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Amanda [17]
3 years ago
13

There are 52 runners in a race. How many ways can the runners finish​ first, second, and​ third?

Mathematics
1 answer:
elena55 [62]3 years ago
5 0

Answer:

126

Step-by-step explanation:

52 * 3 = 126

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Please help me 30 points please help me
Romashka [77]

Answer:

y = + 1x - 4y

Step-by-step explanation:

This could be the wrong way of writing it but thats the pattern ❤

4 0
2 years ago
A five​-digit number starts with a number between 4​-9 in the first​ position, with no restrictions on the remaining 4 digits. a
Maurinko [17]

Answer:

(a) Pr = 0.3024

(b) Pr = 0.6976

(c) Pr = \frac{^9P_{n-1}}{10^{n-1}}

Step-by-step explanation:

Given

Start = \{5,6,7,8\} i.e. between 4 and 9

n(Start) =4

Digits = 5

Solving (a): Probability that each of the 5 digit are different

Since there is no restriction;

The total possible selection is as follows:

First\ digit = 4 (i.e. any of the 4 start digits)

Second\ digit = 10\\ (i.e. any of the 10 digits 0 - 9)

Third\ digit = 10 (i.e. any of the 10 digits 0 - 9)

Fourth\ digit = 10 (i.e. any of the 10 digits 0 - 9)

Fifth\ digit = 10 (i.e. any of the 10 digits 0 - 9)

So, the total is:

Total = 4 * 10 * 10 * 10 * 10

Total = 40000

For selection that all digits are different, the selection is:

First\ digit = 4 (i.e. any of the 4 start digits)

Second\ digit = 9 (i.e. any of the remaining 9)

Third\ digit = 8 (i.e. any of the remaining 8)

Fourth\ digit = 7 (i.e. any of the remaining 7)

Fifth\ digit = 6 (i.e. any of the remaining 6)

So:

Selection =4 * 9 * 8 * 7 * 6

Selection =12096

So, the probability is:

Pr = \frac{Selection}{Total}

Pr = \frac{12096}{40000}

Pr = 0.3024

Solving (b): At least 1 repeated digit

The probability calculated in (a) is the all digits are different i.e. P(None)

So, using laws of complement

We have:

P(At\ least\ 1) = 1 - P(None)

So, we have:

Pr= 1 - 0.3024

Pr = 0.6976

Solving (c): An expression to model the probability.

<em>Using (a) as a point of reference, we have;</em>

Pr = \frac{Selection}{Total}

Where

Selection =4 * 9 * 8 * 7 * 6 ---- for selection of 5 i.e. n = 5

Total = 4 * 10 * 10 * 10 * 10

Selection =4 * 9 * 8 * 7 * 6

This can be rewritten as:

Selection = 4 * ^9P_4

4 can be expressed as: 5 - 1

So, we have:

Selection = (5-1) *^9P_{5-1}

Substitute n for 5

Selection = (n-1) *^9P_{n-1}

Selection = (n-1)^9P_{n-1}

Total = 4 * 10 * 10 * 10 * 10

This can be rewritten as:

Total = 4 * 10^4

Total = (5-1) * 10^{5-1}

Total = (n-1) * 10^{n-1}

Total = (n-1) 10^{n-1}

So, the expression is:

Pr = \frac{(n-1)^9P_{n-1}}{(n-1)10^{n-1}}

Pr = \frac{^9P_{n-1}}{10^{n-1}}

<em>Where n represents the digit number</em>

5 0
3 years ago
When jack went to the movie he paid $8 for his popcorn and $4 for each additional order of popcorn. if i represents the total co
melamori03 [73]
I = 8 + 4x

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8 0
3 years ago
Read 2 more answers
What is 2 3/5 multiplied by 2 as a mixed number or fraction
vivado [14]

Answer:

26/5 or 5 1/5

Step-by-step explanation:

First convert 2 3/5 into an improper fraction:  13/5.

Then multiply this result by 2:  2(13/5) = 26/5.  This is the answer as an improper fraction.

26/5 as a mixed number would be 5 1/5.

6 0
3 years ago
A picture of a cougar is 3/4in long, and the legend below it says 1 : 80. How long is the actual cougar?
stealth61 [152]
Basically the real one is 80 times the picture
80 times 3/4=80/1 times 3/4=240/4=60in=5ft
it is 5ft long or 60in
8 0
3 years ago
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