Answer: 6 ≤ h ≤ 9
Step-by-step explanation:
Hi, since He charges $40 as a fixed rate for the first hour plus $20 for each additional hour, the cost of the tutoring service is equal to the fixed rate(40) plus, the product of the additional hours (h-1) and the cost per additional hour (20).
40+20(h-1)
40+20h-20
20+20h
Since a student can spend between $140 and $200, the previous expression must be greater o equal than 140, and less or equal than 200.
140≤20+20h≤200
Subtracting 20
140-20 ≤20-20+20h ≤200-20
120 ≤ 20h ≤ 180
Dividing by 20
120/20 ≤ 20h/20 ≤ 180/20
6 ≤ h ≤ 9
One nice thing about this situation is that you’ve been given everything in the same base. To review a little on the laws of exponents, when you have two exponents with the same base being:
– Multiplied: Add their exponents
– Divided: Subtract their exponents
We can see that in both the numerator and denominator we have exponents *multiplied* together, and the product in the numerator is being *divided* by the product in the detonator, so that translates to *summing the exponents on the top and bottom and then finding their difference*. Let’s throw away the twos for a moment and just focus on the exponents. We have
[11/2 + (-7) + (-5)] - [3 + 1/2 + (-10)]
For convenience’s sake, I’m going to turn 11/2 into the mixed number 5 1/2. Summing the terms in the first brackets gives us
5 1/2 + (-7) + (-5) = - 1 1/2 + (-5) = -6 1/2
And summing the terms in the second:
3 + 1/2 + (-10) = 3 1/2 + (-10) = -6 1/2
Putting those both into our first question gives us -6 1/2 - (-6 1/2), which is 0, since any number minus itself gives us 0.
Now we can bring the 2 back into the mix. The 0 we found is the exponent the 2 is being raised to, so our answer is
2^0, which is just 1.
To getyour answer, just divided 3.24 by 12. You will get 0.27. So the answer is each pencil costs 27 cents or 0.27.
Nope! I have the correct answers here .. it’s a little blurry but you can see where the marks should be https://www.teacherspayteachers.com/Product/Exponential-Growth-Decay-Maze-1005592#