The equivalent expression to the 4^-3 / 4^-1 is 4^-2 or it is also equals to 1/16 .
What is Algebraic expression ?
Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The fundamentals of algebra taught us a way to express an unknown price using letters which includes x, y, z, and so on. these letters are referred to as here as variables. An algebraic expression can be a combination of both variables and constants. Any value this is located earlier than and accelerated with the aid of a variable is a coefficient.
Given
expression ,
4^-3 / 4^-1
= 4 ^ (-3-(-1))
= 4^ (-3+1)
= 4^(-2)
= 1/4^2
= 1/16 .
Therefore , The equivalent expression to the 4^-3 / 4^-1 is 4^-2 or it is also equals to 1/16 .
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Question 8
A scientist determines a plot of forest has a stable population of about 100 deer. Deer live in the interior of ecosystems. Then, a highway is built, splitting the forest into two plots of equal size.
After a couple of years, the scientist checks the number of deer in the two plots and finds the total population to be 60 deer.
Why did the carrying capacity of the habitat drop when the forest was split into two plots?
Select all that apply.
Responses
The two plots of forest have more edges than a single plot, causing a decrease in interior species. The two plots of forest have more edges than a single plot, causing a decrease in interior species.
The highway changed the climate of the region, making it less suitable for deer.The highway changed the climate of the region, making it less suitable for deer.
The two plots of forest provided more interior habitat for species other than deer. The two plots of forest provided more interior habitat for species other than deer.
The highway affected the growth of many plant species, which serve as food for the deer.
Question 9
A chicken-sized, flightless bird lives on an island in the middle of an ocean. The bird has some natural predators, which it avoids.
When people arrive at this island, they bring cats with them. Cats also hunt the bird.
What is the impact in the short term of bringing cats to the island?
Responses
The number of birds will remain the same.The number of birds will remain the same.
It is not possible to know whether there will be fewer or more birds.It is not possible to know whether there will be fewer or more birds.
There will be fewer birds.There will be fewer birds.
There will be more birds.
a) The highway affected the growth of many plant species, which serve as food for the deer. Option D
b) There will be fewer population of the birds. Option C
What is the carrying capacity?The carrying capacity of an ecosystem is the maximum number of individuals of a particular species that can be supported by the available resources in that ecosystem.
It is the point at which the population growth rate becomes zero, as the resources needed to sustain the population (such as food, water, and space) become limited. Carrying capacity can change over time due to factors such as climate change, pollution, and human activity.
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- A person has a beginning balance of $660. She pays $90 on the ninth day, and she
charges $320 on the 28th day. What amount of interest is due on her account if it has an
APR of 26 percent?
The total amount of interest due on the account is $8.36.
What is the simple interest?
Simple interest is a method of calculating the interest on a loan or deposit. It is calculated as the principal amount multiplied by the interest rate, multiplied by the number of time periods (usually in years).
To calculate the interest due on the account, we first need to determine the number of days for which the interest will accrue. Since the payment was made on the 9th day and the charge was made on the 28th day, the interest will accrue for 28 - 9 = 19 days.
We then use the formula for simple interest: Interest = Principal x Rate x Time
In this case, the Principal is the beginning balance of $660, the Rate is the APR of 26% (which must be converted to a decimal by dividing by 100), and the Time is the number of days for which the interest will accrue (19 days).
So the Interest = $660 x 0.26 x (19/365) = $8.36
Therefore, the total amount of interest due on the account is $8.36.
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You owe $278.94
on your credit card. Because you have not paid your bill on time, you have to add a past due charge of $23 , an over-limit fee of $ 30 , and a service charge of 8% of the amount owed on the credit card (without the past due charge and over limit fees). If you wish to send a check for the total amount immediately, how much should you write the check for?
Answer:
chnbntyehjejejdbhdhehgeuru382863yrh
a marketing agency selected a random sample of television viewers to test the claim that the proportion of viewers who watch a particular show is less than 0.20 at a level of significance of 0.05. the test yielded a p -value of 0.47. assuming all conditions for inference were met, which of the following is the correct conclusion?
