
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...

Math
The easiest way I have for knowing the difference between linear and nonlinear is the exponent value on the variable x. It is important to understand the root word in linear. It is LINE. A...

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)...

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...

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(1r)^x such that r is the decay...

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...

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...

Math
Reallife limits are used any time you have some type of realworld application approach a steadystate solution. As an example, we could have a chemical reaction in a beaker start with two...

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...

Math
A sequence is an ordered set; usually the objects in the set (often numbers) are written with commas between them. e.g. 1,3,5,7 is a finite sequence, 1,3,5,7,... is an infinite sequence as is...

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...

Math
A die is a cube and there are 6 numbers, {1,2,3,4,5,6}, that can turn up when the die is thrown. When two two dice are thrown the sum of the numbers that turn up is 10. This is the case when the...

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...

Math
It has to be shown that `cos (2pi/7)+cos (4pi/7) + cos (6pi/7) = 1/2` `cos (2pi/7)+cos (4pi/7) + cos (6pi/7)` Multiply and divide by `sin(pi/7)` => `(sin(pi/7)cos(2pi /7)+sin(pi /7)cos(4pi...

Math
1 year consists of 365 days. 1 day has 24 hours, each hour has 60 minutes and each minute has 60 seconds. This gives the number of seconds in an hour as 60*60 = 3600 and the number of seconds in a...

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 +... +...

Math
To find the area of the largest square that can be fit in a circle, let’s see what happens when the square is drawn. We find that for a square all four corners of which lie on the circle, the...

Math
A linear function is one that has the form f(x) = ax + b. Here for each value of x there is only one corresponding value of f(x) and every value of f(x) is due to only one particular value of x. In...

Math
When you were 4 years old, your sister was half your age. Half of 4 is 2, your sister was 2 years old when you were 4 years old or she is 2 years younger to you. Your present age is 100, as your...

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...

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

Math
The probability that the coin when tossed turns up heads is 1/2. This means that when the coin is tossed, the probability of tails is 1 – 1/2 = 1/2. When the coin is tossed twice, the probability...

Math
Right now, the man is 24 and his son is 6. Here is how you figure this out: Let the man's age by M and the son's age be S. Right now M = 4S In three years M + 3 = 3(S + 3) So you put the 4S in to...

Math
Suppose there is a legal limit to the angle an entrance ramp can be. If I have the horizontal length of a ramp and the vertical height I can compute the angle by using the inverse tangent to find...

Math
A square and a rectangle each have 4 sides and 4 angles. The only difference between them is that a square is a rectangle with equal sides. Both have 4 90 degree (right) angles. A triangle has 3...

Math
The domain and range of the function f(x) = x  2 has to be determined. The domain of a function is all values of x for which the value of f(x) is defined. The range of the function is all values...

Math
Probability is 13/52, or one in four, or 25%. The "math" is simply the number of cards that fit the description "diamond" over the total number of cards or chances available.

Math
There is a story behind this problem. It is said that a famous mathematician by the name of Carl Gauss was punished for poor behavior in class, so he was told to stay after school. As punishment,...

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...

Math
Since the line is perpendicular to the xaxis, then, the line is vertical. And if the line passes throught the point (2,1), hence the equation is x = 2. Answer: Equation of the line is x=2 .

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...

Math
The pages of the book are numbered starting from 1. A total of 3189 digits are used to number all the pages. For pages 1  9, 9*1 = 9 digits are required. For pages 10  99, 90*2 = 180 digits are...

Math
We have to find the value of 11 3/4 divided by 2. First convert 11 3/4 to an improper fraction 11 3/4 = (11*4 + 3)/4 = 47/4 Divide 47/4 by 2 => 47/8 This can be converted to a mixed number form...

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...

Math
Let x and y be the two numbersWe want xy = 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...

Math
A confidence of 95% implies that `alpha=.05,alpha/2=.025` `hatp=40/200=.2` `n=200` `z_(alpha/2)=1.96` from a table. The interval we seek is given by:...

Math
The first 4 terms of the series are 1, 3, 9 and 27. It is seen that `(3/1)= (9/3) = (27/9) = 3` . The ratio between consecutive terms is the same and equal to 3. This is the characteristic of a...

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=(xp)(xq) where p,q are the xintercepts. One way to...

Math
The square root of 169 is 13. This is so because 13 times 13 gives 169  the definition of a square root of a number k is the number such that when you multiply it by itself you get k. Note that...

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...

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...

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 +...

Math
`121 = 11 X 11` `==> sqrt121 = sqrt(11X 11) = 11` `==> sqrt121 = 11` `` ``

Math
The product of n natural numbers can only be found by multiplying the n numbers. There is no formula for that. If you have tables for the factorials of numbers you could find the value of the...

Math
x^2  5x + 6 =< 0 First let us factor: (x3)(x2) =< 0 Then we have two cases: case 1: x3 =< 0 and x2 => 0 x =< 3 and x => 2 ==> x = [ 2, 3] case 2: x3...

Math
According to logarithm; `log_ab = (log_kb)/(log_ka)` If we consider k = 10 which is log in base 10 then; `log_ab = (logb)/(loga)` Similarly we can write;...

Math
The letters of the word EQUATION are arranged in a row. The probability that all the vowels are together has to be determined. All the letters of the word EQUATION are unique. The vowels can be...

Math
All you have to do here is to multiply. You are going to multiply 5/6 by 18. To do that, the best way is to make 18 into a fraction  that is, write it as 18/1. From there, you know what to do....

Math
In statistics, if we have a set of observations expressed in numbers (for example, lengths of trees in meters, weights of animals in kilograms and so on), then the difference between maximum and...

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...