Which property justifies rewriting the equation 1/6 x 6 + z = 8 as 1 + z = 8?

A group of hikers buys 8 bags of mixed nuts. Each bag contains 3 and 1/2 cups of mixed nuts. the mixed nuts are shared evenly am

nika2105 [10]

Answer:

2 1/3 cups for each hiker

Step-by-step explanation:

8bags x 3.5 cups in each bag =28 cups in total
28 cups shared among 12 hikers = 28/12 = 2 1/3 cups for each hiker

4 0

2 years ago

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

2 years ago

Can 8/45 be simplified as a fraction

max2010maxim [7]

Answer:

Step-by-step explanation:

isn't it already a fraction or is it a division

if it's a division then yes

the answer is 5 and 2/8

8 0

3 years ago

Triangle ABC has vertices A(-2, 3), B(0, 3), and C(-1,-1). Find the coordinates of the image after a reflection over the

motikmotik

Given:

Given that the triangle ABC has vertices A(-2,3), B(0,3) and C(-1,-1).

We need to determine the coordinates of the image after a reflection over the x - axis.

Let A'B'C' denote the coordinates of the triangle after a reflection over the x - axis.

Coordinates of the point A':

The general rule to reflect the coordinate across the x - axis is given by

$(x,y)\rightarrow (x,-y)$

Substituting the point A(-2,3), we get;

$(-2,3)\rightarrow (-2,-3)$

Thus, the coordinates of the point A' is (-2,-3)

Coordinates of the point B':

The general rule to reflect the coordinate across the x - axis is given by

$(x,y)\rightarrow (x,-y)$

Substituting the point B(0,3), we get;

$(0,3)\rightarrow (0,-3)$

Thus, the coordinates of the point B' is (0,-3)

Coordinates of the point C':

The general rule to reflect the coordinate across the x - axis is given by

$(x,y)\rightarrow (x,-y)$

Substituting the point C(-1,-1), we get;

$(-1,-1)\rightarrow (-1,1)$

Thus, the coordinates of the point C' is (-1,1)

Hence, the coordinates of the image after a reflection over the x - axis is A'(-2,-3), B(0,-3) and C(-1,1)

8 0

3 years ago

Which statements are true regarding elements of the given sets? Check all that apply. Paris ∈ F. The Statue of Liberty ∈ A. The

jek_recluse [69]

Answer:

Paris F, Abraham Lincoln belongs to none of these sets, and The Eiffel Tower is in more than one of these sets

Step-by-step explanation:

8 0

3 years ago