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3 years ago

If an item has a retail price retail price = $1,995 and a discount of 15%, how much is the discount? It is $ .

Mathematics

1 answer:

vovikov84 [41]3 years ago

6 0

I think the answer is 299.25

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How many integers in the set {n ∈ Z | 1 ≤ n ≤ 700} are divisible by 2 or 7?

sukhopar [10]

$\large\begin{array}{l}\\\\ \textsf{This question gives us a set}\\\\ \mathsf{S=\{n \in\mathbb{Z}:~1\le n\le 700\}}\\\\ \mathsf{S=\{1,\,2,\,3,\,\ldots,\,699,\,700\}}\\\\\\ \bullet~~\textsf{Set of integers that are divible by 2 (even integers):}\\\\ \mathsf{A=\{n\in \mathbb{Z}:~n=2k,\,k\in\mathbb{Z}\}}\\\\ \mathsf{A=\{\ldots,\,-4,\,-2,\,0,\,2,\,4,\,\ldots\}}\\\\\\ \bullet~~\textsf{Set of integers that are divible by 7:}\\\\ \mathsf{B=\{n\in \mathbb{Z}:~n=7k,\,k\in\mathbb{Z}\}}\\\\ \mathsf{A=\{\ldots,\,-14,\,-7,\,0,\,7,\,14,\,\ldots\}} \end{array}$

___________

$\large\begin{array}{l}\\\\ \textsf{We want to know how many elements there are in the}\\\textsf{following set:}\\\\ \mathsf{S\cap (A\cup B)=(S\cap A)\cup(S\cap B)\qquad(i)} \end{array}$

____________

$\large\begin{array}{l}\\\\ \bullet~~\mathsf{S\cap A=\{n\in\mathbb{N}:~n=2k~~and~~1\le n\le 700,\,k\in\mathbb{Z}\}}\\\\ \mathsf{S\cap A=\{2,\,4,\,6,\,\ldots,\,698,\,700\}}\\\\ \mathsf{S\cap A=\{1\cdot 2,\,2\cdot 2,\,3\cdot 2,\,\ldots,\,349\cdot 2,\,350\cdot 2\}}\\\\\\ \textsf{So, there are 350 elements in }\mathsf{S\cap A:}\\\\ \mathsf{\#(S\cap A)=350.} \\\\\\ \bullet~~\mathsf{S\cap B=\{n\in\mathbb{N}:~n=7k~~and~~1\le n\le 700,\,k\in\mathbb{Z}\}}\\\\ \mathsf{S\cap B=\{7,\,14,\,21,\,\ldots,\,693,\,700\}}\\\\ \mathsf{S\cap B=\{1\cdot 7,\,2\cdot 7,\,3\cdot 7,\,\ldots,\,99\cdot 7,\,100\cdot 7\}} \\\\\\ \textsf{So, there are 100 elements in }\mathsf{S\cap B:}\\\\ \mathsf{\#(S\cap B)=100.} \end{array}$

____________

$\large\begin{array}{l}\\\\ \textsf{Therefore,}\\\\ \mathsf{\#\big[S\cap (A\cup B)\big]}\\\\ =\mathsf{\#\big[(S\cap A)\cup(S\cap B)\big]}\\\\ =\mathsf{\#(S\cap A)+\#(S\cap B)-\#\big[(S\cap A)\cap(S\cap B)\big]}\\\\ =\mathsf{350+100-50}\\\\ =\mathsf{450-50}\\\\ =\mathsf{400~elements.}\\\\\\ \textsf{There are 400 integers in S that are divisible by 2 or 7.} \end{array}$

If you're having problems understanding the answer, try to see it through your browser: brainly.com/question/2105863

$\large\begin{array}{l}\\\\ \textsf{Any doubts? Please, comment below.}\\\\\\ \textsf{Best wishes! :-)} \end{array}$

Tags: <em>set theory divibilility divisible integers union intersection</em>

3 0

4 years ago

10 POINTS!!!!! Which of the following statements is true about 63 and 20?

uysha [10]

The answer is: A) They are relatively prime. This is because both of them aren't divisible by any other number than 1. (or 0 if you really want to do that)

4 0

4 years ago

Read 2 more answers

Which is equivalent ratio to 4:5 (select all that are true)

Sever21 [200]

It is b only b I think sorry If I am wrong have a good day

8 0

3 years ago

A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collecte

allsm [11]

Answer:

The degrees of freedom are given by;

$df =n-1= 5-1=4$

The significance level is 0.1 so then the critical value would be given by:

$F_{cric}= 7.779$

If the calculated value is higher than this value we can reject the null hypothesis that the arrivals are uniformly distributed over weekdays

Step-by-step explanation:

For this case we have the following observed values:

Mon 25 Tue 22 Wed 19 Thu 18 Fri 16 Total 100

For this case the expected values for each day are assumed:

$E_i = \frac{100}{5}= 20$

The statsitic would be given by:

$\chi^2 = \sum_{i=1}^n \frac{(O_i-E_i)^2}{E_i}$

Where O represent the observed values and E the expected values

The degrees of freedom are given by;

$df =n-1= 5-1=4$

The significance level is 0.1 so then the critical value would be given by:

$F_{cric}= 7.779$

If the calculated value is higher than this value we can reject the null hypothesis that the arrivals are uniformly distributed over weekdays

5 0

3 years ago

Write an equation and solve each problem. The ages of three brothers are consecutive integers with the sum of 96. How old are th

Alexxx [7]

Hi,

Let the

Youngest brothers age = x+2

Middle brothers age = x+4

Oldest brothers age = x+6

So,

Youngest brothers age = x+2 = 28+2 = 30 years of age

Middle brothers age = x+4 = 28+4 = 32 years of age

Oldest brothers age = x+6 = 28+6 = 34 years of age

Have a great day!

4 0

3 years ago