.99

Number of cams = 24

Total sp = 10.99 x 24 = 263.76

Loss = 336 - 263.76 = 72.24

6 0

2 years ago

A store finds that its sales revenue changes at a rate given by S'(t) = −30t2 + 420t dollars per day where t is the number of da

allochka39001 [22]

Answer:

Step-by-step explanation:

Give the rate of change of sales revenue of a store modeled by the equation $S'(t)= -30t^{2} + 420t$ . The Total sales revenue function S(t) can be gotten by integrating the function given as shown;

$\int\limits {S'(t)} \, dt = \int\limits ({-30t^{2}+420t }) \, dt \\S(t) = \frac{-30t^{3} }{3}+\frac{420t^{2} }{2}\\ S(t)= -10t^{3} +210t^{2} \\$

a) The total sales for the first week after the campaign ends (t = 0 to t = 7) is expressed as shown;

$Given\ S(t) = -10t^{3} + 210t^{2}$

$S(0) = -10(0)^{3} + 210(0)^{2}\\S(0) = 0\\S(7) = -10(7)^{3} + 210(7)^{2}\\S(7) = -3430+10,290\\S(7) = 6,860$

Total sales = S(7) - S(0)

= 6,860 - 0

Total sales for the first week = $6,860

b) The total sales for the secondweek after the campaign ends (t = 7 to t = 14) is expressed as shown;

Total sales for the second week = S(14)-S(7)

Given S(7) = 6,860

To get S(14);

$S(14) = -10(14)^{3} + 210(14)^{2}\\S(14) = -27,440+41,160\\S(14) = 13,720$

The total sales for the second week after campaign ends = 13,720 - 6,860

= $6,860

8 0

3 years ago

Thirty percent of all customers who enter a department store will make a purchase. Suppose that 6 customers enter the store and

torisob [31]

Answer:

Step-by-step explanation:

Let's use binomial distribution, because we are interested in find the total number of successes in a sequence of n independent experiments.

In probability, a binomial distribution is used in a Bernoulli process. That is, a sequence of experiments of n independent trials, each asking a dichotomous question, that means it only has two answers. One answer is a success (probability: p) and the other is a failure (probability: 1-p). In this case, every customer who enters in the store is the experiment. If they make a purchase is a success event, taking into account that every purchase decision has to be independent.

$P(X=x) = C(n,x)p^{x} (1-p)^{n-x}$

x= total number of success

n= total number of experiments

p=probability of success on an indivual trial

$C(n,x) = \frac{n!}{x!(n-x)!}$

a) x= 5 ------> customers that make a purchase

n= 6 ------> total customers

p=0.3

$p(X=5)= C(6,5)(0.3)^{5} (1-0.3)^{6-5} \\p(X=5)=0.102$

b) At least 3 customers make a purchase. x ≥ 3

$P(X\geq 3)=1-P (X=0)-P(X=1)-P(X=2)\\P(X\geq 3)=1-(C(6,0)(0.3^{0})(0.7)^{6}) - (C(6,1)(0.3^{1})(0.7)^{5}) - (C(6,2)(0.3^{2})(0.7)^{4})\\ P(X\geq 3) = 1-0.11765-0.30253-0.32414\\P(X\geq3)= 0.2557$

c) At most 2 customers make a purchase. x ≤ 2

$P(X\leq2) = P(X=0) + P(X=1) + P(X=2)\\P(X\leq2) = (C(6,0)(0.3^{0})(0.7)^{6}) + (C(6,1)(0.3^{1})(0.7)^{5}) + (C(6,2)(0.3^{2})(0.7)^{4})\\P(X\leq2) = 0.11765-0.30253-0.32414\\P(X\leq2)=0.7443$