# Math

Math

A very simple example of combinations would be in the number of pizzas one could create given a certain number of criteria. In other word, given that a pizza place has: 3 types of crust -thin,...

Latest answer posted February 10, 2010 1:00 pm UTC

Math

The letters R, Q, N, and Z refers to a set of numbers such that: R = real numbers includes all real number [-inf, inf] Q= rational numbers ( numbers written as ratio) N = Natural numbers (all...

Latest answer posted September 7, 2010 12:47 pm UTC

Math

y= 16(0.25)^x The exponential equation represents an exponential decay because the rate of decay is 0.25 which is less than 1. The general form equation is: y(x)= a(1-r)^x such that r is the decay...

Latest answer posted May 23, 2012 2:05 am UTC

Math

A linear equation has the following form: y = mx + b where m is the slopeb is the y-intercept. You can also perform a vertical line test. If the line touches your graphed function in more than...

Latest answer posted October 7, 2013 8:13 pm UTC

Math

They're already in increasing order, which is obvious. If you want to "prove" it (in quotes because the fact may be considered so basic as to not need proof), you can always write the numbers with...

Latest answer posted October 24, 2012 5:48 am UTC

Math

A "mixed number," in math terms, is a whole number with a fraction attached to it. What you have posted in your question is essentially an "improper fraction," a situation that occurs when the top...

Latest answer posted November 4, 2009 6:52 am UTC

Math

Given that the number of boys and girls in a class is as follows: Number of boys = 11 Number of girls = 9 Then we conclude that the total number of students in the class= 20 students. Then, the...

Latest answer posted November 29, 2010 7:26 am UTC

Math

You are asking how to determine a linear function from a table and a graph. Linear functions graph as a straight line, no curves allowed. So, if the graph is a straight line, it is the graph of a...

Latest answer posted March 9, 2011 7:59 pm UTC

Math

What you have to remember here is the formulas for area and circumference of a circle. The area of a circle is equal to the square of its radius times pi. The circumference of a circle is equal to...

Latest answer posted April 24, 2010 5:49 am UTC

Math

Real-life limits are used any time you have some type of real-world application approach a steady-state solution. As an example, we could have a chemical reaction in a beaker start with two...

Latest answer posted September 2, 2012 3:00 am UTC

Math

Similarity is an important concept in geometry that helps prove some theorems and their corollaries. The statement of similarity is based on the fact that for two shapes to be similar, they have to...

Latest answer posted September 9, 2020 1:31 pm UTC

Math

How do you find the vertex of the graph of a quadratic function written in intercept form? Intercept form is also known as factored form: y=(x-p)(x-q) where p,q are the x-intercepts. One way to...

Latest answer posted February 24, 2015 2:15 am UTC

Math

The answer depends on the margin of how badly you failed your final exam. Here is the equation to calculate your final average, if x=exam grade: .15x + 86 (.85) = Final overall average. So if...

Latest answer posted May 28, 2012 6:30 pm UTC

Math

Given the equation. x + y= xy We need to find dy/dx We will use implicit differentiation. ==> (x+y)' = (xy)' ==> x' + y' = (x)y' + x'(y) ==> 1 + y' = xy' + y Now we will combine terms with...

Latest answer posted December 6, 2011 8:29 am UTC

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)...

Latest answer posted August 17, 2010 8:49 am UTC

Math

We are traveling at a speed S = 60 m/h The distance we are traveling is D = 50 m We know that: Speed (S) = distance (D)/ Time (T) 60 = 50 / T ==> T = 50/60 = 5/6 hour ==> T = 5/6 * 60 minutes...

Latest answer posted August 3, 2010 12:41 am UTC

Math

Let one of the numbers be x. Then the next consecutive number is (x+1) Given that the sum of the squares is 145. ==> x^2 + (x+1)^2 = 145 ==> x^2 + x^2 + 2x + 1 = 145 ==> 2x^2 + 2x - 144 =...

Latest answer posted January 20, 2011 12:56 pm UTC

Math

Problem 1. When a die is thrown the outcome can be any of the numbers from 1 to 6. If two dice are thrown the set of outcomes that ensure the sum is 9 is {(3, 6), (6,3), (4, 5), (5, 4)}. The total...

