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2 years ago

The ratio of yellow marbles to purple marbles was 13 to 4. If there was 102 marbles in the bag, how many were yellow marbles?

Mathematics

1 answer:

Pani-rosa [81]2 years ago

3 0

The total number of yellow marbles in the bag was 78 marbles

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

The ratio of yellow marbles to purple marbles in the bag = 13 : 4

Let the total number of yellow marbles in the bag be = 13x

Let the total number of purple marbles in the bag be = 4x

Now , the equation will be

The total number of marbles in the bag = 102

So , substituting the values in the equation , we get

The total number of marbles in the bag = total number of yellow marbles + total number of purple marbles

The total number of marbles in the bag = 13x + 4x

13x + 4x = 102

17x = 102

Divide by 17 on both sides of the equation , we get

x = 6

Therefore , substituting the value of x in the above expressions , we get

Total number of yellow marbles in the bag = 13x

Total number of yellow marbles in the bag = 13 x 6

Total number of yellow marbles in the bag = 78 marbles

And ,

Total number of purple marbles in the bag = 4x

Total number of purple marbles in the bag = 4 x 6

Total number of purple marbles in the bag = 24 marbles

Hence , The total number of yellow marbles in the bag was 78 marbles

To learn more about proportion click :

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8 0

3 years ago

Read 2 more answers

What is the problem of 200 and 400

user100 [1]

200+400=600 u just add 2 and 6 togather and u get 6 and then annd the two zeros on too it

6 0

3 years ago

Consider the line integral Z C (sin x dx + cos y dy), where C consists of the top part of the circle x 2 + y 2 = 1 from (1, 0) t

pashok25 [27]

Direct computation:

Parameterize the top part of the circle $x^2+y^2=1$ by

$\vec r(t)=(x(t),y(t))=(\cos t,\sin t)$

with $0\le t\le\pi$ , and the line segment by

$\vec s(t)=(1-t)(-1,0)+t(2,-\pi)=(3t-1,-\pi t)$

with $0\le t\le1$ . Then

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)$

$=\displaystyle\int_0^\pi(-\sin t\sin(\cos t)+\cos t\cos(\sin t)\,\mathrm dt+\int_0^1(3\sin(3t-1)-\pi\cos(-\pi t))\,\mathrm dt$

$=0+(\cos1-\cos2)=\boxed{\cos1-\cos2}$

Using the fundamental theorem of calculus:

The integral can be written as

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=\int_C\underbrace{(\sin x,\cos y)}_{\vec F}\cdot\underbrace{(\mathrm dx,\mathrm dy)}_{\vec r}$

If there happens to be a scalar function $f$ such that $\vec F=\nabla f$ , then $\vec F$ is conservative and the integral is path-independent, so we only need to worry about the value of $f$ at the path's endpoints.

This requires

$\dfrac{\partial f}{\partial x}=\sin x\implies f(x,y)=-\cos x+g(y)$

$\dfrac{\partial f}{\partial y}=\cos y=\dfrac{\mathrm dg}{\mathrm dy}\implies g(y)=\sin y+C$

So we have

$f(x,y)=-\cos x+\sin y+C$

which means $\vec F$ is indeed conservative. By the fundamental theorem, we have

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=f(2,-\pi)-f(1,0)=-\cos2-(-\cos1)=\boxed{\cos1-\cos2}$

3 0

3 years ago

Look at the graph below measuring the speed of a truck and answers the following 2 question.

NemiM [27]

X would be equal to time and y be equal to distance

The y axis would be measuring distance and the x axis would be measuring time. Another name for a speed graph is the distance time graph. The y axis would be measuring the distance covered by the truck in meters and the x axis would be for the time it takes to reach that distance in second.

B) 2-6 would represent contact motion, meaning the vehicle is at rest. The time would be increasing from 2-6 to however the distance remains the same which is 20m

4 0

3 years ago

Solve the following system of equations using the substitution method.

sergey [27]

Answer:

y=1; x=2

Step-by-step explanation:

Substitution:

x=2y

2x+5y=9

=> if x=2y, plug in the x value into other equation, so

----------------------------------------------------------------------------

2(2y)+5y=9

4y+5y=9

9y=9

y=1

You have the Y value, so now solve for X

-----------------------------------------------------------------------

plug in y value to x=2y

so x=2(1)

x=2

5 0

3 years ago