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Math

The three numbers that give the same answer whether they are multiplied or added, are 1, 2, and 3. Let's check. Addition of these three numbers: 1 + 2 + 3 = 6 Multiplication of these three numbers:...

Latest answer posted December 3, 2021, 6:25 am (UTC)

1 educator answer

Math

A trophic level is a level in the ecosystem that marks an organism's place in the food web. There are five trophic levels, and organisms are placed in them based on how they get their food. Let's...

Latest answer posted November 6, 2021, 3:51 pm (UTC)

1 educator answer

Math

Given the function y= 1+x-x^2-x^4. We are asked to identify the the intervals where it increasing, decreasing, concave up, concave down, local minima/maxima, and points of inflection. We start with...

Latest answer posted November 9, 2021, 3:51 am (UTC)

1 educator answer

Math

Let’s begin by considering the external angles in this equiangular 12-gon. They must add up to 360 degrees, there are 12 of them, and they are equal—so they each must be 360/12 or 30 degrees. Now,...

Latest answer posted November 18, 2021, 1:24 am (UTC)

1 educator answer

Math

The answer depends on the number system you are using. Either in the reals or the complex numbers, the answer is `1/16`._____________________________________________ Suppose we are asked to...

Latest answer posted November 28, 2021, 11:39 pm (UTC)

1 educator answer

Math

In the given scenario, an adult pays Rs. 80/person and a child pays Rs. 30/child for admission into the zoo. The number of adults is given as "xx" and that of children as "yy". If 1 adult pays Rs....

Latest answer posted November 24, 2021, 9:13 am (UTC)

1 educator answer

Math

Before we can round to the nearest hundred, we have to make sure we know the place values of digits in a number. Let's look at the number 1,325. The 1 is in the thousands place. The 3 is in the...

Latest answer posted November 6, 2021, 3:32 pm (UTC)

1 educator answer

Math

Probability refers to the likelihood that some event will happen. Knowing probability helps us determine the possible outcomes of an event, how likely each one is to happen, and how much of a risk...

Latest answer posted November 6, 2021, 3:10 pm (UTC)

1 educator answer

Math

An equation is called differential if it includes a derivative of an unknown function of the first, second, or greater degree. Such derivatives may also be partial. Also, the unknown function may...

Latest answer posted November 26, 2021, 1:15 pm (UTC)

1 educator answer

Math

A quadratic equation is an equation with one variable, say, `x , ` in the form `a x^2 + b x + c = 0 , ` where `a , b , and c ` are numbers, usually real, and `a != 0 .` It is called "quadratic"...

Latest answer posted November 26, 2021, 12:32 pm (UTC)

1 educator answer

Math

There are `4 0 ` equal intervals between the poles on the road of length `5 2 8 0` feet. Because of this, the length of one interval is `( 5 2 8 0 ) / ( 4 0 ) = ( 5 2 8 ) / 4 = 1 3 2 ( f t ) .` `4...

Latest answer posted November 25, 2021, 7:58 pm (UTC)

1 educator answer

Math

Let's position the vertex between the sides a and b at the origin and incline the 12-gon such that both sides make equal angles with the x-axis. The angle is 15 degrees (pi/12). Each next side has...

Latest answer posted November 25, 2021, 6:33 am (UTC)

1 educator answer

Math

Given an equilateral triangle ABC with side length 8, AD is drawn to meet BC at D so that BD:CD = 5:3. To check : If Area (triangle ABC) : Area (triangle ACD) = BC:CD Solution: Triangles ABC and...

Latest answer posted November 10, 2021, 4:37 am (UTC)

1 educator answer

Math

`a+b=4053+20sqrt(3)~~4087.641016`. We are given that `b(1-sqrt(3)/2)=2016-1001sqrt(3)`. Then `b=(2016-1001sqrt(3))/(1-sqrt(3)/2)`. We can multiply the numerator and denominator by the conjugate to...

Latest answer posted November 22, 2021, 3:57 am (UTC)

1 educator answer

Math

The solutions are `p=+-1, +-4` _______________________________________________ We are asked to solve `p^4-17p^2+16=0`. 1. An efficient way to solve this is to factor the polynomial. This polynomial...

Latest answer posted November 21, 2021, 9:34 pm (UTC)

1 educator answer

Math

To find the range of a graph, figure out how far down the graph goes and how far up the graph goes. How far down the graph goes represents the lowest point on the graph. Meanwhile, how far up the...

Latest answer posted November 21, 2021, 7:17 pm (UTC)

1 educator answer

Math

The mean absolute deviation of any data set refers to the average distance between particular data points and the mean of the entire data set. The mean absolute deviation helps us better understand...

Latest answer posted November 19, 2021, 5:04 pm (UTC)

1 educator answer

Math

In mathematics, algebra is a field of study that deals with mathematical symbols known as variables. Algebra was developed in Ancient Mesopotamia by the Babylonians, who had different mathematical...

Latest answer posted November 22, 2021, 7:23 pm (UTC)

1 educator answer

Math

The largest integer in the set must be 998,877,665,544,332,211, and the smallest must be 112,233,445,566,778,899. The sum of these two numbers is 1,111,111,111,111,111,110, and their mean is...

Latest answer posted November 18, 2021, 1:51 am (UTC)

1 educator answer

Math

Secant is a trigonometric ratio that relates the hypotenuse and adjacent side to a given angle in the right triangle. The ratio of a secant for the adjacent side and the hypotenuse is given by...

Latest answer posted November 18, 2021, 1:50 am (UTC)

1 educator answer

Math

To find the value of bacteria before 6 hours, we will use the double life formula. `f(t)=a*(2)^t`, where f(t) is the final value, a is the initial value, 2 is the growth factor, and t is the time...

Latest answer posted November 18, 2021, 2:25 pm (UTC)

1 educator answer

Math

There are three different ways to graph linear equations. One can use the "x" and "y" intercepts and connect the two points. One can also find values for "x" in the equation and find the "y" value....

Latest answer posted November 14, 2021, 3:13 am (UTC)

1 educator answer

Math

n=189______________________________________________ We are given that a number n has exactly 8 factors: `1=d_1<d_2<...<d_8=n` We are told that `d_4=9` and `d_7=2d_6+3d_2` and are asked to...

Latest answer posted November 17, 2021, 2:02 am (UTC)

1 educator answer

Math

The sum of all inner angles of a 12-gon is `10 pi, ` so each internal angle is `(5pi)/6` and each external angle is `pi/6`. So each next side has an angle with the x-axis `pi/6` greater than that...

Latest answer posted November 17, 2021, 6:06 pm (UTC)

1 educator answer

Math

This question contains 3 different questions. Let us solve them one by one. (1) `3y+6=5y-8` In order to solve this equation, we will use opposite operations. Upon subtracting 5y and 6 from both...

Latest answer posted November 19, 2021, 4:22 pm (UTC)

1 educator answer

Math

In this problem, we are given a sphere with a rectangular box inscribed in it. The surface area of the box is 189 m^2, and and its perimeter is 132 m. We must find the volume of the sphere. Since...

Latest answer posted November 17, 2021, 5:46 am (UTC)

1 educator answer

Math

The critical values are x = 0, 6, and 7. The function is increasing on `(-oo, 0)` with a local maximum at (0, 0), decreasing on (0, 6) with a local minimum at (6, -36), and increasing on (6, 7) and...

Latest answer posted November 17, 2021, 3:02 am (UTC)

1 educator answer

Math

To find a percentage of discount, we multiply the original price of the item by the decimal form of the percentage discounted. In this case, we have an original price of $245, and we want to see...

Latest answer posted November 16, 2021, 5:39 pm (UTC)

1 educator answer

Math

Let's start with the equation `2012 ( 1 - x^10 ) / ( 1 - x ) + x / ( 1 - x )^2 (9x^10 - 10x^9 + 1) + b x^10 + a x^11 = 0 , ` where `x = e^(i pi/6) . ` Let's multiply it by `( 1 - x )^2 ` and open...

Latest answer posted November 18, 2021, 2:01 pm (UTC)

1 educator answer

Math

As the phrase implies, DNA replication refers to the process by which a DNA molecule is copied to create another strand of DNA. The new DNA duplicates the information from the original...

Latest answer posted November 16, 2021, 3:59 pm (UTC)

1 educator answer

Math

Express `c = 9 - a - b ` and substitute it into the second equality: `( 9 - a - b ) ( a + b ) + a b = 2 4 `. It is an ellipse, which is shown on the attached picture. From the picture we see that...

Latest answer posted November 17, 2021, 8:35 am (UTC)

1 educator answer

Math

The discriminant is a part of the quadratic formula, which is used to solve quadratic equations. A quadratic equation takes the form `ax^2+bx+c=0`. The quadratic formula takes the form...

Latest answer posted November 6, 2021, 3:45 am (UTC)

1 educator answer

Math

We have been given that the scores for aptitude tests are normally distributed with a mean of 519 and a standard deviation of 108. We need to find the probability that a person has a score of at...

Latest answer posted November 6, 2021, 5:45 am (UTC)

1 educator answer

Math

This looks like the kind of question you might see on the SAT or ACT, so we’ll talk a little about problem-solving strategy as well as the specific solution to this problem. What do we see in the...

