Answer:
The answer is below
Step-by-step explanation:
The next step to solve the system, would be to divide the second row by 3 and we would be left with: 3 * R2
[1 -5 3 0 -2
0 1 -7/3 0 4/3
0 0 1 2 -2]
Then what we will do is multiply row 3 by 7/3 and then subtract it from row 2, that is, R2 - 7/3 * R3, and it would look like this:
[1 -5 3 0 -2
0 1 0 14/3 -10/3
0 0 1 2 -2]
And these would be the next two steps in the process of solving the system.
The shape shown here is a pentagonal pyramid, because it has a pentagonal base and a pointy tip.
Answer:
0.3
Step-by-step explanation:
The margin of error is calculated as ...
(standard deviation)/√(sample size) × (z*-score)
where the z*-score is chosen based on the desired confidence level.
Here, you have ...
- standard deviation = 2.7
- √(sample size) = √225 = 15
- z*-score for 90% confidence level = 1.645
Putting these values in the above expression for margin of error gives ...
2.7/15·1.645 = 0.2961 ≈ 0.3
Given Information:
Area of rectangle = 16 square feet
Required Information:
Least amount of material = ?
Answer:
x = 4 ft and y = 4 ft
Step-by-step explanation:
We know that a rectangle has area = xy and perimeter = 2x + 2y
We want to use least amount of material to design the sandbox which means we want to minimize the perimeter which can be done by taking the derivative of perimeter and then setting it equal to 0.
So we have
xy = 16
y = 16/x
p = 2x + 2y
put the value of y into the equation of perimeter
p = 2x + 2(16/x)
p = 2x + 32/x
Take derivative with respect to x
d/dt (2x + 32/x)
2 - 32/x²
set the derivative equal to zero to minimize the perimeter
2 - 32/x² = 0
32/x² = 2
x² = 32/2
x² = 16
x =
ft
put the value of x into equation xy = 16
(4)y = 16
y = 16/4
y = 4 ft
So the dimensions are x = 4 ft and y = 4 ft in order to use least amount of material.
Verification:
xy = 16
4*4 = 16
16 = 16 (satisfied)
Hello,
xy+xz=100==>x(y+z)=100
x/5*(3y+3z)+10=3/5*(x(y+z))+10=3/5*100+10=70
Answer C