Correct conclusion , Proportion of viewers is not less than 0.20.
What is proportion ?
A proportion is a way to express the relationship between two or more quantities or values. It is a statement that asserts that two ratios or fractions are equal, such as "2/5 is equal to 4/10". Proportions can be written in different ways, such as "2 to 5 is equal to 4 to 10", or "2:5 = 4:10".
the proportion of viewers who watch the particular show is less than 0.20. The p-value of 0.47 is greater than the level of significance of 0.05, meaning that the results of the test are not statistically significant and do not provide enough evidence to reject the null hypothesis that the proportion of viewers who watch the particular show is greater than or equal to 0.20. Therefore, the marketing agency cannot conclude that the proportion of viewers who watch the particular show is less than 0.20.
Correct conclusion , Proportion of viewers is not less than 0.20.
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Average movie prices in the United States are in general lower than in other countries.It would cost $81.22 to buy three tickets in Japan plus two tickets in Switzerland.Three tickets in Switzerland plus two tickets in Japan would cost $77.03.How much does an average movie ticket cost in each of these countries?
Answer:
It is not possible to determine the average movie ticket price in each of these countries with the given information. The statement "Average movie prices in the United States are in general lower than in other countries" is not relevant to determine the average movie ticket price in Japan and Switzerland. The information provided is the cost of 3 tickets in Japan and 2 tickets in Switzerland, and also the cost of 3 tickets in Switzerland and 2 tickets in Japan. This information cannot be used to determine the average movie ticket price in each country as it is not clear how many people are going to the movies and the different prices of the movies. More information is needed.
Two mechanics worked on a car. The first mechanic charged $115 per hour, and the second mechanic charged $60 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $2600. How long did each mechanic work? First Mechanic hours Seconds Mechanic hours
Answer:
Step-by-step explanation:
Each mechanic worked a total of 12.5 hours each.
the solid whose base is the region bounded by x-y^2 and the line y-1 and whose cross sections perpendicular to the base and parallel to the x-axis are squares
The solid whose base is the region bounded by the parabola y = x^2 and the line y = 1 and whose cross sections perpendicular to the base and parallel to the x-axis are squares is a parabolic pyramid.
A parabolic pyramid is a pyramid whose base is a parabola and whose lateral faces are formed by rectangles that are perpendicular to the base. The height of the pyramid is determined by the y-coordinate of the point where the parabola and the line y = 1 intersect. The length of the side of the square cross section is determined by the x-coordinate of the point where the parabola and the line y = 1 intersect.
The base of the solid is a parabolic region, defined by the parabola y = x^2 and the line y = 1, and the cross sections are squares, perpendicular to the base, and parallel to the x-axis. This solid is called a parabolic pyramid.
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a circular disk is to be manufactured with a radius of 26 cm. use differentials to estimate the maximum error in the calculated area of the disk if the possible error in measuring the radius is 0.25 cm.
The maximum error in calculating the area of the disk is approximately 0.25 cm * 2π * 26 cm = 16.3 cm².
The maximum error in the calculated area of the disk can be estimated using differentials. A = r2, where r is the circle's radius, is the formula for calculating a circle's area.. Differentiating this equation with respect to r gives us A' = 2πr. Plugging in the given values, we get A' = 2π * 26 cm = 161.6 cm². If the possible error in measuring the radius is 0.25 cm, then the maximum error in calculating the area of the disk is 0.25 cm * A' = 0.25 cm * 161.6 cm² = 16.3 cm². Therefore, the maximum error in the calculated area of the disk is approximately 16.3 cm².
