Answer:
1. City A: 150 violent crimes per 100,000 residents.
City B: 161 violent crimes per 100,000 residents.
2. City A
Step-by-step explanation:
City A:
Population = 123,000
Violent crimes = 185
Violent crimes per 100,000 people:
City B:
Population = 84,000
Violent crimes = 135
Violent crimes per 100,000 people:
1. City A: 150 violent crimes per 100,000 residents.
City B: 161 violent crimes per 100,000 residents.
2. Even though it has a bigger number of crimes, City A has the lowest crime rate since its population is larger.
The 2 graphs on the left are exponential
The other 2 are linear
Answer:
The number is -3.
Step-by-step explanation:
Set up an equation:
Variable n = number
12 + 7n = n - 6
Assuming the question is solve for n, isolate the variable:
Subtract n from both sides:
12 + 6n = -6
Subtract 12 from both sides:
6n = -18
Divide by 6 on both sides:
n = -3
Check your work:
12 + 7(-3) = -3 - 6
12 - 21 = -3 - 6
-9 = -9
Correct
Answer:
The pizza that is a better deal is 12" square pan pizza for $3.95.
Step-by-step explanation:
This is because if you get 2 of the 12" square pan pizzas it will be 24" and you will only have to pay $7.90. but if you bought the 24" square pan pizza you would have to pay $14.95 which isnt a fair price.
Answers:
The formula is [f(-1)-f(-4)]/[3]
The value of f(-1) is 3
The value of f(-4) is -3
The average rate of change is 2
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Explanation:
For the first blank, we use the formula
[ f(b) - f(a) ]/[ b - a ]
where 'a' and 'b' are the endpoints for the x interval
In this case, a = -4 and b = -1. When you plug those values into the formula above, you get...
[ f(b) - f(a) ]/[ b - a]
[ f(-1) - f(-4)]/[ -1 - (-4) ]
[ f(-1) - f(-4)]/[ -1+4 ]
[ f(-1) - f(-4)]/[ 3 ]
which is why the answer is choice C for the first blank
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To compute the value of f(-1), we draw a vertical line through -1 on the x axis. This vertical line crosses the diagonal function graph at the point (-1,3). The y value of this point is what we want. Plugging in x = -1 leads to y = 3. This is why f(-1) = 3
If you want, you can draw a horizontal line through (-1,3) and you'll see it touching 3 on the y axis.
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Follow similar steps as above to compute f(-4). Draw a vertical line through x = -4 on the x axis. Mark the point where the vertical line crosses the diagonal line. This point is (-4,-3). Optionally draw a horizontal line over til you hit the y axis and you'll find that y = -3 corresponds to x = -4
This is why f(-4) = -3
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We'll use the last three sections to compute the average rate of change. Everything combines together building up to this moment.
From the first part, we had the formula
[ f(b) - f(a) ]/[ b - a ]
[ f(-1) - f(-4)]/[ 3 ]
We can replace the "f(-1)" with 3 since we found that f(-1) = 3
Similarly, f(-4) = -3 so we can replace the "f(-4)" with -3
Doing those replacements and simplifying leads to...
[ f(-1) - f(-4)]/[ 3 ]
[ 3 - (-3)]/[ 3 ]
[ 3 + 3]/[ 3 ]
6/3
2
So the average rate of change is 2
Note: because the entire graph is a straight line, the average rate of change for any interval a < x < b is going to be equal to the slope m. In this case, the slope of the line is m = 2/1 = 2. We move up 2 units each time we move to the right 1 unit along the diagonal line.
