A car traveled 240 miles in 3 hours. At this rate, how many miles will the car travel in 1/2 hour?

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

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

So

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

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

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

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

3 years ago

Graph y< 1/3 c + 1/2

castortr0y [4]

<h3>The Graph you need above </h3>

<h3>Step-by-step explaination : </h3>

<h3>Combine 1/3and x.</h3>

y<x/3+1/2

<h3>Use the slope-intercept form to find the slope and y-intercept.</h3><h3 />

Slope: 1/3

y-intercept: 1/2

<h3>Graph a dashed line, then shade the area below the boundary line since y is less</h3><h3>than x/3+1/2.</h3>

6 0

2 years ago

What is i + 6i simplified?

kkurt [141]

Answer:

7i..........................

3 0

3 years ago

Ryker wants a new car. The dealership offers him a loan at 9% annual interest for 6 years. If Ryker wants to do some calculation

Contact [7]

The monthly interest rate is 0.75%

<u>Step-by-step explanation:</u>

The rate of interest= 9%

Total time = 6years

Interest rate per month = 9/12

= 0.75%

Monthly payment =cost of the car + 0.75% of cost of car

Interest per month is 0.75%

3 0

3 years ago

The universal set in this diagram is the set of integers from 1 to 15. place the integers in the correct place in the venn diagr

neonofarm [45]

Answer:

Step-by-step explanation:

Given : universal set in this diagram is the set of integers from 1 to 15.

Solution :

The intersection of odd integer,multiples of 3 and Factors of 15 are 3,15

The intersection of odd integer and Factors of 15 are 1,5

The intersection of odd integer,multiples of 3 is 9

The remaining multiples of 3 are 6,12

The remaining odd integers are 7,11,13

Now the remaining integers are 2,4,8,10,14 and these integers must be placed in the boxes outside the circles Since they does not belong any intersection or odd integer or factor of 15 .

Refer the attached figure for the answer.

3 0

3 years ago

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