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6. A parabola has focus (-1, 6) and directrix y = 4. Determine whether each point on
the list is on this parabola. Explain your reasoning.
a. (-1,5)
b. (1,7)
c. (3,9)
a. (-1,5) is on the parabola
b. (1,7) is NOT on the parabola
c. (3,9) is NOT on the parabola
How to find if they are on the parabolaa. (-1,5)
The distance from the point (-1,5) to the focus (-1,6) is sqrt((-1-(-1))^2 + (5-6)^2) = sqrt(0+1) = 1
The distance from the point (-1,5) to the directrix y=4 is the absolute value of the y-coordinate of the point - the y-coordinate of the directrix = abs(5-4) = 1
Since the distances are equal, the point (-1,5) is on the parabola.
b. (1,7)
The distance from the point (1,7) to the focus (-1,6) is sqrt((1-(-1))^2 + (7-6)^2) = sqrt(2^2 + 1^2) = sqrt(5)
The distance from the point (1,7) to the directrix y=4 is the absolute value of the y-coordinate of the point - the y-coordinate of the directrix = abs(7-4) = 3
Since the distances are not equal, the point (1,7) is not on the parabola.
c. (3,9)
The distance from the point (3,9) to the focus (-1,6) is sqrt((3-(-1))^2 + (9-6)^2) = sqrt(4^2 + 3^2) = sqrt(16+9) = sqrt(25)
The distance from the point (3,9) to the directrix y=4 is the absolute value of the y-coordinate of the point - the y-coordinate of the directrix = abs(9-4) = 5
Since the distances are not equal, the point (3,9) is not on the parabola.
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several students wonder which is a better buy a 40 pack of pencil top erasers for $2.82 or a 2 pack of pencil top erasers for $0.12. they use different methods to arrive at an answer
If several students wonder which is a better buy a 40 pack of pencil top The option that is the best is option 2 because it is cheaper.
How to find the option that is the best?Option 1
40 pack of pencil top erasers = 2.82/ 40
40 pack of pencil top erasers = 0.07
40 pack of pencil top erasers = 7 cent cost of each pack
Option 2 :
2 pack of pencil top erasers =0.12/ 2
2 pack of pencil top erasers = 0.06
2 pack of pencil top erasers = 6ent a pack
Based on the above calculation the second option is better than the first option based on the fact that you tend to get pencils cheaper per pack.
Therefore option 2 is better.
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2-2 the following sample data represent the per pound cost of raw materials used in processing batches of a chemical feedstock: $12.01 $14.90 $11.24 $14.40 $12.87 11.30 16.98 15.23 12.38 12.90 12.29 11.51 12.06 15.06 11.16 10.12 14.82 17.02 12.56 13.95 11.13 12.14 13.41 15.67 12.17 12.15 12.57 14.21 13.21 16.50 13.81 15.58 11.10 12.03 11.20 12.27 17.05 12.57 13.11 13.31 13.84 11.62 12.33 16.31 12.74 14.25 18.63 13.34 13.43 14.78 Construct a table for the sample frequency distribution having $2 widths for the class intervals, with $10.00 as the first tower limit Interval 1 frequency Interval 2 frequency - Interval 3 frequency - Interval 4 frequency Interval 5 frequency -
Interval 1: 10 a.m. to 12 p.m., Frequency: 6, Interval 2: 12 p.m. to 14 p.m., Frequency: 8, Interval 3: 14 p.m. to 16 p.m., Frequency 5, Interval 4: 16 p.m. to 18 p.m., Frequency 2, and Interval 5: 18 p.m. to 20 p.m., Frequency 1.
The first lower limit of the sample frequency distribution for the provided data is fixed at $10.00, with an interval width of $2.00. The frequency of Interval 1 is 6, and it runs from 10:00 to 12:00. The frequency of Interval 2 is 8, and it lasts from 12:00 to 14:00. With a frequency of 5, interval 3 runs from 14:00 to 16:00. The frequency of interval 4 is 2, and it lasts from 16:00 to 18:00. With a frequency of 1, interval 5 runs from 18.00 to 20.00. The data range and frequency of each value are shown in this table, giving a comprehensive picture of the data. You can use this table to determine suitable pricing strategies for the product.
