Answer:
$1,641.36
Step-by-step explanation:
You multiply $136.78x 12 and you get your answer.
Well, lets start out small.
If there are 60 seconds in 1 minute... then just multiply 60 by the totaly number of minutes to get how many seconds you need.
Sooooo
60(minutes)=total number of seconds
Therefore, 60(8)=480
Now, just see which number is greater...
480<500
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So, in 8 minutes there are 480 seconds. Meaning, 500 seconds IS ,yes indeed, greater than 8 minutes.
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-Hope this helped :)
Answer:
a
Step-by-step explanation:
Mean: 11
Median: 9
Mode: 7
Mean is when you add up all of the numbers, then you take the sum you get and divide by the amount of numbers you have. So in this case, it’d be 154 (the sum) divided by 14 (the amount of numbers you have).
Median is when you put all of your numbers in ascending order and then find the middle number. In this case, the amount of numbers we had were even, so the middle numbers were 8 and 10. In between of these two numbers, is the number 9. So as a result, 9 is your answer.
Mode is the number that you see the most in a set of number. In this case, 7 is repeated 3 times, unlike other numbers, which happens to be the most. So, 7 is your answer for the mode.
Let g(x) = x^2 and h(x) = mx+b
The piecewise function f(x) is basically a combination of g(x) and h(x) depending on what x is.
If x is equal to 3 or smaller, then f(x) = g(x) = x^2
If x is larger than 3, then f(x) = h(x) = mx+b
Plug in x = 3 into g(x)
g(x) = x^2
g(3) = 3^2
g(3) = 9
And do the same for h(x)
h(x) = mx+b
h(3) = m*3+b
h(3) = 3m+b
In order for f(x) to be differentiable at x = 3, the two functions g(x) and h(x) must meet up at this x value. The function f(x) must be continuous at x = 3. In other words, g(x) = h(x) must be true when x = 3
So we can equate the two function outputs
g(3) = h(3)
9 = 3m+b
Solve for b to get
b = 9-3m
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Now differentiate each function g(x) and h(x) with respect to x. Plug in x = 3 after you differentiated
g(x) = x^2
g ' (x) = 2x
g ' (3) = 2*3
g ' (3) = 6
h(x) = mx+b
h ' (x) = m
h ' (3) = m
If f(x) is differentiable at x = 3, then f ' (x) must be continuous at x = 3
This means,
g ' (x) = h ' (x)
g ' (3) = h ' (3)
6 = m
m = 6
Now use this value of m to find b
b = 9 - 3m
b = 9 - 3*6
b = 9 - 18
b = -9
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In summary, we found that
m = 6
b = -9
which are the values needed to make f(x) differentiable