Which number is not divisible by either of the numbers 3 and 5?
1 answer:
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Answer:
Both functions have negative rates of change
Function B has a greater rate of change than Function A
Step-by-step explanation:
we know that
<em>Function A</em>
The rule for Function A is
This is the equation of a proportional relationship (the line passes through the origin)
The slope is equal to
<em>Function B</em>
Find the equation of the function B
we have the points (-2,0) and (0,-2)
<em>Find the slope</em>
The formula to calculate the slope between two points is equal to
substitute the values
The equation of the function B in slope intercept form is equal to
we have
substitute
<u><em>Verify each statement</em></u>
Option 1) Both functions have negative rates of change
The statement is true
Because, the rate of change is the slope of the linear equation
Function A ---->
Function B ---->
Option 2) Both functions have the same rate of change.
The statement is false (see the explanation)
The rate of change are different ( m=-2/3 and m=-1)
Option 3) When graphed, Function A and Function B are parallel
The statement is false
When graphed, Function A and Function B are intersecting lines, because their slopes are different
Option 4) Function B has a greater rate of change than Function A
The statement is true
Remember that the rate of change can be either positive (increasing function) or negative (decreasing function). To find out which function has a greater rate of change, compare the absolute value of their slopes
therefore
1 > 2/3
Answer:
a) To determine the minimum sample size we need to use the formula shown in the picture 1.
E is the margin of error, which is the distance from the limits to the middle (the mean) of the confidence interval. This means that we have to divide the range of the interval by 2 to find this distance.
E = 0.5/2 = 0.25
Now we apply the formula
n = (1.645*0.80/0.25)^2 = 27.7 = 28
The minimum sample size would be 28.
b) To answer the question we are going to make a 90% confidence interval. The formula is:
(μ - E, μ + E)
μ is the mean which is 127. The formula for E is shown in the picture.
E = 0.80*1.645/√8 = 0.47
(126.5, 127.5)
This means that the true mean is going to be contained in this interval 90% of the time. This is why it doesn't seem possible that the population mean is exactly 128.
Given the following table showing the hourly wages of employees of a movie theater based on their length of employment.
<span>Length of employment (months) Hourly wage (dollars/hour)
6 months 7.55
12 months 7.85
18 months 8.15
24 months 8.45
To obtain an algebraic expression </span>that describes how much Bailey’s employer pays part-time workers, we take two points from the table.
Recall that the equation of a linear function satisfying two points
and 
is given by
Given the two points (6, 7.55) and (12, 7.85), the algebraic expression relating the two points is given by
Therefore, the <span>algebraic expression that describes how much Bailey’s employer pays part-time workers is
</span>
<span>Length of employment (months) Hourly wage (dollars/hour)
6 months 7.55
12 months 7.85
18 months 8.15
24 months 8.45
To obtain an algebraic expression </span>that describes how much Bailey’s employer pays part-time workers, we take two points from the table.
Recall that the equation of a linear function satisfying two points
is given by
Given the two points (6, 7.55) and (12, 7.85), the algebraic expression relating the two points is given by
Therefore, the <span>algebraic expression that describes how much Bailey’s employer pays part-time workers is