The average rate of change from x = -1 to x = 2 is 2
<u>Solution:</u>
Given function is:
f(x) = 2x - 1
We have to find the average rate of change from x = -1 to x = 2
<em><u>The average rate of change is given as:</u></em>
<em><u>The average rate of change from x = -1 to x = 2 is given by formula:</u></em>
<em><u>Find f(2) and f( - 1)</u></em>
<em><u>Substitute x = 2 in given function</u></em>
f(2) = 2(2) - 1 = 4 - 1 = 3
<em><u>Substitute x = -1 in given function</u></em>
f( - 1) = 2(-1) - 1 = -2 - 1 = -3
<em><u>Substitute the values in above formula,</u></em>
Thus average rate of change from x = -1 to x = 2 is 2
Let X be the number of lightning strikes in a year at the top of particular mountain.
X follows Poisson distribution with mean μ = 3.8
We have to find here the probability that in randomly selected year the number of lightning strikes is 0
The Poisson probability is given by,
P(X=k) = 
Here we have X=0, mean =3.8
Hence probability that X=0 is given by
P(X=0) = 
P(X=0) = 
P(X=0) = 0.0224
The probability that in a randomly selected year, the number of lightning strikes is 0 is 0.0224
Given:
Triangle:
height = 6ft
base = 4ft
Rectangle:
length = x
Width = 6 ft
Surface Area = 150ft²
Area of a Triangle = h*b / 2 = (6ft * 4ft) / 2 = 12ft²
Area of a rectangle = Surface Area - Area of a Triangle
A = 150 ft² - 12 ft² = 138 ft²
138 ft² = x * 6ft
138 ft² / 6 ft = x
23 ft = x.
Answer:
Length is 14
Width is 6
Step-by-step explanation:
Length = 2W + 2
Width = W
Perimeter is twice the length + twice the width
P = 40 = 2(2W+2) + 2W first simplify
40 = 4W + 4 + 2W now combine terms
40 = 6W + 4 and subtract 4 from both sides
36 = 6W
Width W = 6
Length = 2W + 2 = 12 + 2 = 14
