A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function
1 answer:
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By definition, the average rate of change is given by:
We evaluate each of the functions in the given interval.
We have then:
For f (x) = x ^ 2 + 3x:
Evaluating for x = -2:
Evaluating for x = 3:
Then, the AVR is:
For f (x) = 3x - 8:
Evaluating for x =4:
Evaluating for x = 5:
Then, the AVR is:
For f (x) = x ^ 2 - 2x:
Evaluating for x = -3:
Evaluating for x = 4:
Then, the AVR is:
For f (x) = x ^ 2 - 5:
Evaluating for x = -1:
Evaluating for x = 1:
Then, the AVR is:
Answer:
from the greatest to the least value based on the average rate of change in the specified interval:
f(x) = x^2 + 3x interval: [-2, 3]
f(x) = 3x - 8 interval: [4, 5]
f(x) = x^2 - 5 interval: [-1, 1]
f(x) = x^2 - 2x interval: [-3, 4]
10 = ax - 3b
First, add 3b to both sides. / Your problem should look like: 10 + 3b = ax.
Second, divide both sides by a. / Your problem should look like:
= x.
Third, switch sides. / Your problem should look like: x = which is your answer.
First, add 3b to both sides. / Your problem should look like: 10 + 3b = ax.
Second, divide both sides by a. / Your problem should look like:
Third, switch sides. / Your problem should look like: x =
Answer:
The z-score (value of z) for an income of $1,100 is 1.
Step-by-step explanation:
We are given that the mean of a normally distributed group of weekly incomes of a large group of executives is $1,000 and the standard deviation is $100.
<em>Let X = group of weekly incomes of a large group of executives</em>
So, X ~ N()
The z-score probability distribution for a normal distribution is given by;
Z = ~ N(0,1)
where, = mean income = $1,000
= standard deviation = $100
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, we are given an income of $1,100 for which we have to find the z-score (value of z);
So, <em><u>z-score</u></em> is given by = =
= 1
<em>Hence, the z-score (value of z) for an income of $1,100 is 1.</em>