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


1. Slope intercept form. First find two points to get slope: (0,-3) and (-3,-4). Slope is
(-4 - -3)/(-3 - 0)= 1/3
Use one of the points of (x,y) to solve for b
Y=1/3x + b
-3 = 1/3(0) + b
-3 = b so your slope intercept equation is
Y = 1/3x - 3
2. Rate of Change is slope. Your points are (0,10) and (24,6) so slope is (6-10)/(24-0)
= - 1/6 which means that for each 1 unit increase in x, y decreases by 1/6.
3. Standard form is ax + by =c
Notice it is the same line as in the first graph so it's the same equation
y = 1/3x - 3
First, you cannot have fractions, so you have to multiply the equation by 3 to get rid of the 1/3.
3y= x - 9. Now move the x over:
-x + 3y = - 9. Now get rid of the negative value on x by multiplying the entire equation by -1:
x - 3y = 9
Answer:
StartFraction negative 1 Over k cubed EndFraction
Step-by-step explanation:
3k / (k + 1) × (k²- 1) / 3k³
= 3k(k² - 1) / (k + 1)(3k³)
= 3k³ - 3k / 3k⁴ + 3k³
= -3k / 3k⁴
= -1/k³
StartFraction k + 1 Over k squared EndFraction
(k + 1) / k²
StartFraction k minus 1 Over k squared EndFraction
(k - 1)/k²
StartFraction negative 1 Over k cubed EndFraction
= -1/k³
StartFraction 1 Over k EndFraction
= 1/k