Answer:
We can write the equation for the first part of this problem as:
16
+
4
x
=
10
+
14
We can now solve for
4
x
:
−
16
+
16
+
4
x
=
−
16
+
24
0
+
4
x
=
8
4
x
=
8
To find the value of
8
x
we can multiply each side of this equation by
2
:
2
×
4
x
=
2
×
8
8
x
=
16
Step-by-step explanation:
Answer:
16/9
Step-by-step explanation:
Answer: given and explained briefly below.
In these questions, we go right to left of the function to solve.
(a)
given that
f(x) = x - 3
g(x) = x + 3
(i) fg(x)
= f(x + 3)
= ( x +3 ) -3
= x
(ii) gf(x)
= g(x-3)
= (x-3)+3
= x
to find inverse, we have to make x the subject,
1)
f(x) = x - 3
f(x) + 3 =x
f^-1(x) = x + 3
2)
g(x) = x + 3
g(x) -3 = x
g^-1(x) = x -3
- f and g are inverses of each other
(b)
given that
f(x) = -1/4x
g(x) = 1/4x
fg(x) =
f(1/4x)
1/4(-1/4x)
= x
2)
gf(x)
g(-1/4x)
-1/4(1/4x)
= -x
<u>to find inverse, we have to make x the subject,</u>
1)
f(x) = -1/4x
-1/f(x) = 4x
f^-1(x) = -1/4x
2)
g(x) = 1/4x
x = 1/4g(x)
g^-1(x) = 1/4x
- f and g are not inverses of each other here.
Answer:
(C) No, the probability of making a second purchase is not equal to the probability of making a second purchase given that a coupon was sent.
Step-by-step explanation:
Let A = the customer makes a second purchase within 30 days and let B = customer is sent a coupon. Events A and B are independent if P(A) = P(A | B).
P(A) = P(the customer makes a second purchase within 30 days) = \frac{50}{100} = 0.5
100
50
=0.5
P(A | B) = P(the customer makes a second purchase within 30 days | customer is sent a coupon) = \frac{34}{60} = 0.567
60
34
=0.567
Because P(A) ≠ P(A | B) making a second purchase is not independent of being sent a coupon.
