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irina [24]
2 years ago
6

A bag contains equal numbers of green marbles and blue marbles. You can divide all of the green marbles into groups of 12 and al

l the blue marbles into groups of 16. Whatis the least number of each color of marble thatcan be in the bag
Mathematics
1 answer:
Furkat [3]2 years ago
6 0

Answer: 48

Step-by-step explanation:

We need to find the least common multiple of 12 and 16.

Finding the prime factorizations of 12 and 16,

12=2^{2} \times 3\\\\16=2^{4}

Thus, the least common multiple is 2^{4} \times 3=\boxed{48}

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Ber [7]
The answers in order is
Bc
Dc
Sas
7 0
3 years ago
A tank contains 60 kg of salt and 1000 L of water. A solution of a concentration 0.03 kg of salt per liter enters a tank at the
charle [14.2K]

Answer:

\dfrac{dy}{dt}=0.27-0.009y(t),$  y(0)=60kg

Step-by-step explanation:

Volume of water in the tank = 1000 L

Let y(t) denote the amount of salt in the tank at any time t.

Initially, the tank contains 60 kg of salt, therefore:

y(0)=60 kg

<u />

<u>Rate In</u>

A solution of concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min.

R_{in} =(concentration of salt in inflow)(input rate of solution)

=(0.03\frac{kg}{liter})( 9\frac{liter}{min})=0.27\frac{kg}{min}

<u>Rate Out</u>

The solution is mixed and drains from the tank at the same rate.

Concentration, C(t)=\dfrac{Amount}{Volume} =\dfrac{y(t)}{1000}

R_{out} =(concentration of salt in outflow)(output rate of solution)

=\dfrac{y(t)}{1000}* 9\dfrac{liter}{min}=0.009y(t)\dfrac{kg}{min}

Therefore, the differential equation for the amount of Salt in the Tank  at any time t:

\dfrac{dy}{dt}=R_{in}-R_{out}\\\\\dfrac{dy}{dt}=0.27-0.009y(t),$  y(0)=60kg

8 0
4 years ago
What type of number is √5? Choose all answers that apply:
Vlada [557]
<h2>SOLVING</h2>

\Large\maltese\underline{\textsf{A. What is Asked}}

What type of number is \bf{\sqrt 5}? Select all that apply

\Large\maltese\underline{\textsf{B. This problem has been solved!}}

Let's start by taking a look at all the four sets of numbers.

<h2>A: Whole number</h2><h3>{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22...∞}</h3>

The set is shown above. To be honest, this is an infinitely small part of the number set; the whole number set would take FOREVER to type ;)

<h2>B: Integers</h2><h3>{∞...-2,-1,0,1,2,3,4,5,6,7,8,9...∞}</h3>

Wow, this set starts at negative infinity and ends at positive infinity!

<h2>C: Rational</h2>

This set consists of all integers, decimals, and fractions.

<h2>D: Irrational</h2>

That's where the desired number \bf{\sqrt{5}} belongs!

\cline{1-2}

\bf{Result:}

                 \bf{=The\;fourth\;option}

\LARGE\boxed{\bf{aesthetics \not1\theta l}}

<em>∞</em>

8 0
2 years ago
Fill in the gaps in this sequence: -8, -19, -30, _ , _.<br> (Geometric and arithmetic sequences)
gavmur [86]

-8, -19, -30, -49 , -60

<u>Step-by-step explanation:</u>

Here we have the following sequence :

-8, -19, -30, _ , _

  • First term of sequence is -8 .
  • Second term of sequence is -19 : -8-11 = -19
  • Third term of sequence is -30 : -19-11 = -30
  • Fourth term of sequence is : -30-11 = -49
  • Fifth term of sequence is : -49-11 = -60  

Following sequence was an AP( Arithmetic Progression ) with first term as -8 i.e. a = -8 and common difference d = -11 having general equation as : -8 -11n .

6 0
3 years ago
Which is an equation of the line that passes through the point (8,7) and is perpendicular to the line whose equation is y = 4x-1
algol [13]

Answer:

Y = -1/4x + 5

Step-by-step explanation:

7 0
3 years ago
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