we have 24= 2^3 x 3 ; 30=2 x 3 x 5 ; 36= 2^2 x 3^2
so lcm of 24, 30, 36 is 2^3 x 5 x 3^2 =360
ok done. Thank to me :>
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.
Answer:
D) 2x²+4x-30
Step-by-step explanation:
You would multiply x and 2x; x and -6; 5 and 2x; 5 and -6
(x)(2x) = 2x²
(x)(-6) = -6x
(5)(2x) = 10x
(5)(-6) = -30
Now just put it back in the order that it was listed in the equation starting with (x)(2x)
This would give you 2x²-6x+10x-30
Simplify even further to get 2x²+4x-30
Answer:
b
Step-by-step explanation:
