# Math

• Math
We are asked to evaluate int_(-oo)^(oo)e^(-x^2)xdx I. The easy way is to recognize xe^(-x^2) as an odd function. ( f(-x)=-f(x) ). Since the limits of integration are symmetric about the origin,...

• Math
We are asked to find a transformation from the list that is equivalent, in the sense that it maps the given quadrilateral to the same image, as a reflection over the y-axis. We are given...

• Math
To determine the bounded region, graph the given equations. (Please see attached figure.) On the bounded region, draw a dot to represent its center of mass. To get its coordinates, we have to solve...

• Math
We are given f''(x)=2x, f'(2)=1, and f(1)=3 and we are asked to find the particular solution to the differential equation. Since we know the second derivative, we can use the indefinite integral...

• Math
We are given that Mary purchased 3 yards of fabric from a roll that started with 8 1/2 yards, and we are asked to find the number of 1/2 yards remaining on the roll. There are a couple of good...

• Math
This math question can be solved by figuring out the relation between the increase in the volume of gallons of water in the tank and the increase in volume of disinfectant. To figure this out, one...

• Math
To determine the bounded region, graph the given equations. See the attached image for the graph I've created. Base on the graph, there are three bounded regions. To get the area of each bounded...

• Math
The primary question asks us to determine the number of cups of bleach to add to 5 gallons of water if 4.5 cups is required for 10 gallons of water. One approach to solving a problem like this is...

• Math
Find the principal (original) amount if $675 "ordinary" interest accrues after 6 months. Depending on your definition of "ordinary" interest as being simple interest: P = ? (the unknown) rate (r... 1 Educator Answer • Math The best way to learn any kind of math is to do it. Watching videos and listening to lectures may be beneficial to an overall understanding, but to become proficient one must use a pencil and paper... 1 Educator Answer • Math We are given that two solids, solid I and solid II, are similar with a scale factor of 3:5. The height of solid I is given as 3 cm, and we are asked to find the height of solid II. A simple... 1 Educator Answer • Math Let's think of this question as: x% of n is a, then what is y% of n. x% of n can be written as (x/100) * n. This means (x/100)*n = a Using this relation, we can find the value of n as: n =... 1 Educator Answer • Math We are given two isosceles triangles with the same base. We are asked to prove that the line joining the vertex angles is the bisector of the base. When asked to do a proof, there are a few general... 1 Educator Answer • Math We are asked to find the critical numbers for f(x)=root(3)(x^3-3x^2) . Critical points of a function occur when the first derivative is 0, or when the first derivative fails to exist. Thus to... 1 Educator Answer • Math We are asked to find the exponential function that contains the points (3,12) and (4,24). Exponential functions can be written in the form y=a*b^x . b is the base of the exponential function. b... 1 Educator Answer • Math We are asked to solve sin(x+pi/4)=2(cos(x-pi/4)) for x. Often, to solve equations involving trigonometric functions, it helps to try to transform the equation to one that involves only one... 1 Educator Answer • Math This question becomes easier by rephrasing the sentences. For example, "a glass of sweet tea is 1/8 of a gallon" can also be understood as "a gallon fills 8 glasses of sweet tea". In other words, 1... 1 Educator Answer • Math We want to solve the given system of equations by graphing and locating the point of intersection (if it exists). The system: y = x - 1y = 3x - 9 A system of two linear equations in two variables... 1 Educator Answer • Math We are given that Jenny has 12 apples, 30 pears, and 42 oranges. If she is making fruit baskets, each of which contain the same number of each fruit, what is the largest number of baskets that she... 1 Educator Answer • Math We are given a four-digit number with leading digits 1, 5, and 5. When this number is divided by 35 the remainder is 15. We are asked to find the last digit. (1) We can try a guess and revise... 1 Educator Answer • Math The initial question gives the following information: Marcy takes two kinds of medicine; one every 4 hours, and the other every 6 hours. We are told that Marcy took both medications at 10 a.m., and... 1 Educator Answer • Math We are asked to find the interval in which we would be unable to reject the null hypothesis. When hypothesis testing we generally state the null hypothesis, the alternative hypothesis, and the... 1 Educator Answer • Math Denote the relative amount of the substance remaining after t years as R( t ). We know that after H years (the half-life period) 1/2 will remain: R(H) = 1/2. Then after H more years the... 1 Educator Answer • Math This subtraction problem is made a bit more complicated by fractions which do not share a common denominator. The first step is to determine the greatest quantity that the gas tank can hold. In... 1 Educator Answer • Math Hello! To find some c such that f(c) = c is actually the same as to solve for c the equation f(c) - c = 0, or to find root(s) of f(c) - c. There is a well-known Bolzano theorem about a... 1 Educator Answer • Math From what I have read, you will need get about 1/2 the questions correct in order to pass the math section of the GED. It does vary from state to state, so it will depend on your specific testing... 1 Educator Answer • Math A logical independent variable to use in regression analysis on BMI might be a measure for class, such as annual family income. As class has an intense affect on people's ability to access healthy... 1 Educator Answer • Math If Sally earns$400 per week and she spends 15% of her earnings on transportation, then Sally spends $60 per week on transportation. Let’s look at how to use multiplication to solve this problem.... 1 Educator Answer • Math We are given a circle with radius 17 cm. There is a chord 9 cm from the center. We are asked to find the perimeter of the minor segment formed by the chord. Let the center of the circle be O, and... 1 Educator Answer • Math This is a linear equation which can be rewritten into the formula y=mx+b, where m is the slope and b is the y-intercept. I will assume that the first part of the equation is 2x2; in many... 1 Educator Answer • Math A normal distribution can be used to find the probability of a given range of scores in the distribution. The probability is the area between two values under the curve given by P(x)=(1/(sigma... 1 Educator Answer • Math We are given that 4 students are wearing red shirts, 11 students are wearing blue shirts, and 10 students are wearing black shirts. We are asked to find the ratio of students wearing red or black... 1 Educator Answer • Math We are asked to find the points of inflection for the graph of f(x)=6sin(x)+sin(2x) Points of inflection occur when the concavity of the graph changes. (Graphs can be concave up, concave down, or... 1 Educator Answer • Math To calculate the APR, you fortunately have all the information you need. The APR is the annual percentage rate, and it is the interest with which the monthly payments are calculated. The first... 1 Educator Answer • Math The null hypothesis is that the mean cost of textbooks is$130. H_0:mu=130 . The alternative hypothesis (and in this case the claim) is that the mean cost of textbooks is greater than \$130....

