Factorize the numerator and denominator. You'll see that they both have a factor of 4 that can be canceled. The introduce a factor of 3 to change the denominator to 36.
Answer:
No this is not a function because the x-values repeat. In a function you can have the the output duplicate but not the input. The input at 3 has duplicates s o this is not a function.
Step-by-step explanation:
Answer: 7 / 18
Step-by-step explanation:
There were 18 students.
Out of them, the scores above 65 are:
73, 73, 69, 68, 71, 76, 70
There are 7 of them.
Probability of picking someone who scored higher than 65 is:
= Number of people who scored above 65/ Total number who took the test
= 7 / 18
Answer:
Length = 4cm
Width = 4cm
Height = 8cm
Step-by-step explanation:
The volume of the box = 128cm^3
LWH = Volume
LWH = 128cm^3
The side of the box = $1 per cm^2
The top and bottom of the box = $2 per cm^2
Let C be the cost function
C(LWH) = (1) 2H (L+W) + (2) 2LW
from LWH = 128cm^39
H = 128/LW
put H = 128/LW in equation for C(LWH)
C(LW) = (1) 2(128/LW) + (L+W) +(2) 2LW
= 256/LW(L+W) + 4LW
= 256(1/L + 1/W) + 4LW
Differentiate C with respect to L
dC/dL = 4W - 256/L^2 = 0
Differentiate C with respect to W
dC/dW = 4L - 256/W^2 = 0
The cost is minimum when the two partial derivatives equal 0
From 4W - 256/L^2 = 0
4W = 256/L^2
W = (256/L^2) 1/4
W = 64/L^2
From 4L - 256/W^2 = 0
4L = 256/W^2
L = (256/W^2) 1/4
L = 64/W^2
Since L = W,
L= W = cuberoot (64)
L = W = 4cm
Recall that H= 128/LW
H = 128/(4*4)
H= 128/16
H= 8cm
therefore;
L= 4cm
B= 4cm
H= 8cm
