Answer:
n=40 boys
Step-by-step explanation:
-Margin of error is given by the formula:
-The z score for a probability of 92% is 1.75
#We make n the subject of the formula and substitute at a 92% confidence:
![E=z\frac{\sigma}{\sqrt{n}}\\\\\sqrt{n}=\frac{z\sigma}{E}\\\\n=[\frac{z\sigma}{E}]^2\\\\\therefore n=[\frac{1.75\times 1.8}{0.5}]^2\\\\=39.69\approx 40](https://tex.z-dn.net/?f=E%3Dz%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%5C%5C%5C%5C%5Csqrt%7Bn%7D%3D%5Cfrac%7Bz%5Csigma%7D%7BE%7D%5C%5C%5C%5Cn%3D%5B%5Cfrac%7Bz%5Csigma%7D%7BE%7D%5D%5E2%5C%5C%5C%5C%5Ctherefore%20n%3D%5B%5Cfrac%7B1.75%5Ctimes%201.8%7D%7B0.5%7D%5D%5E2%5C%5C%5C%5C%3D39.69%5Capprox%2040)
Hence, he needs approximately 40 boys for the study
Answer:
Is that the full question?
Step-by-step explanation:
Answer:
Step-by-step explanation:
The formula for determining the area of a square is expressed as
Area = L²
Where
L represents length of each side of the square.
The side of the square is field us 12 meters long. Therefore
Area of the square field = 12² = 144ft²
The formula for determining the area of a circle is expressed as
Area = πr²
Where
r represents radius if the circle.
π is a constant whose value is 3.14
Diameter of the circular area covered by the sprinkler is 12 meters.
Radius = 12/2 = 6 meters.
Area of the field covered by the sprinkler would be
Area = 3.14 × 6² = 113.04ft²
Therefore, the area of the field that is NOT reached by the sprinkler would be
144 - 113.04 = 30.96ft²
He would most likely be referring to kilometers if it is a large area. So D would be your answer.
Answer:
Length= 19cm
Width= 9cm
Step-by-step explanation:
let the length of the rectangle be L cm and its width be W cm.
Perimeter of rectangle= 56cm
2L +2W= 56
L +W= 56 ÷2
L +W= 28
L= 28 -W -----(1)
Area of rectangle= length ×width
LW= 171 -----(2)
Susbt. (1) into (2):
W(28 -W)= 171
28W -W²= 171 <em>(</em><em>expand</em><em>)</em>
W² -28W +171= 0 <em>(</em><em>bring</em><em> </em><em>everything</em><em> </em><em>to</em><em> </em><em>one</em><em> </em><em>side</em><em>)</em>
(W -19)(W-9)= 0 <em>(</em><em>factorise</em><em>)</em>
W-19=0 or W-9=0
W= 19 or W= 9
Subst into (1):
L=28 -19 or L= 28 -9
L=9 or L= 19
Since we usually take the longer side of the rectangle to be its length, L= 19 and hence W=9.
Therefore its length is 19cm and its width is 9cm.
