Counting / Sets - Algebra 1

Since we are given the mean, we need to find the sum of the numbers. From there we can figure out . We know

We can use this to find the sum by plugging in

So our sum is 96.

So we know that our total sum minus the sum of the given numbers is equal to .

So, .

2 men can be selected:

2 women can be selected out of 4 women:

Finally, after the selection process, these men and women can fill the executive body in ways.

This gives us a total of

This is a sequence that features every other positive, odd integers. The missing number in this case is 9.

You need to evaluate the terms in the sequence to determine the pattern that is shown. In this case, the first term is multiplied by 2 and the second term is found by adding 3.

Find the missing number:

To find the missing number, we need to find the pattern.

If we look closely, our numbers are going up by the same number each time: 13

To check this, find the difference between neighboring numbers

You get the idea.

So, to find the missing number, simply do the following:

Notice that the world parabolic is given. This means that our parent function will be in the form:

The terms resemble a pattern where the parent function is centered at , and the first term starts at and so forth.

We can find the two missing terms by substituting to determine the missing numbers.

The first number is:

The second number is:

The respective numbers are:

Notice that the second and third terms in the set of numbers can be subtracted to determine the displacement of each number in the set.

Subtract negative three from one. Enclose the negative number with parentheses.

Each number is spaced four units.

Subtract four from negative three to find the first number.

Add four to one to find the number for the second question mark.

This number is also four units from nine.

The answer is:

Determine the distance between each number.

The second and the third number are spaced units.

Check the third and fourth number if this is also has the same displacement.

Since this is true, this means that the numbers are also spaced at units.

Notice the fractions are in decreasing order.

Add units to the second term to obtain the first term.

Reduce this fraction.

The first term is:

Subtract units from to obtain the fifth term.

Reduce this fraction.

The fifth term is:

The correct answer is:

, ,

We can simply plug in the values to each occurrence of the variables.

For :

Then :

Then :

Now we can solve.

The prime integers beterrn 20 and 40 are 23, 29, 31, and 37. Their sum is

.

There are four perfect squares between 10 and 50: 16, 25, 36, and 49. There is one perfect cube, 27, in this range. Add:

The smallest perfect square between 100 and 1,000 inclusive is 100 itself, since . The largest can be found by noting that ; this makes the greatest perfect square in this range.

Since the squares of the integers from 10 to 31 all fall in this range, this makes perfect squares.

There are five ways to choose the first scoop, then four ways to choose the second scoop, and finally three ways to choose the third scoop:

5 * 4 * 3 = 60

To calculate the number of integers, find subtract the integers of interest and then subtract 1.

As a proof of concept, calculate the number of integers that fall between 5 and 10 on a number line. We know there are 4 (6, 7, 8, 9).

How many integers are in between the numbers 455, and 467?

An integer is just a whole number.

We can find the number of integers between two numbers in a variety of ways. To start, let's count off.

456,457,458,459,460,461,462,463,464,465,466

There are 11.

However, what if your numbers are really big?

Then just subtract the smaller number from the bigger number and then subtract 1.

Our answer is eleven either way.

To determine the number of integers in between 2 and 8, we can simply write out the numbers and count.

Notice that the number of integers in between two other integers will be one less than the range of the two given numbers.

The answer is: