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1. The points M, N, and O are plotted on the number line below. Plot point P based on the equation: N-M+O=P
2. Which of the following is equivalent to 4^3+12÷4+8^2×3?
3. Solve the equation for x: 3^2+2x=17.
4. Given the sequence represented in the table below, where n represents the position of the term and a_n represents the value of the term, which of the following describes the relationship between the position number and the value of the term?
A. Multiply n by 2 and subtract 4
B. Multiply n by 2 and subtract 3
C. Multiply n by −3 and add 8
D. Multiply n by −4 and add 1
5. Part A: Steven’s class had a pushup contest and the results are recorded below.
What is the median number of pushups the class did?
Part B: What is the difference between the median and the mean number of push ups?
1. M=1/2, N=1 3/4, and O=2 1/4, so N-M+O=3 1/2. The number line is shown below.
2. D: The order of operations states that numbers with exponents must be evaluated first. Thus, the expression can be rewritten as 64+12÷4+64×3. Next, multiplication and division must be computed as they appear from left to right in the expression. Thus, the expression can be further simplified as 64+3+192, which equals 259.
3. X=4: 3^2+2x=17, 9+2x=17, 2x=8, x=4
4. C: The equation that represents the relationship between the position number, n, and the value of the term, a_n, is a_n=-3n+8. Notice each n is multiplied by −3, with 8 added to that value. Substituting position number 1 for n gives a_n=-3(1)+8, which equals 5. Substitution of the remaining position numbers does not provide a counterexample to this procedure.
5. Part A: 33: The median number is the middle number out of the group. In this case there are 18 numbers so it is the average of the 9th and 10th number. However, since the 9th and 10th numbers are both 33 it is just 33.
Part B: 1: The mean can be found by adding all of the numbers together and dividing by 18. If you add all of the numbers up and divide by 18 you get 32. The difference in the mean and median is 1.