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3 years ago

20 POINTS~ 2/5 |5x+10| -14 > -6 Please explain both answers

Mathematics

1 answer:

Pavlova-9 [17]3 years ago

5 0

Answer:

$x2$

Step-by-step explanation:

We have the inequality:

$\frac{2}{5}|5x+10|-14>-6$

First, we can factor out a 5 from our absolute value. This yields:

$\frac{2}{5}(5|x+2|)-14>-6$

Simplify:

$2|x+2|-14>-6$

Add 14 to both sides:

$2|x+2|>8$

Divide both sides by 2:

$|x+2|>4$

Definition of Absolute Value:

$x+2>4\text{ or } -(x+2)>4$

Solve each case individually:

Case 1:

$x+2>4$

Subtract 2 from both sides:

$x>2$

Case 2:

$-(x+2)>4$

Divide both sides by -1. Flip the sign:

$x+2$

Subtract 2 from both sides:

$x$

So, our answers are:

$x2$

Since our inequality is a greater than, we will have an "or" inequality.

So, our answer is all values left to the first solution and all values to the right of the second solution:

$x2$

And we're done!

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Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)

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$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}$

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$\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt$
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The second line segment ( $C_2$ ) can be described by $\mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle$ , again with $0\le t\le1$ . Then

$\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt$
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Answer:

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Step-by-step explanation:

For each voter, there are only two possible outcomes. Either the voter is a Democrat, or he is not. The probability of the voter being a Democrat is independent of other voters. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

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This means that $p = 0.62$

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This is P(X = 2) when n = 2. So

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