-2/3n=12 What is the value n?<br> Use inverse.

Step-by-step explanation: We know that 9 panes of glass cost $26.55, but we should first find how many dollars would it cost per pane of glass, or 1.

So, we can divide 26.55 by 9 to find the price per 1 pan of glass.

26.55/9 = 2.95, or $2.95 per pane of glass.

Now, we want to know how much it will cost for 4 panes of glass. Simply multiply 2.95 by 4.

2.95 x 4 = 11.8, or $11.80 for another 4 panes of glass.

8 0

3 years ago

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If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar

Oksana_A [137]

Answer:

$n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}$

Step-by-step explanation:

Lets divide it in cases, then sum everything

Case (1): All 5 numbers are different

In this case, the problem is reduced to count the number of subsets of cardinality 5 from a set of cardinality n. The order doesnt matter because once we have two different sets, we can order them descendently, and we obtain two different 5-tuples in decreasing order.

The total cardinality of this case therefore is the Combinatorial number of n with 5, in other words, the total amount of possibilities to pick 5 elements from a set of n.

${n \choose 5 } = \frac{n!}{5!(n-5)!}$

Case (2): 4 numbers are different

We start this case similarly to the previous one, we count how many subsets of 4 elements we can form from a set of n elements. The answer is the combinatorial number of n with 4 ${n \choose 4} .$

We still have to localize the other element, that forcibly, is one of the four chosen. Therefore, the total amount of possibilities for this case is multiplied by those 4 options.

The total cardinality of this case is $4 * {n \choose 4} .$

Case (3): 3 numbers are different

As we did before, we pick 3 elements from a set of n. The amount of possibilities is ${n \choose 3} .$

Then, we need to define the other 2 numbers. They can be the same number, in which case we have 3 possibilities, or they can be 2 different ones, in which case we have ${3 \choose 2 } = 3$ possibilities. Therefore, we have a total of 6 possibilities to define the other 2 numbers. That multiplies by 6 the total of cases for this part, giving a total of $6 * {n \choose 3}$

Case (4): 2 numbers are different

We pick 2 numbers from a set of n, with a total of ${n \choose 2}$ possibilities. We have 4 options to define the other 3 numbers, they can all three of them be equal to the biggest number, there can be 2 equal to the biggest number and 1 to the smallest one, there can be 1 equal to the biggest number and 2 to the smallest one, and they can all three of them be equal to the smallest number.

The total amount of possibilities for this case is

$4 * {n \choose 2}$

Case (5): All numbers are the same

This is easy, he have as many possibilities as numbers the set has. In other words, n

Conclussion

By summing over all 5 cases, the total amount of possibilities to form 5-tuples of integers from 1 through n is

$n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}$

I hope that works for you!

4 0

3 years ago

Simplify each expression.<br> (-3)¹/₃ . (-3)¹/₃ . (-3)¹/₃

babymother [125]

The result of simplifying each number (-3)¹/₃ . (-3)¹/₃ . (-3)¹/₃ using the exponent rules is -3

To solve this exercise we have to resolve algebraic operations following the exponent rules.

(-3)¹/₃ . (-3)¹/₃ . (-3)¹/₃

Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:

(-3)¹/₃⁺ ¹/₃ ⁺ ¹/₃

(-3)³/₃

(-3)¹

-3

<h3>What is an exponent?</h3>

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

Learn more about exponent at: brainly.com/question/847241

#SPJ4

4 0

1 year ago

-2/3n=12 What is the value n? Use inverse.