To find the total number of hours that Jerry played with his friends, you will add the amount of times he played with each.
7/8 hour+ 3/4 hour + 3/2 hours; create fractions with common denominators.
7/8 + 6/8 + 12/8
25/8 = 3 1/8 hours.
Jerry played with his friends for 3 1/8 hours.
Since f(x) is (strictly) increasing, we know that it is one-to-one and has an inverse f^(-1)(x). Then we can apply the inverse function theorem. Suppose f(a) = b and a = f^(-1)(b). By definition of inverse function, we have
f^(-1)(f(x)) = x
Differentiating with the chain rule gives
(f^(-1))'(f(x)) f'(x) = 1
so that
(f^(-1))'(f(x)) = 1/f'(x)
Let x = a; then
(f^(-1))'(f(a)) = 1/f'(a)
(f^(-1))'(b) = 1/f'(a)
In particular, we take a = 2 and b = 7; then
(f^(-1))'(7) = 1/f'(2) = 1/5
Divide $32.05 by 15 for the unit rate per gallon. So 32.05/15= $2.14 per gallon.
Answer:
20 sweatshirts and 5 hats
Step-by-step explanation:
So, let's assign our variables.
x = sweatshirts
y = hats
Now, we can set up our system of equations.
x + y = 25
8x + 2.5y = 172.5
In this instance, you can use a variety of methods. I will use substitution.
x + y = 25
x = 25 - y
8(25 - y) + 2.5y = 172.5
200 - 8y + 2.5y = 172.5
200 - 5.5y = 172.5
-5.5y = -27.5
y = 5.5
Now, we can plug in y to solve for x.
8x + 2.5(5.5) = 172.5
8x + 13.75 = 172.5
8x = 158.75
x = 19.84
Now, this was very sloppy work, and now we must make sense of these answers as pertaining to the context of the equation. First, let's try 20 and 5.
20 + 5 = 25
8(20) + 2.5(5) = 172.5 It works!
Answer:
She tipped $25.50 and paid a total of $110.50
Step-by-step explanation:
hope this helps you out