Answer:
See below
Step-by-step explanation:
linear equation: y=2x+10
x=cost per movie rented
10=$10 for the membership
24=2x+10 (24 being total you want to spend)
subtract 10 from each side
14=2x
divide by 2
7=x
He can rent no more than 7 movies if he want to spend $24 or less in the month
The probability of event A and B to both occur is denoted as P(A ∩ B) = P(A) P(B|A). It is the probability that Event A occurs times the probability that Event B occurs, given that Event A has occurred.
So, to find the probability that you will be assigned a poem by Shakespeare and by Tennyson, let Event A = the event that a Shakespeare poem will be assigned to you; and let Event B = the event that the second poem that will be assigned to you will be by Tennyson.
At first, there are a total of 13 poems that would be randomly assigned in your class. There are 4 poems by Shakespeare, thus P(A) is 4/13.
After the first selection, there would be 13 poems left. Therefore, P(B|A) = 2/12
Based on the rule of multiplication,
P(A ∩ B) = P(A) P(B|A)P(A ∩ B) = 4/13 * 2/12
P(A ∩ B) = 8/156
P(A ∩ B) = 2/39
The probability that you will be assigned a poem by Shakespeare, then a poem by Tennyson is 2/39 or 5.13%.
Answer:
Step-by-step explanation:
This kinda looks like the limiting definition of a derivative.
Anyway, what we are doing with the f(2 + h) is evaluating f(x) with 2+h in place for x. That looks like this:
f(2 + h) = 2(2 + h) - 3 which simplifies to
f(2 + h) = 4 + 2h - 3 which simplifies to
2h + 1
From that we are subtracting f(2). What we are doing with that is evaluating f(x) with 2 in place for x. That looks like this:
f(2) = 2(2) - 3 which simplifies to
f(2) = 4 - 3 which simplifies to
f(2) = 1. Now put those together over h to get:
Answer: 3∛2
<u>Step-by-step explanation:</u>
First, factor 128 .... you need three common factors to bring one on the outside of the radical.
![\dfrac{3}{4}\sqrt[3]{128} \\\\\\=\dfrac{3}{4}\sqrt[3]{4\cdot 4\cdot 4\cdot 2} \\\\\\=\dfrac{3}{4}\cdot 4\sqrt[3]{2} \\\\\\=\large\boxed{3\sqrt[3]{2} }](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B4%7D%5Csqrt%5B3%5D%7B128%7D%20%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B3%7D%7B4%7D%5Csqrt%5B3%5D%7B4%5Ccdot%204%5Ccdot%204%5Ccdot%202%7D%20%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B3%7D%7B4%7D%5Ccdot%204%5Csqrt%5B3%5D%7B2%7D%20%5C%5C%5C%5C%5C%5C%3D%5Clarge%5Cboxed%7B3%5Csqrt%5B3%5D%7B2%7D%20%7D)
