For a standard normally distributed random variable <em>Z</em> (with mean 0 and standard deviation 1), we get a probability of 0.0625 for a <em>z</em>-score of <em>Z</em> ≈ 1.53, since
P(<em>Z</em> ≥ 1.53) ≈ 0.9375
You can transform any normally distributed variable <em>Y</em> to <em>Z</em> using the relation
<em>Z</em> = (<em>Y</em> - <em>µ</em>) / <em>σ</em>
where <em>µ</em> and <em>σ</em> are the mean and standard deviation of <em>Y</em>, respectively.
So if <em>s</em> is the standard deviation of <em>X</em>, then
(250 - 234) / <em>s</em> ≈ 1.53
Solve for <em>s</em> :
16/<em>s</em> ≈ 1.53
<em>s</em> ≈ 10.43
Answer:
7(2a +7)
Step-by-step explanation:
Answer: 6 feet
Step-by-step explanation:
Given that a 4-foot by 8-foot rectangular piece of plywood will be cut into 4 congruent rectangles with no wood left over and no wood lost due to the cuts
Let assume that the 4 rectangles will be of the same area since they are congruent.
The area of the big rectangle will be
Area = 4 × 8 = 32
Divide 32 by 4
32/4 = 8
Suggest the two possible numbers in which their product will be equal to 8
4 and 2 or 8 and 1
If 4 and 2
The perimeter = 2L + 2B
Substitute the 4 and 2 into the formula
Perimeter = 2(4) + 2(2)
Perimeter = 8 + 4
Perimeter = 12
If 8 and 1
Perimeter = 2(8) + 2(1)
Perimeter = 16 + 2 = 18
The positive difference, in feet, between the greatest possible perimeter of a single piece and the least possible perimeter of a single piece will be:
18 - 12 = 6 feet
Answer:
x = 21
Step-by-step explanation:
8 + 3x = 29 + 2x
8 + 3x - 2x = 29
8 + x = 29
x = 29 - 8 = 21
x = 21
Answer:
x=1 y = -1/2
(1,-1/2)
Step-by-step explanation:
7x-2y=8
5x+2y=4
I would use elimination since we have 2y in one equation and -2y in the other
7x-2y=8
5x+2y=4
--------------------
12x = 12
Divide each side by 12
12x/12 = 12/12
x =1
The substitute back into equation 2
5(1) +2y = 4
5 +2y = 4
Subtract 5
5-5+2y = 4-5
2y = -1
Divide by 2
2y/2 = -1/2
y = -1/2
