<h3>
Answer: -6</h3>
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Explanation:
Plug in x = 1
f(x) = 17-x^2
f(1) = 17-1^2
f(1) = 17-1
f(1) = 16
Repeat for x = 5 to find that f(5) = -8
Now we'll use the formula below to find the average rate of change from x = a to x = b.
![m = \frac{f(b)-f(a)}{b-a}\\\\m = \frac{f(5)-f(1)}{5-1}\\\\m = \frac{-8-16}{4}\\\\m = \frac{-24}{4}\\\\m = -6\\\\](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7Bf%285%29-f%281%29%7D%7B5-1%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B-8-16%7D%7B4%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B-24%7D%7B4%7D%5C%5C%5C%5Cm%20%3D%20-6%5C%5C%5C%5C)
The average rate of change is -6
The formula is basically the slope formula, more or less. So that's why I used 'm' to represent the average rate of change.
The average rate of change on the interval [1,5] is the same as finding the slope through the lines (1, 16) and (5, -8)
C. (5,7) is the correct answer for this problem. First you look at the x axis (across) then the y axis (up and down).
Answer:
B
Step-by-step explanation:
x = y-4x^2 can be rearranged to get y = 4x^2 + x, which is a function
Answer:
a) 0.2588
b) 0.044015
c) 0.12609
Step-by-step explanation:
Using the TI-84 PLUS calculator
The formula for calculating a z-score is is z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
From the question, we know that:
μ = 119 inches
standard deviation σ = 17 inches
(a) What proportion of trees are more than 130 inches tall?
x = 130 inches
z = (130-119)/17
= 0.64706
Probabilty value from Z-Table:
P(x<130) = 0.7412
P(x>130) = 1 - P(x<130) = 0.2588
(b) What proportion of trees are less than 90 inches tall?
x = 90 inches
z = (90-119)/17
=-1.70588
Probability value from Z-Table:
P(x<90) = 0.044015
(c) What is the probability that a randomly chosen tree is between 95 and 105 inches tall?
For x = 95
z = (95-119)/17
= -1.41176
Probability value from Z-Table:
P(x = 95) = 0.07901
For x = 105
z = (105 -119)/17
=-0.82353
Probability value from Z-Table:
P(x<105) = 0.2051
The probability that a randomly chosen tree is between 95 and 105 inches tall
P(x = 105) - P(x = 95)
0.2051 - 0.07901
= 0.12609