The weight of 10,000 identical samples of a substance is 100 pounds. What is the weight of 10 samples?

It is 2.8km from David’s house to the nearest mailbox. How far is it in meters?

Ganezh [65]

Solution

Distance in km = 2.8 km

Distance in m = 2.8 x 1000m

Distance in m = 2,800m

5 0

1 year ago

Your friend says that the solutions to the inequality 5x - 14x < - 18 are x ≤2. Solve the inequality correctly. What error di

katrin2010 [14]

<h3>Answer: x > 2</h3>

Work Shown:

5x - 14x < - 18

-9x < - 18

x > -18/(-9)

x > 2

The inequality sign flips when dividing both sides by a negative number.

Here's another approach you could take.

5x - 14x < - 18

-9x < -18

0 < -18+9x

18 < 9x

9x > 18

x > 18/9

x > 2

It's a slightly longer pathway, but it avoids a sign flip when you divide both sides by the positive number 9.

The sign flip happens two steps earlier when going from 18 < 9x to 9x > 18. In other words, A < B is the same as B > A.

6 0

2 years ago

Naval intelligence reports that 99 enemy vessels in a fleet of 1818 are carrying nuclear weapons. If 99 vessels are randomly tar

oee [108]

Answer:

0.001687 = 0.1687% probability that no more than 1 vessel transporting nuclear weapons was destroyed.

Step-by-step explanation:

The vessels are destroyed and then not replaced, 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 18 means that $N = 18$

9 are carrying nuclear weapons, which means that $k = 9$

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

What is the probability that no more than 1 vessel transporting nuclear weapons was destroyed?

This is:

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

In which

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

$P(X = 0) = h(0,18,9,9) = \frac{C_{9,0}*C_{9,9}}{C_{18,9}} = 0.000021$

$P(X = 1) = h(1,18,9,9) = \frac{C_{9,1}*C_{9,8}}{C_{18,9}} = 0.001666$

Then

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.000021 + 0.001666 = 0.001687$

0.001687 = 0.1687% probability that no more than 1 vessel transporting nuclear weapons was destroyed.

4 0

3 years ago

What is the value of the expression (2 x 5)^3

Tom [10]

Deal with the brackets first
(2x5) = 10
Then 10 cubed = 1000

Hope this helps

3 0

3 years ago

Twenty percent of a number is 14. find the number

7nadin3 [17]

The answer is: 70 .
___________________________________________
Explanation:
_________________________________

(20/100) x = 14; solve for "x".

(20/100) = 2/10 = 1/5 ;

(1/5) x = 14

x/5 = 14 ;

x = 14 * 5 ;

x = 70 . The answer is: 70 .
___________________________________

5 0

3 years ago

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