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den301095 [7]
3 years ago
15

The route used by a certain motorist in commuting to workcontains two intersections with traffic signals. The probabilitythat he

must stop at the first signal is .4, the analogousprobability for the second signal is .5, and the probability thathe must stop at least one of the two signals is .6. What is theprobability that he must stop.
a.) At both signals?

b.) At the first signal but not at the second one?

c.) At exactly on signal?

Mathematics
2 answers:
Masja [62]3 years ago
8 0

Answer:

a) 0.3

b) 0.1

c) 0.3

Step-by-step explanation:

Lets call:

a = stop at first signal,  b = stop at second signal

The data we are given is P(a) = 0.4, and P(b)=0.5

Stoping at least at one is the event (a or b) = a ∪ b

P(a U b) = 0.6 is the other data we are given

a) Stoping at both signals is the event (a and b = a ∩ b)

The laws of probability say that:

P(a ∪ b)= P(a) + P(b) - P( a ∩ b) = 0.4 + 0.5  - P( a ∩ b) = 0.6

Then we get P( a ∩ b) = 0.3

b) The event is (a and not b) = a ∩(¬b).

P( a ∩(¬b) ) = P(a) - P( a ∩ b) = 0.1

c) The event is (a or b) without the cases in which (a and b)

P(a ∪ b) - P( a ∩ b) = 0.3

The Venn diagram can help you understand how the events are related to each other

zavuch27 [327]3 years ago
7 0

Answer:

a) 0.2

b) 0.2

c) 0.5

Step-by-step explanation:

Let S be the event "the car stops at the signal.

In the attached figure you can see a tree describing all possible scenarios.

For the first question the red path describes stopping at the first light but not stopping at the second. We can determine the probability of this path happening by multiplying the probabilities on the branches of the tree, thus

P(a)=0.4\times0.5=0.2

For the second one the blue path describes the situation

P(b)=0.4\times 0.5=0.2

For the las situation the sum of the two green path will give us the answer

P(c)=0.6\times 0.5 + 0.4\times 0.5=0.3+0.2=0.5

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Step-by-step explanation:

It is given that,

A 2-liter bottle of juice costs $2.80.

It means that 1 liter bottle of juice costs $1.4.

A box containing six 12-liter bottles sells for $3.90.  

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It is clear that "A box containing six 12-liter bottles sells for $3.90." have higher cost per liter. Its cost is $0.05416 per liter. Hence, the correct option is (D).

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3 years ago
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4.45*10 to the second power

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Evaluate the equation. -4x = 14 A.10 B. 7/2 C. -7/2 D. -10
Alex_Xolod [135]

Answer:

c) -7/2

Step-by-step explanation:

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How do you find the equations of the vertical and horizontal asymptotes for a graph when you only have the graph and no function
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Answer:

See below for answer and explanations (as well as an attached graph)

Step-by-step explanation:

Pay attention to the behavior of the asymptotes. If the asymptotes are approaching a certain x-value or y-value, then that value is undefined for the function.

Take for example y=\frac{1}{x}:

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See the graph for a visual.

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2 years ago
Solve the system and give your answer as a coordinate point in the form (k, c) k+c=100 51k+11c=2500
Aleks [24]

Answer:

k = 35, c = 65

Step-by-step explanation:

Solve the following system:

{c + k = 100 | (equation 1)

{11 c + 51 k = 2500 | (equation 2)

Swap equation 1 with equation 2:

{11 c + 51 k = 2500 | (equation 1)

{c + k = 100 | (equation 2)

Subtract 1/11 × (equation 1) from equation 2:

{11 c + 51 k = 2500 | (equation 1)

{0 c - (40 k)/11 = -1400/11 | (equation 2)

Multiply equation 2 by -11/40:

{11 c + 51 k = 2500 | (equation 1)

{0 c+k = 35 | (equation 2)

Subtract 51 × (equation 2) from equation 1:

{11 c+0 k = 715 | (equation 1)

{0 c+k = 35 | (equation 2)

Divide equation 1 by 11:

{c+0 k = 65 | (equation 1)

{0 c+k = 35 | (equation 2)

Collect results:

Answer: {c = 65 , k = 35

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