400² = I don’t know what this is
2 answers:
You might be interested in
Answer:
(a) The probability of an adult using non-prescription antidepressants given that he visited the therapist is 0.78.
(b) The probability of an adult visited the therapist given that he was using non-prescription antidepressants is 0.46.
Step-by-step explanation:
Conditional probability of an event <em>X</em> given that another event <em>Y</em> has already occurred is:
Let <em>A</em> = an adult visited the therapist and <em>B</em> = an used non-prescription antidepressants.
Given:
P (A) = 0.27
P (B) = 0.46
P (A ∩ B) = 0.21
(a)
Compute the probability that a randomly selected adult who visited a therapist during the past year also used non-prescription antidepressants as follows:
Thus, the probability of an adult using non-prescription antidepressants given that he visited the therapist is 0.78.
(b)
Compute the probability that a randomly selected adult visited a therapist during the past year, given that he or she used non-prescription antidepressants as follows:
Thus, the probability of an adult visited the therapist given that he was using non-prescription antidepressants is 0.46.
Answers:
- -1 in the first box
- 19/2 or 9.5 in the second box
- -12 in the third box
=================================================
Work Shown:
We'll use the template y = ax^2 + bx + c
- If (x,y) = (2,3) is on the parabola, then y = ax^2+bx+c turns into 3 = a(2)^2 + b(2) + c. That simplifies to 4a+2b+c = 3
- If (x,y) = (6,9) is on the parabola, then y = ax^2+bx+c turns into 9 = a(6)^2 + b(6) + c. That simplifies to 36a+6b+c = 9
- If (x,y) = (8,0) is on the parabola, then y = ax^2+bx+c turns into 0 = a(8)^2 + b(8) + c. That simplifies to 64a+8b+c = 0
The system of equations is
We have 3 equations and 3 unknowns.
-----------------------------------
Let's solve the first equation for c
4a+2b+c = 3
2b+c = 3-4a
c = 3-4a-2b
c = -4a-2b+3
Plug that into the second equation and simplify
36a+6b+c = 9
36a+6b+(-4a-2b+3) = 9
32a+4b+3 = 9
32a+4b = 9-3
32a+4b = 6
2(16a+2b) = 6
16a+2b = 6/2
16a+2b = 3 .... we'll use this later
Plug that value of c into the third equation as well
64a+8b+c = 0
64a+8b+(-4a-2b+3) = 0
60a+6b+3 = 0
3(20a+2b+1) = 0
20a+2b+1 = 0
20a+2b = -1
--------------------------
We have a new system of equations. This time it deals with 2 variables instead of 3. We can think of this as a reduced equivalent system.
Note how subtracting the terms straight down has the b terms canceling (since 2b-2b = 0b = 0)
The 'a' terms subtract to 16a-20a = -4a
The terms on the right hand side subtract to 3-(-1) = 3+1 = 4
We end up with the equation -4a = 4 which solves to a = -1
Use this value of 'a' to find b
16a+2b = 3
16(-1)+2b = 3
-16+2b = 3
2b = 3+16
2b = 19
b = 19/2
b = 9.5
Now use the values of a and b to find c
4a+2b+c = 3
4(-1)+2(9.5)+c = 3
-4+19+c = 3
15+c = 3
c = 3-15
c = -12
--------------------------
Summary:
The values of a,b,c we found were
- a = -1
- b = 19/2 = 9.5
- c = -12
So the function is
f(x) = -x^2 + (19/2)x - 12
which is equivalent to
f(x) = -x^2 + 9.5x - 12
To check this answer, plug in x = 2, x = 6, x = 8 one at a time. You should get y = 3, y = 9 and y = 0 in that order.
Answer: v = - 9
Step-by-step explanation:
Since two points on the line are given, we use formula for slope.
Let (a,b) and (c,d) be two points on the line, the slope of the line is given by
m=.
Hence, using this we have
-4=
Thus, we have
-4×(-3)=3-v⇒12=3-v⇒12-3=-v⇒v=-9