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4 years ago

3 times a number,n, minus 4 is less than -11

Mathematics

1 answer:

weqwewe [10]4 years ago

6 0

Answer:

The number you are looking for is n < -2.333...

Step-by-step explanation:

Here is the modeled equation for this problem:

3n - 4 < -11.

Add 4 to both sides to isolate 3n.

3n - 4 + 4 < -11 + 4.

3n < -7.

Divide 3 to both sides to get the value of n.

3n/3 < -7/3.

n < -2.333...

So n must be less than -2.333... to make the equation true. Any number equal to or greater than -2.333 will result in the equation being false.

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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

3 years ago

Factor the expression: 84x – 12x

liberstina [14]

Subtract 12x from 84x = 72x

6 0

3 years ago

Read 2 more answers

Numerical coefficient of the term x over 7

Over [174]

Answer:

1/7

Step-by-step explanation:

In the term x/7, the numerical multiplier of x is 1/7.

3 0

4 years ago

Four added to twice a number yield 26/5. Find the number.<br>

avanturin [10]

Answer:

3/5 is the answer

sry if it's wrong

8 0

3 years ago

Read 2 more answers

$2,000 IN AN ACCOUNT THAT PAID 6.25% SIMPLE INTEREST ANNUALLY

valkas [14]

$\bf ~~~~~~ \textit{Simple Interest Earned Amount}\\\\
A=P(1+rt)\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to& \$2000\\
r=rate\to 6.25\%\to \frac{6.25}{100}\to &0.0625\\
t=years\to &3
\end{cases}
\\\\\\
A=2000(1+0.0625\cdot 3)\implies A=2000(1.1875)$

8 0

3 years ago