Answer: each guest gets 4.19 cm²
Step-by-step explanation:
The cake is a circle. The area which he cuts for himself is a sector with a central angle of 120 degrees. The formula for determining the area of a sector is expressed as
Area of sector = θ/360 × πr²
Where
θ represents the central angle
π is a constant whose value is 3.14
r represents the radius of the circle.
From the diagram,
r = 4cm
Therefore, area of the cake that he cut for himself is
120/360 × 3.14 × 4²
= 16.75 cm²
The total area of the cake is
3.14 × 4² = 50.24 cm²
Therefore, the rest of the cake is
50.24 - 16.75 = 33.49 cm²
The amount that each guest gets would be
33.49/8 = 4.19 cm²
If the question is, "What is the scale factor." That would be a scale (factor) of 2.
Answer:
C. m∠4 = m∠8
D. m∠2 = m∠7
Step-by-step explanation:
Here, we use the principles of alternate angles, corresponding angles and vertically opposite angles to confirm which of the statements are true. Alternate angles are always equal, corresponding angles are equal, likewise vertically opposite angles.
From the given question, it was given that a is parallel to b. Thus, it can be observed and deduced that;
m∠4 = m∠8 (corresponding angles)
and
m∠2 = m∠3 (vertically opposite angles)
m∠3 = m∠7 (corresponding angles)
So that,
m∠2 = m∠7
Thus in the question, statements C and D are true.
Answer:
5.98
Step-by-step explanation:
The probability that a randomly selected professor is female and feels "About Right" is 0.40
The distribution table :
____About right _ Oweight _ Uweight __ Total
Female _ 80 _____ 39 ______ 3 _______ 122
Male ___ 52 _____ 10 ______ 16 _______ 88
Total ___ 132 ____ 49 ______ 19 _______ 200
Oweight = Overweight
Uweight = Underweight
Recall :
Probability = required outcome / Total possible outcomes
Probability that a selected professor is female and feels 'About right' :
Required outcome = number of female professors who feels 'About right' = 80
Total number of professors = 200
Hence,
P(Female and 'About right') = 80/200 = 0.40
Learn more : brainly.com/question/11234923
