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3 years ago

Which of the following inequalities matches the graph? (1 point)

Mathematics

1 answer:

Aleksandr [31]3 years ago

7 0

Answer: 2x + y < 7

Step-by-step explanation:

In the graph we can see that:

The line is a dashed line, and the shaded area is below the dashed line, then we will have something like:

y < a*x + b

We also can see that the slope of the line is negative, and that the y-intercept is +7

Then the inequality will be something like:

y < a*x + 7

Now we can see that the line passes through the points (0, 7) and (3, 1)

Then the slope will be:

a = (1 - 7)/(3 - 0) = -6/3 = -2

that is negative, as we already said.

Then we have:

y < -2*x + 7

we can rewrite this as:

2x + y < 7

This is the first solution shown.

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3 years ago

I have no clue how to do this please help

mel-nik [20]

Answer:

Max = (6,0); min = (-2, 4)

Step-by-step explanation:

1. Summarize the constraints

$\text{Constraints} = \begin{cases}(a)\qquad 2x - y & \leq 12\\(b)\qquad 4x+ 2y & \geq 0\\(c) \qquad x + 2y & \leq 6\\ \end{cases}$

2. Optimization equation

z = 5x + 2y

3. Graph the constraints to identify the feasible region

See the figure below.

The "TRUE" regions for each graph are the shaded areas to the side of the line indicated by the arrows.

The "feasibility region" is the dark green area where all three areas overlap and all three conditions are satisfied.

5. Determine the points of intersection among the constraints

(i) Constraints (a) and (b)

$\begin{array}{rcr}2x - y & = & 12\\4x + 2y & = & 0\\4x - 2y & = & 24\\8x&=&24\\x & = & \mathbf{3}\\6 - y & = & 12\\-y & = &6\\y & = & \mathbf{-6}\\\end{array}\\$

The lines intersect at (3,-6).

(ii) Constraints (a) and (c)

$\begin{array}{rcr}2x - y & = & 12\\x + 2y & = & 6\\4x - 2y & = &24\\5x & = & 30\\x & = & \mathbf{6}\\6 + 2y & = & 6\\2y & = &0\\y & = & \mathbf{0}\\\end{array}$

The lines intersect at (6,0).

(iii) Constraints (b) and (c)

$\begin{array}{rcr}4x+ 2y &= & 0\\x + 2y &=& 6\\3x & = & -6\\x & = & \mathbf{-2}\\-2 +2y & = & 6\\2y & = &8\\y & = & \mathbf{4}\\\end{array}$

The lines intersect at (-2,4).

6. Determine the x- and y-intercepts of the feasible region

The five black dots at (3,-6), (6,0), and (-2,4) are the vertices of the polygon that represents the feasible region.

Each vertex is a possible maximum or minimum of z.

7. Calculate the maxima and minima

Calculate z at each of the vertices.

(i) At (-2,4)

z = 5x + 2y = 5(-2) + 2(4) = -10 + 8 = 2

(ii) At (3,-6)

z = 5(3) + 2(-6) = 15 - 12 = 3

(iii) At (6,0)

z = 5(6)+ 2(0) = 30 + 0 = 30

The maximum of z occurs at (6,0).

The minimum of z occurs at (-2, 4).

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3 years ago

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3 years ago

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Julia enjoys shooting paper balls into the wastebasket across her office. She misses the first shot 50% of the time. When she mi

Marianna [84]

Answer:

a) Probability that Julia misses two shots in a row = $\frac{1}{2}\frac{1}{5} =\frac{1}{10}$

b) We can use the complement rule on this case. Let X the number of shoots successful, we want this probability:

$P(X \geq 1)$

And using the complement rule we have this:

$P(X \geq 1) = 1-P(X$

And P(X=0) correspond to the probability that Julia misses two shots in a row founded on part A so then we have:

$P(X\geq 1) = 1- \frac{1}{10}= \frac{9}{10}$

Step-by-step explanation:

Part a

For this case we know that Julia enjoys shooting paper balls into the basket across her office.

She misses the first shot 50% of the time.

Probability that Julia misses the first shot = $\frac{1}{2}$

When she misses on the first shot, she misses the second shot 20% of the time.

Probability that Julia misses the second shot = $\frac{1}{5}$

For this case we need to find the probability of missing two shots in a row

So we can multiple the two probabilities like this

Probability that Julia misses two shots in a row = $\frac{1}{2}\frac{1}{5} =\frac{1}{10}$

Part b

For this case we want probability of making at least one successful throw

And we can use the complement rule on this case. Let X the number of shoots successful, we want this probability:

$P(X \geq 1)$

And using the complement rule we have this:

$P(X \geq 1) = 1-P(X$

And P(X=0) correspond to the probability that Julia misses two shots in a row founded on part A so then we have:

$P(X\geq 1) = 1- \frac{1}{10}= \frac{9}{10}$

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3 years ago

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3 years ago

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