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Josiah takes a multiple-choice quiz that has three questions. Each question has five answer options. if he randomly chooses his answers, what is the probability that he will get all three correct
Answer: 1/15
Step-by-step explanation: 3*5=15
Use the zoom controls to magnify the Moon until it fills the entire Sky Chart. Read the field of view display on the bottom left corner of the Status Bar. Roughly, what is the angular diameter of the Moon?
59 arc minutes (59')
30 arc minutes (30')
30 arc seconds (30")
15 arc minutes (15')
We frequently have no idea of their distance from us when we observe things in the night sky. For instance, although having the appearance of being inside a sphere with a very big radius that surrounds the Earth, the stars are actually all located at vastly different distances from our Solar System.
The angle that an object makes (subtends) as observed by an observer is its angular diameter. This is illustrated in the image below, where an observer at A (who is closer to the object) perceives the object's angular diameter as being larger than an observer at B. The terms "angular diameter" and "distance between two objects, measured on the celestial sphere" are interchangeable.
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determine whether each of the following formulas is a tautology, contingency, or contradiction (this means always true, sometimes true, never true). show how you arrived at each answer. use equivalence-style proofs.
From the given formulas, formula A is a tautology or always true. Formula B is a contradiction or never true. And, formula C is contingency or sometimes true.
Using the truth table, a given expression is said to be in tautology when all the values are true. The given expression is said to be a contradiction when all the values are false or never true. And the given expression is said to be contingency when the values are either true or false.
In the given formulas, formula A (p→q)∨(q→r) is a tautology. This is because the values in all rows are true (T).
In the given formulas, formula B (¬(¬(p∧q)→(p→¬q))) is a contradiction. This is because the values in all rows are false (F).
In the given formulas, formula C ((¬p∨q)→q) is a contingency. This is because some values are true and some are false.
The complete question is -
Determine whether each of the following formulas is a tautology, contingency, or contradiction (this means always true, sometimes true, never true). Show how you arrived at each answer. Use equivalence-style proofs.
A. (p→q)∨(q→r)
B. ¬(¬(p∧q)→(p→¬q))
C. ((¬p∨q)→q)
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For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. f(x)=4x²-7 on (1,b)
On the interval (1,b), f(x)=4x2-7 changes at an average rate of 8b-11. To determine this, divide the difference between the function at b and 1 (4b2-7-3) by the difference between the intervals (b-1).
The average rate of change of a function on an interval is a measure of the change in the output of the function over the given interval. It can be calculated by taking the difference of the output between the endpoints of the interval, and dividing by the difference between the endpoints of the interval. For the given function f(x)=4x²-7 on the interval (1,b), the average rate of change is 8b-11This is obtained by dividing the output difference between 1 and b (4b2-7-3) by the output difference between the intervals (b-1). Our average rate of change is given by this formula: (4b2-7-3) / (b-1) = 8b-11. This average rate of change provides us with a general understanding of the function's rate of change across the specified interval. The output of the function increases at a constant rate as the input increases in this situation because the rate of change grows linearly as b increases.
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Need help with #4 please :)
Answer:
Step-by-step explanation:
the answer is 69
Answer:yes
Step-by-step explanation:
The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Here we see two sides being congruent and one angle, this means that the other angles are also congruent, as only one triangle can be formed with two set sides and an angle. therefore we know both triangles are congruent
according to the social class model developed by gilbert, which is based on weber's analysis of the class structure, the upper class in the united states includes about of the population. group of answer choices 3 percent 1 percent 8 percent 12 percent
According to the social class model developed by Gilbert and Kahl, and based on the theory of Weber, the upper (capitalist) class of the United States includes about b) 1 percent of the population.
In the United States, the upper class, or capitalist class, is estimated to comprise about 1 percent of the population.
This is according to the social class model developed by Gilbert and Kahl, which is based on the theory of Weber.
This model suggests that the upper class is made up of those who own the majority of the nation's wealth and power, and are thus able to influence governmental decisions.
While the upper class may be small in size, it is highly influential and its members often have the resources to enact large-scale change.
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please help me with math
Answer: 3rd Picture
Step-by-step explanation: Equation: y=1/3x+4
Intercepts y axis at 4, and with the slope equation (rise/run), then it rises 1 and runs 3, thus being the 3rd picture.
Find the equation for the plane through the points Po(5,5,2), Qo(-4,0,-2), and Ro(-4,-1,1).
Using a coefficient of - 19 for x, the equation of the plane is
Ax+by is c is the equation for a line in two dimensions, the equation for a line in three dimensions.
What is the equation of plane formula?The equation of a plane in R has the generic form an x + b y + c z + d = 0, where a, b, and c are the elements of the normal vector n = (a, b, c) that is perpendicular to the plane or any vector parallel to the plane.A line and a point that is not on the line can only be crossed by one plane.Ax+by=c is the equation for a line in two dimensions. It is logical to assume that ax+by+cz=d is the equation for a line in three dimensions. However, this assumption is incorrect since it turns out that this is really the equation for a plane. In contrast to a line, a plane lacks an evident "direction."(5,5,2), Qo(-4,0,-2), and Ro(-4,-1,1).5x + 5y =2-4x + y = -2-4x -y = 1To learn more about equation of the plane refer to:
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What is the ratio of 1.5-inch screws to 2.5-inch screws, written in three different ways? Do not reduce.
The ratio of two screws written in three different forms are,
2.5 : 1.5, 5 : 3 and 1.5/2.5.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, Two screws are in the ratio of 1.5 inches and 2.5 inches.
It can be written as 2.5 : 1.5
It can also be written as 2.5×10 : 1.5×10 = 25 : 15 = 5 : 3.
It can also be written as a fraction as, 1.5/2.5.
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place value 75,232 = ___ in expanded form
7 × 10000 + 5 × 1000 + 2 × 100 + 3 × 10 + 2 × 1
help me please (asap)!!!!
Answer:
no more Fortnight gift cards
Step-by-step explanation:
Please help me, I will give best answer a brainlist
Here we are interested in finding the slope of the line. From the given graph we can see that that the line passes through points (-5,0) and (0,-3) . We know that slope can be calculated by ,
[tex]\longrightarrow slope \ (m)=\dfrac{y_2-y_1}{x_2-x_1} =\tan\theta [/tex]
hence here ,
[tex]\longrightarrow m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]
[tex]\longrightarrow m =\dfrac{0-(-3)}{-5-0}\\[/tex]
[tex]\longrightarrow m =\dfrac{3}{-5}\\ [/tex]
[tex]\longrightarrow m =\dfrac{-3}{5}\\ [/tex]
[tex]\longrightarrow \underline{\underline{ m = -0.6}}[/tex]
And we are done!
What is 4 ÷ 1⁄5?
- Answers are appericated.
Answer: 20
Step-by-step explanation:
Answer:
[tex] \sf \: 4 \div \frac{1}{5} = 20[/tex]
Step-by-step explanation:
Given problem,
[tex] \sf \rightarrow \: 4 \div \frac{1}{5} [/tex]
Let's solve the problem,
[tex] \sf \rightarrow \: 4 \div \frac{1}{5} [/tex]
[tex] \sf \rightarrow \: 4 \times \frac{5}{1} [/tex]
[tex] \sf \rightarrow \: 4 \times 5[/tex]
[tex] \sf \rightarrow \: 20[/tex]
Hence, the answer is 20.
you can assess normality of data using what?
You can assess normality of data using D. Pearson's Measure of Normality
What is Pearson's Measure of Normality ?Pearson's Measure of Normality, also known as Pearson's Test for Normality, is a statistical test that is used to assess whether a set of data is normally distributed.
It is based on the skewness and kurtosis of the data, and it provides a p-value which indicates the probability that the data is from a normal distribution. Pearson's test is considered as one of the most common statistical test used to check normality of data.
