## Math Questions and Answers

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

### 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

### 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

### State and prove Raabe's Test.

Raabe's test is the ratio test for convergence of a series. Consider the limit `lim_(n->) |a_(n+1)/a_n| = L` Raabe's test says that if `L<1` then the series converges. If `L>1` then the...

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

### 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

### 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 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

### When I was 4 years old, my sister was half my age. Now am 100. How old is my sister?

You can make use of equations. For instance, let the number of years you need to grow to become 100 years old be x. Then 4 + x = 100 x = 100 - 4 = 96 When you are 4 years old, your sister is half...

Math

### Is there a formula to find the product of n natural numbers. For example can I determine the value of 19! by the...

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

### Solve for the value of log 20 without using calculator

`log20 = log(2*(10))` I assume you are using the base 10 in your log. According to logarithm laws, we know, `log(ab) = loga + logb` Therefore, `log20 = log2+log10` From table, `log20 = 0.3010 +...

Math

### Solve for b2:A= 1/2h (b1+b2)

A = 1/2h(b1+b2) Multiply both sides by 2 2A = h(b1+b2) Multiply both sides by 1/h 2A/h = b1+b2 Add -b1 to both sides 2A/h + -b1 = b2 Answer: b2 = 2A/h - b1

Math

### An exam has a weightage of 30%. If a student has a score of 82% before the exam what is the student's score if the...

An exam has a weightage of 30%. The student's score before the exam is 82%. If the student scores 40% in the exam, the score of the student is 0.82*0.7 + 0.4*0.3 = 0.694. Similarly, if the student...

Math

### What is the integral of:`x/(x-1)^2`

`int x/(x-1)^2 dx ` `u= x-1 ==gt x= u+1` du = dx `==gt int x/(x-1)^2 dx = int (u+1)/u^2 du` `= int u/u^2 du+ int 1/u^2 du ` `= int 1/u du + int 1/u^2 du ` `= ln u - 1/u + C = ln (x-1) - 1/(x-1) + C...

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

### 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

### What is 11 3/4 divided by two

The answer to this is 47/8. You can simplify that to 5 7/8. Here is how to get to this answer. First, you can convert 11 3/4 to a simple fraction. You do this by multiplying 11 by 4 and adding...

Math

### If 1 year is equal to 365 days, how many seconds are there in a year.

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

### If a^2 - b^2 = 8 and a*b = 2, find a^4 + b^4.

We have a^2 - b^2 = 8 and ab = 2 Now (a - b)^2 = a^2 + b^2 + 2ab => (a^2 - b^2)^2 = a^4 + b^4 - 2*a^2*b^2 a^4 + b^4 => (a^2 - b^2)^2 + 2*a^2*b^2 => 8^2 + 2* (ab)^2 => 64 + 2*2^2 =>...

Math

### The product of two positive numbers is 16. Find the numbers if their sum is least and if the sum of one and the...

The product of the two positive numbers is 16. Let one of the numbers be X, the other number is `16/X` . The sum of the two numbers is `S = X + 16/X` . The value of S is minimized for X such that...

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

### 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

### With numbers 1 to 9, we have to make the answer 100. How? You have numbers 1,2,3,4,5,6,7,8,9. You cannot change their...

Here are some ways to write the number 100 using only +- or 2 digit numbers.: 1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 = 100 12 + 3 - 4 + 5+ 67 + 8 + 9 = 100 1 +2 + 3 - 4+ 5 + 6 + 78 + 9 = 100

Math

### Prove that log(a) b = 1/(log(b) a)

We have to prove that `log_a b = 1/(log_b a)` Use the property for changing the base of logarithms: `log_a b = (log_c b)/(log_c a)` Change the base of `log_a b` to b `log_a b = (log_b b)/(log_b...

Math

### What is the domain and range of the function f(x) = |x - 2|

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

### How many combinations of 6-digit number between 000001 to 999999 that contains the digit 1 or multiples of digit 1?...

We will find how many numbers contain no ones: There are 9 choices of numbers for the first digit: 0,2,3,4,5,6,7,8,9 Simarly there are 9 choices for the second, third, fourth, fifth,and sixth...

Math

### In a basket of fruits , 1/3 are apples , 1/4 are oranges , 1/5 are bananas. The remaining are mangoes. What part of...

1/3 of 240 = 80 apples 1/4 of 240 = 60 oranges 1/5 of 240 = 48 bananas 80+60+48 = 188 mixed fruits/240 total fruits 240-188 = 52 mangoes/ 240 as a reduced fraction = divide both the numerator...

Math

### what is the reciprocal of -2?

The reciprocal of a number is the number's multiplicative inverse: in other words the number that when you multiply by that number you get 1. The reciprocal of -2 is `-1/2` since `(-2)(-1/2)=1` **...

Math

### Q. `a = log_(1/2)sqrt0.125` and `b = log_3{1/(sqrt24 - sqrt 17)}` then a) `a>0 and b>0` b)`a<0 and...

The answer is a): a > 0 and b > 0 A logarithm is positive when the base is greater than 1 and the argument is greater than 1, and it is also positive when the base is less than 1 and the...

Math

### A rectangle has a perimeter of 20m. Express the area of the rectangle as a function of the length of ones of its sides.

The perimeter of a rectangle can be written as P=2l+2w where w is the width and l the length. Here P=2l+2w or 20=2l+2w The area of a rectangle is A=lw. We can express the width of the rectangle in...

Math

### The value of (log2(3))(log3(4))(log4(5))(log5(6))(log6(7))(log7(8)) is equal to; A) 2 B) 4 C) log7(8) D) log2(7)...

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

### How are integers and their opposites related?

First, I think we should go over what integers mean. A clear definition of integers will lead to a discussion about opposites, which should reveal how the two are related. Integer is another word...

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

### If the minimum point on the graph of the equation y=f(x) is (-1,-3), what is the minimum point on the graph of the...

`y = f(x)+5` is just the same shape as `y=f(x)` except shifted up 5 units since 5 has been added to every y value. So if the first graph has the point (-1, -3), the second graph will have the...

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

### How can 0.99999... be converted into a proper fraction. Why is that the answer?

We have to convert 0.99999..... into a proper fraction. Let 0.99999... = f 10f = 9.9999... 10f - f = 9.99999... - 0.99999 => 9f = 9 => f = 9/9 => f = 1/1 The representation of .9999... as...

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

### If the circumference of a circle is 12pi, what is the area?

The circumference of a triangle is given by 2*pi*r where r is the radius and the area is pi*r^2. Here circumference = 12*pi = 2*pi*r => r = 6 The area = pi*r^2 = 36*pi The area of the circle is...

Math

### Find the exact value of log2 32

Given the logarithm expression : log2 (32) We need to find the value. We will assume that the value of log2 (32) = x Now we will rewrite the equation using the exponent form. ==> log2 (32) = x...

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

### A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was...

The commission of the real estate agent is 6% on the selling price of the house. The commission received is 8880. Let the selling price be S. We have 6% of S equal to 8880 => .06* S = 8880 =>...

Math

### If a child pulls a sled through the snow on a level path with a force of 30 N exerted at an angle of 36° above the...

See the attached image with the steps. The child pulls the sled at an angle 36 degrees above horizontal. Vertical component `F_V` = 30sin36 = 17.6N Horizontal component `F_H` = 30cos36 = 24.3N

Math

### The GCF of three numbers is 6 and their LCM is 900. If two of the numbers are 36 and 60, find the other number.

Hello! Denote the unknown number as `x.` Factor the given numbers into primes: `36 = 2^2*3^2,` `60 = 2^2*3*5,` `6 = 2*3,` `900 = 2^2*3^2*5^2.` The `GCF(36,60)=2^2*3=12,` not `6.` Therefore to...

Math

### The sum of three consecutive even integers is equal to 84. Find the numbers

The sum of three consecutive even number is 84. Let the number be 2*n , 2*n + 2 and 2*n + 4. We have 2n + 2n + 2 + 2n + 4 = 84 => 6n + 6 = 84 => 6n = 84 - 6 => 6n = 78 => 2n = 78/3...

Math

### When is tan undefined?

The value of a trigonometric function is undefined when the ratio for the function involves division by zero. The function thus has an asymptote at such a point. The trigonometric function y =...

Math

### If you are dealt 3 cards from a shuffle deck of 52 cards, find the probability that all 3 cards are clubs

Find the probability of drawing 3 clubs from a shuffled, standard deck of cards: The probability is the number of possible ways to draw 3 clubs divided by the total number of 3 card draws....

Math

### The difference between maximum and minimum value is called what?

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

### what is 11 3/4 divided by 2

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

### 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

### 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)`...

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