
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`...

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...

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...

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 =...

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...

Math
We are asked to find the critical numbers for `f(x)=root(3)(x^33x^2)` . Critical points of a function occur when the first derivative is 0, or when the first derivative fails to exist. Thus to...

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...

Math
We are asked to solve sin(x+pi/4)=2(cos(xpi/4)) for x. Often, to solve equations involving trigonometric functions, it helps to try to transform the equation to one that involves only one...

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...

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...

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...

Math
We are given a fourdigit 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...

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...

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...

Math
Denote the relative amount of the substance remaining after `t` years as `R( t ).` We know that after `H` years (the halflife period) `1/2` will remain: `R(H) = 1/2.` Then after `H` more years the...

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...

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 wellknown Bolzano theorem about a...

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...

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...

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....

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...

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 yintercept. I will assume that the first part of the equation is 2x2; in many...

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...

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...

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...

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...

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: `328.54200=128.54` Silvio's earnings...

Math
Can the two triangles be proved congruent? If so, by which method: sss, sas, asa, aas, or hl. Please help me with this problem.
Can the two triangles be proved congruent? If so, by which method: sss, sas, asa, aas, or hl.
Here are the...
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,...

Math
Sqrt(135*b*c^2*d^3) * sqrt(5*b^2*d) The first thing to remember is that when you’re multiplying square roots, you can combine everything underneath the radical as if it’s not there, so let’s...

Math
The position function is given as `s(t)=6.5+4t^2t^4` for t>0 The velocity function is the first derivative of the position function, and the acceleration function is the derivative of the...

Math
First, arrange them in order from smallest to largest so you can see where your number line will start and end: `x> 3; x>= 5/2; x<=2; x<5/2` On a number line the ones that are only...

Math
We are asked to find the number of 4 letter "codes" that can be created using the 26 letters of the alphabet. There are a couple of considerations. Are we allowed to repeat letters (e.g., is AAAA a...

Math
Every year that you own this comic book, it will appreciate 9%. So, you will multiply the initial amount by 1.09 every year. This works out to a fairly straightforward equation. Assuming Y is the...