Answer:
- The shaded region is 9.83 cm²
Step-by-step explanation:
<em>Refer to attached diagram with added details.</em>
<h2>Given </h2>
Circle O with:
- OA = OB = OD - radius
- OC = OD = 2 cm
<h2>To find</h2>
<h2>Solution</h2>
Since r = OC + CD, the radius is 4 cm.
Consider right triangles OAC or OBC:
- They have one leg of 2 cm and hypotenuse of 4 cm, so the hypotenuse is twice the short leg.
Recall the property of 30°x60°x90° triangle:
- a : b : c = 1 : √3 : 2, where a- short leg, b- long leg, c- hypotenuse.
It means OC: OA = 1 : 2, so angles AOC and BOC are both 60° as adjacent to short legs.
In order to find the shaded area we need to find the area of sector OADB and subtract the area of triangle OAB.
Area of <u>sector:</u>
- A = π(θ/360)r², where θ- central angle,
- A = π*((mAOC + mBOC)/360)*r²,
- A = π*((60 + 60)/360))(4²) = 16.76 cm².
Area of<u> triangle AO</u>B:
- A = (1/2)*OC*(AC + BC), AC = BC = OC√3 according to the property of 30x60x90 triangle.
- A = (1/2)(2*2√3)*2 = 4√3 = 6.93 cm²
The shaded area is:
- A = 16.76 - 6.93 = 9.83 cm²
308 slices would be sold.
38*8= 304, plus 4 slices in half a pizza makes 308 slices.
Answer:
The statement in the question is wrong. The series actually diverges.
Step-by-step explanation:
We compute
Therefore, by the series divergence test, the series 
diverges.
EDIT: To VectorFundament120, if 
is a sequence, both 
and 
are common notation for its limit. The former is not wrong but I have switched to the latter if that helps.
Answer:
a) 47.55
b) 58
c) 47.88
Step-by-step explanation:
Given that the size of the orders is uniformly distributed over the interval
$25 ( a ) to $80 ( b )
<u>a) Determine the value for the first order size generated based on 0.41</u>
parameter for normal distribution is given as ; a = 25, b = 80
size/value of order = a + random number ( b - a )
= 25 + 0.41 ( 80 - 25 )
= 47.55
<u>b) Value of the last order generated based on random number (0.6)</u>
= a + random number ( b - a )
= 25 + 0.6 ( 80 - 25 )
= 25 + 33 = 58
<u>c) Average order size </u>
= ∑ order 1 + order 2 + ----- + order 10 ) / 10
= (47.55 + ...... + 58 ) / 10
= 478.8 / 10 = 47.88
