Answer:
Step-by-step explanation:
Number 5 is L because you have 18 coins but you only want to find the probability of the pennies. So take 3/18 and simplify to 1/6 by dividing both the numerator and the denominator by 3.
Number 6 can be (-6x - 3), just use the distributive property on the original expression.
Answer:
A darts player practices throwing a dart at the bull’s eye on a dart board. Her probability of hitting the bull’s eye for each throw is 0.2.
(a) Find the probability that she is successful for the first time on the third throw:
The number F of unsuccessful throws till the first bull’s eye follows a geometric
distribution with probability of success q = 0.2 and probability of failure p = 0.8.
If the first bull’s eye is on the third throw, there must be two failures:
P(F = 2) = p
2
q = (0.8)2
(0.2) = 0.128.
(b) Find the probability that she will have at least three failures before her first
success.
We want the probability of F ≥ 3. This can be found in two ways:
P(F ≥ 3) = P(F = 3) + P(F = 4) + P(F = 5) + P(F = 6) + . . .
= p
3
q + p
4
q + p
5
q + p
6
q + . . . (geometric series with ratio p)
=
p
3
q
1 − p
=
(0.8)3
(0.2)
1 − 0.8
= (0.8)3 = 0.512.
Alternatively,
P(F ≥ 3) = 1 − (P(F = 0) + P(F = 1) + P(F = 2))
= 1 − (q + pq + p
2
q)
= 1 − (0.2)(1 + 0.8 + (0.8)2
)
= 1 − 0.488 = 0.512.
(c) How many throws on average will fail before she hits bull’s eye?
Since p = 0.8 and q = 0.2, the expected number of failures before the first success
is
E[F] = p
q
=
0.8
0.2
= 4.
You're looking for the extreme values of 
subject to the constraint 
.
The target function has partial derivatives (set equal to 0)
so there is only one critical point at 
. But this point does not fall in the region . There are no extreme values in the region of interest, so we check the boundary.
Parameterize the boundary of by
with 
. Then 
can be considered a function of 
alone:
has critical points where 
:
but 
for all , so this case yields nothing important.
At these critical points, we have temperatures of
so the plate is hottest at (1, 0) with a temperature of 14 (degrees?) and coldest at (-1, 0) with a temp of -12.
Answer:
40%
Step-by-step explanation: If you have five equal-sized sectors, then the probability that the spinner will stop on 4 and 5 is 40%.
First start with the squares we know that they have four equal sides. This means that all of the square sides are 10.
