Answer:
2
Step-by-step explanation:
You want the largest possible greatest common divisor of consecutive terms of the sequence an = n! +n.
SequenceThe sequence starts off 2, 4, 9, 28, 125, ...
The first two terms have a GCD of 2. The remaining pairs of terms have a GCD of 1.
The maximum possible GCD of adjacent terms is 2.
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Is this question right I just want to check?
Not quite, but really close. All you need to do is switch -4/3 and -0.2, because -4/3 is about -1.3, and negative numbers get greater as they get closer to 0
please view the image and fill in the blanks if possible.
Two of the ways that we can factor the cubes are the addition of cubes and subtraction of the cubes.
How do you factor expressions step by step?The steps below can be used to determine an expression's GCF.
If there are any variables, list them separately and write each term as the prime factorization of the coefficient or constant. As an illustration, write x. y. as x. y. and x. as x. x. The elements that each phrase has in common should be noted. Add together those typical elements.
The set containing all items found in both sets A and B, or both sets A and B taken together, is referred to as the union of two sets A and B. With the symbol "," you can represent the union of the set.
First, we change the equation's form to read as ax2+bx+c=0, where a, b, and c are the coefficients. As a result, we enter these coefficients into the formula: (-b(b2-4ac))/(2a).
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Given:
R is the midpoint of QS
Prove: PRQ = TRS
Answer:
Step-by-step explanation: Hello!
I don't remember all of the postulates to these, but I hope this will help you! Vertical angles are congruent, so both angles SRT and PRQ are congruent. This also means that line segments PQ and ST are congruent. You also know that angles Q and S are congruent which is given. By the ASA Theorem, when two angles and a side are congruent, then the triangles are congruent.
The arrows represent the forces acting on the object. Use the highlighter and draw an arrow to represent the direction that the object would be accelerating. Put an "X" if it is not accelerating.
Answer:
see attached
Step-by-step explanation:
You want the given diagram annotated with an arrow to show the direction of acceleration.
AccelerationAcceleration is a result of a net force on an object. It is in the direction of that net force.
ApplicationHere, the forces to the left and right are equal and opposite, so have a sum of zero.
The forces up and down are opposite, but unequal. The downward force is larger, so the direction of the net force is downward. (+5 +(-10) = -5)
The object will be accelerated downward in the direction of the 10 N force.
explain how the probability associated with the roll of each individual die in the pair explains the higher variability in the total outcome of the roll of each pair. how do the concepts of permutations and combinations apply to this example? discuss how the notion of degree of freedom can be used to illustrate the accumulating results of a set of dice rolls.
The probability of each individual dying in the pair explains the higher variability in the total outcome of the roll of each pair because there are more possible combinations of outcomes.
The concepts of permutations and combinations apply to this example by showing the different ways the dice can be rolled to achieve a specific total outcome. Each die in a pair of dice has a probability of 1/6 of rolling any number between 1 and 6.
When rolling two dice, there are 36 different possible outcomes (6x6) and each one has a different probability of happening. This is where the concepts of permutations and combinations apply, as each possible combination of dice rolls will result in a different total outcome.
The notion of degree of freedom can be used to illustrate the accumulating results of a set of dice rolls by showing how the total outcome is affected by the roll of each individual die.
For example, if the first die rolls a 4, the second die has 5 degrees of freedom as it can roll any number between 1 and 6 (except for 4) and still achieve a total outcome of 9. As the number of dice being rolled increases, the degree of freedom decreases, making the probability of rolling a specific total outcome less likely.
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Which equation matches the graph? f( x) = ( x + 4) 2 – 2 f( x) = ( x – 2) 2 + 4 f( x) = ( x + 2) 2 + 4 f( x) = ( x – 4) 2 + 2 f( x) = ( x + 2) 2 – 4
The quadratic equation that matches the graph is f(x) = (x - 2)² + 4.
The correct option is B.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The graph shows the function.
The graph is given in the attached image.
In the interval, [x = 0, x = 2],
we have a line that passes through the points (0, 8) and (2, 4).
That means, the points satisfies then function.
Let the f(x) = (x - 2)² + 4.
That means,
f(0) = 8
And f(2) = 4
Therefore, the quadratic function is f(x) = (x - 2)² + 4.
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A bag of Skittles has 3
green, 2 purple, 4 yellow, 6 red, and 5 orange candies.
If you pick one candy 10 times and replace it after each draw, how many times would you expect to get a candy that isn't green or purple?
Therefore , the solution of the given problem of probability comes out be probability of don't get green or purple candy = 0.75 .
