Answer:
114 yards
456 yards
Step-by-step explanation:
Given that:
Area of square parking lot = 12,996 square yards
The lenght of one side of the parking lot :
Area of a square = a² ; a = side length
Hence ;
12996 = a²
√12996 = a
114 = a
Hence, length of one side = 114 yards
Yards of fence needed to enclose parking lot :
Perimeter of a square = 4a ; a = side length
Perimeter = 4(114)
Perimeter = 456 yards
Answer:
or in slope y-intercept form :
Step-by-step explanation:
The easiest way of find the answer for this is to use what is called the "point-slope" form of a line, because you are in fact given the value of the slope (m) and also a point 
it goes through:
In our case the equation becomes:
This can also be written in the slope-intercept form by solving for "y" and operating to remove the parenthesis:
We know that
in a right triangle
Applying the Pythagoras Theorem
c²=a²+b²
in this problem
c=√87 yd
a=√23 yd
b=?
so
b²=c²-a²-----> b²=(√87)²-(√23)²----> b²=87-23----> b²=64----> b=8 yd
the answer is
8 yd
Answer:
1 .4x2-9= 2x+3,2x-3
2 .16x2-1=4x-1,4x+1
3 .16x2-4=4(2x+1)(2x-1)
4 .4x2-1=(2x+1)(2x-1)
Step-by-step explanation:
16x² − 1 = (4x − 1)(4x + 1) ; 16x² − 4 = 4(2x + 1)(2x − 1); 4x² − 1 = (2x + 1)(2x − 1) ;
4x² − 9 = (2x + 3)(2x − 3)
16x² − 1 is the difference of squares. This is because 16x² is a perfect square, as is 1. To find the factors of the difference of squares, take the square root of each square; one factor will be the sum of these and the other will be the difference.
The square root of 16x² is 4x and the square root of 1 is 1; this gives us (4x-1)(4x+1).
16x² − 4 is also the difference of squares. The difference of 16x² is 4x and the square root of 4 is 2; this gives us (4x-2)(4x+2). However, we can also factor a 2 out of each of these binomials; this gives us
2(2x-1)(2)(2x+1) = 2(2)(2x-1)(2x+1) = 4(2x-1)(2x+1)
4x² − 1 is also the difference of squares. The square root of 4x² is 2x and the square root of 1 is 1; this gives us (2x-1)(2x+1).
4x² − 9 is also the difference of squares. The square root of 4x² is 2x and the square root of 9 is 3; this gives us (2x-3)(2x+3).
Answer:
a. n=4148
b. n=3909
c. The sample size is smaller if a known proportion from prior study is used. The difference in sample sizes is 239
Step-by-step explanation:
a. For sample where no preliminary estimate is given, the minimum sample size is calculated using the formula:
Where:
Margin of error
is the assumed proportion
#Let p=0.5, substitute in the formula to solve for n:
Hence, the minimum sample size is 4148
b. If given a preliminary estimate p=0.38, we use the same formula but substitute p with the given value:
Hence, the minimum sample size is 3909
c. Comparing the sample sizes from a and b:
Hence, the actual sample size is smaller for a known proportion from prior a prior study.
