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Reil [10]
3 years ago
13

At the Bristol County Fair, there is a baking contest that awards a first prize and a second prize to the best pies baked. There

are 56 entrants to the contest this year.
In order to determine how many ways there are to award prizes, you should use a __[blank 1]__. There are __[blank 2]__ ways to award the prizes.

Enter either the word permutation or the word combination for blank 1, and then enter the number that correctly fills in blank 2.
Mathematics
1 answer:
4vir4ik [10]3 years ago
3 0

Answer:

1: Permutation

2: 3080

Step-by-step explanation:

As order matters, (first place as opposed to second place) this must be a permutation.

For first place, there are 56 different contestants that could win it, while once first place is selected, there are only 55 to get second. This means that

56*55=3080

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The number of people arriving for treatment at an emergency room can be modeled by a Poisson Distribution with a rate parameter
AlekseyPX

Answer:

a) 0.052 = 5.2% probability that exactly three arrivals occur during a particular hour

b) 0.971 = 97.1% probability that at least three people arrive during a particular hour

c) 5.25 people are expected to arrive during a 45-min period

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given interval.

Poisson Distribution with a rate parameter of seven per hour.

This means that \mu = 7

(a) What is the probability that exactly three arrivals occur during a particular hour?

This is P(X = 3).

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 3) = \frac{e^{-7}*7^{3}}{(3)!} = 0.052

0.052 = 5.2% probability that exactly three arrivals occur during a particular hour.

(b) What is the probability that at least three people arrive during a particular hour? (Round your answer to three decimal places.)

Either less than three people arrive, or at least three does. The sum of the probabilities of these events is 1. So

P(X < 3) + P(X \geq 3) = 1

We want P(X \geq 3), which is

P(X \geq 3) = 1 - P(X < 3)

In which

P(X \geq 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-7}*7^{0}}{(0)!} = 0.001

P(X = 1) = \frac{e^{-7}*7^{1}}{(1)!} = 0.006

P(X = 2) = \frac{e^{-7}*7^{2}}{(2)!} = 0.022

So

P(X \geq 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.001 + 0.006 + 0.022 + 0.029

P(X \geq 3) = 1 - P(X < 3) = 1 - 0.029 = 0.971

0.971 = 97.1% probability that at least three people arrive during a particular hour

(c) How many people do you expect to arrive during a 45-min period?

During an hour(60 minutes), 7 people are expected to arrive. So, using proportions:

\frac{45*7}{60} = \frac{3*7}{4} = \frac{21}{4} = 5.25

5.25 people are expected to arrive during a 45-min period

5 0
3 years ago
Brian spins a fair spinner numbered 1 - 5 and flips a fair coin.
Greeley [361]

Answer:  0.1

Step-by-step explanation:

If we spin a fair spinner numbered 1 - 5 and flips a fair coin.

Then, the possible outcomes will be :-

(1,T),(2,T), (3,T), (4,T), (5,T)\\\\(1,H),(2,H), (3,H), (4,H), (5,H)

i.e. total 10 possible outcomes.

The favorable outcomes = a 2 and a head  i.e. only 1 .

Now, the probability of obtaining a 2 and a head will be :_

\dfrac{\text{Number of favorable outcome}}{\text{Total outcomes}}\\\\=\dfrac{1}{10}=0.1

Hence, the  probability of obtaining a 2 and a head = 0.1

7 0
2 years ago
3.5x-81=360 <br> Please help this is due tomorrow
postnew [5]

Answer:

Step-by-step explanation:

so what your gonna do is you are going to add 81 to 360 and then sum it up. after you are going to divide it by 3.5.

This might be wrong but there is always a point where you have to try :)

3 0
2 years ago
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Write the following equation in slope-intercept form: 2x + 3y = 6
Leokris [45]

Answer:

y=-2/3x+2

Step-by-step explanation:

2x+3y=6

3y=6-2x

3y=-2x+6 /:3

y=-2/3x+6/3

y=-2/3x+2

Slope=-2/3

7 0
2 years ago
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Johnny was walking down the street and he found 20$ so he went into the shop and bout three ice cream cones boxes how much money
timofeeve [1]

Answer:

he has 1 $ left

Step-by-step explanation:

7 0
3 years ago
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