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Math
We are asked to solve the following system using the Gauss-Jordan elimination method: 2x+3y-2z=122x-3y+2z=-44x-y+3z=-4 We put the coefficients into an augmented matrix:...
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Math
We are asked to find the amount of three different foodstuffs to prepare in order to meet the requirements of particular vitamins/minerals. The amount of each for each foodstuff is given below:...
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Math
In simpler terms, this question is asking, "arrange this group in order of increasing age, then identify the top 25% of eldest members of the group". The ages need to be tallied, with each...
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Math
We are given that identically sized bags of fertilizers contain ingredients as follows: formulation A has 18 parts nitrogen, 4 parts phosphorous, and 5 parts potassium, while formulation B has 20...
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Math
We are asked to approximate the definite integral `int_(0)^(3) e^(-x^2)dx` One method is to use upper and lower sums. We divide the region into n rectangles bounded by the x-axis and the curve such...
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Math
I'm not able to solve this exact problem for you per the eNotes terms of use, but let me talk through a similar problem for you. Afterward, you should be able to use the steps shown here to solve...
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Math
We are asked to find the midpoint of the segment joining the intersection points of the curve `y=x^2-4x+4` and the line `y=x+c` (we are told that m is a constant and m=1—we let c vary.) **If you...
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Math
Let us assign variables: let m be the price of the system at Mary's and let c be the price of the system at Cal's. We are told that the price at Mary's, m, is $220 less than twice the price at...
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Math
Hello! Essentially, there are two unknowns: the price at marys, denote it as `x` (dollars), and the price at cals as `y` (dollars). We are given two statements about these prices. The first...
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Math
In order to subtract one fraction from another fraction, you will need to find the lowest common denominator. The lowest common denominator is the smallest number that can be exactly divided...
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Math
We are asked to find the equation of the line with slope `m=3/4` and containing the point (-8,4). Recognize that a line is determined by two points (through two points there is exactly one line.)...
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Math
This problem is solved by looking at the definitions of certain terms. APR (annual percentage return) is the percent that you would pay on the balance if you left it in the bank for a year with no...
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Math
We are given that `int_(0)^(1)(15xsqrt(x^2+9))dx=50sqrt(10)-135` and we are asked to evaluate `int_(1)^(0)(15usqrt(u^2+9))du` . These are definite integrals. If we restrict the variables to the...
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Math
We are asked to create the 95% confidence interval for the mean number of nights that people stayed for vacation. We are told that the sample size was 1500, and the sample mean is 7.5. We are also...
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Math
Hello! Although $10000 is a number, it does not influence the answer. Let's select 4 students one by one. The first student may be any of those 8 possible. After this choice, one less student...
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Math
We are asked to find the confidence level of the mean of the population that a sample was drawn from. The data from the sample is `bar(x)=21, n=32, sigma=3` with a 95% confidence (`alpha=.05` )...
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Math
To determine the bounded region, graph the given equations.(See Figure 1). Then, shade the bounded region. Since the axis of rotation is horizontal, in cylindrical method, the rectangular strip to...
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Math
We are given the following information about chicken sandwiches. Let x represent the grams of fat. Then the mean of 11 sandwiches is `bar(x)=20.6` with a standard deviation of `s_x=9.8` Let y (the...
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Math
We are given a matrix which has the prices of models of buildings in three different areas. The prices of all houses will be increased by 3%; we are asked to write a matrix with the new prices. The...
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Math
Use the information given to set up equations as follows: Assign variables: Let x be the amount invested in stocks, y the amount invested in bonds, and z the amount invested in money markets. (1)...
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Math
We are given that there are a maximum of 19.15 hours of sunlight on June 21 (day 172) and a minimum of 5.62 hours on December 21 (day 355.) We are told that the underlying function is periodic, and...
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Math
We are asked to show that the system of equations 2x-y=-4 and 8x-4y=8 has no solutions. A system of linear equations is said to be consistent if it has solutions. If there are two linear equation...
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Math
We are asked to solve the system of equations using Gaussian elimination (or Gauss-Jordan elimination.) The system: 3x-2y+z=3x+3y-4z=-72x-3y+5z=8x-8y+9z=17 The idea is to place the coefficients...
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Math
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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Math
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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Math
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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Math
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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Math
(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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Math
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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Math
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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Math
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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Math
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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Math
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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Math
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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Math
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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Math
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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Math
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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Math
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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Math
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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Math
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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Math
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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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,...
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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...
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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...
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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...
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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...
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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...
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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...
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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...
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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`...