To find the IQR you first need to write it in numerical order
77, 81, 83, 84, 86, 86, 88, 92
IQR is just Q3 - Q1
Q1 is the middle of the first have, since it has an even set of 4 numbers in the first half you need to take the average of the two middle ones.. which is 82
Q3 done the same process would be 87.
87 - 82 = 5
IQR = 5
Answer:
The baker uses 15 cups of cereal for 10 cups of marshmallows
Step-by-step explanation:
The proportion 6:4 has to stay true in the answer, so both numbers have to be multiplied by the same number
6 x 2.5 = 15
4 x 2.5 = 15
both numbers were multiplied by the same number in this answer and it is the only answer that stays true to the ratio
Answer:
Step-by-step explanation:
If you want to determine the domain and range of this analytically, you first need to factor the numerator and denominator to see if there is a common factor that can be reduced away. If there is, this affects the domain. The domain are the values in the denominator that the function covers as far as the x-values go. If we factor both the numerator and denominator, we get this:

Since there is a common factor in the numerator and the denominator, (x + 3), we can reduce those away. That type of discontinuity is called a removeable discontinuity and creates a hole in the graph at that value of x. The other factor, (x - 4), does not cancel out. This is called a vertical asymptote and affects the domain of the function. Since the denominator of a rational function (or any fraction, for that matter!) can't EVER equal 0, we see that the denominator of this function goes to 0 where x = 4. That means that the function has to split at that x-value. It comes in from the left, from negative infinity and goes down to negative infinity at x = 4. Then the graph picks up again to the right of x = 4 and comes from positive infinity and goes to positive infinity. The domain is:
(-∞, 4) U (4, ∞)
The range is (-∞, ∞)
If you're having trouble following the wording, refer to the graph of the function on your calculator and it should become apparent.
Given that the sides of the acute triangle are as follows:
21 cm
x cm
2x cm
Stated that 21 cm is one of the shorter sides of the triangle2x is greater than x, so it follows that 2x MUST be the longest side
For acute triangles, the longest side must be less than the sum of the 2 shorter sides
Therefore, 2x < x + 21cm
2x – x < 21cm
x < 21cm
If x < 21cm, then 2x < 42cm
Therefore, the longest possible length for the longest side is 42cm