Find v(w+3) for v(w)=2w-1

1 answer:

6 0

So we have v(w) = 2w - 1

Now we make the following change: w ---> w +3.
So we change every "w" into a "w+3" as follows:

v(w) = 2w - 1 --------> v(w+3) = 2*(w+3) - 1

Let's solve this.
2*(w+3) - 1
2*w + 2*3 - 1
2w + 6 - 1
2w + 5

So

v(w+3) = 2w + 5

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Strands Copper wire from a manufacturer are analyzed forstrenghth and conductivity. The Results from 100 strands are asfollows:S

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Answer and explanation:

Given : Strands Copper wire from a manufacturer are analyzed forstrenghth and conductivity. The Results from 100 strands are as follows :

Strength Strength

High Low

High conductivity 74 8

Low conductivity 15 3

To find :

a) If a stand is randomly selected, the probability that is conductivity is high and its strength is high

The favorable outcome is 74

The probability is given by,

$P=\frac{74}{100}=0.74$

b) If a stand is randomly selected, the probability that its conductivity is low or strength is low

Conductivity is low A= 15+3=18

Strength is low B= 8+3=11

Conductivity is low and strength is low $A\cap B=3$

Probability is given by,

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

$P(A\cup B)=\frac{18}{100}+\frac{11}{100}-\frac{3}{100}$

$P(A\cup B)=0.18+0.11-0.03$

$P(A\cup B)=0.26$

c) Consider the event that a strand low conductivity and the event that the strand has a low strength. Are these tow events mutually exclusive?

Since the events the stand has low conductivity and the stand has low strength are not mutually exclusive, since there exists some cases in which both the events coincide. i.e. Intersection of both the events exists with probability 0.03.

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3 years ago

Calculator

Sedaia [141]

Check the picture below.

so let's find the lengths of those two sides in red, since are the length and width of the rectangle.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d = \sqrt{[-3-(-6)]^2+[6-3]^2}\implies d=\sqrt{(-3+6)^2+(6-3)^2} \\\\\\ d=\sqrt{9+9}\implies \boxed{d=\sqrt{18}} \\\\[-0.35em] ~\dotfill$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1})~\hfill d=\sqrt{[-2-(-6)]^2+[-1-3]^2} \\\\\\ d=\sqrt{(-2+6)^2+(-1-3)^2}\implies d=\sqrt{16+16}\implies \boxed{d=\sqrt{32}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the rectangle}}{(\sqrt{18})(\sqrt{32})}\implies \sqrt{18\cdot 32}\implies \sqrt{576}\implies 24$