# Math

• Math
To calculate the APR, you fortunately have all the information you need. The APR is the annual percentage rate, and it is the interest with which the monthly payments are calculated. The first...

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The null hypothesis is that the mean cost of textbooks is $130. H_0:mu=130 . The alternative hypothesis (and in this case the claim) is that the mean cost of textbooks is greater than$130....

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To determine Silvio's gross sales, first subtract his base salary from his gross earnings to determine the amount of earnings Silvio made on commission alone: 328.54-200=128.54 Silvio's earnings...

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Triangles are congruent if they have three equal sides and three equal internal angles. Congruent triangles can be exact copies or mirror images. Here are the rules for congruent triangles: 1....

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To convert a decimal into a percentage, all you have to do is multiply the decimal by 100 and add the percent symbol. For example, 0.14 x 100 = 14% The word percent means “per hundred” (in...

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Each die has 6 sides, each of them has the same probability to show itself (of course, this probability is 1/6). There are 3 even numbers on each die, 2, 4 and 6. Also, the outcome of the second...

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Hello! Denote a number of groups as n . Because each of n groups should have the same number of boys, this number n must divide the number of boys, i.e. 24 . The same way, because each of...

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In order to answer this question, it is important to know what is being asked in mathematical terms. Here, the real question is to find the lowest common multiple between 12 and 16. Here's why....

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Because the angles are not the same (even though the heights of the buildings are), we know that the observer isn’t standing exactly halfway between both buildings. The building closest to the...

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In order to find the monthly payment on a mortgage or other fixed rate loan, there is a relatively straightforward equation. The equation uses the term (length) and interest rate to determine the...

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It looks like you are trying to collect like terms in order to solve for y. This can be tricky when both numbers you are working with are negative. And working with fractions can be tricky, too. So...

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When you are graphing the equation y = mx + b (or - b, it doesn’t matter), you need to first find one of the intercepts. It is easiest to find the y intercept because the equation is set up to show...

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Each person either always tells the truth or always tells a lie. In these kinds of problems, such persons are usually called "knights" and "liars," respectively. Consider two possibilities: the...

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To find the mean absolute deviation, you have to take several steps. The mean absolute deviation is the average distance away from the mean value of a dataset of each datapoint. First, you need to...

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A rational number is any number that can be written as a ratio (i.e., a fraction). When the fraction is divided to form a decimal value, it becomes a terminating or repeating decimal. For example,...

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Sqrt(135*b*c^2*d^3) * sqrt(5*b^2*d) The first thing to remember is that when you’re multiplying square roots, you can combine everything underneath the radical as if it’s not there, so let’s...

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The position function is given as s(t)=6.5+4t^2-t^4 for t>0 The velocity function is the first derivative of the position function, and the acceleration function is the derivative of the...

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First, arrange them in order from smallest to largest so you can see where your number line will start and end: x> -3; x>= -5/2; x<=2; x<5/2 On a number line the ones that are only...

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We are asked to find the number of 4 letter "codes" that can be created using the 26 letters of the alphabet. There are a couple of considerations. Are we allowed to repeat letters (e.g., is AAAA a...

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Every year that you own this comic book, it will appreciate 9%. So, you will multiply the initial amount by 1.09 every year. This works out to a fairly straightforward equation. Assuming Y is the...

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1) 4.24/8.5 = 2.5/n ; 4.25 N =2.5 times 8.5 ; N = 21.25 divided by 4.25 ; N = 52) Slope = 6/0 9/1 12/2 15/3 That means you go over 0 up six; over 1 up 9 and so on.3) 12yds/1 day = Xfeet...

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Due to how the question is written, I'm not sure exactly what you're asking. If it is 1 - 7/13 = n/d, then it is 6/13, and n = 6 and d = 13. If it (1-7)/13, then it is -6/13, and n = -6 and d...

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2x + a = 4 2x = 4 - a x = (4 - a) / 2 You can simplify this further to: x = 2 - a/2

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The volume of the cube (v)= (side)^3= s^3 100 = S^3 ==> s= (100)^1/3 = 4.643 Now to calculate the diagonal (d): We know that: d^2= s^2 + s^2 = 2s^2= 2(4.643)^2= 43.1148 ==> d =...

• Math
x*y= 2(x-1)(y-1)+1 To solve x*2 we will substitute y =2 x*2 = 2(x-1)(2-1)+1=25 x*2 = 2(x-1)+1 = 25 2x-2 +1 =25 2x-1= 25 2x= 26 x= 13

• Math
(x+3)^1/2 = 2 ==> (x+3) = 2^2 ==> x+ 3 = 4 ==> x= 1 To check: (1+3)^1/2 = 2 4^1/2 =2 2=2

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(m-3)/(3-m) Let us rewrite 3-m as (-1)(-3+m) (m-3)/ (-1)(-3+m) = (m-3)/ (-1)(m-3) = (-1)*(m-3)/(m-3) = (-1)*1= -1

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444 *111 444= 2*2*3*37 111= 3*37 Then: sqrt 444*111 = sqrt(2*2*3*37)*(3*37) = 2*3*37 = 222

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log (x +2) - log x = log 5 We know that log a - log b = log (a/b) ==> log (x+2)/x = log 5 ==> (x+2)/x = 5 Now cross multiply: ==> x + 2 = 5x ==> 2 = 4x ==> 2/4 = x ==> x= 1/2

• Math
Given the points: A(2,5) B(a,b) and m(-1,3) is midpoint of AB We need to determine the point B(a,b) Then we will use the midpoint formula to solve for B: We know that: mx = ( Ax+Bx)/2 ==> -1 =...

