Think of 5 positive integers that have a mode of 4, a median of 8, a mean of 9 and a range of 12 what are the 5 integers

{4, 4, 8, 13, 16}

Step-by-step explanation:

If we have a set of N numbers in order:

{x₁, x₂, ..., xₙ}

The median is the middle number of the set.

The mode is the value that is repeated more times in the set

The mean is computed as:

And the range is the difference between the largest value and the smallest value.

Here we want 5 positive integers, so we have something like:

{x₁, x₂, x₃, x₄, x₅}

We know that the median is 8.

Then the middle value, x₃, is equal to 8.

We also know that the mode is 4, then we can have the number 4 repeated two times, and because 4 is smaller than 8 and this must be in order, then we can have:

x₁ = x₂ = 4

Replacing these in the set we have:

{4, 4, 8, x₄, x₅}

Now we know that the range is 12, and this was the difference between the largest and smallest value.

We know that the smallest value is 4, and the largest value is x₅, then we will have:

x₅ - 4 = 12

x₅ = 12 + 4 = 16

Then our set is:

{4, 4, 8, x₄, 16}

Finally, we know that the mean is 9.

Remember that the equation for the mean is:

Then we need to solve:

Then the set of five positive integers is:

{4, 4, 8, 13, 16}

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions