Answer:
.
Step-by-step explanation:
We use the Venn diagram to calculate the desired probabilities.
Note that there are 6 possible results in the sample space
S = {1, 2, 3, 4, 5, 6}
Then note that in the region representing the intercept of A and B there are two possible values.
So
In the region that represents event A there are 4 possible outcomes {4, 5, 1, 2}
So
In the region that represents event B there are 3 possible outcomes {1, 2, 6}
So
.
Now
Answer:
1. He added 5 instead of subtracted 5.
2. He should have subtracted 5.
3. 2 2/3
Step-by-step explanation:
3x+5=13
subtract 5 to both sides 3x=8
divide both sides by 3 x=8/3 or 2 2/3
9514 1404 393
Answer:
-13/11
Step-by-step explanation:
Straightforward evaluation of the expression at x=1 gives (1 -1)/(1 -1) = 0/0, an indeterminate form. So, L'Hopital's rule applies. The ratio of derivatives is ...
![\displaystyle\lim_{x\to 1}\dfrac{n}{d}=\dfrac{n'}{d'}=\left.\dfrac{\dfrac{4}{3\sqrt[3]{4x-3}}-\dfrac{7}{2\sqrt{7x-6}}}{\dfrac{5}{2\sqrt{5x-4}}-\dfrac{2}{3\sqrt[3]{2x-1}}}\right|_{x=1}=\dfrac{4/3-7/2}{5/2-2/3}=\dfrac{8-21}{15-4}\\\\=\boxed{-\dfrac{13}{11}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto%201%7D%5Cdfrac%7Bn%7D%7Bd%7D%3D%5Cdfrac%7Bn%27%7D%7Bd%27%7D%3D%5Cleft.%5Cdfrac%7B%5Cdfrac%7B4%7D%7B3%5Csqrt%5B3%5D%7B4x-3%7D%7D-%5Cdfrac%7B7%7D%7B2%5Csqrt%7B7x-6%7D%7D%7D%7B%5Cdfrac%7B5%7D%7B2%5Csqrt%7B5x-4%7D%7D-%5Cdfrac%7B2%7D%7B3%5Csqrt%5B3%5D%7B2x-1%7D%7D%7D%5Cright%7C_%7Bx%3D1%7D%3D%5Cdfrac%7B4%2F3-7%2F2%7D%7B5%2F2-2%2F3%7D%3D%5Cdfrac%7B8-21%7D%7B15-4%7D%5C%5C%5C%5C%3D%5Cboxed%7B-%5Cdfrac%7B13%7D%7B11%7D%7D)
The line is parallel so it has the same slope as the other line, -4.
Substitute the x and y variables with the given points and find the y-intercept.
(-8, 6)
y = -4x + b
6 = -4(8) + b
6 = -32 + b
6 + 32 = b
38 = b
So the equation is:
y = -4 + 38
