F(x) = 3x + 1
let f(x) = y
y = 3x + 1
y - 1 = 3x
3x = y - 1
x = (y - 1)/3
From y = f(x), x = f⁻¹(y)
<span>x = (y - 1)/3
</span>
f⁻¹(y) = (y - 1)/3
f⁻¹(7) = <span>(7 - 1)/3 = 6/3 = 2
</span>f⁻¹(7)<span> = 2</span>
Answer:
The bottom 3 is separated by weight 7.8896 g and the top 3 is separated by weight 8.1904 g.
Step-by-step explanation:
We are given that
Mean, 
Standard deviation, 
We have to find the two weights that separate the top 3% and the bottom 3%.
Let x be the weight of machine components


=0.03
From z- table we get

Therefore, we get







Hence, the bottom 3 is separated by weight 7.8896 g and the top 3 is separated by weight 8.1904 g.
Answer:
V = 301 ft^3
Step-by-step explanation:
The volume of a cone is given by
V =1/3 pi r^2 h
We know pi = 3.14 r =6 and
We need to determine h
We can find h from the Pythagorean theorem where 6 is a leg and 10 is the hypotenuse
h^2 +6^2 = 10^2
h^2 +36 = 100
h^2 = 64
Taking the square root of each side
h = 8
V =1/3 pi r^2 h
V = 1/3 (3.14) (6)^2 * 8
V = 301.44 ft^3
Rounding to the nearest cubic foot
V = 301 ft^3
Answer:
The value of k is -11
Step-by-step explanation:
If (x+2) is a factor of x3 − 6x2 + kx + 10:
Then,
f(x)=x3 − 6x2 + kx + 10
f(-2)=0
f(-2)=(-2)³-6(-2)²+k(-2)+10=0
f(-2)= -8-6(4)-2k+10=0
f(-2)= -8-24-2k+10=0
Solve the like terms:
f(-2)=-2k-22=0
f(-2)=-2k=0+22
-2k=22
k=22/-2
k=-11
Hence the value of k is -11....