Answer: a) Required minimum sample size= 219
b) Required minimum sample size= 271
Step-by-step explanation:
As per given , we have
Margin of error : E= 5% =0.05
Critical z-value for 90% confidence interval : 
a) Prior estimate of true proportion: p=28%=0.28
Formula to find the sample size :-

Required minimum sample size= 219
b) If no estimate of true proportion is given , then we assume p= 0.5
Formula to find the sample size :-

Required minimum sample size= 271
Answer:
104 units
Step-by-step explanation:
Given
Shape: Rhombus


Required
Determine the perimeter
The given parameter are the diagonals of the rhombus.
The perimeter (from diagonals) is calculated as thus:

Substitute values for JL and KM





<em>Hence, the perimeter is 104 units</em>
Answer:
(a) x = 
(b) x = 
Step-by-step explanation:
A. sum of angles in a polygon = (n - 2) 180
The polygon given is an irregular pentagon, where n = 5
So that;
sum of angles in a pentagon = (5 - 2) 180
= 3 x 180
= 
Thus,
x + 90 + 76 + 110 + 136 = 
x + 412 = 
x =
- 412
x = 
B. The polygon given is an irregular pentagon, where n = 5.
Let the supplementary angle with angle 38 be represented by y,
y + 38 = 180
y = 180 - 38
= 
y = 
Let the supplementary angle with x be represented by z, so that;
z + 72 + 120 + 100 + 142 = 
z + 434 = 
z =
- 434
= 
z = 
But, x + z = 
Then;
x +
= 
x =
- 
= 
x = 
<span>Given the two end of the diameter of the circle, we are able to compute the center of the circle as 0.5*[(-1,3)+(7,-7)]=(3,-2). The radius of the circle is 0.5*sqrt[(-1-7)^2+(3+7)^2]=sqrt(41). Therefore the equation of the circle is (x-3)^2+(y+2)^2=41.</span>
Answer:

Step-by-step explanation:
Let be
, the range of the function corresponds to the set of values of
. The sine function is a bounded function between -1 and 1. Hence, the range of the function is:
