Answer:
-x^3+5x^2-8x+1, which is choice A
======================================
Work Shown:
f(x) = x^3 - x^2 - 3
f(x) = (x)^3 - (x)^2 - 3
f(2-x) = (2-x)^3 - (2-x)^2 - 3 ................ see note 1 (below)
f(2-x) = (2-x)(2-x)^2 - (2-x)^2 - 3 ........... see note 2
f(2-x) = (2-x)(4-4x+x^2) - (4-4x+x^2) - 3 ..... see note 3
f(2-x) = -x^3+6x^2-12x+8 - (4-4x+x^2) - 3 ..... see note 4
f(2-x) = -x^3+6x^2-12x+8 - 4+4x-x^2 - 3 ....... see note 5
f(2-x) = -x^3+5x^2-8x+1
----------
note1: I replaced every copy of x with 2-x. Be careful to use parenthesis so that you go from x^3 to (2-x)^3, same for the x^2 term as well.
note2: The (2-x)^3 is like y^3 with y = 2-x. We can break up y^3 into y*y^2, so that means (2-x)^3 = (2-x)(2-x)^2
note3: (2-x)^2 expands out into 4-4x+x^2 as shown in figure 1 (attached image below). I used the box method for this and for note 4 as well. Each inner box or cell is the result of multiplying the outside terms. Example: in row1, column1 we have 2 times 2 = 4. You could use the FOIL rule or distribution property, but the box method is ideal so you don't lose track of terms.
note4: (2-x)(4-4x+x^2) turns into -x^3+6x^2-12x+8 when expanding everything out. See figure 2 (attached image below). Same story as note 3, but it's a bit more complicated.
note5: distribute the negative through to ALL the terms inside the parenthesis of (4-4x+x^2) to end up with -4+4x-x^2
Answer:
Bob drove from home to work at 75 mph. After work the traffic was heavier, and he drove home at 40 mph. His driving time to and from work was 1 hour and 9 minutes. How far does he live from his job?
=================
Avg speed for the round trip = 2*75*40/(75+40) = 6000/115 = 1200/23 mi/hr
RT distance = 1200/23 * 69 minutes * 1 hr/60 mins =
= 60 miles
30 miles each way
Step-by-step explanation:
Answer:
a. The probability that a customer purchase none of these items is 0.49
b. The probability that a customer purchase exactly 1 of these items would be of 0.28
Step-by-step explanation:
a. In order to calculate the probability that a customer purchase none of these items we would have to make the following:
let A represents suit
B represents shirt
C represents tie
P(A) = 0.22
P(B) = 0.30
P(C) = 0.28
P(A∩B) = 0.11
P(C∩B) = 0.10
P(A∩C) = 0.14
P(A∩B∩C) = 0.06
Therefore, the probability that a customer purchase none of these items we would have to calculate the following:
1 - P(A∪B∪C)
P(A∪B∪C) =P(A) + P(B) + P(C) − P(A ∩ B) − P(A ∩ C) − P(B ∩ C) + P(A ∩ B ∩ C)
= 0.22+0.28+0.30-0.11-0.10-0.14+0.06
= 0.51
Hence, 1 - P(A∪B∪C) = 1-0.51 = 0.49
The probability that a customer purchase none of these items is 0.49
b.To calculate the probability that a customer purchase exactly 1 of these items we would have to make the following calculation:
= P(A∪B∪C) - ( P(A∩B) +P(C∩B) +P(A∩C) - 2 P(A ∩ B ∩ C))
=0.51 -0.23 = 0.28
The probability that a customer purchase exactly 1 of these items would be of 0.28
Answer:
3
Step-by-step explanation:
3x=9
3(3)=9
3/3=0=9/3=3
answer=3
The key features of the above given functions are correctly matched to their corresponding definition.
<h3>Definition of terms</h3>
- Negative sections of the graph: They are the parts where the graph is below the x-axis. That is option C.
- End behaviour: This is what happens to the graph on the far left or far right. That is option E.
- Positive sections of the graph: This is the parts where the graph is above the x-axis. That is option D.
- Intercepts: This is the points where the graph crosses an axis. That is option B
- Relative extrema: This is the points of relative minimum or maximum in a graph. That is option A.
Learn more about graphs here:
brainly.com/question/25799000
#SPJ1
