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3 years ago

mark ran 11.3 miles on Monday 12.64 miles on Wednesday and 11.9 miles on Friday how many miles did mark run together?

Mathematics

1 answer:

Blizzard [7]3 years ago

7 0

The answer is 35.84.
You just add all of them up

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You’ve bought a half-dozen (six) eggs from the store but you forgot to check them first! The probability that no eggs are broken

GREYUIT [131]

Answer:

$P(X = 0) = C_{6,0}.(0.1416)^{0}.(0.8584)^{6} = 0.4$

$P(X = 1) = C_{6,1}.(0.1416)^{1}.(8584)^{5} = 0.3960$

$P(X = 2) = C_{6,2}.(0.1416)^{2}.(8584)^{4} = 0.1633$

$P(X = 3) = C_{6,3}.(0.1416)^{3}.(8584)^{3} = 0.0359$

$P(X = 4) = C_{6,4}.(0.1416)^{4}.(8584)^{2} = 0.0044$

$P(X = 5) = C_{6,5}.(0.1416)^{5}.(8584)^{1} = 0.0003$

$P(X = 6) = C_{6,6}.(0.1416)^{6}.(8584)^{0} = 0.00001$

b) 56.77% probability that an even number of eggs is broken.

Expectation: 0.8496

Variance: 0.7293

Step-by-step explanation:

For each egg, there are only two possible outcomes. Either it is broken, or it is not. The probability of an egg being broken is independent from other eggs. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

There are 6 eggs

So $n = 6$

The probability that no eggs are broken is 0.4.

This means that $P(X = 0) = 0.4$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{6,0}.p^{0}.(1-p)^{6}$

$(1 - p)^{6} = 0.4$

Taking the sixth root from both sides of the equality

$(1 - p) = 0.8584$

p = 0.1416

Each egg has a 0.1416 probability of being broken

(a) Write out the pmf of X.

Probability of each value, from 0 to 6

$P(X = 0) = C_{6,0}.(0.1416)^{0}.(0.8584)^{6} = 0.4$

$P(X = 1) = C_{6,1}.(0.1416)^{1}.(8584)^{5} = 0.3960$

$P(X = 2) = C_{6,2}.(0.1416)^{2}.(8584)^{4} = 0.1633$

$P(X = 3) = C_{6,3}.(0.1416)^{3}.(8584)^{3} = 0.0359$

$P(X = 4) = C_{6,4}.(0.1416)^{4}.(8584)^{2} = 0.0044$

$P(X = 5) = C_{6,5}.(0.1416)^{5}.(8584)^{1} = 0.0003$

$P(X = 6) = C_{6,6}.(0.1416)^{6}.(8584)^{0} = 0.00001$

(b) Compute the probability that an even number of eggs is broken.

0, 2, 4 or 6

$P = P(X = 0) + P(X = 2) + P(X = 4) + P(X = 6) = 0.4 + 0.1633 + 0.0044 + 0.00001 = 0.5677$

56.77% probability that an even number of eggs is broken.

(c) Compute the expectation and variance of X.

Expectation:

$E(X) = np = 6*0.1416 = 0.8496$

Variance:

$V(X) = np(1-p) = 6*0.1416*0.8584 = 0.7293$

7 0

4 years ago

Convert 120 kilometers per hour into miles per hour using dimensional analysis

musickatia [10]

Answer:

74.56 miles / h

Step-by-step explanation:

1 mile = 1.609 km

Using the dimensional analysis you multiply the number you want to convert by 1 (using a fraction with the needed units)

Since 1 mile = 1.609 km then:

$1= \frac{1 mile}{1.609 km}$

Now to convert 120 kilometers per hour to miles per hour :

$120 \frac{km}{h} * \frac{1 mile}{1.609 km} = \frac{120}{1.609}\frac{miles}{h} = 74.56 \frac{miles}{h}$

4 0

4 years ago

Helpppp me on thisss

Delvig [45]

Answer:

Step-by-step explanation:

3600/30/16=15/2=7 1/2

5 0

3 years ago

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Select the proper inverse operation to check the answer to 25 − 13 = 12. A. 12 × 13 = 25 B. 12 + 13 = 25 C. 12 × 25 = 13 D. 12 ÷

Olenka [21]

B. 12 + 13 = 25 is the answer

4 0

4 years ago

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Simplify. 11 + 10 × 4 ÷ 5 – 11

gizmo_the_mogwai [7]

Answer:

The answer is 8 using PEMDAS

Step-by-step explanation:

3 0

3 years ago

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