What exactly does the probability process entail?Calculating the likelihood that a statement is true or that an event will occur is the focus of the branch of mathematics known as probability theory. Any number from range 0 to 1, where 1 represents certainty and 0 normally represents possibility, may be used to represent chance. The likelihood that a particular event will occur is depicted in a probability diagram.
Here,
Given :
there are 3 green, 2 purple, 4 yellow, 6 red, and 5 orange candies in the skittles.
total candies = 3 + 2 + 4 + 6 +5 =20
To find the probability that you don't get green or purple candy :
So , the probability of green candies is = 3/20 = 0.15
and the probability of purple candies is = 2/20 = 1/10 = 0.1
The probability of don't get green or purple candy
=> 0.15 + 0.1
=> 0.25
and 1 - 0.25 = 0.75
Therefore , the solution of the given problem of probability comes out be probability of don't get green or purple candy = 0.75 .
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lydia went on a trip with her family. for three hours they drove east and drove 40 miles per hour. then, they drove north for one hour and drove 50 miles. how far was lydia and her family from their home after 4 hours
Answer:
170 miles
Step-by-step explanation:
first, for 3 hours they drove 40 mph. this means you have to multiply 40 mph by the 3 hours.
40*3=120
then you have to add the extra 50 miles that they drive north because their speed changed.
120+50=170
Why doesn’t 100% of the data fall within 3 standard deviations of the mean?
As per the Empirical Rule and the properties of a Normal distribution , 99.7% of the data lies within three standard deviation not 100%.
What is Empirical Rule?
According to the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, practically all observed data for a normal distribution will lie within three standard deviations of the mean or average.
In specifically, the empirical rule predicts that 68 percent of observations will fall within the first standard deviation, 95 percent will fall within the first two standard deviations, and 99.7 percent will fall within the first three standard deviations.
Hence, as per the Empirical Rule and the properties of a Normal distribution , 99.7% of the data lies within three standard deviation not 100%.
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No need to explain. check picture.
Answer: What you chose was correct :>
A small company has one manager and 5 other employees. The manager’s salary is 25% of the company’s salary budget. If the company’s salary budget is x dollars, which expressions represent the amount of money, in dollars, from the salary budget that is left for the 5 other employees?
The amount of money left for the 5 other employees is 0.75x dollars.
How to determine the amount of moneyFrom the question, we have the following parameters that can be used in our computation:
Employees = 5
Salary = 25%
If the manager's salary is 25% of the company's salary budget, and the company's salary budget is x dollars, we can represent the manager's salary as 0.25x.
To find the amount of money left for the 5 other employees, we need to subtract the manager's salary from the total salary budget.
We can represent this using the following expression: x - 0.25x
Simplifying this further, we get
x(1-0.25) = 0.75x dollars
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Determine whether the probability given is experimental or theoretical probability. There are 120 seniors out of a total school population of 400. Elizabeth says the probability of randomly choosing a senior from a list of all the students is 3/10.
Answer:
Theoretical.
Step-by-step explanation:
120/400 = 30/100 = 3/10
She is correct.
It is the theoretical probability since it is based on calculations alone.
What is an equivalence class example?.
An example of equivalence class is the equivalence relation Congruence Modulo n. Here, two integers say "a" and "b" are equivalent if they results same remainder after dividing by n.
Equivalence classes are constructed such that elements a and b belong to the same equivalence class if and only if a and b are equivalent. Formally, the set S and the equivalence relation ~ on S, the equivalence class of the element a in S is the set [a] = { x Ε X | and ~ x} = S / ~. Example 1 : If X is the set of all pens and ~ is the "has the same color as" equivalence relation, then one particular equivalence class consists of all black pens.
Example 2: A well-known example is itthe equivalence relation Congruence Modulo n . Two integers "a" and "b" are equivalent if they have the same remainder after division by n. For example, consider the congruence relation modulo 2 on the set of integers,
R ≈ { (a,b) | a ≡ b mod 2}
The possible remainders for n = 2 are 0 and 1. An equivalence class consists of those integers that have the same remainder. Hence, there are 4 equivalence classes in this example:
[0] = { ...........,-8,-6,-4,-2,0,2,4,6,8,......}
[1] = {..........-7, -5, -3,1,3,5,7,........}
Similarly, one can show that the relation of congruence modulo n has (n -1) equivalence classes, [0], [1], ...., [ n - 1].
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What is the y-intercept of the graph with the equation 2x 3y − 6?.
The y-intercept of line 2x - 3y = -6 is (0,2).
The y-intercept of a line is the point where the line intersects the y-axis. It can be found by setting x to 0 and solving for y. In this case, we have the equation 2x - 3y = -6.
By setting x to 0, we get:
2(0) - 3y = -6
Which simplifies to: -3y = -6
And finally, by dividing both sides by -3, we get the value of y: y = 2
It means the line will intersect the y-axis at point (0,2) which means
when x =0 the line will be at y = 2.
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hi may you help if you can thanks
Answer: A 4 91/100
Step-by-step explanation: its 491/100 because the 100 is 1 and 4 is the number 4 and 91/100 is .91
In 1992, Jason bought a gallon of gas for $1.20. Yesterday, he bought a gallon of gas for $2.17. What is the percentage increase of the price of a gallon of gas from 1992 to yesterday? If necessary, round to the nearest tenth of a percent.
The percentage increase in the price of a gallon of gas is 80.84 %.
Given,
Jason bought a gallon of gas in 1992 = $1.20
He bought a gallon of gas yesterday = $2.17
Using the formula for the percentage increase in the price,
= ( New Price - Old Price) / Old Price × 100
= ( 2.17 - 1.20) / 1.20 × 100
= 80.84%
Therefore, the percentage increase in the price of a gallon of gas from 1992 to yesterday is 80.84 %.
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Which ordered pair is a solution of the equation?
y + 5 = 2(x+1)
Choose 1 answer:
Only (5, 10)
B Only (-1,-5)
Both (5, 10) and (-1,-5)
Neither
Answer:
i tried to solve it and the solution is : x=3/2 or 1.5 so ig its neither
Select the best Measures of Center for the data set:
4, 6, 9, 10, 6, 7
Question 3 options:
Either the Mean or the Median
The Median Only
The Mode Only
Answer:
either the mean or the median
What is a partial sum example?.
A partial sum is basically a addition of series and adding number upto a partial value.
For example,
635 + 312 is calculated by adding 600 + 300 = 900, 30 + 10 = 40 and 5 + 2 = 7.
These partial sums are then added as 900 + 40 + 7 = 947
A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.
A partial sum is the total of a limited number of the series' terms. To see how the infinite sum behaves, we can examine a collection of these sums. The index of the final term in the sum is used to denote each of these partial sums.
When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total.
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For what values of k will the system of equations KX 2y 5 3x Y 1 have a no unique solution?.
For k=6 the system of equations have a no unique solution
So,we have given 2 equations from the question:
kx+2y=5…(1)
3x+y=1 …(2)
First multiply the second equation by 2
We get:
6x+2y=2
Now subtracting (2) from (1), we get:
kx+2y−6x−2y=5−2
(k−6)x=3
x= 3/K-6
So, here if we put any value in k, then we will get a corresponding value of x but if we put k=6, then we will not get any value of x.
So, for k=6 this equation has no unique solution.
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If 13 is added to a number and the sum is multiplied by 3, the result is 7 times the number decreased by 9. Find the number
Answer: 47/4
Step-by-step explanation:
Convert the words into math:
The number = x
( 13 + x ) * 3 = 7 * x - 9
Expand:
39 + 3x = 7x - 9
Subtract 3x from both sides:
38 = 4x - 9
Add 9 to both sides:
47 = 4x
x = 47/4
Is an angle a defined term?.
The figure in which two rays intersect at a single location known as the vertex is referred to as an angle. The symbol "" is used to indicate an angle.
An angle is the figure formed when two rays cross at a common endpoint, according to the definition of angles. Simply put, an angle is a shape made up of two lines or rays that diverge from a central point (the vertex). The letter "a" stands for an angle.Vertex: The intersection of two angles is referred to as a vertex. It is the location where two rays converge. Arms: The two angle sides that are connected at a single endpoint. The initial side is also referred to as the reference line.
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J.5 Unit rates
2NB
You have prizes to reveal!
Go to your game board.
Finn ran a total of 6 miles over the course of 2 track practices. How many miles would Finn have run after 6 track practices? Solve using unit rates.
miles
Finn would run 18 miles after 6 track practices.
What are the total miles?Generally, A unit rate is a ratio of two measurements with a denominator of 1. To find the number of miles Finn would run after 6 track practices, we can use the unit rate of miles per practice to multiply by the number of practices.
Unit rate: 6 miles / 2 practices = 3 miles per practice
To find the total number of miles Finn would run after 6 practices, we can multiply the unit rate of 3 miles per practice by the number of practices, 6.
Total miles: 3 miles/practice * 6 practices = 18 miles
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How to solve 3 equations with 3 variables using scientific calculator?.
