ANSWER:
E[X] ≈ m ln m
STEP-BY-STEP EXPLANATION:
Hint: Let X be the number needed. It is useful to represent X by
m
X = ∑ Xi
i=1
where each Xi is a geometric random variable
Solution: Assume that there is a sufficiently large number of coupons such that removing a finite number of them does not change the probability that a coupon of a given type is draw. Let X be the number of coupons picked
m
X = ∑ Xi
i=1
where Xi is the number of coupons picked between drawing the (i − 1)th coupon type and drawing i th coupon type. It should be clear that X1 = 1. Also, for each i:
Xi ∼ geometric 
P r{Xi = n} =
Such a random variable has expectation:
E [Xi
] =
= 
Next we use the fact that the expectation of a sum is the sum of the expectation, thus:
m m m m
E[X] = E ∑ Xi = ∑ E Xi = ∑ = m ∑ 
= mHm
i=1 i=1 i=1 i=1
In the case of large m this takes on the limit:
E[X] ≈ m ln m
Assuming that the actual question reads lines b and c are perpendicular to line d
we are given that c is perpendicular to line d and parallel to line a. Since b is also perpendicular to line d, a b and c must all be parallel (draw it out will make a lot more sense)
So b is also parallel to line a
Answer:
B. 33
Step-by-step explanation:
The side opposite the 45° angle has measure 11√6×sin(45°). The side opposite the 60° angle has measure tan(60°) times that, so we have ...
x = 11√6×sin(45°)×tan(60°) = 11√6×(√2/2)×√3 = 11×(√6)²/2
x = 33
_____
The mnemonic SOH CAH TOA can be a useful reminder of the definitions of the trig functions. It tells you ...
Sin = Opposite/Hypotenuse
Tan = Opposite/Adjacent
Using these relations, we can find the sides of interest:
Opposite = Hypotenuse × Sin . . . . for the 45° triangle
Opposite = Adjacent × Tan . . . . . . for the 60° triangle
where the side opposite the 45° angle is the side adjacent to the 60° angle.
Answer:
135
Step-by-step explanation:
The supplement of an angle is 80° less than three times the measure of the complement of the angle find the measure of the supplement of the angle
Two Angles are Supplementary when they add up to 180 degrees.
Two Angles are Complementary when they add up to 90 degrees
Let the angle = x
Supplement of the angle = y
The supplement of an angle is 80° less than three times the measure of the complement of the angle find the measure of the supplement of the angle
x - 180 = 3(x - 90)
x - 180 = 3x - 270
Collect like terms
3x - x = 270 - 180
2x = 90
x = 90/2
x = 45
x+ y = 180
45 + y = 180
y = 180 -45
y = 135
Answer:
$34,000
Step-by-step explanation:
Jerry will get $1,750 for every year that his money stays in the account thus for 8 years he will get:
8*1,750 = $14,000
Together with the deposited money:
$20,000 + $14,000 = $34,000
By the end of year 8 there will be $34,000 of Jerry's account.
