Answer: the cubic equation is
L^3 - 52L +144 =0
Lenght= 4inches
Width = 2inches
Height = 3 inches
Step-by-step explanation:
Let the lenght= L
Let the width = W
Let the height = H
Volume of the box = 24 cubic inch
Total surface area of the box = 52 sq. Inches
W = L/2
W, = 0.5L
Volume = L * B * H
Insert W = 0.5L
L * 0.5L * H = 24
0.5L^2 * H = 24
H = 24/0.5L^2
= 48/L^2
Surface area equation
2(L*W) + 2(L+H) + 2(W+H)= 52
Divide through by 2
(L*W) + (L+H) + (W*H) = 26
Insert W= 0.5L
(L*0.5L) + (L*H) + (0.5L*H) = 26
0.5L^2 + LH + 0.5LH = 26
0.5L^2 + 1.5LH = 26
Insert H = 48/L^2
0.5L^2 + 1.5*48/L = 26
0.5L^2 + 72/L = 26
Multiply through by L to get rid of the denominator
0.5L^3 + 72 - 26L = 0
0.5L^3 - 26L + 72 = 0
Multiply through by 2, we have
L^3 - 52L +144 =0
Try L= 4
4*3 -52(4)+ 144 =0
0= 0
(L - 4) is a factor of cubic equation
Therefore Length (L) = 4 inch
Recall that W= L/2
W= 4/2
W= 2 inches
H= 48/L*2
= 48/4*2
= 48/16
= 3 inches
Answer:
a. 2
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean 
and standard deviation 
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation 
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean 
and standard deviation 
Standard deviation is known to be 14.
This means that 
Sample of 49
This means that 
The standard error of the mean is
So the correct answer is given by option a.
You can use this equation to help you: (ab)^2 = a^2 b^2. And also (a^m)^n = a^m*n
So, here it is:
(7ab^3)^2 = 7^2 a^2 b^3*2 = 49a^2b^6
The correct answer is the third one - 49 a^2 b^6.
Step-by-step explanation:
M is the midpoint of AB. First, find the coordinates of M.
M = ((4 + 0) / 2, (2 + 4) / 2)
M = (2, 3)
Now find the slope of MC:
m = (15 − 3) / (8 − 2)
m = 12 / 6
m = 2
Find the slope of AB:
m = (4 − 2) / (0 − 4)
m = 2 / -4
m = -1/2
The slopes are opposite inverses, so the two are indeed perpendicular.
