# Tutor profile: Paola T.

## Questions

### Subject: Pre-Algebra

Sarah solved the following problem. $(2-1(3+2)=?$) Here is her answer: $(2-1(3+2)=1(3+2)=1(5)=5$) Is she correct? If not, where is her mistake?

She is not correct. Order of operations tells us that we must do parenthesis first, so the first step should be to add 3 and 2 inside the parenthesis $(2-1(5)$) Next, order of operations tells us we should do multiplication, so next, we multiply 1 and 5 $(2-5$) Finally we subtract $(2-5=-3$) The answer should be $$-3$$

### Subject: Statistics

The Pearson correlation coefficient ($$r$$) is a measure of the linear correlation between two variables. Given the following Pearson correlation coefficients, what can you say about the equation/model that it represents? a) $$ r= -0.95$$ c) $$ r= -0.12$$ d) $$ r= 1$$

a) The coefficient is negative, this means that there is a negative linear correlation between the two variables, as one increases the other one decreases. Since the number is close to -1, this means that the linear equation is a good representation of the data. b.) The coefficient is close to zero, this means that there is really no correlation between the two variables. The equation/model would not but useful in representing the data. c.) The coefficient is positive, this means that there is a positive linear correlation, as one variable increases so does the other one. The number is 1, this means that the equation/model represents the data perfectly.

### Subject: Algebra

James has 19 nickles and dimes in his pocket. If he has a total of $1.50, how many nickles and how many dimes does he have?

To begin, we must take our context and turn into something we can work with mathematically. That is, make equations that we can solve. First, let's choose which variables we want to use. N = the number of nickles James has D = the number of dimes James has Now we use these variables and the information given to us in the problem to write our equations. We know that James has a total of 10 nicles and dimes in his pocket. So one of the equations is: $( N + D = 19$) We also know that he has a total of $12, which is 1200 cents. Using that information, along with our knowledge of the values of nickels (5 cents) and dimes (10 cents), and have the second equation. $(5N + 10D = 150$) Are these equations enough to answer the question? We have two equations and two unknown variables, this is a 2x2 SYSTEM OF LINEAR EQUATIONS which we can solve. \begin{cases} N + D = 19\\ 5N + 10D = 150 \\ \end{cases} There are a few ways to solve a 2x2 system of linear equations. Today, we will be using the substitution method. We take the first equation and solve for N subtracting D from both sides of the equation. $(N +D - D = 19 - D $) This leaves us with $(N = 19 - D $) Now, we take this new equation and plug it into the second equation of our system. $(5(19-D)+10D=150$) We focus our attention on this new equation. We only have one variable, D. This means we can easily solve for D. We use the DISTRIBUTIVE PROPERTY to expand the left side, multiplying by 5 everything inside the parenthesis. $(5 \times 19 - 5D+10D=150$) $(95 - 5D+10D=150$) We combine LIKE-TERMS $(95 +5D=150$) We subtract 95 from both sides. $(95 +5D -95=150-95$) Which leaves us with $(5D=55$) Finally, we divide both sides by 5 $( \frac{5D}{5}= \frac{55}{5}$) We simplify $(D=11$) We have part of our answer! $$D=11$$, James has 11 dimes. Now, how many nickles does he have? Well, we know he has a total of 19 nickles and dimes, that is: $( N + D = 19$) We substitute 11 in for D and we have $( N + 11 = 19$) We subtract 11 from both sides $( N + 11-11 = 19-11$) and we are left with $(N=9$) Now we have the answer, James has 11 dimes and 8 nickles.

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