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Given the expression E = 200m^4 + 80m^3 + 8m^2. We need to simplify as mush as possible. First we will need to factor all terms is order to find a common factor. Let us factor each term. 200m^4 =...

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Let the integers be x, y and z. Given that the sum of the three integers is 66. ==> x + y + z = 66..............(1) Also, given that the second integer (y) is 2 more than the first (x). ==> y...

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Using the properties of absolute value yields: Hence, evaluating the solutions to absolute value equation yields and .

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Given y= (x-2) / (x^2 - 3) We need to find y'. Since y is a quotient, then we will use the quotient rule to find the derivative. ==> Let y= u/v such that: u= x-2 ==> u' = 1 v= x^2 -3...

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You need to evaluate the determinant of the matrix to check if there exists a inverse for the given matrix, such that: det A = [(1,2,-1),(3,7,-1),(-5,-7,-15)] = -26 != 0 Since the determinant of...

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The right triangle has two sides of length 4 and 3. The third side can have a length which can be calculated using the Pythagorean Theorem. As it is not given that 4 and 3 are the lengths of the...

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The sum of 3/4 + 3/20 can be calculated in the following way 3/4 + 3/20 make the denominator the same, here it would be 20 3*5 / 4*5 + 3/ 20 => 15/20 + 3/ 20 => (15 + 3) / 20 => 18/20...

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To find which value if greater, we will calculate the value of each percentage. ==> 10% of 325 = 10/100 * 325 = 32.5 ==> 15% of 295 = 15/100 * 295 = 44.25 ==> 25% of 250 = 25/100 * 250 =...

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In a decimal number each digit is a power of 10, for example in 123 is equal to 1*10^0 + 2*10^1 + 3*10^2. For binary numbers the base is 2 instead of 10. So 11001011 = 1*2^0 + 1*2^1 + 0*2^2 + 1*2^3...

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If an amount P is invested for n terms at a rate of interest of r, it grows to P*(1 + r)^n. Here, the annual rate of interest is 4%, as the compounding is done semi-annually, the effective rate for...

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The area of a triangle if two sides and the enclosed angle are given is (1/2)*s1*s2*cos A Here the sides are 6 yd and 2 yd and the enclosed angle is 10 degrees. The area of the triangle is...

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The equation to be solved is 8^(6x+5)-2/8=0 8^(6x+5) = 2/8 => 2^3^(6x + 5) = 1/4 = 2^-2 As the base 2 is the same, equate the exponent 3*(6x + 5) = -2 18x + 15 = -2 => 18x = -17 => x =...

• Math
Let the width of the rectangle be x, then the length is 3x +2. Now we are given that the area if 33. Then we know that x*(3x+2) = 33 Let us solve. ==> 3x^2 + 2x = 33 ==> 3x^2 +2x - 33 = 0...

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We know that cos (pi/6) = (sqrt 3)/2 cos (pi/6) = cos 2*(pi/12) = 2*[cos (pi/12)]^2 - 1 => (sqrt 3)/2 = 2*[cos (pi/12)]^2 - 1 => 2*[cos (pi/12)]^2 = 1 + (sqrt 3)/2 => [cos (pi/12)]^2 = 1/2...

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We have to solve the equation: x/(x+4) + 4/(x+4) + 2 = 0 x/(x+4) + 4/(x+4) + 2 = 0 => x/(x+4) + 4/(x+4) = -2 => (x + 4)/(x + 4) = -2 => 1 = -2 This is not possible. The given equation has...

• Math
The endpoints of the diameter of the circle are (4, 7) and (7, 11). The distance between the points or the length of the diameter is given as: sqrt[ (4 - 7)^2 + (7 - 11)^2] => sqrt[3^2 + 4^2]...

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We have to find the value of Sum(100 + k), for k = 1 to 100 Sum(100 + k), k = 1 to 100 => 100*100 + Sum(k), k = 1 to 100 The sum of the numbers from 1 to n is given by n*(n + 1)/2 => 100*100...

• Math
First (A + B + C)/3 = 2709 so (1345 + 568 + x)/3 = 2709 1345 + 568 + x = 3*2709 1913 + x = 8127 x = 8127 - 1913 x = 6214 Check - (1345 + 568 + 6214)/3 = 8127/3 = 2709 So the answer is 6214.

The answer is if a>b>0 then a^n > b^n Proof by induction a) a>b ==> a^1 > b^1 by definiton.b) suppose a^(n-1) > b^(n-1)c) We know that if a>b>0 and c>d>0 then...