Can a function have no holes?
Yes, a function can have no holes when it has no common factor at both numerator and denominator.
What is a function?In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range).
What is a hole?In Mathematics, a hole can be defined as a point on the graph wherein the input value of a given function is undefined or not defined. This ultimately implies that, a hole is a point on the graph of a rational function where the input value causes both its numerator and denominator to be equal to zero (0).
In conclusion, we can reasonably infer and logically deduce that it is very possible for a function to have no holes.
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Question 7 *
2 points
Consider five-digit integers that have the following properties. Each of the digits is
1, 2 or 3, and each of 1, 2, 3 occurs at least once as a digit; also, the number is not
divisible by 2 nor divisible by 3.
What is the difference between the largest and the smallest of these integers?
O
Answer:
22098
Step-by-step explanation:
You want the difference between the largest and smallest 5-digit numbers whose digits are from the set {1, 2, 3} and include each of these at least once. The numbers cannot be divisible by 2 or 3.
DigitsThe number will be divisible by 3 when its sum of digits is a multiple of 3. Since 1, 2, and 3 are prescribed digits, the remaining two digits must not have a total of 3 or 6. The largest possible remaining digits are {2, 3}, and the smallest remaining digits are {1, 1}. (Using {3, 3} for the largest digits would give a number divisible by 3.)
The number will be divisible by 2 if the least significant digit is 2. The largest and smallest digits are not 2, so that will not be an issue.
LargestThe largest number will place the largest available digit in the place with the highest place value: 33221.
SmallestThe smallest number will place the smallest available digit in the place with the highest place value: 11123.
DifferenceThe desired difference is the difference of these numbers:
33221 -11123 = 22098 . . . . difference of largest and smallest
The difference between the two numbers will be 1998.
What is a number system?A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.
Given that Consider five-digit integers that have the following properties. Each of the digits is 1, 2 or 3, and each of 1, 2, 3 occurs at least once as a digit; also, the number is not divisible by 2 nor divisible by 3.
The largest number will be 3211.
The smallest number will be 1213.
The difference between the largest and the smallest number will be calculated as,
D = 3211 - 1213
D = 1998
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A committee consisting of 2 faculty members and 4 students is to be formed. Every committee position has the same duties and voting rights. There are 8 faculty members and 13 students eligible to serve on the committee. In how many ways can the committee be formed?
Answer:
Thus there are 3150 ways to select the 2 faculty members and 4 students for the committee.
Step-by-step explanation:
How do I solve this, or set it up
What is the mean of the following data 2 3 5 7 8?
Mean of the given numbers is 5.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
given numbers are 2 3 5 7 8
Mean is given by the formula
Mean = Sum of all the items/Number of items
x = 2 +3 + 5 + 7 + 8/5
x = 25/5
x = 5
Mean of the given numbers is 5.
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Which function is always discontinuous?
A function can have an asymptote if it approaches a horizontal or vertical line but never touches it. There are several types of functions that can have asymptotes, including rational functions, exponential functions, and logarithmic functions.
A continuous function in mathematics is a function without discontinuities, or any sudden changes in value. If we can guarantee arbitrarily small changes in the input of a function by limiting small enough changes, then the function is continuous.
There is no function that is always discontinuous. A function is either continuous or discontinuous at a particular point, but it is not necessarily either one at all points.
For example, the function f(x) = x^2 is continuous at all points, but the function g(x) = |x| is discontinuous at x=0.
On the other hand, there are functions that are discontinuous at an infinite number of points, such as the Dirichlet function, which is defined as follows:
f(x) = { 1 if x is irrational
{ 0 if x is rational
This function is discontinuous at all rational points, but it is continuous at all irrational points
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The function f(x) = x^2 is continuous at all points, but the function g(x) = |x| is discontinuous at x=0.
On the other hand, there are functions that are discontinuous at an infinite number of points, such as the Dirichlet function, which is defined as follows:
f(x) = { 1 if x is irrational
{ 0 if x is rational
This function is discontinuous at all rational points, but it is continuous at all irrational points
a population grows exponentially, doubling in 4 hours. how long, to the nearest tenth of an hour, will it take the population to triple?
Answer: 6.3 hours
Step-by-step explanation:
I have attached an image of how I solved it!
I NEED ANSWER FASTTT PLEASEE!!!!
Use the drawing tool(s) to form the correct answer on the provided graph. The graph of function f(x)=|x| is vertically stretched by a factor of 2, shifted 6 units down, and then shifted 4 units to the right. Draw the transformed function on the provided graph.
