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mezya [45]
3 years ago
15

A lawyer owns 4 pairs of pants, 5 dress shirts and 6 ties. How many days can the lawyer go without wearing the same combination

of three items?
Mathematics
2 answers:
Naddik [55]3 years ago
8 0

Answer: 4 × 5 × 6 = 120

Explanation:

1) This is a direct use of the counting principle, which states that the number of different ways a combination of independent events can happen is equal to the product of the number of different outcomes for each event.

That is, if event A can have m different outcomes, event B can have n different outcomes, and event C can have p different outcomes, the total number of different combinations is m × n × p.

2) In this case, the lawyer can use 4 different pais of pants, 5 different shirts, and 6 different ties, so the number of different combinations of the three items is: 4 × 5 × 6 = 120.

3) You can see that if you make a diagram (may be a tree diagram).

With that you can see that each pair of pants, can go with 5 shirts, which make 4 × 5 different couples of pants - shirts. After that, each different couple of pants - shirts can go with 6 different ties, so you have 4 × 5 × 6 three-piece combinations.

RideAnS [48]3 years ago
7 0
6 x 4 x 5 = 120 days

Answer is 120 days.
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Step-by-step explanation:

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Nick does not has enough money to follow this recommendation.

Step-by-step explanation:

Given: A self-service car wash charges $4 for the initial 5 minutes plus an additional $0.75 for each minute after that.

Let y be the cost for car wash for m minutes then

y=4+0.75(m-5) such that at m= 5 , y=4 which is the cost for car wash (dollars) for first 5 minutes.

Also, A car enthusiast magazine recommends spending at least 15 minutes to properly wash a car.

For m\geq15

\\\Rightarrow\ y=4+0.75(m-5)\geq4+0.75(15-5)\\\Rightarrow\ y\geq4+0.75(10)\\\Rightarrow\ y\geq4+7.5\\\Rightarrow\ y\geq11.5

But Nick has $10 which is less than $11.5, so he does not has enough money to follow this recommendation.

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Step-by-step explanation:

The trigonometric ratio for cosine is given as follows;

Cos(\theta) = \dfrac{Adjacent\, side \, to\,  angle}{Hypothenus\, side \, length \ of\, the \  triangle}

7. The adjacent leg length to ∠X = 27

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8. The adjacent leg length to ∠X = 15

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∴ cos(Y) = 13·√3/26 = (√3)/2 ≈ 0.8660

cos(Y) = (√3)/2 ≈ 0.8660.

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