# Tutor profile: Tali R.

## Questions

### Subject: Calculus

Perform the function evaluation for: f(x) = 3 - 5x - 2x^2 a. f(4) b. f(6-t)

When presented with problems like this, what is being asked is to perform the substitution and them to simplify. This is one of the first concepts that needs to be mastered before moving onto more complicated calculus problems. a. This is a simple numerical substitution, replace x with 4 in the given function. This evaluates to 3 - 5(4) - 2(4)^2 Now, using the correct order of operations, this further evaluates to -49. b. While still a matter of substitution, this requires a little more work when simplifying than just basic arithmetic. Here is a break down, step by step, for solving this more involved substitution: First, simply sub for x: f(6-t) = 3 - 5(6-t) - 2(6-t)^2 Next, start with exponents f(6-t) = 3 - 5(6-t) - 2(36-12t+t^2) Now, we can distributed the multiplication throughout the parentheses: f(6-t) = 3 - 30 +5t -72 + 24t - 2t^2 Finally, add like terms to simplify to it's final stage: f(6-t) = -99 + 29t - 2t^2

### Subject: Statistics

Consider the following three data sets: A = {9,10,11,7,13} B = {10,10,10,10,10} C = {1,1,10,19,19} a) Calculate the mean of each data set. b) Calculate the standard deviation of each data set.

This is a very traditional type of question when introducing the early concepts of statistics, namely mean and standard deviation. a) To find the mean of any data set, it is just a matter of finding the average. Simply add all of the Data points and divide it by the total number of Data points. For A, 9+10+11+7+13 is 50. There are 5 data points giving us the the mean of 10: 50/5 = 10. Note that B and C will also have means of 10 because, although they have different values for some of the data points, the total is the same as well as the number of data points. b) While there is an equation for finding the mean, it is simpler to explain it as an average: a total divided by the number of items added. The standard deviation, however, is best conceptualized by the equation. It needs to be shown as a picture or written on paper because it is a summation formula and would end up being very confusing if typed out... so I will do my best to explain this without that visual: There are 4 steps here: 1] Find the mean, which we just did (10 for all 3 data sets), and call it μ, pronounced "mu". 2] Next, subtract each data point in a particular set by the mean of that set, then square it. For A, this would be : (9-10)^2 or (-1)^2 or 1 (10-10)^2 or (0)^2 or 0 (11-10)^2 or (1)^2 or 1 and so on to get {1, 0, 1, 9, 9} 3] Then, just like how we found the mean of the original data set, now we will find the average of these numbers. For A (remember that a negative squared is positive): (1+0+1+9+9)/5 is 20/5 is 4. 4] The very last step is taking the square root of the results from step 3. For A, the square root of 4 is 2, giving us the standard deviation! Now, notice that the standard deviation for B is 0. The reason is because all data points are 10 and the mean "mu" is also 10. Since our standard deviation is calculated by subtracting those (10-10), our standard deviation equation comes to 0/5, which of course is 0. See if you can use these steps to find that the solution for C is 8.05!

### Subject: Algebra

Evaluate the following --> -24 + 3*(6 ÷ 2)^2

In algebra, and other subjects in math and science, you'll often be faced with questions that require you to utilize the principle of PEMDAS - also referred to as the order of operations. This stands for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction and simply points to the order in which you execute the calculation. Some problems will ask you to solve one calculation, as in this example, while other, more wordy problems, will involve many different areas that need to be evaluated using this method in order to find the overall solution. It is important to practice these types of examples so it can become second nature. For this example, we start with the Parentheses (6÷2) resulting in 3: -24 + 3*(3)^2 We then move to the next step of evaluating the Exponent, 3^2, which is 9. The equation at this step is shown below (notice how nothing has changed on the left side of the multiplication): -24 + 3*9 Multiplication/Division comes next, 3*9 = 27, giving us: -24 + 27 At this point, you can "add a negative and a positive" or, if it helps, rearrange to a subtraction: 27 - 24 We now arrive at our final answer, 3.

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