• Math
To determine Silvio's gross sales, first subtract his base salary from his gross earnings to determine the amount of earnings Silvio made on commission alone: 328.54-200=128.54 Silvio's earnings...

• Math
Triangles are congruent if they have three equal sides and three equal internal angles. Congruent triangles can be exact copies or mirror images. Here are the rules for congruent triangles: 1....

• Math
To convert a decimal into a percentage, all you have to do is multiply the decimal by 100 and add the percent symbol. For example, 0.14 x 100 = 14% The word percent means “per hundred” (in...

• Math
Each die has 6 sides, each of them has the same probability to show itself (of course, this probability is 1/6). There are 3 even numbers on each die, 2, 4 and 6. Also, the outcome of the second...

• Math
Hello! Denote a number of groups as n . Because each of n groups should have the same number of boys, this number n must divide the number of boys, i.e. 24 . The same way, because each of...

• Math
In order to answer this question, it is important to know what is being asked in mathematical terms. Here, the real question is to find the lowest common multiple between 12 and 16. Here's why....

• Math
Because the angles are not the same (even though the heights of the buildings are), we know that the observer isn’t standing exactly halfway between both buildings. The building closest to the...

• Math
In order to find the monthly payment on a mortgage or other fixed rate loan, there is a relatively straightforward equation. The equation uses the term (length) and interest rate to determine the...

• Math
It looks like you are trying to collect like terms in order to solve for y. This can be tricky when both numbers you are working with are negative. And working with fractions can be tricky, too. So...

• Math
When you are graphing the equation y = mx + b (or - b, it doesn’t matter), you need to first find one of the intercepts. It is easiest to find the y intercept because the equation is set up to show...

• Math
Each person either always tells the truth or always tells a lie. In these kinds of problems, such persons are usually called "knights" and "liars," respectively. Consider two possibilities: the...

• Math
To find the mean absolute deviation, you have to take several steps. The mean absolute deviation is the average distance away from the mean value of a dataset of each datapoint. First, you need to...

• Math
A rational number is any number that can be written as a ratio (i.e., a fraction). When the fraction is divided to form a decimal value, it becomes a terminating or repeating decimal. For example,...