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3 years ago

(IF ANSWERED CORRECTLY WILL GIVE BRAINLIEST)

Mathematics

1 answer:

ahrayia [7]3 years ago

8 0

172 ÷ 4 = 43 miles per hour

43 ÷ 5 = 10.75 miles per 12 minutes

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

sukhopar [10]

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

___________

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

____________

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

____________

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

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

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

3 0

4 years ago

Neeeeed helpppppp please

MissTica

Answer:

Scale factor = 7

Step-by-step explanation:

Dilation with scale factor to map HEFG to DABC will be,

Scale factor = $\frac{\text{Dimension of Image DABC}}{\text{Dimension of preimage HEFG}}$

= $\frac{\text{Length of CD}}{\text{Length of GH}}$

Length of CD = Distance between two points C(0, -7) and D(-7, 0)

= $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

= $\sqrt{(-7-0)^2+(0+7)^2}$

= $\sqrt{98}$

= $7\sqrt{2}$

Length of GH = Distance between G(0, -1) and H(-1, 0)

= $\sqrt{(-1-0)^2+(0+1)^2}$

= $\sqrt{2}$

Scale factor = $\frac{7\sqrt{2} }{\sqrt{2} }$

= 7

6 0

3 years ago

Sue deposited $52 into her bank account, so she currently has $12 in her account. What was her balance before the deposit?

Semenov [28]

Answer:

-40

Step-by-step explanation:

12 - 52 = -40

hope this helps...

7 0

3 years ago

Read 2 more answers

Please help me with another problem

lorasvet [3.4K]

"one" will fill both blanks.

8 0

3 years ago

Marta bought new fish for her home aquarium. She bought 3 guppies and 2 platies for a total of $13.95. Hank also bought guppies

ratelena [41]

Hank bought same guppies as Marta but 2more platies so
18.33-13.95=4.38
2platies=4.38
4.38/2=2.19
2.19 price of platies
13.95-4.34=9.61
9.61/3=3.20
3.29 price of guppies

3 0

3 years ago