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3 years ago

What are the coordinates of the image of the point (2, –6) under a dilation with a center of (0, 0) and a scale factor of 1/2

Mathematics

1 answer:

ycow [4]3 years ago

8 0

That would be (1, -3) because you basically divide the coordinates by the scale factor, in this case 2.

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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

3 years ago

trygg has 3/4 package of marigold seeds. He plants 1/6 of those seeds in his garden and divides the rest equally into 10 flowerp

meriva

The answer is just 1/16

3 0

3 years ago

Read 2 more answers

g At a certain gas station, 30% of all customers use the restroom. What is the probability that, out of the next 10 customers, (

Kruka [31]

Answer:

$P(x=4) = 0.200$

Step-by-step explanation:

Given

$n=10$ --- selected customers

$x = 4$ --- those that are expected to use the restroom

$p =30\% = 0.30$ --- proportion that uses the restroom

Required

$P(x = 4)$

The question illustrates binomial probability and the formula is:

$P(x) = ^nC_x * p^x * (1 - p)^{n - x}$

So, we have:

$P(x=4) = ^{10}C_4 * (0.30)^4 * (1 - 0.30)^{10 - 4}$

$P(x=4) = ^{10}C_4 * (0.30)^4 * (0.70)^6$

$P(x=4) = 210* (0.30)^4 * (0.70)^6$

$P(x=4) = 0.200$

4 0

3 years ago

Is there a way to understand inequalities better? I don't get them at all!

AlekseyPX

Ok for inequalities it's this < and > that so here's a example prob 3>2 so as my teacher used it put it "it's like the little number eats the bigger number." For negatives the one that's being eaten would be the one that's the closest to 0 so -3>-5 also alone way of doing this is to make a number line that's another way I was taught how to do these. I hope this helps you!

7 0

3 years ago

If one-sixth of a number plus one-third returns two-thirds of that number What is the number

Solnce55 [7]

Answer:

$x= \frac{2}{3}$