Answer:
1:6
Step-by-step explanation:
Given that there are 10 circles and 2 triangles, the total number of shapes is equal to 10+2.
10+2=12
Because there are 2 triangles, the ratio of triangles to total shapes is equal to 2:12.
However, this ratio can be simplified because both sides are multiples of 2. Divide both sides of the ratio by 2 to simplify the ratio.
2:12
1:6
Therefore, the simplest ratio of triangles to total shapes is 1:6.
I hope this helps!
Answer:
23 males and 12 females
Step-by-step explanation:
x = # of females
y = # of males
x + y = 35
x + x + 11 = 35
2x + 11 =35 (SUBTRACT 11 FROM BOTH SIDES)
2x = 24 (DIVIDE BOTH SIDES BY 2)
x = 12 females
x + y =35
12 + y = 35 (SUBTRACT 12 FROM BOTH SIDES)
y = 23 males
23 males + 12 females = 35 students
Answer:
The probability of getting two of the same color is 61/121 or about 50.41%.
Step-by-step explanation:
The bag is filled with five blue marbles and six red marbles.
And we want to find the probability of getting two of the same color.
If we're getting two of the same color, this means that we are either getting Red - Red or Blue - Blue.
In other words, we can find the independent probability of each case and add the probabilities together*.
The probability of getting a red marble first is:

Since the marble is replaced, the probability of getting another red is: 
The probability of getting a blue marble first is:

And the probability of getting another blue is:

So, the probability of getting two of the same color is:

*Note:
We can only add the probabilities together because the event is mutually exclusive. That is, a red marble is a red marble and a blue marble is a blue marble: a marble cannot be both red and blue simultaneously.
Recall that the area under a curve and above the x axis can be computed by the definite integral. If we have two curves
<span> y = f(x) and y = g(x)</span>
such that
<span> f(x) > g(x)
</span>
then the area between them bounded by the horizontal lines x = a and x = b is
To remember this formula we write