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alex41 [277]
1 year ago
14

Solve the equation. 3x-3(4+x)=3/4(3x+2)-1

Mathematics
1 answer:
bonufazy [111]1 year ago
8 0

Answer:

x=\frac{10}{3}

Step-by-step explanation:

3x-3(4+x)=\frac{3}{4}(3x+2)-1

Solve the parenthesis ↑

3x-12+3x=\frac{9}{4}x+\frac{6}{4}-1

Multiply everything by 4 to get rid of the denominators.

\frac{12x}{4}-\frac{48}{4}+\frac{12x}{4}=\frac{9}{4}x+\frac{6}{4}-\frac{4}{4}

Rid the denominators.

12x-48+12x=9x+6-4

Solve.

12x+12x-9x=6-4+48

15x=50

x=\frac{50}{15}

Simplify.

x=\frac{10}{3}

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3 years ago
What is the inequality?
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Answer:

y\leq \frac{1}{2}x+2

Step-by-step explanation:

we know that

The solution of the inequality is the shaded area below the solid line (the inequality is of the form y\leq mx+b)

The y-intercept of the solid line is (0,2)

The x-intercept of the solid line is (-4,0)

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therefore

The linear inequality represented by the graph is

y\leq \frac{1}{2}x+2

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3 years ago
An certain brand of upright freezer is available in three different rated capacities: 16 ft3, 18 ft3, and 20 ft3. Let X = the ra
ruslelena [56]

Answer:

E(X)=16\cdot 0.3+18\cdot 0.1+20\cdot 0.6=18.6

E(X^2)=16^2\cdot 0.3+18^2\cdot 0.1+20^2\cdot 0.6=349.2

V(X) = E(X^2)-[E(X)]^2=349.2-(18.6)^2=3.24

The expected price paid by the next customer to buy a freezer is $466

Step-by-step explanation:

From the information given we know the probability mass function (pmf) of random variable X.

\left|\begin{array}{c|ccc}x&16&18&20\\p(x)&0.3&0.1&0.6\end{array}\right|

<em>Point a:</em>

  • The Expected value or the mean value of X with set of possible values D, denoted by <em>E(X)</em> or <em>μ </em>is

E(X) = $\sum_{x\in D} x\cdot p(x)

Therefore

E(X)=16\cdot 0.3+18\cdot 0.1+20\cdot 0.6=18.6

  • If the random variable X has a set of possible values D and a probability mass function, then the expected value of any function h(X), denoted by <em>E[h(X)]</em> is computed by

E[h(X)] = $\sum_{D} h(x)\cdot p(x)

So h(X) = X^2 and

E[h(X)] = $\sum_{D} h(x)\cdot p(x)\\E[X^2]=$\sum_{D}x^2\cdot p(x)\\ E(X^2)=16^2\cdot 0.3+18^2\cdot 0.1+20^2\cdot 0.6\\E(X^2)=349.2

  • The variance of X, denoted by V(X), is

V(X) = $\sum_{D}E[(X-\mu)^2]=E(X^2)-[E(X)]^2

Therefore

V(X) = E(X^2)-[E(X)]^2\\V(X)=349.2-(18.6)^2\\V(X)=3.24

<em>Point b:</em>

We know that the price of a freezer having capacity X is 60X − 650, to find the expected price paid by the next customer to buy a freezer you need to:

From the rules of expected value this proposition is true:

E(aX+b)=a\cdot E(x)+b

We have a = 60, b = -650, and <em>E(X)</em> = 18.6. Therefore

The expected price paid by the next customer is

60\cdot E(X)-650=60\cdot 18.6-650=466

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Stacey: 1 1/2 hours
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