All categories

2 years ago

Bag A: Two thirds of the candies are yellow. What portion of the candies is green

Mathematics

1 answer:

dalvyx [7]2 years ago

7 0

Answer: $\frac{1}{3}$ proportion of candies are green.

Solution:

In bag A, $\frac{2}{3}$ candies are yellow.

$\frac{2}{3}$ this proportion shows ratio of favorable over total candies.

Here numerator number is 2.

So, Total number of yellow candies should be 2x

Total number of candies in Bag A would be 3x

Number of green candies in bag A = 3x-2x = x

Now we find the portion of green candies in bag A

$\therefore,$ $\frac{x}{3x}$

$\frac{1}{3}$ portion of candies are green in bag A

You might be interested in

The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep

Alchen [17]

Ooh, fun

geometric sequences can be represented as
$a_n=a(r)^{n-1}$
so the first 3 terms are
$a_1=a$
$a_2=a(r)$
$a_2=a(r)^2$

the sum is -7/10
$\frac{-7}{10}=a+ar+ar^2$
and their product is -1/125
$\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3$

from the 2nd equation we can take the cube root of both sides to get
$\frac{-1}{5}=ar$
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
$\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r$
subsituting -1/5 for ar
$\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r$
which simplifies to
$\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}$
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for $ax^2+bx+c=0$
$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
so
for 2r²-5r+2=0
a=2
b=-5
c=2

$r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}$
$r=\frac{5 \pm \sqrt{25-16}}{4}$
$r=\frac{5 \pm \sqrt{9}}{4}$
$r=\frac{5 \pm 3}{4}$
so
$r=\frac{5+3}{4}=\frac{8}{4}=2$ or $r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

use them to solve for the value of a
$\frac{-1}{5}=ar$
$\frac{-1}{5r}=a$
try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

6 0

3 years ago

Enter the y coordinate of the solution to this system of equations. -2x+3y=-6 5x-6y=15

julia-pushkina [17]

Y coordinate on solving both equations comes out to be 0
-2x+3y=-6
3y = -6+2x
put the value of 3y in equation 2nd
5x-2(-6+2x) =15
5x+12-4x = 15
x=3
put value of X in 3y = -6+2x
3y = -6+2*3 = -6+6 = 0
thus y = 0

7 0

3 years ago

Graph y= 3/4x - 1/2

Elenna [48]

I hope this helps! :)

4 0

3 years ago

Read 2 more answers

How to take 1.20 into a faction

sergejj [24]

Answer:

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is 1 number to the right of the decimal point, place the decimal number over

10 1

(10 ). Next, add the whole number to the left of the decimal.

1 2 /10

Reduce the fractional part of the mixed number.

1 1 /5

Reduce the fraction.

6/ 5

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

5(1+4K)+7k=4(7k+2) Help

stepladder [879]

Answer:

k = -3

Step-by-step explanation:

1) Simplify

5+20k+7k=28k+8

2) Combine the k's

5+27k=28k+8

3) Subtract 27k on both sides

5=k+8

4) Subtract 8 on both sides

-3=k or k= -3

5 0

2 years ago