Latest answer posted July 30, 2014 7:20 am UTC

Math

Hello! A common ratio is a term which applies to a geometric sequence. A geometric sequence starts from any number a and any next term is equal to the previous term multiplied by a fixed number...

Latest answer posted January 18, 2016 7:49 am UTC

Math

The equivalent resistance of two resistances connected in parallel is given by 1/R = 1/R1 + 1/R2 R = (R1*R2)/(R1 + R2) (dR)/(dt) = ((R1*(dR2)/dt + R2*(dR1)/dt)(R1 + R2) - (R1*R2*((dR1)/dt +...

Latest answer posted March 8, 2012 10:14 pm UTC

Math

A lot of it has to do with what perspective you are looking at. If you consider the chart on the webpage given, there are 36 combination of rolls you can get from two dice. When you consider the...

Latest answer posted August 8, 2014 2:20 pm UTC

Math

We can view a function as something that maps things of one type to things of another type. The inverse of a function tells you how to get back to the original value. We do this a lot in everyday...

Latest answer posted August 10, 2011 4:01 am UTC

Math

To write sin x in terms of cos x use the relation sin^2x + cos^2x=1 => sin^2x = 1 - cos^2x Taking the square root of both the sides gives two values of sin x sin x = sqrt(1 - cos^2x) and...

Latest answer posted May 15, 2012 7:13 am UTC

Math

Looking at the series of numbers, you can see that any number is 3 times the number right before it. So with each additional term, you have multiplied a number by 3 one more time. This means that...

Latest answer posted July 5, 2012 7:22 pm UTC

Math

We have to find the sum of 1+2+3+. . . +100. Here n=100 We have a formula to calculate the sum of n numbers as: Sum=(n(n+1))/2 So we have:  Sum=(100(100+1))/2=5050  Hence the sum is 5050.

Latest answer posted October 9, 2017 12:54 am UTC

Math

Hello! The formula for an average speed is a distance travelled divided by a time spent, V=d/t. In our problem the average speed V and the distance d are given, and we are looking for the...

Latest answer posted February 25, 2016 6:48 pm UTC

Math

We have to prove that tan A + tan B + tan C = tan A*tan B*tan C for any non-right angle triangle. For any triangle the sum of the angles is equal to 180 degrees. If we take a triangle ABC, A + B +...

Latest answer posted June 5, 2011 10:53 pm UTC

Math

In arithmetic the least common multiple (LCM) of two numbers a and b is the smallest positive integer that is a multiple of both a and b. So, the multiples of 3 are : 3, 6, 9, 12, ...The multiples...

Latest answer posted September 12, 2010 12:21 pm UTC

Math

f(x)= ax^3 + bx^2 + cx + d f(0)= 0 ==> d = 0 f(2)= 4 ==> 8a + 4b + 2c = 4 ==> 4a + 2b + c = 2 .............(1) f'(x)= 3ax^2 + 2bx + c f'(2)= 0 ==> 12a + 4b + c = 0...........(2) 8a...

Latest answer posted November 13, 2011 10:17 am UTC

Math

X = 3 and Y = 2. Here is how we find this. What we have to do is use the first equation to get a value for y. This is quite easy because all we must do is say x + y = 5 so y = 5 -x Now we plug...

Latest answer posted August 15, 2010 8:53 am UTC

Math

If a line has no y-intercept, that means it never intersects the y-axis, so it must be parallel to the y-axis. This means it is a vertical line, such as x=3 . This slope of this line is...

Latest answer posted September 26, 2012 12:10 am UTC

Math

When adding a zero to the numbers, the mean will get smaller. Let us prove it by an example. For example: Let "2, 3, 5, 7, 9" be numbers that their mean is as follow. m = (2+ 3 + 5+ 7+ 9) / total...

Latest answer posted November 29, 2010 7:12 am UTC

Math

Let x and y be the two numbersWe want x-y = 8 and xy=P as small as possibleAs you wrote, x=8+yOnce you have that, you can substitute into the other equation, and getP=(y+8)y = y^2 + 8yJust as you...

Latest answer posted December 13, 2012 12:39 am UTC

Math

Probability is determined by the number of desired answers divided by the total number of answers. There are 12 possible balls you can draw so the denominator will be 12, there are 4 red balls and...

