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2 years ago

15

How many meters did Nathan jog

1 answer:

marin [14]2 years ago

6 0

Answer:

x meters

Step-by-step explanation:

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Which graph best represents the feasibility region for the system shown above? ( pics are in this)

zalisa [80]

Consider the system of inequalities

$\left\{ \begin{array}{l} y\ge 2 \\ x\le 6 \\ y\le 3x+2 \\ y\le -x+10. \end{array}\right.$

1. Plot all lines that are determined by equalities (see attached diagram)

$\left\{ \begin{array}{l} y=2 \text{ (red line)} \\ x= 6 \text{ (blue line)}\\ y=3x+2 \text{ (green line)} \\ y= -x+10 \text{ (orange line)}. \end{array}\right.$

2. Determine which bounded part of the plane you should select:

$y\ge 2$ means that you should take points with y-coordinates greater than or equal to 2 (top part of the coordinate plane that was formed by the red line);
$x\le 6$ means that you should take points with x-coordinates less than or equal to 6 (left part of the coordinate plane that was formed by the blue line);
for $y\le 3x+2$ you can check where the origin is placed. Since $0\le 3\cdot 0+2$ , the origin belongs to the needed part and you have to take the right part of the coordinate plane that was formed by green line.
for $y\le -x+10$ you can check where the origin is placed. Since $0\le -1\cdot 0+10$ , the origin belongs to the needed part and you have to take the bottom part of the coordinate plane that was formed by orange line.

3. According to the previous explanations, the shaded region is as in A diagram.

Answer: correct choice is A.

5 0

3 years ago

Read 2 more answers

(Anderson, 1.14) Assume that P(A) = 0.4 and P(B) = 0.7. Making no further assumptions on A and B, show that P(A ∩ B) satisfies 0

Goshia [24]

Answer with Step-by-step explanation:

We are given that

P(A)=0.4 and P(B)=0.7

We know that

$P(A)+P(B)+P(A\cap B)=P(A\cup B)$

We know that

Maximum value of $P(A\cup B)$ =1 and minimum value of $P(A\cup B)$ =0

$0\leq P(A\cup B )\leq 1$

$0\leq P(A)+P(B)-P(A\cap B)\leq 1$

$0\leq 0.4+0.7-P(A\cap B)\leq 1$

$0\leq 1.1-P(A\cap B)\leq 1$

$0\leq 1.1-P(A\cap B)$

$P(A\cap B)\leq 1.1$

It is not possible that $P(A\cap B)$ is equal to 1.1

$1.1-P(A\cap B)\leq 1$

$-P(A\cap B)\leq 1-1.1=-0.1$

Multiply by (-1) on both sides

$P(A\cap B)\geq 0.1$

Again, $P(A\cup B)\geq P(B)$

$0.4+0.7-P(A\cap B)\geq 0.7$

$1.1-P(A\cap B)\geq 0.7$

$-P(A\cap B)\geq -1.1+0.7=-0.4$

Multiply by (-1) on both sides

$P(A\cap B)\leq 0.4$

Hence, $0.1\leq P(A\cap B)\leq 0.4$

3 0

3 years ago

Plz help me with the problem below

zalisa [80]

Answer:

10

Step-by-step explanation:

4 0

2 years ago

A frame is marked down by 22 percent from an original price of $14.50. What is the new price?

Valentin [98]

22% = 22/100 22/100 * 14.50 = 3.19 (this is the amount discounted off original price) 14.50 - 3.19 = $11.31

7 0

3 years ago

Read 2 more answers

You cut a circular hole 1/4 -inch in diameter in a piece of cardboard. With the cardboard 30 inches from your face, the Moon fit

Stolb23 [73]

Answer:

The Moon's diameter is greater than $1,500$ miles

Step-by-step explanation:

we know that

$1\ mile=63,360\ inches$

$1,500\ miles=1,500*63,360=95,040,000\ inches$

$240,000\ miles=240,000*63,360=15,206,400,000\ inches$

by proportion

Find the Moon's diameter

Let

x-----> the Moon's diameter in inches

$\frac{x}{15,206,400,000}=\frac{0.25}{30}\\ \\x= 15,206,400,000*0.25/30\\ \\x=126,720,000\ inches$

Compare

$126,720,000\ inches> 95,040,000\ inches$

therefore

The Moon's diameter is greater than $1,500$ miles

3 0

3 years ago