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Serhud [2]
3 years ago
7

Economists predict that Americans will spend $1,180 on Summer Vacation in 2015, this is up 5.6% from 2014. What did Americans sp

end in 2014?
Mathematics
1 answer:
netineya [11]3 years ago
3 0

Answer: $1117.42

Step-by-step explanation:

Given: The amount predicted by Economist =$1180

Let x be the amount spent by Americans on Summer vacation in 2014.

Therefore,  According to the question, we have

5.6% of x+x=1180

\Rightarrow0.056\timesx+x=1180\\\Rightarrow x(0.056+1)=1180\\\Rightarrow\ x=\frac{1180}{1.056}=1117.42\approx

Hence, the amount spent by Americans on Summer vacation in 2014 = $1117.42

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The CPU of a personal computer has a lifetime that is exponentially distributed with a mean lifetime of six years. a) What is th
amm1812

Answer: Our required probability is 0.39.

Step-by-step explanation:

Since we have given that

X be the exponentially distributed with mean life = 6 years

So, E[x]=6

\dfrac{1}{\lambda}=6\\\\\lambda=\dfrac{1}{6}

So, our cumulative distribution function would be

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4 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}.

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

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-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.

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\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}.

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By the same logic, c = 38.

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

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