Answer:
(
h
∘
f
∘
g
)
(
x
)
is known as a composite function. Here's how composite functions work:
let's say that
x
=
1
. Your function
g
(
x
)
=
1
3
(
x
)
now produces a
y
output of
1
3
, since
g
(
1
)
=
1
3
(
1
)
. Within a composite function, the y-value of one function becomes the x-value of the next, like so:
g
(
1
)
=
1
3
⇒
f
(
1
3
)
=
17
3
⇒
h
(
17
3
)
=
17
Therefore,
(
h
∘
f
∘
g
)
(
1
)
=
17
Based on this, to find the function for
(
h
∘
f
∘
g
)
(
x
)
(combined from right to left, by the way), simply replace
x
in
f
(
x
)
with the function
g
(
x
)
, and replace
x
in
h
(
x
)
with the function of
(
f
∘
g
)
(
x
)
, to get
(
h
∘
f
∘
g
)
(
x
)
.
This, simplified, is equal to
2
x
+
15
, and therefore
(
h
∘
f
∘
g
)
(
1
)
=
2
(
1
)
+
15
=
17
Hope that helps!
Answer: 1¹/₈ hours
Step-by-step explanation:
Joelle spent 1¹/₂ hours reading and Rileigh spent 3/4 of that time.
To find out how much time Rileigh spent, multiply the fractions but first convert the improper fraction to a proper fraction:
= 1¹/₂ = 3/2
= 3/2 * 3/4
= 9/8
= 1¹/₈ hours
Answer:
5/6
Step-by-step explanation:
1/3 + 1/2 = 5/6
Answer:
r(t) and s(t) are parallel.
Step-by-step explanation:
Given that :
the lines represented by the vector equations are:
r(t)=⟨1−t,3+2t,−3t⟩
s(t)=⟨2t,−3−4t,3+6t⟩
The objective is to determine if the following lines represented by the vector equations below intersect, are parallel, are skew, or are identical.
NOTE:
Two lines will be parallel if 
here;
Thus;
∴
Hence, we can conclude that r(t) and s(t) are parallel.
Answer:
Yes, the company can expect a profit in the long term
Step-by-step explanation:
In this question, we are to project if a company is expected to make a profit or loss given the information in the question.
Let’s use the scenario of 50 gadgets produced.
1 is expected to be faulty, while 49 is thus expected to work perfectly.
Now, on this 49 sold, there is an expectancy of $3 profit. Hence, this means that for a batch of 50 gadgets produced, the amount of expected profit will be 49 * 3 = $147
The amount that would be used to repair the faulty unit is $80. If we subtract this from the total expected profit, we have $147-$80 = $67
Hence, per 50 gadgets sold, a total of $67 in profit is to be expected
This means profit is expected in the long tey
