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frosja888 [35]
3 years ago
14

Write the solution in interval notation: 4v+2>-2 or 3v-5<7

Mathematics
1 answer:
kari74 [83]3 years ago
8 0

For this case we must find the solution of the following inequalities:

4v + 2> -2\ or\ 3v-5

From the first inequality we have:

4v + 2> -2

Subtracting 2 from both sides of the inequality:

4v> -2-2

Equal signs are added and the same sign is placed.

4v> -4

Dividing between 4 on both sides of the inequality:

v> \frac {-4} {4}\\v> -1

Thus, the solution is given by all values of "v" greater than -1.

From the second inequality we have:

3v-5

Adding 5 to both sides of the inequality we have:

3v

Dividing by 3 to both sides of the inequality we have:

v

Thus, the solution is given by all values of "v" less than 4.

Then, the solution set is given by the union of both intervals.

The union consists of all the elements that are contained in each interval.

(-∞,∞)

Answer:

The solution set is: (-∞,∞)

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p_R(r)=\begin{cases}\dfrac18&\text{for }r\in\{-2,-1,\ldots,5\}\\\\0&\text{otherwise}\end{cases}

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We want to find P\left(\dfrac RK\equiv0\pmod n\right), where n is any integer.

We have six possible choices for K:

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(iii) if K=4, then \dfrac RK is an integer when R=0,4;

(iv) if K=5, then \dfrac RK is an integer when R=0,5;

(v) if K=6 or K=7, then \dfrac RK is an integer only when R=0 in both cases.

If the selection of R,K are made independently, then the joint distribution is the product of the marginal distribution, i.e.

p_{R,K}(r,k)=p_R(r)\cdot p_K(k)=\begin{cases}\dfrac1{48}&\text{for }(r,k)\in[-2,5]\times[2,7]\\\\0&\text{otherwise}\end{cases}

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3 years ago
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Problem 1

<h3>Answers:</h3><h3>angle 6 = 50</h3><h3>angle 7 = 50</h3><h3>angle 8 = 40</h3>

--------------------

Work Shown:

point E = intersection point of diagonals.

x = measure of angle 6

y = measure of angle 8

angle 7 is also x because triangle AED is isosceles (AE = ED)

Focus on triangle AED, the three angles A, E, D add to 180

A+E+D = 180

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2x = 180-80

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Turn to angle 8. This is adjacent to angle 7. The two angles form a 90 degree angle at point A. This is because a rectangle has 4 right angles.

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=================================================

Problem 2

<h3>Answers:</h3><h3>angle 2 = 61</h3><h3>angle 3 = 61</h3>

--------------------

Work Shown:

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x = measure of angle 3

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