Real Numbers - Algebra

Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.

x + (x + 2) + (x + 4) = 72

3x + 6 = 72

3x = 66

x = 22.

This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.

The answer is 13728.

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:

Divide the absolute values to get the magnitude of the answer.

Remember the following rules:

Positive divided by negative is negative.

Positive divided by positive is positive.

Negative divided by negative is positive.

Since we are dealing with two negatives, our answer will be positive.

This is a classic order of operations question, and if you are not careful, you can end up with the wrong answer!

Remember, the order of operations says that you have to go in the following order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (also known as PEMDAS). In this equation, you will start with the parentheses. In the parentheses, we have

.

But within the parentheses, you still need to follow PEMDAS. First, we will solve the exponent, and the square of 2 is 4. Then, we'll divide 16 by 4, which gives us 4, so we can rewrite our original equation as

.

We can now divide into , which gives us

.

The last step is to add and subtract the numbers above, paying careful attention to negative signs. In the end, we end up with because added to equals , and minus equals .

All of these choices are equivalent to the correct answer. But only is in scientific notation.

For a number A to be divisible by another number B, A must share all of the prime factors of B. For example, 100 is divisible by 10 because the prime factors of 10 (5 and 2) are found in the prime factors of 100 (2, 2, 5, and 5).

In this problem, we have a number A that is divisible by 9 and 12. First, find the prime factors of 9 and 12. The factors of 9 are (3, 3). The factors of 12 are (2,2,3). So, to be divisible by 9 and 12, the number A must have the factors (2,2,3,3). Multiply those together, and we get 2*2*3*3= 36.

So, A must be divisible by 36. It could be divisible by the other answer choices, but since the question asked which choice must be right, we can only choose 36.

One way to do this:

Divide 100 by 6. The remainder will be the last digit.

Now divide the quotient by 6. This remainder will be the second-to-last digit.

The quotient is less than 6, so it is the first digit. The base-six equivalent of 100 is .

Write the factors of the two numbers.

If a number is divisble by some number , then it is also divisible by all of its factors. Hence, if a number is divisible by , it is also divisible by , and . Thus, I and II are both true.

When you are dealing with negative numbers, the following rules apply.

If there are no negative signs, the answer is positive.

If there is one negative sign, the answer is negative.

If there are two negative signs, the answer is positive.

, and since there is only one negative sign the answer is negative. is the solution.

Rewrite the expression in fraction form.

Write out the common factors of both the numerator and denominator.

We can then see that the fraction can be reduced to without having to conduct long division.

The answer is .

Rewrite the expression as a fraction.

Write out the multiples of the numerator and denominator.

The twos can be cancelled. Simplify what remains of the fraction.

The answer is: