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Algebra
The use of letters to substitute unknown numbers to form an equation. Solve the equation to get the unknown number using different methods such as simultaneous equations and more.
227,579 Questions
Well, honey, 440 can be equal to a lot of things. For starters, it's the product of 10 multiplied by 44. It's also the sum of 220 and 220, or even the result of subtracting 60 from 500. So take your pick, there are plenty of ways to skin a cat when it comes to making 440.
How many 3 digit numbers are possible from the digits 012345?
Assuming that the first digit can't be zero:
If repetition of digits is permitted: (5 x 6 x 6) = 180 numbers of 3 digits.
If repetition of digits is not permitted: (5 x 5 x 4) = 100 numbers of 3 digits.
What is the probability of rolling a number less than 5 on a six-sided die?
A way to visulize this is to start with asking "what situation has the least probability" on one roll of a six-sided die. The answer is any particular number, say a 1. Since there are six possible numbers, the probability is 1-in-6 or 1/6 = 0.17 (17%); now, since the total probability of any set added to the probability of the opposite outcome must be 1, then it stands that the probability of getting any of the 5 remaining numbers (2 through 6) is 1 - 0.17 = 0.83 (83%).
In fact, for any n-sided die, the probability, on one roll, of getting one of m numbers in the set of nnumbers is m/n.
Answer: if n = 6, and m = 4, because there are only 4 numbers on a six-sided die less than 5, the probability, P = 4/6 = 0.67 (67%).
Now let's extend the question and ask: what is the probability of getting a number less than 5 in each of two rolls. To answer, we must accept that each roll is a mutully exclusive set. That means the each roll has no impact whatsoeveron any other roll. Now, one could argue that this is never the case, because when the die bounces on the table, it changes the surface structure, or your hand muscles are stressed from the first roll, etc., but you would dramatically change the nature of the probability sets and make this far too technical a situation to be handled here. But in general, we say that these two die rolls have no impact on one another and are therefore mutually exclusive.
To find the probability of two mutually exclusive sets, we simply multiply the separate probabilities. Keep in mind that while the two sets are mutually exclusive, the sum of the combined probabilities, plus the opposite of the two, must be 1 (or 100%).
So, if the probability of rolling a 1,2,3, or 4 in one throw is 0.67, the doing the same in two throws is 0.67 * 0.67 = 0.44 (44%); hopefully you intuitively predicted that the probability would go down. Therefore, the probability of not throwing anything less than a 5 twice in a row is P = 1 - 0.44 = 0.56 (56%); keep in mind: this is not the probability of throwing a 5 or 6 twice in a row; it simply means not throwing a 1, 2, 3, or 4 twice in a row; for example, this could mean throwing a 1,2,3, or 4 the first time, but then throwing a 5 or 6 the second time. You have to ask "what are all the situations where it wouldn't be true?". Knowing that the probability of the opposite occurring is 56%, this should intuitively tell you that this "opposite" probability set has more possibilities.
Try this on your own: What is the probability of rolling exactly a 5, then rolling exactly a 1? Hint: what is the probability of each case on its own?
The volume of a cube with sides 10 feet?
Oh, dude, it's like super easy. So, the volume of a cube is just the length of one side cubed. Since all sides of a cube are the same length, you just have to cube the length of one side. In this case, the sides are 10 feet long, so the volume would be 10 feet cubed. Math is cool, right?
What are the perfect cubes between 1000 and 3000?
There are only two. They are 13^3 = 1331 and 14^3 = 2744.
You need speed to calculate this. Distance is speed / time
The volume of the rectangular prism base area 56 in. and height 6 in.?
The base area cannot be 56 inches because 56 inches is NOT a measure of area - it is a measure of distance.
If, the base area was 56 SQUARE inches, the area would be 56*6 = 336 CUBIC inches.
To solve for x in the proportion StartFraction 7 over 8 EndFraction = StartFraction x over 24 EndFraction, you can cross multiply. This means multiplying 7 by 24 and 8 by x, which gives you 168 = 8x. To isolate x, divide both sides by 8, resulting in x = 21. Therefore, x equals 21 in this proportion.
What is the gradient for 2y equals 4x plus 1?
To find the gradient of the equation 2y = 4x + 1, we first need to rewrite it in slope-intercept form, y = mx + b, where m is the gradient. Dividing by 2 on both sides gives y = 2x + 0.5. Therefore, the gradient is 2.
The cube root of 4 to the power of 3 is the same as the cube root of 64, which equals 4. This is because raising a number to the power of 3 and then taking the cube root of that result cancels out the exponentiation. In this case, 4 cubed is 64, and the cube root of 64 is 4.
93 Horses and 36 cows. ( 3 legs / cow * x cow + 4 legs / horse * y horse = 480 legs and 1 head / cow * x cow + 1 head / horse * y horse = 129 are two equations in two unknowns, which can easily be solved )
Oh, dude, you've thrown me back to high school math class with that one. So, X2 - 16x + 28 is a quadratic expression that can be factored as (X - 14)(X - 2). That's like the math version of solving a puzzle, but like, who even uses this stuff in real life, am I right?
What is the diameter of a circle with circumference 208 centimetres?
Oh, what a happy little question! To find the diameter of a circle when you know the circumference, you can use the formula: diameter = circumference / π. So, for a circle with a circumference of 208 centimeters, the diameter would be 208 / π ≈ 66.12 centimeters. Just remember, there are no mistakes, only happy little accidents in math!
How do you factor the polynomial 2x 16?
To factor the polynomial 2x^2 + 16, we first look for a common factor. In this case, both terms are divisible by 2, so we can factor out a 2 to get 2(x^2 + 8). Next, we check if the remaining quadratic expression x^2 + 8 can be factored further. Since x^2 + 8 cannot be factored further over the real numbers, the factored form of the polynomial is 2(x^2 + 8).
They have the same value! Want to know why?
When you round the numbers, if the number is 5 or larger, you add 1 to the number to the left. Making 4.59, 4.6
What is x to the 2nd power minus x minus 56?
x^(2) - x - 56
is a Quadratic EXPRESSION.
This can be factored to
( x + 7)(x - 8)
To find the values of 'x' , it needs to be equated to 'zero'
Hence it is Quadratic EQUATION
x^(2) - x - 56 = 0
( x + 7)(x - 8) = 0
x + 7 = 0
x = -7
& / or
x - 8 = 0
x = 8
How do you find an angle of a triangle with only three sides given?
By Trigonometry.
There are two Rules.
Sine Rule ; SinA/a = SinB / b = SinC/c
For this rule you need either two angles and one side, or two sides and one angle.
Cosine Rule ; a^(2) = b^(2) + c^(2) - 2bcCosA
This can be rearranged to
CosA = (a^(2) - b^(2) - c^(2)) / (-2bc)
For this rule you need three sides only, in order to calculate an angle.
The 2 nonadjacent angles formed by two intersecting line are?
They are of EQUAL size, and described as 'Vertically Opposite'.
