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3 years ago

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Mathematics

1 answer:

Reil [10]3 years ago

7 0

Answer:

A. 1

B. 7

C. 2

D. 10

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nika2105 [10]

The answer for part b is 6

3 0

3 years ago

A bag contains 4 red, 5 blue, and 3 black marbles. Find the probability that if you pick 3 marbles

Fofino [41]

Answer:

3/12 =1/6

Step-by-step explanation:

4+5+3=12

probability of picking 3 marbles is

3/12which in lowest term is 1/6

3 0

3 years ago

monica sells lemonade over the summer and uses conical paper cups to serve the lemonade. Each cup is 8 centimeters tall.She star

GaryK [48]

Answer:

(a)205

(b)5 Packages

Step-by-step explanation:

$\text{One gallon is equivalent to 3785 } cm^3$

Therefore: $\text{10 gallon= 3785X 10 =37850 } cm^3$

Therefore, Volume of the lemonade Monica Started with is $\text{37850 } cm^3$

The diameter of the cup =8cm

Therefore, Radius =8/2 =4cm

Height of the Cup =11cm

Volume of a Cone= $\frac{1}{3}\pi r^2 h$

$\text{Volume of the Cup}=\frac{1}{3}\pi *4^2*11 \\=184.31cm^3$

The number of cups needed to empty the 10 gallon cooler =37850÷184.31

=205.36

$\approx 205$ Cups

(b)If the Cups are sold in packages of 50

Number of Package to be bought =205 ÷ 50 =4.1

She would need to buy 5 packages.

5 0

3 years ago

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

3 years ago

Please please help please please ASAP please I'm begging you please I have 10 minutes please y'all help please any ACE that can

Finger [1]

Answer:

Step-by-step explanation:

ML:RQ = MN:RS = LN:QS (corr side, similar triangles)

8 0

2 years ago

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