Hi, Lydia! This question is very common in a log unit. The basic outline for solving this question is to use the information they gave you (year = 1995, pop = 1400) to find k. Once you know k, find t for the year 2010 and plug everything in to find the population in...

## Answers by Patricia S.

Hi, Prasenjeet! Proving an equation in mathematics almost always means to simplify each side individually and try to get them to equal the same thing. With that being said, let's take a look at the two questions you listed above: 1.) log2 + 16*log(16/15) +...

Hi, Tevell! Before I show you the truth table for the statement that you gave above, let me make sure that you understand all the parts of the statement. If you have a statement p, the statement ~p is read as "not p" and understood to be the opposite of what p says...

Hi, Abby! A sector is simply a piece of a circle. The easiest way to find the area of a sector is to find the area as if it were a complete circle (Area of a circle is pi*r2.) and then multiply it by a ratio to represent the size of the sector compared to a whole circle (degree/360)...

PJ, A term is defined as a number, variable, or some combination of numbers and/or variables being multiplied together. Even though 2x has two parts (2 and x), since they are being multiplied together, 2x is considered a single term (a monomial expression). In expressions...

Hi, Lila! Vivian and Ken are correct in that two of the roots are +/-3. However, you need to be careful "canceling" out a k on both sides, as this removes one of the possible roots. This type of problem is traditionally solved using factoring: 3k3 =...

Hi, Chani. This might be a little difficult to explain given that it has fractions in it and the formatting of this response window doesn't have the best display options for fractions, but I'll do what I can! So, we have: (4b2c)3 * 5a5c...

Hi, Denisha! Let me rewrite the question to make sure that I understand it. You are trying to simply the following expression: (m1/4n1/4)2 * (m2n3)1/2 There are a couple things from middle school math that will help with simplifying this expression...

Victoria, Are the 4x and 3(x+6) on opposite sides of the quadrilateral? If so, you can solve for x by setting them equal to each other (opposite sides of a parallelogram have equal lengths). It would look like this: 4x = 3(x+6) 4x = 3x+18 x...

Hi, Mondrea! This equation could be solved a few different ways, depending on what is underneath the square root sign on the left side of the equation. In this solution, I assumed that the entire left side of the equation is under the square root symbol. √(3x+13)...

Hi, Abby! When simplifying math expressions that have radical symbols in them (like square roots), "like terms" are terms that have the same radicand (number under the radical symbol). With that in mind, these directions are instructing you to rewrite √80 in such...

Hi, Amy! What are you trying to solve about this scenario? - If you are given a C and told to solve for N, then I would recommend plugging in the domains for N to determine a range of C values for each part of the piecewise function. Then use the equation...

Mary, I want to make sure I understand what each of the three equations are: EQ1: 6x+5y+2z=830 EQ2: 3x+7y+4z=820 EQ3: x=x-22 Is this correct? If so, the last equation (EQ3) does not make any sense. There is no number...

Hi, Danny! This question requires a little bit of background in statistics. According to statistics, when data is represented using a standard bell-shaped curve (also known as a "Normal Distribution"), 68.2% of the data should fall within 1 standard deviation of...

A fraction is just another way to write a division problem: The top number (numerator) divided by the bottom number (denominator). If you were writing the division problem in terms of the square division bar (like in long division), the numerator would go under the bar and the denominator...

Hi, Haley! Once you've used the Law of Cosines to solve for another piece of information, there are many different ways to find the remaining missing angle and segment measurements. Given that you asked about the Law of Cosines in the question title, I will show how to apply...

Hi, Pamela! The set that you described can be written as "The set of all numbers x such that x is a Natural number and is greater than or equal to 1000." If you recall, Natural numbers are counting numbers (0, 1, 2, 3, 4, 5...). They are non-negative integers...

To calculate Mary's opportunity cost of moving to New York, calculate Mary's net income in New York City for a year (after rent and insurance are paid) and compare it to her net income in Princeton, NJ for a year (after rent and insurance are paid). NYC: Salary...

This question seems kind of silly given that they already told you what the price of a chair is, but if you pretend you don't know that information, you are left with this: x = cost of 1 chair Need: 6 chairs Table costs: $419.99 Budget: $2000 The question...

Hi, Serenity! First of all, let me make sure I understand your question: You are trying to add two fractions, 2/(1+i) and 3/(1-i). To begin this question, the first step is the same as any other time when you are adding or subtracting two or more fractions:...