Solving a system of 3 equations with 3 variables using a scientific calculator can be done by using matrix operations. The method is called Gaussian elimination or Gauss-Jordan elimination. Here is an overview of the steps you can follow:
Write the system of equations in matrix form. For example, if the equations are
a₁x + b₁y + c₁z = d₁
a₂x + b₂y + c₂z = d₂
a₃x + b₃y + c₃z = d₃
the matrix form would be:
| a₁ b₁ c₁ | |x| |d₁|
| a₂ b₂ c₂ | |y| = |d₂|
| a₃ b₃ c₃ | |z| = |d₃|
Enter the matrix of coefficients (on the left side of the equations) into your calculator, usually by using the matrix function or the linear equation solver function.
Enter the constant terms of the equations (on the right side of the equations) into your calculator as a column matrix or vector.
Perform row operations to make the matrix of coefficients into an upper-triangular matrix.
Solve the system by back-substitution using the values of x, y, z in the matrix of coefficients and the matrix of constant terms.
The calculator will give you the solution of the system in terms of x, y, z.
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What is the formula of product in math?.
The multiplication formula in maths is given as follows Multiplier × Multiplicand = Product.
The product meaning in maths is a number you get to by multiplying two or more other numbers. For example, if you multiply 3 and 5 together, you get a product of 15.
Multiplication is an important part of maths. Learning and understanding how to find the product in maths is an important basis for developing their skills in maths.
You can help children learn the maths definition of the product by reminding them that it is produced when two or more numbers are multiplied together.
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if micheal's pool hold 21,000 gallons of water and it is 90 percent full, how many gallons of water are there?
The number of gallons of water that Michael's pool holds for the given condition will be 18,900 gallons.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
If Michael's pool holds 21,000 gallons of water and it is 90 percent full.
The number of gallons of water that Michael's pool holds will be given as,
⇒ 90% of 21,000
⇒ 0.90 x 21,000
⇒ 18,900 gallons
The number of gallons of water that Michael's pool holds for the given condition will be 18,900 gallons.
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What is the inverse of a convex function?.
The concept is Inverse function. The answer is, the inverse of a convex differentiable function with a non-zero derivative is strictly concave.
In mathematics, an inverse function is a function used to "cancel" another function. In other words, if f(x) yields y, then setting y to be the inverse of f yields x.
A convex function is a continuous function whose value at the middle of each interval of its domain does not exceed the arithmetic mean of its values at the ends of the interval.
The convex function has an increasing first derivative, making it appear curved upwards. Conversely, the concave function has a decreasing first derivative, so it curves down.
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How do you find the area of a 45 45 90 triangle with only the hypotenuse?.
The area of a 45-45-90 triangle, with a hypotenuse of 8mm in length is [tex]4mm^{2}[/tex]
This is a 45-45-90 triangle the base of the triangle and the height of the triangle are equal. So we simply need to find the values of the two sides and plug them into the formula.
[tex]a^{2} +b^{2} = 8^{2}[/tex]
[tex]a=b[/tex]
[tex]a^{4} =16[/tex]
[tex]a^{2} =8[/tex]
[tex]a=\sqrt{8}[/tex]
[tex]Area = 1/2 *base.height[/tex]
[tex]area=1/2*\sqrt{8} .\sqrt{8}[/tex]
[tex]Area= 4mm^{2}[/tex]
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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Complete Question:
What is the area of a 45-45-90 triangle, with a hypotenuse of 8mm in length?
Find the length of the arc on a circle of radius r intercepted by a central angle θ?
A circle's arc length can be determined from its radius and central angle using the formula Length of an Arc = r, where is in radians.
How to Find Arc Length With the Radius and Central Angle?Length of an Arc = r, where is in radians, is a formula that may be used to calculate the arc length of a circle given its radius and central angle. A circle's length is equal to (r/180)r, where r is the radius and is the angle. The length of the arc on a circle of radius r intercepted by a central angle is S = r.
Multiply the radius (6 in) by the central angle's measurement in radians to determine the length of the arc. Remember that the angle must be expressed in radians in order to employ the calculation s = r.
Assuming that is measured in radians, the formula for the length s of the arc that is intercepted on a circle with radius r by a central angle is: s = r.
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What does it mean when you substitute a value into an equation and the result is a true statement?.
When you substitute a value into an equation and the result is a true statement it means solution to an equation is a value of a variable.
The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions. According to what the name implies, this method entails determining the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation.
We can solve and determine the value of the y-variable in this method. Finally, we may use any of the above equations to obtain x by substituting the value of y. This procedure can also be switched around so that we first solve for x before solving for y.
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