A movie theater has a seating capacity of 179. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults.
2 answers:
Answer:
31 adults, 62 children, and 86 students.
Step-by-step explanation:
The seating capacity of the movie theatre = 179
- c+s+a=179
Children's(c) Ticket = $5.00
Student's(s) Tickets = $7.00
Adult's(a) Tickets = $12.00
There are half as many adults as there are children.
The total ticket sales was $1284
- 5c+7s+12a=1284
We then solve the three resulting equations simultaneously.
c+s+a=179
c=2a
5c+7s+12a=1284
We substitute c=2a into the first and third equation
Substitute s=179-3a into 22a+7s=1284
Recall:
c=2a
c=2*31
c=62
Finally:
c+s+a=179
62+s+31=179
s=179-62-31
s=86.
Therefore:
31 adults, 62 children, and 86 students attended the movie theatre.
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Answer:
(a) 0.343
(b) 0.657
(c) 0.189
(d) 0.216
(e) 0.353
Step-by-step explanation:
Let P(a vehicle passing the test) = p
Let P(a vehicle not passing the test) = q
q = 1 - p
q = 1 - 0.7 = 0.3
(a) P(all of the next three vehicles inspected pass) = P(ppp)
= 0.7 × 0.7 × 0.7
= 0.343
(b) P(at least one of the next three inspected fails) = P(qpp or qqp or pqp or pqq or ppq or qpq or qqq)
= (0.3 × 0.7 × 0.7) + (0.3 × 0.3 × 0.7) + (0.7 × 0.3 × 0.7) + (0.7 × 0.3 × 0.3) + (0.7 × 0.7 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.3)
= 0.147 + 0.063 + 0.147 + 0.063 + 0.147 + 0.063 + 0.027
= 0.657
(c) P(exactly one of the next three inspected passes) = P(pqq or qpq or qqp)
= (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7)
= 0.063 + 0.063 + 0.063
= 0.189
(d) P(at most one of the next three vehicles inspected passes) = P(pqq or qpq or qqp or qqq)
= (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7) + (0.3 × 0.3 × 0.3)
= 0.063 + 0.063 + 0.063 + 0.027
= 0.216
(e) Given that at least one of the next 3 vehicles passes inspection, what is the probability that all 3 pass (a conditional probability)?
P(at least one of the next three vehicles inspected passes) = P(ppp or ppq or pqp or qpp or pqq or qpq or qqp)
= (0.7 × 0.7 × 0.7) + (0.7 × 0.7 × 0.3) + (0.7 × 0.3 × 0.7) + (0.3 × 0.7 × 0.7) + (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7)
= 0.343 + 0.147 + 0.147 + 0.147 + 0.063 + 0.063 + 0.063
= 0.973
With the condition that at least one of the next 3 vehicles passes inspection, the probability that all 3 pass is,
= 0.353
Answer:
c = 50
Step-by-step explanation:
Using the Pythagorean Theorem:
Plug in the values of a = 14, and b = 48