# Tutor profile: Aleksandra B.

## Questions

### Subject: SAT

f(x) = 2x + 4; Find f(4) + f(6): a) f(2) b) f(4) c) f(12) d) f(28)

Be very careful with this one. A lot of my students have trouble with functions and they don't even realize it. So, in this case, we have a function: f(x) = 2x + 4. We are asked to find f(4) + f(6). Let's break this up into 2 problems. First, we have to find f(4). This means we plug in the 4 where the x is in the equation and solve. So f(4) means 2(4) + 4 which equals 8 + 4 which equals 12. Now, let's find f(6). f(6) means 2(6) + 4 which equals 12 + 4 which equals 16. So f(4) + f(6) is going to be 12 + 16 which equals 28. HOWEVER, not so fast. The answer choices are NOT just numbers. They gives us MORE functions. So you may think the answer is d, f(28), but that is NOT the same thing as our answer, 28. f(28) means you are plugging in 28 to the original function, so f(28) means 2 (28) + 4 which equals 60. That is not correct. So, we now have to go through and plug in the answer choices to find the one that also equals 28. a) f(2) is 2(2) + 4 which equals 4 + 4 which equals 8. b) f(4) is 2(4) + 4 which equals 8 + 4 which equals 12. c) f(12) is 2(12) + 4 which equals 24 + 4 which equals 28. So our answer is c) f(12).

### Subject: Java Programming

What is the difference between an object and a class?

Java is an object-oriented programming language. What this means is that every single time you write a program in Java, you represent things in the real world using objects and classes. So a class is like a BLUEPRINT or a DICTIONARY DEFINITION of what something is. For example, let's say we want to make a video game, and we need a way to represent a DOG. We are going to create a CLASS that represents what a DOG is, to tell the computer what a dog is, what it can do, and what characteristics define it. public class Dog { String color; int age; public void bark() { } public void eat() { } public void wagTail() { } } So in the above class, we have defined a dog using fields (also called attributes) and methods (which represent behavior). The fields are VARIABLES (so the fur color, the age, etc.) that describe what each specific dog is like. The methods are VERBS (so actions that a dog can do that make it a dog). This class describes a dog in general. This code does NOT create an actual dog. It's just a definition for the computer of what a dog IS. Now, let's create a dog OBJECT using this class definition: Dog() Antoni = new Dog(); NOW, we have created a SPECIFIC dog, and his name is Antoni. We can create a few new dogs for him so that he has friends: Dog() Polly = new Dog(); Dog() Ted = new Dog(); So each of these dogs could have their OWN characteristics, which we describe using those FIELDS we created earlier in the class definition. Let's say Antoni is a 5-year-old dog with brown fur, Polly is a 1-year-old Puppy with black fur, and Ted is a 6-year-old dog with white fur. Antoni.color = "brown"; Antoni.age = 5; Polly.color = "black"; Polly.age = 1; Ted.color = "white"; Ted.age = 6; So now, we have used both a class and an object. Remember, a CLASS is just a DEFINITION or a BLUEPRINT or a MAP of how to make something, so that we can represent it. An OBJECT is every specific individual we create that is a model of the thing defined by the CLASS.

### Subject: GRE

The average (arithmetic mean) high temperature for x days is 90 degrees. The addition of one day with a high temperature of 95 degrees increases the average to 97 degrees. Quantity A: x Quantity B: 6 Choose the correct answer below: (A) Quantity A is greater. (B) Quantity B is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given.

To find the average of a few different numbers, we add up all of the numbers to get the SUM, and then we divide the SUM by how many numbers there are. We can apply that to this question: Since we know that the original average is 90, we can say that: (the total of all of the temperatures) / x = 90. So (the total of all of the temperatures) is equal to 90x. We are then told that adding one day (which makes X + 1 temperatures now, not just x) increases the average. So the original average, 90, is now wrong. Our new average is 97. We can do the same calculation: (the total of all of the temperatures) / (x + 1) = 97. We can substitute 90x + 95 for (the total of all of the temperatures), since that is our newly added day (with a temperature of 95) added to what we found earlier (90x). So now, our equation is: (90x + 95) / (x + 1) = 97. And now, we can just solve this equation to find x: Multiply both sides by (x + 1) to get rid of any fractions in the equation (this makes things easier to solve). We get 90x + 95 = 97 * (x + 1). Multiply out the right side using the distributive property, and we get: 90x + 95 = 97x + 97. Subtract 95 from both sides. 90x = 97x + 2. Subtract 97x from both sides. -7x = 2. Divide both sides by -7. x = -2/7. So x is, in fact, NOT greater than 6. Therefore, quantity B, 6, is greater. Therefore, the answer is (B) Quantity B is greater.

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