The probability that the person uses exactly one of the facilities = 95/130 .
<h3>What is Probability ?</h3>
Probability is the branch of Mathematics which helps to determine the likeliness of an event to happen.
The data is given and the probability that the person uses exactly one of the facilities is asked
73 people use the gym. P(G)
62 people use the swimming pool. P (S)
58 people use the track. P (T)
22 people use the gym and the pool. P (G ∩ P)
29 people use the pool and the track. P (P ∩ T)
25 people use the gym and the track. P (G ∩ T)
11 people use all three facilities. P (P∩G∩T)
P (PUGUT) = P(G) + P (S) + P (T) - P (G ∩ P) - P (P ∩ T) - P (G ∩ T) - 2 P (P∩G∩T)
73 + 62 + 58 -22-29-25 -11-11 = 95
The probability that the person uses exactly one of the facilities = 95/130 .
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Very easy!
6 people= 12 servings so 1 person= 2 servings
We have 112 people so we need 112 x 2= 224 servings
So she will make 224 servings with an 8 servings pan, 224/8= 28 pans.
The minimum number of pans she need in order to serve 112 people is 28 pans!
<h3>
Answer: 42</h3>
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Work Shown:
The two angle bisectors intersect to form the incenter. The incenter is the center of the inscribed circle (aka "incircle"). This circle is the largest possible, but is completely inside the triangle. No portions of the circle spill outside the triangle.
The two segments marked with lengths x+8 and 2x-5 are two radii of the incircle. This is because the sides of the triangle are tangent to the incircle.
Since all radii are the same length, we can set those expressions equal to one another and solve for x
x+8 = 2x-5
x-2x = -5-8
-x = -13
x = 13
This x value then leads to
- x+8 = 13+8 = 21
- 2x-5 = 2*13-5 = 26-5 = 21
Both radii are 21 units long, which helps confirm we have the proper x value. We double the length of the radius ot get the diameter.
So the diameter of the incircle is 2*21 = 42 units long.
Answer:
Break-even point in units= 20,000
Step-by-step explanation:
Giving the following information:
Selling price per unit= $29.99
Unitary variable cost= $14.25
Fixed costs= $314,800
<u>To calculate the break-even point in units, we need to use the following formula:</u>
Break-even point in units= fixed costs/ contribution margin per unit
Break-even point in units= 314,800 / (29.99 - 14.25)
Break-even point in units= 20,000