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1 year ago

Can someone help me? With all the problems and with work

Mathematics

1 answer:

Lemur [1.5K]1 year ago

4 0

Answer:

5.006

41.056

31.289

51.977

7.884

Step-by-step explanation:

1) sin x = opposite side / hypotenuse

sin 24.3° = 2.06 / hyp

hyp = 2.06 / sin 24.3 = 5.0059006616019108320511866543651

rounding to 3 significant figures

= 5.006

2)cos x = adjacent side / hypotenuse

cos 47 = 28 / x

x = 28 / cos 47 = 41.055817197909497891901840157945

= 41.056

3) cos x = adjacent side / hypotenuse

cos 56.1 = x / 56.1

x = 56.1 * cos 56.1 = 31.289500613760617368691451544764

= 31.289

4) tan x = opposite side / adjacent side

tan 68 = x / 21

x = 21 * tan 68 = 51.9768239217422123300402781676

= 51.977

5) sin x = opposite side / hypotenuse

sin 21 = x / 22

x = 22 * sin 21 = 7.8840948899966060166510313670963

= 7.884

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Naval intelligence reports that 4 enemy vessels in a fleet of 17 are carrying nuclear weapons. If 9 vessels are randomly targete

icang [17]

Answer:

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

Step-by-step explanation:

The vessels are destroyed without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

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

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

In this question:

Fleet of 17 means that $N = 17$

4 are carrying nucleas weapons, which means that $k = 4$

9 are destroyed, which means that $n = 9$

What is the probability that more than 1 vessel transporting nuclear weapons was destroyed?

This is:

$P(X > 1) = 1 - P(X \leq 1)$

In which

$P(X \leq 1) = P(X = 0) + P(X = 1)$

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 0) = h(0,17,9,4) = \frac{C_{4,0}*C_{13,9}}{C_{17,9}} = 0.0294$

$P(X = 1) = h(1,17,9,4) = \frac{C_{4,1}*C_{13,8}}{C_{17,9}} = 0.2118$

Then

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0294 + 0.2118 = 0.2412$

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.2412 = 0.7588$

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

8 0

2 years ago

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Anna11 [10]

Answer:

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Step-by-step explanation:

First, convert the mixed numbers into improper fractions, 11/4*7/8

Next, you can just multiply the fractions for your answer!

Hope this helped<3

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Answer:

Step-by-step explanation:

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