The simplest form of this sum is 670.
This is a probability problem with two dependent events and conditional probability. Note that after the first donut is chosen, it is not replaced into the data set, so only 23 donuts remain. If we set A=selection of a lemon-filled, and B=selection of a custard-filled, then P(A and B) = P(A)*P(B|A), where P(B|A) means the probability of B happening given that A has already occurred.P(A) = 8/24 = 1/3 = 0.333333P(B|A) = 12/23 = 0.521739P(A and B) = 1/3(12/23) = 12/69 = 0.1739130435 or 17.4%
https://www.wyzant.com/resources/answers/296921/find_the_probability_of_selecting_a_a_lemon_filled_d...
When it says 'which has a greater rate of change' it is referring to 'what has a greater slope.' So, let's calculate each thing's slope:
Table:
I'm going to pick the easiest values to work with, so I'll pick the points (0, -2) and (1, -9/5) - I simplified the mixed fraction. So, here we go, the slope formula is:



So, the table's slope is
-1/5.
Graph
We can, again, pick two points. I'll pick the two given: (5, 0) and (0, -3). Let's start off with the same formula:


The graph's slope is
3/5.
Now, we just have to decide which is bigger:
-1/5 or
3/5. So, clearly:
3/5 > -1/5.
The
3/5 slope was the graph, hence it has the greater rate of change (
that's why it's B). If anything doesn't make sense, feel free to DM me or ask!
Answer:
5 + 4 - (8 * 3 - 22)⁴ * 4 = -55
Step-by-step explanation:
5 + 4 - (8 * 3 - 22)⁴ * 4
Follow PEMDAS which states you need to do equations in the order of:
Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction.
Knowing this, simplify inside the parenthesis by multiplying 8 and 3 first.
5 + 4 - (24 - 22)⁴ * 4
Now subtract 22 from 24 inside the parenthesis.
5 + 4 - (2)⁴ * 4
Since we are done with parenthesis, move on to the next part of PEMDAS which says to do exponents next. Take 2 to the power of 4.
5 + 4 - 16 * 4
Now that we are done with exponents, move on to the next part of PEMDAS which says to multiply/divide next. Multiply -16 and 4.
5 + 4 - 64
Now that we are done with multiplication/division, move on to the last part of PEMDAS which says to add/subtract. Add 5 and 4.
9 - 64
Finally, subtract 64 from 9 to get:
-55.
22 - 5(6v - 1) = -63 First, you distribute 5 to the parentheses.
22 - 30v + 5 = -63
27 - 30v = -63
-30v = -90
v = 3