The average rate of change of <em>g(x)</em> over the interval [2, 8] is given by
(<em>g</em> (8) - <em>g</em> (2)) / (8 - 2)
In other words, it's the slope of the line through the points (2, <em>g</em> (2)) and (8, <em>g</em> (8)).
Use the definition of the function to evaluate it at the points in the numerator:
• 8 ≥ 4, so using the second piece, <em>g</em> (8) = -0.5(8) + 8 = 4
• 2 < 4, so <em>g</em> (2) = 5(2) + 1 = 11
Then the average rate of change is
(<em>g</em> (8) - <em>g</em> (2)) / (8 - 2) = (4 - 11) / 6 = -7/6
9514 1404 393
Answer:
In step 4, Jim's answer is incorrect.
Step-by-step explanation:
In step 1, Jim swaps the order of addends using the commutative property of addition.
In step 2, Jim uses the distributive property to factor -1 from the final two terms. (The associative property lets Jim move parentheses.)
6.1 +(-8.5 -1.3) . . . associative property
6.1 +(-1)(8.5 +1.3) . . . distributive property
In step 3, Jim has used the properties of real numbers to form the sum of two of them.
In step 4, Jim wrote an answer of 1.1, when the answer should have been -3.7. Jim's answer is incorrect.
__
The descriptive statements about steps 2 and 4 are both true.
From the given options we can say that the only one that represents the area of the sector is; A = n/360 * πr²
<h3>What is the Area of the Sector?</h3>
In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.
The formula for Area of a sector is given as;
θ/360 * πr²
where;
θ is the central angle of the sector
r is radius
Now, looking at the given options we can say that the only one that represents the area of the sector is;
A = n/360 * πr²
where n is the central angle of the sector
Read more about Area of Sector at; brainly.com/question/16736105
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Y = (-3/2)x + 1 is the equatjon
Answer:
A sample of 1077 is required.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of 
.
The margin of error is of:
42% of freshmen do not visit their counselors regularly.
This means that 
98% confidence level
So 
, z is the value of Z that has a pvalue of 
, so 
.
How large of a sample size is required?
A sample size of n is required, and n is found when M = 0.035. So
Rounding up:
A sample of 1077 is required.
