Answer:
Any polynomial of the form f(x)=rx²+(1-4r)x+(3r+6) passes through these points.
Step-by-step explanation:
Let f(x)=rx²+bx+c be a polynomial that passes through (1,7) and (3,9). This means that f(1)=7 and f(3)=9, that is,
f(1)=r(1)²+b(1)+c=r+b+c=7, and
f(3)=r(3)²+b(3)+c=9r+3b+c=9
We have the equations r+b+c=7 and 9r+3b+c=9. Substract the second equation minus 9 times the first to obtain -6b-8c=-54, then 6b+8c=54 or equivalently b=9-4c/3.
Substract the second equation minus 3 times the first to obtain 6r-2c=-12. Then 2c=6r+12, thus c=3r+6. We have written c in terms of r. Substitute in b=9-4c/3 to obtain b=9-4(r+2)=-4r+1. The polynomial acquires the form
f(x)=rx²+(1-4r)x+(3r+6).
Answer:
what is the Question
Step-by-step explanation:
Let y = f(x)
f(x) = sin x
g(x) = (2x^2 + 3x - 4)
Use the chain rule.
We want y' = f' (g(x)) • g'(x).
y' = cos(2x^2 + 3x - 4) • (4x + 3)
Done.
Answer:
The value of Q is 350.
Step-by-step explanation:
Denote the events as follows:
X = the test is positive
Y = the test is negative
A = the person is telling the truth
B = the person is telling a lie.
It is provided that:
P (B ∩ X) = 0.90
P (A ∩ Y) = 0.50
Then:
P (B ∩ Y) = 1 - P (B ∩ X) = 1 - 0.90 = 0.10
P (A ∩ X) = 1 - P (A ∩ Y) = 1 - 0.50 = 0.50
To test the accuracy of lie-detector a police officer tests 1000 suspected criminals.
It is assumed that 700 per 1,000 suspected criminals tell the truth during polygraph tests.
The table needed to be completed is:
Truth (A) Lie (B) TOTAL
Positive (X) Q __ __
Negative (Y) __ P __
TOTAL __ __ __
For the 1000 suspected criminals selected complete the table as follows:
Given:
Truth (A) Lie (B) TOTAL
Positive (X) Q __ __
Negative (Y) __ P __
TOTAL 700 300 1000
n (A ∩ X) = P (A ∩ X) × n (A)
= 0.50 × 700
= 350
n (A ∩ Y) = P (A ∩ Y) × n (A)
= 0.50 × 700
= 350
n (B ∩ X) = P (B ∩ X) × n (B)
= 0.90 × 300
= 270
n (B ∩ Y) = P (B ∩ Y) × n (B)
= 0.10 × 300
= 30
n (X) = n (B ∩ X) + n (A ∩ X)
= 270 + 350
= 620
n (Y) = n (B ∩ Y) + n (A ∩ Y)
= 30 + 350
= 380
Complete table is:
Truth (A) Lie (B) TOTAL
Positive (X) Q = 350 270 620
Negative (Y) 350 P = 30 380
TOTAL 700 300 1000
Thus, the value of Q is 350.
Answer: 5/33
Step-by-step explanation: There are 12 fruits and 5 are oranges.
If you draw an orange, then there are 11 fruits and 4 oranges. (5/12)x(4/11)=20/132 or 5/33 in simplest form.
Answer:
x=-11/12
Step-by-step explanation:
Given an equation for x
x -2/3(3x - 4) + 3x = 5/6
We are asked to find the value of x.
We use equation rules to solve
To get rid of denominator in fraction, let us multiply the whole equation by 6.
6x-4(3x-4) +18x = 5
Simplify:
-6x+18x+16 =5
12x = 5-16 = -11
x = -11/12
Answer:
- 11/6
Step-by-step explanation: