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A manager gives gift cards to every 80th customer. On Saturday, 1210 customers entered, while on Sunday, 1814 customers entered. We are asked to find the number of people who received gift cards....

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We are given that Jenny finished 12 of 20 piano lessons from her book and that Liam finished the same percentage from his book of 30 lessons. We are asked to find the number of lessons Liam...

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I assume you are asked to show that the finite sum (this is a series; the sum of the elements of some sequence): 3+6+9+...+3n=(3n(n+1))/2 We can rewrite the equation as :...

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The equations indeed represent two straight lines, because they are both linear (have the form A x + B y = C ). To find the point of intersection is the same as to solve the system of these...

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(1) We are asked to find the point of intersection of the lines y=3x+4 and y=-2x+9. There are several methods to find this point, assuming it exists. Given the equations of two lines, the graphs of...

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In this question, x represents the quantity demanded in units of 1000, and p represents unit price in dollars. The equation of the demand curve is 3x + 4p - 48 = 0. We rewrite this equation in the...

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Let's start by looking at the component parts of the number sentence. Five is being multiplied by zero. The product of that answer then has one fifth added to it. Everything in the parentheses is...

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1) For f(x) = 3x + 9, we can rewrite as y = 3x + 9 and the reverse the x and y, which yields x = 3y + 9. If we solve for y, we'll have the inverse function. x = 3y + 9x - 9 = 3yy = 1/3x - 3 2)...

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We are asked to graph the functions C(x)=12x+17000 and C(x)=20x+16000. See the attachment for the graphs. C(x)=12x+17000 is in green while C(x)=20x+16000 is in blue. C(x)=12x+17000 is a linear...

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There are 4 answers for each multiple choice question and each of them has only one correct answer. If any answer is chosen at random the probability of it being correct is 1/4. The probability...

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The boat moves up and down with the passing waves. I take the height of the boat to be a sinusoidal function. And the height of the boat is zero at the start of the cycle. The distance between the...

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f(x) = 2x g(x) = x + 3 First let us find (fog)(x) (fog)(x) = f(g(x) = f(x+3) = 2(x+3) = 2x + 6 ==> (fog)(x) = 2x + 6 Now let us find (gof)(x): (gof)(x)...

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You need to evaluate the definite integral of the given funtion to find the area under its graph such that: int_1^n (x^2+ sqrt(1+2x)) dx  You need to use the property of linearity of integrals...

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The given relation  tan lambda = (cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda)  cannot be proved. As seen from the link provided in the question the back drive efficiency is given by...

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You need to find the limit of the function tan 2x , x-gtpi/2 , hence you need to substitute pi/2 for x in the equation of the function such that: lim_(x-gtpi/2) tan 2x = tan 2(pi/2)...

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In the problem we are given the length of two of the sides of the triangle and we have two of the angles. The sum of the three angles of a triangle is equal to 180 degrees. Using this, the third...

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First, it depends on how you interpret the dv term. The most obvious way is to interpret it as (dv)/dx which is how I'll treat it. There are two things to remember with regard to differential...

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Hello! Because the task contains expressions dx / dt and dy / dt, we know that x and y are functions of t : x = x ( t ), y = y ( t ) . Here t is an independent variable....

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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,...

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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...

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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...

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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...

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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...

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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...

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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...

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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...

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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....

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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...

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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...