Respuesta :
The best way to approach this problem is to assign values that fit the ratios.
First we consider the ratio of white and black shapes. Since it's [tex]5:11[/tex], let's assume that there are [tex]500[/tex] white shapes and [tex]1,100[/tex] black shapes.
Next we look at the ratio of white circles to white squares which is [tex]3:7[/tex]. This means that [tex] \frac{3}{10} [/tex] of the white shapes are circle and [tex] \frac{7}{10} [/tex] are square. This will lead us to have [tex] \frac{3}{10}*500=150 [/tex] white circles and [tex] \frac{7}{10}*500=350 [/tex] white squares.
Then, we look at the ratio of black circles to black squares ([tex]3:8[/tex]). We can get at the number of black circles and black squares by performing the same step as before:
[tex] \frac{3}{11}*1100=300 [/tex] black circles
[tex] \frac{8}{11}*1100=800 [/tex] black squares
Now that we have all the assumed values, we just proceed to get the fraction of circles by counting the assumed number of circles and dividing it by the total number of assumed shapes. (We can get the total number of assumed shapes by adding the number of black and white shapes).
[tex] \frac{150+300}{500+1100} = \frac{450}{1600}=\frac{9}{32} [/tex]
ANSWER: [tex] \frac{9}{32} [/tex] of all shapes are circles.
(This method will work since we have maintained the given ratios.)
First we consider the ratio of white and black shapes. Since it's [tex]5:11[/tex], let's assume that there are [tex]500[/tex] white shapes and [tex]1,100[/tex] black shapes.
Next we look at the ratio of white circles to white squares which is [tex]3:7[/tex]. This means that [tex] \frac{3}{10} [/tex] of the white shapes are circle and [tex] \frac{7}{10} [/tex] are square. This will lead us to have [tex] \frac{3}{10}*500=150 [/tex] white circles and [tex] \frac{7}{10}*500=350 [/tex] white squares.
Then, we look at the ratio of black circles to black squares ([tex]3:8[/tex]). We can get at the number of black circles and black squares by performing the same step as before:
[tex] \frac{3}{11}*1100=300 [/tex] black circles
[tex] \frac{8}{11}*1100=800 [/tex] black squares
Now that we have all the assumed values, we just proceed to get the fraction of circles by counting the assumed number of circles and dividing it by the total number of assumed shapes. (We can get the total number of assumed shapes by adding the number of black and white shapes).
[tex] \frac{150+300}{500+1100} = \frac{450}{1600}=\frac{9}{32} [/tex]
ANSWER: [tex] \frac{9}{32} [/tex] of all shapes are circles.
(This method will work since we have maintained the given ratios.)
The white shapes and black shapes are used in the game and the fraction of circle in all the shapes are 9/32. While the total number of shapes are 1600.
Given information:
White shapes and black shapes are used in a game. Some of the shapes are circle and all other shapes are square.
The ratio of number of white shapes to the number of black shapes is 5:11
The ratio of number of white circle [tex]W_c[/tex] to number of white squares [tex]W_s[/tex] is 3:7
The ratio of number of black circles [tex]B_c[/tex] to the number of black squares [tex]B_s[/tex] is 3:8
Let, the number of white shapes are [tex]W=500[/tex]
And number of black shapes are [tex]B=1100[/tex]
So the expression formed using above information will be:
[tex]\dfrac{W}{B}=\dfrac{500}{1100}[/tex]
Now, according to the question, the expression for white circle and white square can be written as,
[tex]\dfrac{W_c}{W_s} =\dfrac{3}{7}[/tex]
So, the value of white circles will be,
[tex]W_c=\dfrac{3}{10}\times 500 \\\\W_c=150[/tex]
Similarly, the value of white squares will be,
[tex]W_s=\dfrac{7}{10} \times 500\\\\W_s=350[/tex]
Now, according to the question, the ratio of black circle and black squares will be,
[tex]\dfrac{B_c}{B_s}=\dfrac{3}{8}[/tex]
So, the value of black circles will be,
[tex]B_c=\dfrac{3}{11}\times 1100\\\\B_C=300[/tex]
Similarly, the value of black squares will be,
[tex]B_s=\dfrac{8}{11}\times 1100\\\\B_C=800[/tex]
The shapes, that are circle [tex]C[/tex] is the summation of the white circles and black circles.
[tex]C=B_c+W_c\\C=300+150\\C=450[/tex]
Now, calculate the number of all shapes [tex]S[/tex] to find the faction of circle,
[tex]S=W_c+W_s+B_c+B_s\\S=150+350+300+800\\S=1600\\[/tex]
Hence, the fraction of circle [tex]X[/tex] in all the shapes will be,
[tex]X=\dfrac{450}{1600}\\\\X= \dfrac{9}{32}[/tex]
Hence, the fraction of circle in all the shapes are 9/32. While the total number of shapes are 1600.
For mote information, visit link:
https://brainly.com/question/23340550
