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jasenka [17]
3 years ago
5

In 2019, approximately 97.4% of all the runners who started the Boston Marathon (in Boston, Massachusetts, USA) were able to com

plete the 42.2 km (26.2 mile) race. If 100 runners are chosen at random, find the probability that exactly 97 of them finished the marathon​
Mathematics
1 answer:
PtichkaEL [24]3 years ago
6 0

Answer:

The probability that exactly 97 of them finished the marathon​ is 0.221.

Step-by-step explanation:

We are given that in 2019, approximately 97.4% of all the runners who started the Boston Marathon were able to complete the 42.2 km race.

100 runners are chosen at random.

The above situation can be represented through the binomial distribution;

P(X = x) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x = 0,1,2,3,......

where, n = number of trials(or samples) taken = 100 runners

           r = number of success = exactly 97

           p = probability of success which in our question is the probability

                 that runners finished the marathon​, i.e; p = 0.974

So, X ~ Binom(n = 100, p = 0.974)

Now, the probability that exactly 97 of them finished the marathon​ is given by = P(X = 97)

         P(X = 97) = \binom{100}{97} \times 0.974^{97} \times (1-0.974)^{100-97}

                          = 161700 \times 0.974^{97} \times 0.026^{3}

                          = 0.221

Hence, the required probability is 0.221.

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Tammy has 35 coins nickels and quarters. In all she has $4.15. How many of each kind of coin does she have
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The currency called the U.S dollar can be split into smaller forms or currency value of itself. Examples of these smaller forms are: <u><em>dimes, nickels, pennies, and quarters.</em></u>

Tammy has 23 nickels and 12 quarters.

Let's represent the number of:

Nickels = n

Quarters = q

It is important to note that the value of:

<em>1 nickel = $0.05</em>

<em>1 quarter = $0.25</em>

<em />

Tammy has 35 coins nickels and quarters. This statement can be represented using an algebraic equation below:

n + q = 35

This can be rewritten as :

n = 35 - q

In all, she has $4.15. This statement can be represented using an algebraic equation below:

0.05n + 0.25q = 4.15

We substitute 35 - q for n in the above equation.

0.05(35 - q) + 0.25q = 4.15

1.75 - 0.05q + 0.25q = 4.15

Collect like terms

- 0.05q + 0.25q = 4.15 - 1.75

0.2q = 2.4

Divide both sides by 0.2

0.2q/0.2 = 2.4/0.2

q = 12

Therefore, the number of quarters Tammy has is 12.

Solving for the number of nickels, we have the equation:

n = 35 - q

n = 35 - 12

n = 23

Therefore, the number of nickels Tammy has is 23.

To learn more, visit the link below:

brainly.com/question/13312288

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3 years ago
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Help me out with number 8!!! I’m confused and I need this by tomorrow HELP PLEASE
ivann1987 [24]
We can use elimination for these set of systems.
First, we need to set up our variables.
Belts=b
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Now, the situation is 6 belts and 8 hats for $140. The situation after is 9 belts and 6 hats for $132.
Let’s set up our system of equations.
6b+8h=140
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We need to eliminate a variable. Since b has coefficients of 6 and 9, we can easily eliminate b by multiplying the top equation by 3 and the bottom by -2.
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We can also use the first equation to check our answers.
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So, the price of a belt is $6 while the price of a hat is $13.
































3 0
3 years ago
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