Determine the smallest and largest fractions by rewriting all the fractions to a similar denominator.  

Multiply all three denominators together to get the least common denominator, and multiply the numerators by what was multiplied by the denominator to obtain the new numerators.

It can then be seen that the smallest fraction is  and the largest fraction is .

Write the range formula and solve.

The range of scores is from 75 to 100, which is a range of 25 points.

You take the highest score and subtract the lowest score from it. 

The highest score is 100 and the lowest score is 75 therefore the range is as follows.

First, we want to solve for x. Since we know the average of all the prices is $1.90, then we can say

Now, we can find the range of the prices. The range is represented by the highest value minus the lowest value in any set. With that in mind, our range is given by:

The total value of the tiles is 

There are 100 tiles, so the mean value is 

To find range of any set of data, simply subtract the smallest number from the largest number. It is easiest if you order the numbers first. Thus,

Add up the total number of jellybeans, 20 + 45 + 30 + 5 = 100. 

Divide the number of watermelon jellybeans by the total: 20/100 and reduce the fraction to 1/5.

The probability of the point being inside the circle is the ratio of the area of the circle to the area of the square. If we suppose that the circle has radius r, then the square must have side 2r. The area of the circle is πr² and the area of the square is 〖(2r)〗²=〖4r〗², so the proportion of the areas is (πr²)/〖4r〗²  =π/4.

The bowl has 54 marbles, half green and half blue. This gives us 27 green and 27 blue marbles:

27 G / 27 B

John then takes 3 green and 6 blue from the bowl. This leaves the bowl with:

24 G / 21 B

If there are going to be more blue than green marbles after John's 13 marbles, he has to take at least 4 more green marbles than blue marbles, because right now there are 3 less blue marbles. Therefore, we need to take at least 9 green marbles, which would mean 4 or less of the marbles would be blue (8 green and 5 blue would leave us with equal green and equal blue marbles, so it would have to be more than 8 green marbles, which gives us 9 green marbles).

We can also solve this as an inequality. You take the difference in marbles, which is 3, which means you need the difference in green and blue marbles to be greater than 3, or at least 4. You have b + g = 13 and g - b > 3, where b and g are positive integers.

b + g = 13 (Subtract g on both sides of the equation)

b = 13 - g

g - b > 3 (Substitute above equation)

g - (13 - g) > 3 (Distribute negative sign in parentheses)

g - 13 + g > 3 (Add both g variables)

2g - 13 > 3 (Add 13 to both sides of the inequality)

2g > 16 (Divide both sides of the inequality by 2)

g > 8 so g has to be 9 or greater.

If x is chosen at random from the set (4, 6, 7, 9, 11) and y is chosen at random from the set (12, 13, 15, 17) then what is the probability that xy is odd?

Here we have 5 possible choices for x and 4 possible choices for y, giving us 5 * 4 = 20 possible outcomes.

We know that odd times odd = odd; even times even = even; and even times odd = even. Thus we need all of the outcomes where x and y are odd. We have 3 possibilities of odd numbers for x, and 3 possibilities of odd numbers for y, so we will have 9 outcomes of our total 20 outcomes where xy is odd, giving us a probability of 9/20.

There are 18 marbles in total. One of them is removed so now there are 17 marbles. This is our denominator. All of the original white marbles are still in the bag so there is a 4 out of 17 or 4/17 chance that the next marble taken out of the bag will be white.