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harina [27]
3 years ago
9

A contractor is paving 1 mile 201.25 yards of a county road. How long is this portion of the road in feet and inches?

Mathematics
1 answer:
Natali5045456 [20]3 years ago
5 0

A contractor is paving 1 mile 201.25 yards of a county road

Given distance is 1 mile and 201.25 yards

First we will convert 1 mile in feet.

1 mile = 5280 feet

Now we will convert 201.25 yards in feet

1 yard = 3 ft

201.25 yards = 201.25\times3=603.75 feet

So total distance in feet is = 5280+603.75 = 5883.75 feet

1 foot = 12 inches

0.75 feet = 12\times0.75=9 inches

This is 5883 feet and 9 inches.


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Four cards are dealt from a standard fifty-two-card poker deck. What is the probability that all four are aces given that at lea
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Answer:

The probability is 0.0052

Step-by-step explanation:

Let's call A the event that the four cards are aces, B the event that at least three are aces. So, the probability P(A/B) that all four are aces given that at least three are aces is calculated as:

P(A/B) =  P(A∩B)/P(B)

The probability P(B) that at least three are aces is the sum of the following probabilities:

  • The four card are aces: This is one hand from the 270,725 differents sets of four cards, so the probability is 1/270,725
  • There are exactly 3 aces: we need to calculated how many hands have exactly 3 aces, so we are going to calculate de number of combinations or ways in which we can select k elements from a group of n elements. This can be calculated as:

nCk=\frac{n!}{k!(n-k)!}

So, the number of ways to select exactly 3 aces is:

4C3*48C1=\frac{4!}{3!(4-3)!}*\frac{48!}{1!(48-1)!}=192

Because we are going to select 3 aces from the 4 in the poker deck and we are going to select 1 card from the 48 that aren't aces. So the probability in this case is 192/270,725

Then, the probability P(B) that at least three are aces is:

P(B)=\frac{1}{270,725} +\frac{192}{270,725} =\frac{193}{270,725}

On the other hand the probability P(A∩B) that the four cards are aces and at least three are aces is equal to the probability that the four card are aces, so:

P(A∩B) = 1/270,725

Finally, the probability P(A/B) that all four are aces given that at least three are aces is:

P=\frac{1/270,725}{193/270,725} =\frac{1}{193}=0.0052

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