Answer:
The transformed function is
g(x)=2*|x-4|-6
Step-by-step explanation:
First, you would have to stretch it vertically which is g(x)=2*f(x)
Then you would have to move it 6 units down and 4 units to the right which is g(x)=2*f(x-4)-6
resulting in the actual function
g(x)=2*|x-4|-6
Just type that function into the DESMOS calculator and you should be good
What is a set in math Grade 7?
In math set refers the collection of unique objects that is no two objects can be the same.
In a set, the objects that belong in a set are called members or elements. And the elements of set can be anything that is numbers, animals, sport teams.
In order to represent the Sets either we have to List out the elements that are separated by commas and enclosed by curly brackets
For example,
W = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
Otherwise, we have to specify in words that objects in the set must have certain characteristics/properties by describing elements using words proves useful when we are describing sets of large sizes.
For example,
N = {Even numbers between 1 and 25}
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Can someone please help me please
Answer:
3 (for the box), p=1
Step-by-step explanation:
Since they want you to follow the instructions, divide by 2 to get (5p-2p) alone.
6p/2 = 3p (exactly like 6/2)
You will get 3p=5-2p
To solve the rest of the equation, add 2p to both sides (once you add 2p to the left side, it gets rid of it on the right side by canceling it out)
3p=5-2p
+2p +2p
5p=5
Divide 5p by 5 to get p by itself.
5p/5 = 5/5
That is p = 1
What is the coefficient of y2 in the expression 2x2y 10xy2 5y²?
Let x be the coefficient of y^2 in the expression 2x^2y+10xy^2-5y^2. So x=5.
What is co-efficient?A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves.
Write an example of co-efficient.As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.
The given algebraic expression is 2yx^2+10xy^2-5y^2.
The terms are xy^2, yx^2 any y^2
So the co-efficient of y^2 is 5.
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What is the factor form of 3x² 10x 3?
The factor form of 3x² 10x 3 is 3x(x+3)(x-3). This is because 3x² 10x 3 can be factored into three linear terms: 3x(x+3)(x-3).
What is factor?Factor is a quantity or an expression that is multiplied to another quantity or expression to obtain a product. Factors are used in mathematics to solve problems involving multiplication, division, and equations. Factors can also be used in financial analysis to calculate interest payments, loan repayments, and other financial transactions. Factors can also be used to analyze supply and demand, market trends, and other economic indicators.
This is achieved by using the 'FOIL' method, which stands for First, Outer, Inner, Last. The first two terms, 3x and x+3, are multiplied together to give 3x². The outer two terms, 3x and x-3, are multiplied together to give 3x-9. The inner two terms, x+3 and x-3, are multiplied together to give x²-3. The last two terms, 3x² and x²-3, are added together to give 3x² + x²-3 = 3x² + 10x - 3.
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How do you do 300-84848393
Answer:
Step-by-step explanation:
84848093
How do you find the zeros and holes of a function?
To find the zeros and poles of a function, you can use the following steps:
Write the function in standard form, with the independent variable (usually x) in the denominator.Find the zeros by setting the numerator equal to zero and solving for x. In the example above, the zeros are the solutions to the equation x^2 + 3x + 2 = 0. You can solve this equation using the quadratic formula or by factoring.Find the poles by setting the denominator equal to zero and solving for x. In the example above, the poles are the solutions to the equation x - 1 = 0, which means that the pole is x = 1.Plot the zeros and poles on the complex plane. The zeros correspond to points where the function is equal to zero, and the poles correspond to points where the function is undefined.How do you find the zeros and poles of a function?Generally, It's also important to note that a function can have multiple zeros and poles, and they can be complex numbers as well as real numbers. In that case, you can use the same steps above to find all of the zeros and poles.
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CQ
How do you find the zeros and poles of a function?
Is a function continuous at a hole?
continuous function can be represented by a graph without holes. A function whose graph has holes is a discontinuous function
What is the hole of a function ?Hole is a point on the graph where the value of the function is not defined. If the numerator and denominator of a rational function have a common factor they will cancel when simplifying.
Therefore to find the hole of a function is to consider numerator and denominator. If there is the same factor in the numerator and denominator there is a hole.
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Using the histogram, determine the median and the range (spread) of the quiz scores.
The median is 12 range 16
Information can not be determined by histogram
Median 18 range 10
Median 15 range is 14
Information can not be determined by histogram.
What is histogram?
