Answer:
<h3>
- The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth. </h3><h3>
- The area of the shaded sector depends on the length of the radius. </h3><h3>
- The area of the shaded sector depends on the area of the circle</h3>
Step-by-step explanation:
Given central angle PQR = 45°
Total angle in a circle = 360°
Ratio of the measure of central angle PQR to the measure of the entire circle is
. This shows ratio that <u>the measure of central angle PQR to the measure of the entire circle is one-eighth</u>.
Area of a sector = 
= central angle (in degree) = 45°
r = radius of the circle = 6
Area of the sector

<u>The ratio of the shaded sector is 4.5πunits² not 4units²</u>
From the formula, it can be seen that the ratio of the central angle to that of the circle is multiplied by area of the circle, this shows <u>that area of the shaded sector depends on the length of the radius and the area of the circle.</u>
Since Area of the circle = πr²
Area of the circle = 36πunits²
The ratio of the area of the shaded sector to the area of the circle = 
For length of an arc

ratio of the length of the arc to the area of the circle = 
It is therefore seen that the ratio of the area of the shaded sector to the area of the circle IS NOT equal to the ratio of the length of the arc to the area of the circle
This is the concept of sinusoidal, to solve the question we proceed as follows;
Using the formula;
g(t)=offset+A*sin[(2πt)/T+Delay]
From sinusoidal theory, the time from trough to crest is normally half the period of the wave form. Such that T=2.5
The pick magnitude is given by:
Trough-Crest=
2.1-1.5=0.6 m
amplitude=1/2(Trough-Crest)
=1/2*0.6
=0.3
The offset to the center of the circle is 0.3+1.5=1.8
Since the delay is at -π/2 the wave will start at the trough at [time,t=0]
substituting the above in our formula we get:
g(t)=1.8+(0.3)sin[(2*π*t)/2.5]-π/2]
g(t)=1.8+0.3sin[(0.8πt)/T-π/2]
Answer: 0.0026
Step-by-step explanation:
Given: Mean : 
Standard Deviation : 
Sample size : 
Formula to calculate z-score :-

For X=7.6 hours.


Hence, the probability that their mean rebuild time is less than 7.6 hours = 0.0026