Section B: Multiples and factors 1. Why is the number 17 classified as a prime number?
2 answers:
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Answer: Chris reached Boston at 10:24 a.m.
Explanation:
Since we have given that
Speed at which Chris ran from Newton to Boston = 15 km/h
Speed at which Goffy ran from Newton to Boston = 12 km/h
Time at which both started = 10:00 a.m.
Time at which Goffy reached Boston = 10:30 a.m.
That means Goffy takes half an hour to reach Boston,
so, Distance between Newton and Boston is given by
So, Time taken by Chris to ran from Newton and Boston is given by
So, Chris reached Boston at 10:24 a.m.
Answer:
(a) The probability that the second part is the one with excessive shrinkage is 0.2000.
(b) The probability that the third part is the one with excessive shrinkage is 0.2000.
Step-by-step explanation:
Let the variable <em>X </em>ₙ denote the <em>n</em>th part that has suffered excessive shrinkage.
(a)
It is provided that two parts are selected at random.
The parts are selected without replacement.
Now, for the two parts selected it is possible that either both have excessive shrinkage or only the second part has excessive shrinkage.
The probability that the second part is the one with excessive shrinkage is:
P (X₂) = P (X₂ ∩ X₁) + P (X₂ ∩ X₁')
(without replacement)
Thus, the probability that the second part is the one with excessive shrinkage is 0.2000.
(b)
It is provided that three parts are selected at random.
The parts are selected without replacement.
Now, for the three parts selected it is possible that either all three have excessive shrinkage or any two of the three has excessive shrinkage or only the third part has excessive shrinkage.
The probability that the third part is the one with excessive shrinkage is:
P (X₃) = P (X₃ ∩ X₂ ∩ X₁) + P (X₃ ∩ X₂ ∩ X₁')
+ P (X₃ ∩ X₂' ∩ X₁) + P (X₃ ∩ X₂' ∩ X₁')
Thus, the probability that the third part is the one with excessive shrinkage is 0.2000.