A histogram is an approximation of the distribution of numerical data. This term was first introduced by Karl Pearson. The first step in creating a histogram is to "bin" (or "bucket") the range of values. That is, divide the entire range of values into a series of intervals and count the number of values. At each interval fall. Bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) must be contiguous and often (but not necessarily) the same size.
If the bins are the same size, bars are drawn across the bins, with heights proportional to frequencies (number of cases in each bin). Histograms can also be normalized to display "relative" counts, which indicate the proportion of cases falling into each of multiple categories with sum of heights equal to 1.
Information can not be determined by histogram.
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What are the 6 steps to solving a standard equation or inequality?
The six steps to solve inequality are -:
Add the same number to both sides.
Subtract the same number from both sides.
Multiply both sides by the same positive number.
Divide both sides by the same positive number.
Multiply both sides by the same negative number and reverse the sign.
Divide both sides by the same negative number and reverse the sign.
Inequality—the state of not being equal, especially in status, rights, and opportunities1—is a concept very much at the heart of social justice theories. However, it is prone to confusion in public debate as it tends to mean different things to different people. Some distinctions are common though.
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Add the same number to both sides.
Subtract the same number from both sides.
Multiply both sides by the same positive number.
Divide both sides by the same positive number.
Multiply both sides by the same negative number and reverse the sign.
Divide both sides by the same negative number and reverse the sign.
What is the mean of 1 2 3 4 5?
Answer:
Step-by-step explanation:
answer is 3 because formula of mean is Mean = {Sum of Observation} ÷ {Total numbers of Observations}.
so 1+2+3+4+5=15/5=3
so 3
The mean or arithmetic mean* is represented with this symbol [tex]\boldsymbol{\sf{\overline{x}}}[/tex], and it is calculated by adding all the data, and dividing them in total, by the total number of data there is.
We calculate the mean.1 ➕ 2 ➕ 3 ➕4➕ 5 = 15➗5=3The mode of 1,2,3,4,5 is 3✅.
The correlation coefficient, r, is a number between 0 and 1 O and on O-o and o 0-10 and 10 0 and 10 0 and 100 0-1 and 1
The correlation coefficient is a numerical measure of the strength of the linear relationship between two variables. It ranges from 0 to 1, with 0 indicating no linear relationship, and 1 indicating a perfect linear relationship. A value of 0.5 or higher is considered a strong correlation.
The correlation coefficient is calculated by taking the covariance between two variables and dividing it by the product of the standard deviations of the two variables. The formula is as follows:
r = covariance(x,y) / (stdDeviation(x) * stdDeviation(y))
The correlation coefficient is a statistical measure used to quantify the strength of the linear relationship between two variables. It takes a value between 0 and 1, with 0 indicating no linear relationship, and 1 indicating a perfect linear relationship. The correlation coefficient is calculated by taking the covariance between the two variables and dividing it by the product of their standard deviations. A negative correlation coefficient means that as one variable increases, the other decreases. A value of 0.5 or higher is considered a strong correlation. The correlation coefficient can be used to determine the strength of the relationships between variables, whether they are linear or non-linear. It is an important tool for data analysis and can help to identify relationships between different variables.
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A 292929-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 777 meters per minute. At a certain instant, the bottom of the ladder is 212121 meters from the wall.
Answer: The rate of change of the distancebetween the bottom of the ladder and the wall at that instant is 6.67 meter per minute.Let us consider that distance between the top of the ladder and the ground is x meterand distance between the bottom of the ladder and the wall is y meter.So, A right angle triangle is formed.Since, the bottom of the ladder is 21 meters from the wall.So, Applying Pythagoras theorem, Given that, the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. Differentiate below equation with respect to time. Thus, the rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute
Step-by-step explanation:
How can you verify congruence?
If any two angles and side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent.
There are 5 main rules of congruency for triangles:
SSS Criterion: Side-Side-SideSAS Criterion: Side-Angle-SideASA Criterion: Angle-Side- AngleAAS Criterion: Angle-Angle-SideRHS Criterion: Right angle- Hypotenuse-SideThree Ways To Prove Triangles Congruent:
SSS (Side-Side-Side) Postulate: If there exists a correspondence between the vertices of two triangles such that three sides of one triangle are congruent to the corresponding sides of the other triangle, the two triangles are congruent.
SAS (Side-Angle-Side) Postulate: If there exists a correspondence between the vertices of two triangles such that the two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.
ASA (Angle-Angle-Side)Postulate: If there exits a correspondence between the vertices of two triangles such that two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.
