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larisa86 [58]
1 year ago
6

ali goes for cycle ride. he starts at 3pm . he finished at 5 38pm .he has a total of 25 minutes rest during the ride. how long h

e spends cycling?
Mathematics
1 answer:
nordsb [41]1 year ago
4 0

Answer:

two hours and thirteen minutes.

Step-by-step explanation:

count up from 3pm to 5pm to start with. That gives you two hours

we already have 38 minutes, now just subtract the 25 minutes he spent resting.

That leaves you with 2 hours and 13 minutes.

Correct me if I'm wrong I'm currently responding to this at a major lack of sleep lol

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Given a right triangle with hypothenus of measure 34, the side opposite the angle θ of measure 30, and the side adjacent the angle theta of measure 16.

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The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.80. It is also known that P(A1 ∩ A2) = 0. Suppose P(
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Answer:

(a) A_1 and A_2 are indeed mutually-exclusive.

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(c) \displaystyle P(B) = \frac{9}{100}.

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Step-by-step explanation:

<h3>(a)</h3>

P(A_1 \; \cap \; A_2) = 0 means that it is impossible for events A_1 and A_2 to happen at the same time. Therefore, event A_1 and A_2 are mutually-exclusive.

<h3>(b)</h3>

By the definition of conditional probability:

\displaystyle P(B \; | \; A_1) = \frac{P(B \; \cap \; A_1)}{P(B)} = \frac{P(A_1 \; \cap \; B)}{P(B)}.

Rearrange to obtain:

\displaystyle P(A_1 \; \cap \; B) = P(B \; |\; A_1) \cdot  P(A_1) = 0.25 \times 0.20 = \frac{1}{20}.

Similarly:

\displaystyle P(A_2 \; \cap \; B) = P(B \; |\; A_2) \cdot  P(A_2) = 0.80 \times 0.05 = \frac{1}{25}.

<h3>(c)</h3>

Note that:

\begin{aligned}P(A_1 \; \cup \; A_2) &= P(A_1) + P(A_2) - P(A_1 \; \cap \; A_2) = 0.20 + 0.80 = 1\end{aligned}.

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<h3>(d)</h3>

By Bayes' Theorem:

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\begin{aligned} P(A_2 \; |\; B) &= \frac{P(B \; | \; A_2) \cdot P(A_2)}{P(B)} \\ &= \frac{0.05 \times 0.80}{9/100} = \frac{0.04 \times 100}{9} = \frac{4}{9}\end{aligned}.

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They'll reach the same population in approximately 113.24 years.

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