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The full question is:
You can assess normality of data using A. Pearson's Index of Skewness B. Pearson's Test C. Pearson's p-value D. Pearson's Measure of Normality
In the expression n +23 23 is a?
Hey there!
We are given the expression [tex]n + 23[/tex].
In this expression, [tex]n[/tex] represents the dependent variable; this changes with the input value once determined.Now [tex]23[/tex] on the other hand represents the constant; this variable never changes.Hence, 23 is the constant.
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Which of the following variables are quantitative?Number zip codeFavorite colorShoe sizeArea code
Quantitative variables can be used to measure and contrast data because they have numerical values. Measurements like shoe size, height, weight, and temperature are examples of quantitative variables.
Quantitative variables can be used to measure and contrast data because they have numerical values. They come in discrete or continuous forms. While continuous variables have an infinite number of possible values, such as decimal numbers, discrete variables have specific values, such as integers or whole numbers. Measurements like shoe size, height, weight, and temperature are examples of quantitative variables. Quantitative variables can be used to describe a population's varied characteristics, such as the median age or annual income of a given group. The average height of men and women, for example, might be used to compare two populations. The use of quantitative variables is crucial for comprehending and analyzing data. They enable academics to spot patterns and trends in data They enable researchers to find patterns and trends in data, anticipate the future, and form conclusions.
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the complete question is
Which of the following variables are quantitative? Number zip codeFavorite colorShoe sizeArea code and Shoe size.
compare the original function with the 1st through 4th order approximations for different values of x,
First order approximation = (sin(x+dx)/(x+dx)^3 - sin(x)/x^3)/dx and ((sin(x-(2*dx))/(x-(2*dx))3) is a formula for calculating the fourth-order
Function output for the first order approximation is first order approx (x,dx)
(x3*(cos(x)) analytical derivative =
-sin(x)*3*x^2)/x^6;
First order approximation: % forward differencing = (f(x+dx) - f(x))/dx%
first-order approximation = (sin(x)/x3 - sin(x)/x+dx)/(x+dx)3)/dx;
output is equal to Abs(FirstOrderApproximation - AnalyticalDerivative);
end
Function output for the fourth-order approximation is fourth-order approx (x,dx)
(x3*(cos(x)) analytical derivative =
-sin(x)*3*x^2)/x^6;
((sin(x-(2*dx))/(x-(2*dx))3) is a formula for calculating the fourth-order approximation. 8*(sin(x-dx))/(x-dx) + 8*(sin(x+dx))/(x+dx) - ((sin(x+(2*dx))/(x+(2*dx))3))/(12*dx);
output for the error term is abs(approximation of first order - analytical derivative);
end
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Chang received a $50.00 gift card for a photo center. He used it to buy prints that cost 6 cents each. The remaining balance, B (in dollars) on the card after buying x prints is giving by the following functions?
Answer: B = 50 - 0.06x
Step-by-step explanation:
This equation shows that the remaining balance on the gift card (B) is equal to the initial amount of the gift card (50) minus the cost of the prints (0.06x) where x is the number of prints purchased.
The expression 16n-24 factored using GCF
The G.C.F. of the expression 16n - 24 is evaluated to be 8(2n - 3).
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The given expression is - 16n - 24.
The greatest common factor, which is the product of two or more numbers, is the largest number (GCF). A natural number is created by dividing them by the biggest number (factor).
First of all find the G.C.F of 16n and 24 separately.
It can be written that -
16n = 2 × 2 × 2 × 2 × n
24 = 2 × 2 × 2 × 3
The common prime factor between the two is 2 × 2 × 2 = 8.
So, the GCF of 16n and 24 is 8.
Now use the GCF to factor the expression -
= 16n - 24
= 8(2n) - 8(3)
Using the distributive property -
= 8(2n) - 8(3)
= 8(2n - 3)
Therefore, the GCF value is 8(2n - 3).
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