By using these rules, If two angles and one side of a triangle are respectively equal to two angles and the matching side of another triangle, then the two triangles are congruent.
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How do you find the missing leg length of the hypotenuse?
Answer:
Hello,
Step-by-step explanation:
Just find the longest measure.
Lines L and M are parallel. O 1/6 38 7 3/4 2/5 Find : m
Answer:
∠ 6 = 38°
Step-by-step explanation:
∠ 6 and 38° are vertically opposite angles and are congruent , then
∠ 6 = 38°
For a ride on a rental scooter, Bob Paid 3$ fee to start the scooter plus 11 cents per minute of the ride. the total bill for Bob's ride was 13.67. for how many minutes did Bob ride the scooter?
After solving the equation, the time in minutes Bob rides the scooter will be equal to 97 minutes.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
Total price paid to start the scooter = $3
Price of ride per minute = 11 cents
1 dollar = 100 cents
So, 11 cents = 11/100 = $0.11 per minute
Then, the equation will be,
$3 + $0.11(x) = $13.67
Here, x is the total number of minutes.
0.11x = 13.67 - 3
0.11x = 10.67
x = 97 minutes.
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Ex 2: A car can get 10 miles on 1 ½ gallons of gas. How many gallons of gas are needed
if you need to go 150 miles?
Answer: 22.5 gallons of gas
Step-by-step explanation:
1 1/2 = 3/2 or 1.5
Take 1.5 divided by 10 = 0.15 gallon per mile
Then take 0.15 times 150 miles = 22.5 gallons of gas
what is 20% of 18
(include explanation please)
Answer: 3.6
Step-by-step explanation:
20/100= 1/5
1/5*18=18/5 or 3.6
Answer:
Twenty percent of 18 is 3.6. To find 20% of a number, simply multiply the number by 0.20. For example, 20% of 18 can be calculated by multiplying 18 by 0.20, which gives us 3.6.
Step-by-step explanation:
What are the solutions to this quadratic equation 2x2 − 7x − 4 0?
The solutions of the given quadratic equation are -1/2 and 4
What is a quadratic equation?The meaning of quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.
Given is a quadratic equation, 2x²-7x-4 = 0
Factoring,
2x²-8x+x-4 = 0
2x(x-4)+1(x-4) = 0
(2x+1)(x-4) = 0
x = -1/2
x = 4
Hence, The solutions of the given quadratic equation are -1/2 and 4
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Find the product.
(6t - 3ax)(t+ ax)
Enter the corr
Answer:
Step-by-step explanation:
(6t - 3ax)(t+ ax)
use FOIL
6[tex]t^{2}[/tex] +6tax - 3tax -3[tex](ax)^{2}[/tex]
6[tex]t^{2}[/tex] + 3tax - 3[tex](ax)^{2}[/tex]
How do you rewrite an expression in equivalent form?
To rewrite an expression in equivalent form, you can use the distributive property, combine like terms, apply the commutative property, or use identities to simplify and rearrange the expression.
The distributive property states that multiplying a term and a sum of two or more terms is the same as multiplying each individual term and then adding the products together. It can be used to simplify expressions by breaking down larger terms into smaller ones. For example, 8(x + 2) can be rewritten as 8x + 16.Combining like terms is another way to rewrite expressions in equivalent form. This involves adding (or subtracting) two or more terms with the same variables. For example, 5x + 3x can be rewritten as 8x.The commutative property states that changing the order of two numbers or variables does not change their value. This can be used to rearrange expressions in equivalent forms. For example, 5x + 2y can be rewritten as 2y + 5x.Finally, identities are equations that are always true. They can be used to simplify and rearrange expressions in equivalent form. For example, (x + y)2 can be rewritten as x2 + 2xy + y2 using the identity (x + y)2 = x2 + 2xy + y2.
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Four girls have a mean height of
1.4m. Six boys have a mean
height of 1.7m.
Work out the mean height of all 10
children.
Answer:
To find the mean height of all 10 children, we need to find the total height of all the children and divide it by the number of children. The total height of the four girls is 4 * 1.4 = <<41.4=5.6>>5.6m
The total height of the six boys is 6 * 1.7 = <<61.7=10.2>>10.2m
The total height of all 10 children is 5.6 + 10.2 = <<5.6+10.2=15.8>>15.8m
The mean height of all 10 children is 15.8/10 = <<15.8/10=1.58>>1.58m. Answer: \boxed{1.58}.
Step-by-step explanation: