Answer:
We can conclude that on this case we have identical processes but excersise 17 use another way to present the probability distribution and as we can see the expected value can be viewed as a dot product of two vectors with one vector containing the outcomes and the other the probabilities for each possible outcome.
Step-by-step explanation:
Assuming this previous info:
Exercise 17. Suppose that we convert the table on the previous page displaying the discrete distribution for the number of heads occurring when two coins are flipped to two vectors.
Let vector
Because if that point is true than everything on that side of the number line is true. Visa versa.
9514 1404 393
Answer:
$3400
Step-by-step explanation:
The way these tax tables are structured, you pay 3% on the first $10,000, 5% on the next $40,000, and 5.5% on the remaining $20,000 above $50,000.
tax = 0.03·10,000 +0.05·(50,000 -10,000) +0.055·(70,000 -50000)
= 300 + 2000 +1100
= 3400 . . . dollars
The tax owed on $70,000 is $3,400.
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<em>Additional comment</em>
I like to rewrite this sort of table to a different format:
- 3% of income . . . . . . . . . . . . . . . applies for income ≤ 10,000
- (5% of income) -$200 . . . . . . . . applies for 10,000 < income ≤ 50,000
- (5.5% of income) -$450 . . . . . . .applies for 50,000 < income ≤ 100,000
For an income of $70,000, the tax computation using this form is one multiplication and one addition, rather than 3 multiplications and 4 additions as used when navigating the given table.
Answer:
12
Step-by-step explanation:
There are many ways to approach this problem. I like a method that uses the least amount of computation. We could figure how much Wendy makes on a bag of chips, the additional amount Wendy wants to make, then divide the latter by the former to find the number of additional bags to sell.
We could use a proportion to figure the number of bags corresponding to $126 in earnings, then subtract the 72 bags already sold. Essentially, we will do this, but without the intermediate numbers.
__
The additional fraction of 72 bags will be ...
(126/108) -1 = 18/108 = 1/6
Then Wendy must sell an additional ...
(1/6)×(72 bags) = 12 bags
to increase her earnings to $126.
Yay, implicit differnentiation
when you take the derivitive of y, you multiply it by dy/dx
example
dy/dx y^2=2y dy/dx
for x, the dy/dx dissapears
ok
so differnetiate and solve for dy/dx
3y² dy/dx-(y+x dy/dx)=0
expand
3y² dy/dx-y-x dy/dx=0
3y² dy/dx-x dy/dx=y
dy/dx (3y²-x)=y
dy/dx=y/(3y²-x)
so at (7,2)
x=7 and y=2
dy/dx=2/(3(2)²-7)
dy/dx=2/(3(4)-7)
dy/dx=2/(12-7)
dy/dx=2/5
answer is 2/5
