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lesya692 [45]
1 year ago
3

A family has a day of 7 activities planned: shopping, picnic, hiking, swimming, bike ride, video games, and movie. To make it mo

re adventurous they decide to randomly pick the order of the activities out of a hat. Find the probability that bike ride and movie are chosen consecutively, in either order.
Mathematics
1 answer:
timama [110]1 year ago
4 0

Answer:

Pr= \frac{1}{21}

Step-by-step explanation:

Given

n(S) = 7 --- number of games

Required

Probability of bike and movie in consecutive order

This probability is represented as:

Pr = P(Bike\ and\ Movie) \ or\ P(Movie\ or\ Bike)

So, we have:

Pr = P(Bike\ and\ Movie) \ +\ P(Movie\ or\ Bike)

The probability is an illustration of selection without replacement;

So, we have:

P(Bike\ and\ Movie) = P(Bike) * P(Movie)

P(Bike\ and\ Movie) = \frac{n(Bike)}{n(S)} * \frac{n(Movie)}{n(S) - 1} ---- without replacement

Bike and Movie appear in the game list 1 time.

So, the equation becomes

P(Bike\ and\ Movie) = \frac{1}{7} * \frac{1}{7 - 1}

P(Bike\ and\ Movie) = \frac{1}{7} * \frac{1}{6}

P(Bike\ and\ Movie) = \frac{1}{42}

Similarly,

P(Movie\ and\ Bike) = \frac{1}{42}

So, we have:

Pr = P(Bike\ and\ Movie) \ +\ P(Movie\ or\ Bike)

Pr= \frac{1}{42}+\frac{1}{42}

Take LCM

Pr= \frac{1+1}{42}

Pr= \frac{2}{42}

Pr= \frac{1}{21}

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Answer:

the base of the ladder is 27.89  ft away from the building

Step-by-step explanation:

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cos(\theta)=\frac{adjacent}{hypotenuse} \\cos(29.37^o)=\frac{x}{32\,\,ft}\\32 \,\,cos(29.37^o)\,\,ft=x\\x=27.887\,\,ft

which rounded to the nearest hundredth gives;

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2 years ago
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Using sin rule:
a/sin A =b/sin B=c/sin c
SIN A=sin 46=0.72
THEN:sin B =(0.72*26)/33=0.57
then B= 34° 
AS the sum of triangle angles=180 
then C=180-(46+34)=100°
then c =(a*sin C)/sin A
sin C=sin 100=0.98
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Use equation A=P(1-r)^{t}

Question 1: Need to find A:
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Question 2: Need to find t, use LOGARITHM:
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