Latest answer posted November 3, 2021, 3:40 pm (UTC)

1 educator answer

Math

A student scoring 595 on the GMAT would be in the 73rd percentile, while a student scoring 310 on the GRE would be in the 65th percentile. The score on the GMAT is better than the score on the...

Latest answer posted November 10, 2021, 11:44 pm (UTC)

1 educator answer

Math

The term "discriminant" is most often used in conjunction with quadratic equations. A quadratic equation is an equation in the form `a x^2 + b x + c = 0`, where `x ` is considered to be an unknown...

Latest answer posted November 9, 2021, 12:18 pm (UTC)

1 educator answer

Math

In order to get the answer, you perform the scalar multiplication as give, so you multiply u by -7, v doesn't change, and multiply w by -1/5. Finally you add the resulting vectors....

Latest answer posted March 5, 2012, 4:31 am (UTC)

1 educator answer

Math

Given `z=1+isqrt(3)` we are asked to describe the angles and moduli of the roots: (1) First we write in polar form: if `z=a+bi` then `r=sqrt(a^2+b^2)` and then `z=rcostheta+(rsintheta)i` or...

Latest answer posted February 18, 2013, 9:14 pm (UTC)

1 educator answer

Math

A(-2,6) B (2,-4) The equation for the line passing through A and B is: y- y1 = m (x-x1) m is the slope: ==> m = (yB-yA)/(xB-xA) = (-4-6)/(-2-2) = -10/-4 = 5/2 Then the equation is: y- -4 =...

Latest answer posted September 9, 2010, 1:45 pm (UTC)

1 educator answer

Math

30 , 29 , 27, 24, 20 , ... Let us try and determine the difference between terms.\ a2-a1 = 20 - 30 = -1 a3- a2= 27- 29 = -2 a4- a3= 24- 27 = -3 a5- a4= 20 - 24 = -4 .... We notice that we do not...

Latest answer posted October 27, 2010, 10:56 pm (UTC)

1 educator answer

Math

`h(t) = -10t^2+500t+9050` `First take -10 out of the expression. h(t) = -10(t^2-50t-905)` Now we have to complete a square in the left side. Look at following expression. `(t-a)^2 =...

Latest answer posted October 30, 2012, 3:33 am (UTC)

1 educator answer

Math

The formula for volume of a cylinder is... V = r^2 * h * pi Given that the volume is 144pi and the height is 9, you can write the following equation using substitution 144(pi) = 9r^2(pi) Divide...

Latest answer posted July 8, 2011, 7:21 pm (UTC)

1 educator answer

Math

The product of slopes of two perpendicular lines is equal to -1. The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. Let us say that the...

Latest answer posted November 9, 2021, 12:41 pm (UTC)

1 educator answer

Math

LCM stands for the Least Common Multiple. It may be of two integer or natural numbers. In this case, one may use prime factorization. It is known that any natural number n has (unique)...

Latest answer posted November 9, 2021, 12:47 pm (UTC)

1 educator answer

Math

We can first begin by finding all numbers that can be expressed as a sum of two palindromes (including one-digit ones). One-digit palindromes are all one-digit numbers (`1 . . 9 `). This way,...

Latest answer posted November 11, 2021, 8:24 am (UTC)

1 educator answer

Math

r=16cos3theta r=6sintheta 1)To test for symmetry with respect to theta= pi/2: replace theta with pi-theta, r=16cos3theta r= 16cos3(pi-theta)= 16cos(3pi-3theta) = -16cos3theta thus we get r=...

Latest answer posted May 20, 2012, 8:57 am (UTC)

1 educator answer

Math

Let's call the length of the squares x.We need to figure out the length, width, and heigth of the resulting box, and use that to get the volume.You start with a length of 10, but then you fold up a...

Latest answer posted June 28, 2012, 6:06 pm (UTC)

1 educator answer

Math

The methods we use to find the equation of a line depends on the information given. The least information we need to form the equation of a line is its slope (also known as the 'gradient' ) and the...

Latest answer posted November 3, 2021, 2:06 pm (UTC)

1 educator answer

Math

To find sample standard deviation, we will use the following formula: `s=sqrt((sum (x_i-barx))^2/(N-1))`, where s represents sample standard deviation, `barx` represents sample mean, and N...

Latest answer posted November 8, 2021, 1:27 pm (UTC)

1 educator answer

Math

Slope of a line is the measure of the steepness and direction of the line. Slope of a line is equal to rise divided by run. Rise is the difference between two y-coordinates, and run is the...

Latest answer posted November 8, 2021, 2:05 pm (UTC)

1 educator answer

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