1/42
First, find the probability of Willie winning the grand prize. He has 1 ticket out of the 7 total tickets, so the probability is 1/7.
Now, find the probability of Emily winning the second prize. After the grand prize winner has been announced, there are only 6 tickets left. Emily has 1, so the probability is 1/6.
Finally, multiply the two probabilities together to find the probability that they will both happen together. To multiply fractions, multiply the numerators together and multiply the denominators together. This leaves us with (1 * 1) / (7 * 6), which is easy to simplify to 1/42, which is the final probability.
Answer:
f
(
x
)
=
3
x
3
−
5
x
2
−
47
x
−
15
Explanation:
If the zero is c, the factor is (x-c).
So for zeros of
−
3
,
−
1
3
,
5
, the factors are
(
x
+
3
)
(
x
+
1
3
)
(
x
−
5
)
Let's take a look at the factor
(
x
+
1
3
)
. Using the factor in this form will not result in integer coefficients because
1
3
is not an integer.
Move the
3
in front of the x and leave the
1
in place:
(
3
x
+
1
)
.
When set equal to zero and solved, both
(
x
+
1
3
)
=
0
and
(
3
x
+
1
)
=
0
result in
x
=
−
1
3
.
f
(
x
)
=
(
x
+
3
)
(
3
x
+
1
)
(
x
−
5
)
Multiply the first two factors.
f
(
x
)
=
(
3
x
2
+
10
x
+
3
)
(
x
−
5
)
Multiply/distribute again.
f
(
x
)
=
3
x
3
+
10
x
2
+
3
x
−
15
x
2
−
50
x
−
15
Combine like terms.
f
(
x
)
=
3
x
3
−
5
x
2
−
47
x
−
15
Answer:
True.
Step-by-step explanation:
y = -3x + 20
Put x as 5, then y output should be 5.
y = -3(5) + 20
y = -15 + 20
y = 5
True, the line with slope -3 passes through points (5, 5).
It is tripled as well. You are tripling every distance and thus tripling the sum of the distances as well.
