The City Housing Authority has received 50 applications from qualified applicants for eight low-income apartments. Three of the
2 answers:
The probability that both specific qualified applicants will be among the eight selected is given by:
The probability that the two will get apartments on the North side is given by:
The probability that the two will get apartments on the South side is given by:
The events '2 apartments on North side' and '2 apartments on South side' are mutually exclusive. Therefore the probability the two specific qualified applicants will be on the same side of town is 0.107 + 0.357 = 0.464.
Finally, the probability that two specific qualified applicants will be selected for apartments on the same side of town is found from:
The probability that the two will get apartments on the North side is given by:
The probability that the two will get apartments on the South side is given by:
The events '2 apartments on North side' and '2 apartments on South side' are mutually exclusive. Therefore the probability the two specific qualified applicants will be on the same side of town is 0.107 + 0.357 = 0.464.
Finally, the probability that two specific qualified applicants will be selected for apartments on the same side of town is found from:
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Answer:
<u>Problem 1:</u>
x = 12 unit ; y = 120 ; z = 60 ; perimeter = 58 unit
<u>Problem 2:</u>
FG = 16 unit ; EG = 2√153 unit ; y = 5 unit
Step-by-step explanation:
<u>Problem 1</u>
Since ABCD is a parallelogram. so,
∠ABC = ∠ADC [Since opposite angles of a parallelogram are equal]
but, ∠ADC = 120° [given]------------(1)
So, ∠ ABC = y° = 120° ----------------(2)
Again, sum of two consecutive angles of a parallelogram is, 180°, so,
∠BCD + ∠ADC = 180°
So, ∠BCD =z° = 180° - 120° = 60° [Putting the value of ∠ADC from (1)]-----(3)
Again, since opposite sides of a parallelogram are equal,
so, BC = AD
⇒ (x + 5) = 17
⇒ x = 12------------------------(4)
So, AB = 12 unit , AD = 17 unit
So, the perimeter of the parallelogram is given by,
2(AB + AD)
= unit
= 58 unit --------------------------------------------------------------(5)
<u>Problem 2</u>
Perimeter of parallelogram EFGH = 52 unit
So, 2(EH + GH) = 52 unit
⇒ 2 ( x + x + 6) = 52
⇒ 4x = 40
⇒ x = 10
Now, FG = EH [since opposite sides of a parallelogram are equal]
= (x + 6) unit
= (10 + 6) unit = 16 unit ------------------------------(1)
Again for a parallelogram, the diagonals bisect each other.
so, EG =
= 2√153 unit -----------------------------------------(2)
and,
3y - 10 = y
⇒ y = 5 -----------------------------------------------(3)