Answer:
The third choice, which would be:
Line 
intersects the line 
.
Step-by-step explanation:
On a graph, line 
and line 
do intersect each other, but not in the x-axis, y-axis, or at the origin.
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 and Step-by-step explanation:
We are given a <u>composite function</u>, which are functions inside of functions.
When solving composite functions, we solve the function on the inside first, then the function on the outside.
s(5) = s(x)
x = 5
<u>Plug 5 into the function s(x)</u>
= 2(5) + 1
= 11
<u>Now we plug 11 in for x for the function t(x).</u>
= 
= -2(121) + 2
= -242 + 2
= -240
<u>So, the answer to t(s(5) is -240.</u>
<em><u>#TeamSeas #PAW (Plant And Water)</u></em>
<em><u>I hope this helps!</u></em>
Answer:
4
Step-by-step explanation:
Answer:
length= 24 inches
width= 7 inches
Step-by-step explanation:
Start by writing down what you know.
width= w
length= 3w+3
Then, we can substitute into the perimeter of a rectangle equation, P=2l+2w.
62= 2(3w+3) + 2(w)
62=6w+6+2w
62=8w+6
56=8w
7=w
Now, plug this into our original equations for length and width:
width=7
length= 3(7)+3, so 24
