Answer:
a) 0.857
b) 0.571
c) 1
Step-by-step explanation:
Based on the data given, we have
- 18 juniors
- 10 seniors
- 6 female seniors
- 10-6 = 4 male seniors
- 12 junior males
- 18-12 = 6 junior female
- 6+6 = 12 female
- 4+12 = 16 male
- A total of 28 students
The probability of each union of events is obtained by summing the probabilities of the separated events and substracting the intersection. I will abbreviate female by F, junior by J, male by M, senior by S. We have
- P(J U F) = P(J) + P(F) - P(JF) = 18/28+12/28-6/28 = 24/28 = 0.857
- P(S U F) = P(S) + P(F) - P(SF) = 10/28 + 12/28 - 6/28 = 16/28 = 0.571
- P(J U S) = P(J) + P(S) - P(JS) = 18/28 + 10/28 - 0 = 1
Note that a student cant be Junior and Senior at the same time, so the probability of the combined event is 0. The probability of the union is 1 because every student is either Junior or Senior.
Answer:
C
Step-by-step explanation:
The Hypotenuse is y
The side opposite the given angle (60o) is 12.
You must use one of the trig functions to relate the angle, the side opposite and the hypotenuse.
It turns out that the function you need to use is the sine.
angle = 60o
Side opposite = 12 cm
hypotenuse = h = ???
Sin(60o) = opposite / hypotenuse multiply both sides by the hypotenuse.
hypotenuse * sin(60o) = side opposite
Divide by sin(60o)
hypotenuse = side opposite / sin(60)
hypotenuse = 12/sin(60)
Sin(60) radical form = sqrt(3)/2
hypotenuse = 12 // sqrt(3)/2
hypotenuse = 24 // sqrt(3) Rationalize the denominator.
hypotenuse = 24 * sqrt(3) // ( (sqrt(3)*sqrt(3) )
hypotenuse = 8 sqrt(3)
C
Answer:
It has two solutions.
Step-by-step explanation:
Let as consider the given options are
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
The given equation is
Multiply both sides by 4z(4z-3).
It is a quadratic equation.
Therefore, it has two solutions.
Answer: c
Step-by-step explanation:
Answer:
672
Step-by-step explanation:
If there must be at least 4 people in each group, then the number of people in the group for tennis must be 4, 5, or 6.
There are
(10/k)=(10!)/(k!(10−k)!)
ways of choosing k people from a group of 10, and so there are
(10/4)+(10/5)+(10/6)=(10!)/(4!6!)+(10!)/(5!5!)+(10!)/(6!4!)
=2×(10×9×8×7)/(4×3×2×1)+(10×9×8×7×6)/(5×4×3×2×1)
=2×(10×3×1×7)/(1×1×1×1)+(1×3×2×7×6)/(1×1×1×1×1) =420+252=672
