Answer:f⁻¹(x) =
Explanation:To get the inverse of a function, we have to follow these steps:1- replace f(x) with y
2- swap the x and y variables
3- solve for y
4- replace y with f⁻¹(x)
Applying this to the given as follows:f(x) =
Step 1: replace f(x) with y:y =
Step 2: swap the x and y variables:x =
Step 3: solve for y:7x = 4y - 3
4y = 7x - 3
y =
Step 4: replace y with f⁻¹(x):f⁻¹(x) =
Hope this helps :)
Answer:
3. D) 
2. D) 
1. B) 
Step-by-step explanation:
3.
{y = 3x + 7
{y = x - 9
x - 9 = 3x + 7
-3x - 3x
____________
−2x - 9 = 7
+ 9 + 9
__________
−2x = 16
____ __
−2 −2
[Plug this back into both equations above to get the y-coordinate of −17]; 
__________________________________________________________
2.
{−4x + 3y = 12
{−2x + 3y = −18
−½[−4x + 3y = 12]
{2x - 1½y = −6 >> New Equation
{−2x + 3y = −18
_______________
1½y = −24
____ ____
1½ 1½
[Plug this back into both equations above to get the x-coordinate of −15]; 
__________________________________________________________
1.
{−10x - 3y = −18
{−7x - 8y = 11
−⅜[−7x - 8y = 11]
{−10x - 3y = −18
{2⅝x + 3y = −4⅛ >> New Equation
_________________
−7⅜x = −22⅛
______ _____
−7⅜ −7⅜
[Plug this back into both equations above to get the y-coordinate of −4]; 
I am joyous to assist you anytime.
Answer:
Answer explained below
Step-by-step explanation:
Alex has in the past committed 55% of the burglaries committed by the three, Becky 31%, and Carl the rest, hence
probability, P(Carl doing a burglary) = 1 - P(Alex or Becky doing a burglary)
= 1 - (0.55 + 0.31)
= 0.14
a) P(next burglary in town is the burglary of a residence) = P(Alex did a burglary of a residence) + P(Becky did a burglary of a residence) + P(Carl did a burglary of residence
= 0.55*1/3 + 0.31*0.5 + 0.14*1
= 0.4783
b)From Bayes' Theorem: P(A | B) = P(A & B) / P(B)
Hence,
P(Becky | a resident reports a home burglary) = P(Becky did a burglary of a residence) / P(burglary of a residence)
= (0.31 * 0.5)/0.4783
= 0.3240
