## Math Questions and Answers

Math

### Give a real-world example of how permutations and combinations can be used. Explain what your numeric result means in...

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,...

Math

### What do the letters R, Q, N, and Z mean in 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

### Determine if its a growth or decay.Then find the percent increase of decrease. 1.y=16(.25)^x 2.y=0.8(1.28)^x...

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...

Math

### How do I determine if this equation is a linear function or a nonlinear function?

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...

Math

### How do you place 0.2, 0.22, 0.222, 0.2222, and 0.22222 on a number line?

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

### 5/3 As A Mixed Number

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

### A class has 11 boys, 9 girls. Two students will be selected at random to serve on committee. What's probability that...

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

### How do you determine a linear function from a table and graph?

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...

Math

### If the radius of a circle is doubled, what effect does this have on the area of the circle? On the circumference? ...

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

### How are limits (Calculus limits) used or applied to daily life? Or applied to the real world problems? I need a...

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...

Math

### What is a similarity statement?

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...

Math

### How do you find the vertex of a function in intercept form?

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...

Math

### what if you have an B 86% in a class and you fail your final exam that is 15 % of your grade, then what percentage...

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

### If x + y = xy, then dy/dx = Please explain step by step.

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...

Math

### Given f(x) and g(x), please find (fog)(X) and (gof)(x) f(x) = 2x g(x) = x+3

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

### If you are traveling 50 miles at 60mph how long would it take you to get there????

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

### The sum of the squares of two consecutive numbers is 145. Find the numbers.

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 =...

Math

### 1. When 2 dice at thrown, what is the probability of the sum being 9? 2. Two cards are picked at random from a...

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

### What's the common ratio for 4, 12, 36, 108, ... ?

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...

Math

### If two resistors with resistances R1 and R2 are connected in parallel, then the total resistance R measured in ohms...

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

### When 2 dice are thrown the sum of the numbers that turns up is 10. What is the probability that one of the dice has a...

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...

Math

### Give a practical example of the use of inverse functions.

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...

Math

### How do I write sin x in terms of cos x?

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...

Math

### Find the nth term of the series 1, 3 , 9 , 27...

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...

Math

### Add 1 plus 2 plus 3 plus 4. . . all the way to 100.

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.

Math

### How long will your trip take (in hours) if you travel 350 km at an average speed of 80 km\hr? What is the formula...

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...

Math

### Prove that tanA + tanB + tanC = tanA tanB tanC for any non-right angle triangle

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 +...

Math

### What is the common and least multiples of 3 and 6?

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

### Consider the cubic function f(x) = ax^3 + bx^2 + cx + d. Determine the values of the constants a, b, c and d so that...

`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

### x+ y = 5 2x-y = 4 solve x and y

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...

Math

### If a line has no y-intercept, what can you say about the line? What if a line has no x-intercept? Think of a...

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...

Math

### What happens to the mean of a set of numbers when a zero is added to the set?

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

### Find two numbers whose difference is 8 and whose product is a minimum.

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...

Math

### A bag contains 4 red balls, 3 green balls, and 5 yellow balls. What is the probability of drawing a red or a green...

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...

Math

### Why is it important to learn how to solve inequalities? Does it enhance critical thinking? How can it be applied to...

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...

Math

### Prove that the set {1,w,w^2}, where w(omega) is a cube root of unity, is a cyclic group with respect of multiplication.

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...

Math

### A number from 1 to 10 is chosen at random. What is the probability of choosing a 5 or an even number?

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...

Math

### Find the inverse function of f(x)=x^3+2?

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

Math

### What Is The Probability Of Getting A 6 Each Time If A Die Is Rolled 4 Times?

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

### You are dealt one card from a standard 52 card deck. Find the probability of being dealt a diamond.

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...

Math

### What is the equation of the circle with its center at (0,0) that passes through (3,4).

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...

Math

### Calculate sin^2 1+sin^2 2 +...+ sin^2 90.

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

### There are 12 boys and 16 girls in a class. What is the ratio of boys to girls? Write as a fraction in simplest form.

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...

Math

### The digits of which two digit number are reversed when 27 is added to it.

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 =>...

Math

### find the production level that will maximize profit. If C(x) = 15000 + 600x − 2.8^2+ 0.004x^3 is the cost function...

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...

Math

### A driver in a 1000.0 kg car traveling at 20 m/s slams on the brakes and skids to a stop. If the coefficient of...

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`...

Math

### 3/5 Of 15

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...

Math

### A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and...

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

### What is the double integral of:f(x,y)=e^(x+y) when R is the area bounded by y=x+1, y=x-1, y=1-x, y=-1-x? How to find R?

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)`...

Math

### What is a term to term rule and a position to term rule in 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...

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