Latest answer posted June 22, 2010 7:21 am UTC

Math

Inequalities are arguably used more often in "real life" than equalities. Businesses use inequalities to control inventory, plan production lines, produce pricing models, and for...

Latest answer posted August 9, 2013 12:15 pm UTC

Math

Show that G={1,w,w^2} where w is a cube root of unity is a cyclic group. It suffices to show that the only subgroup H of G that contains w is G itself. Let H<=G,winH . Now the...

Latest answer posted August 3, 2012 6:58 pm UTC

Math

The numebers chosen are from 1 to 10. Then possible outcomes are: 1,2,3,4,5,6,7,8,9,10 The probability of chosen a 5 OR and even number = probability of chosen a 5 + probability of chosen an even...

Latest answer posted November 8, 2010 12:12 pm UTC

Math

f(x)=x^3+2 To find the inverse function f(x)^-1 , we will assume" y=x^3+2 y-2= x^3 ==> x= (y-2)^1/3 ==> f(x)-1= (x-2)^1/3

Latest answer posted May 29, 2010 12:54 am UTC

Math

The roll has 6 sides, the probability of rolling a six when the die is rolled once is 1/6 When rolled 4 times, each time has a probability of 1/6. Then the probability is: 1/6 * 1/6 *1/6 *1/6...

Latest answer posted June 25, 2010 10:03 pm UTC

Math

Calculate the probability of being dealt a diamond from a standard deck of 52 cards. Since there are 4 suits in a deck of cards (hearts, clubs, spades and diamonds) we can find the number of...

Latest answer posted November 8, 2013 9:03 pm UTC

Math

The general equation of a circle is (x - a)^2 + (y - b)^2 = r^2, where the center is at (a , b) and the radius is r. Now we have the center of the circle at (0,0). It passes through the point...

Latest answer posted January 20, 2011 12:10 pm UTC

Math

We have to find the sum of the series (sin 1)^2 + (sin 2)^2 +...+ (sin 90)^2 (sin 1)^2 + (sin 2)^2 +...+ (sin 90)^2 => (sin 1)^2 + (sin 2)^2 +...+ (sin 90)^2 => (sin 1)^2 + (sin 2)^2 +... +...

Latest answer posted June 21, 2011 1:07 am UTC

Math

TThe ratio of boys to girls is 12 to 16, 12:16 or 12/16 (all different ways this can be written). The fraction form 12/16 can be reduced by dividing by the greatest common factor. Both 12 and 16...

Latest answer posted November 11, 2008 1:14 pm UTC

Math

Let the digits of the number we need to find be ab. So the number is 10*a + b. The digits are reversed when 27 is added to it. We can use this to create the equation: 10*a + b + 27 = a + 10*b =>...

Latest answer posted January 17, 2011 10:41 pm UTC

Math

The cost function is C(x)=15000+600x-2.8x^2+0.004x^3 and the revenue function is P(x)=4200-7x Here we have to find the production level that will maximize the profit. For maximum profit, the...

Latest answer posted September 14, 2017 6:41 pm UTC

Math

Using F = ma to the direction of travel; -F = 1000*a -F is due to the reverse direction of the frictional force. F = 0.8*1000*9.81 = 7850 N -7850 = 1000*a a = -7.85m/s^2...

Latest answer posted October 28, 2012 6:29 pm UTC

Math

ok - the question is 3/5 of what number = 15. Try writing an equation to solve the problem. "of" means to multiply. put in a variable (x) for the unknown number. 3/5 * x = 15 to get rid of a...

Latest answer posted August 26, 2015 2:45 am UTC

Math

Probability of head and 3 on a die is: P( head and 3 ) = p(head )* P(3) We multiply probabilities because we have 2 independent events. We know that p(head) = 1/2 Also p(3) = 1/6 Then P( head and...

Latest answer posted November 8, 2010 12:27 pm UTC

Math

You need to solve for y the inner integral, considering x as constant, such that: int_(x-1)^(x+1) e^(x+y) dy = e^(x+y)|_(x-1)^(x+1) int_(x-1)^(x+1) e^(x+y) dy = e^(x+x+1) - e^(x+x-1)`...

Latest answer posted March 11, 2012 12:04 am UTC