A shopper buys 3 notebook for $5 each the percent of sales tax is 8% how much is the total sale

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

erma4kov [3.2K]

Answer:

$\frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}$

Step-by-step explanation:

Given

5 tuples implies that:

$n = 5$

$(h,i,j,k,m)$ implies that:

$r = 5$

Required

How many 5-tuples of integers $(h, i, j, k,m)$ are there such that $n\ge h\ge i\ge j\ge k\ge m\ge 1$

From the question, the order of the integers h, i, j, k and m does not matter. This implies that, we make use of combination to solve this problem.

Also considering that repetition is allowed: This implies that, a number can be repeated in more than 1 location

So, there are n + 4 items to make selection from

The selection becomes:

$^{n}C_r => ^{n + 4}C_5$

$^{n + 4}C_5 = \frac{(n+4)!}{(n+4-5)!5!}$

$^{n + 4}C_5 = \frac{(n+4)!}{(n-1)!5!}$

Expand the numerator

$^{n + 4}C_5 = \frac{(n+4)!(n+3)*(n+2)*(n+1)*n*(n-1)!}{(n-1)!5!}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5!}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5*4*3*2*1}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}$

<u><em>Solved</em></u>

6 0

3 years ago

The graph of the function f(x) = –(x + 1)2 is shown. Use the drop-down menus to describe the key aspects of the function. The ve

eimsori [14]

The graph of the function f(x) = -(x+1)^2 shows that the domain of the function f(x) = -(x+1)² is: -∞ < x < ∞. The range of the function is f(x) ≤ 0.

<h3>What is the graph of a function?</h3>

The graph of a function is the arrangement of all ordered pairs of the function. Typically, they are expressed as points in a cartesian coordinate system. The graph of f is the collection of all ordered pairings (x, f(x)) such that x lies inside the domain of f.

The graph of a function might similarly be defined as the graph of the equation y = f(x). As a result, the graph of a function is a subset of the graph of an equation.

From the given information: the graph of the function f(x) = -(x+1)² can be determined if the domain, the range, and the vertex of the function are known.

The domain of the function f(x) = -(x+1)² is: -∞ < x < ∞
The range of the function is f(x) ≤ 0
The x-intercepts and the y-intercepts are (-1,0) and (0, -1) respectively
The vertex is maximum at (-1,0)

Since the parabola curve from the graph shows that the graph is facing down, then the function is negative and decreasing.

Learn more about the graph of a function here:

brainly.com/question/24696306

#SPJ1

8 0

2 years ago

a student played a computer game 500 times and won 370 of these game. he then won the next "x" games and lost none. he has now w

a_sh-v [17]

So, this is a proportion problem. If we express 75% as a fraction (3/4ths), we have:

$\frac{370+x}{500+x}=\frac{3}{4}$

Since he won all of his games, we add the number won (x), to the number previously won and divide it by the total games played which is just the previous games played plus the number of current games played, so since he lost no games we still add x to the denominator as well. Solving this gives us:

$4(370+x)=3(500+x) \implies\\ 1480+4x=1500+3x \implies \\ x=20$

That x value is 20.

3 0

3 years ago

Which relationships describe angles 1 and 2?

djverab [1.8K]

Supplementary and adjacent.

Two angles are called supplementary when their measures add up to 180 degrees.

Adjacent angles are two angles that have a common vertex and a common side but do not overlap.

4 0

3 years ago

Read 2 more answers

8 + 3b = -13<br> help pleaseee

sergiy2304 [10]

8 + 3b= -13
-8. -8
3b= -21
Divide by 3
B= -7

5 0

3 years ago

Read 2 more answers