Write the arithmetic series in summation notation.

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

Can someone please help me with this question?? It’s really hard and once you understand it, can you please give me an explanati

Thepotemich [5.8K]

We want to subtract 8x + 3 from -2x+5. We can create an expression to represent this.

-2x + 5 - (8x + 3).

After this, lets distribute the - sign (think of this like expanding something with -1).

-2x + 5 - 8x - 3

Lastly, we just need to combine like terms.

-2x + 5 - 8x - 3

Combine the 5 and -3 to get 2.

-2x + 2 - 8x

Combine the -2x and -8x to get -10x.

-10x + 2

The final answer to the question is therefore A.

3 0

3 years ago

Please help!!! i'll give brainliest and offering 20 pts each!!!

Aleks04 [339]

Answer:

5(x +1.5)^2
10(x +1)^2
1/4(x +2)^2
3(x +5/6)^2

Step-by-step explanation:

When your desired form is expanded, it becomes ...

a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2

This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.

a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2

b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2

c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2

d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2

_____

<em>Additional comment</em>

If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.

8 0

2 years ago

Can someone please help me? I just need to get the variable alone to see what it equals, if it doesn’t have a solution, or if it

love history [14]

Answer:

the answer would be p= -4

13-3p = -5(3+2p)

13-3p = -15-10p

13 = -15-7p

28 = -7p

p = -4

4 0

3 years ago

Read 2 more answers

What angles are supplementary?

vova2212 [387]

8 and 5 and I hate IXL ugh

5 0

3 years ago