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tangare [24]
3 years ago
11

Mary and tom park their cars in an empty parking lot with n ≥ 2 consecutive parking spaces (i.e, n spaces in a row, where only o

ne car fits in each space). mary and tom pick parking spaces at random. (all pairs of distinct parking spaces are equally likely.) what is the probability that there is at most one empty parking space between them?
Mathematics
1 answer:
Luda [366]3 years ago
5 0

Answer:

  p(at most one space between) = (4n-6)/(n(n-1))

Step-by-step explanation:

There are n-1 ways the cars can be parked next to each other, and n-2 ways they can be parked with one empty space between. So, the total number of ways the cars can be parked with at most one empty space is ...

  (n -1) +(n -2) = 2n-3

The number of ways that 2 cars can be parked in n spaces is ...

  (n)(n -1)/2

So, the probability is ...

  (2n-3)/((n(n-1)/2) = (4n -6)/(n(n -1))

___

If the cars are considered distinguishable and order matters, then the number of ways they can be parked will double. The factor of 2 cancels in the final probability ratio, so the answer remains the same.

__

<em>Check</em>

For n=2 or 3, p=1 as you expect.

For n=4, p=5/6, since there is only one of the 6 ways the cars can be parked that has 2 spaces between.

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astra-53 [7]

Answer: C

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
A bank loaned out ​$​12,00, part of it at the rate of 9% per year and the rest at 19% per year. If the interest received in one
Crazy boy [7]

Answer:

$7,800 was invested at 9% and $4,200 at 19%.

Step-by-step explanation:

Given that a bank loaned out $ 12,000, part of it at the rate of 9% per year and the rest at 19% per year, if the interest received in one year totaled $ 1,500, to determine how much was loaned at 9% the following calculation must be performed:

12,000 x 0.09 + 0 x 0.19 = 1,080

10,000 x 0.09 + 2,000 x 0.19 = 1,280

8,000 x 0.09 + 4,000 x 0.19 = 1,480

7,900 x 0.09 + 4,100 x 0.19 = 1,490

7,800 x 0.09 + 4,200 x 0.19 = 1,500

Thus, $ 7,800 was invested at 9% and $ 4,200 at 19%.

6 0
2 years ago
alex is building a circular base for a fountain. The radius of the circle is 4 ft. what is the area of the base ?
romanna [79]
The area of a circle is measure by
A=pi(r)^2
So we would do
Area= pi(4)^
ANSWER
Area=16pi
Area is about=50.24 if using 3.14 as pi
7 0
3 years ago
Can someone please help me on this question?
solniwko [45]

ANSWER:

According to question, our g(x) becomes f(x) - 5.

When x = 1,

f(x) - 5 = 5 - 5 = 0.

When x = 2,

f(x) - 5 = 7 - 5 = 2.

When x = 3,

f(x) - 5 = 11 - 5 = 6.

When x = 4,

f(x) - 5 = 19 - 5 = 14.

So, <u>Correct choice</u> - [D]

4 0
2 years ago
A train ticket was £4.50. The price then increased by 3%. What price is the train ticket now
mihalych1998 [28]

0.14 pounds (rounded; 0.135 unrounded); To calculate the % of something, divide it by 100 and multiply the result by the percentage you want to find.

0.0450 (=1%)

0.0450 x 3 = 0.135


8 0
3 years ago
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