Factor Trees are diagrams that show the prime factorization of a number by breaking it down into smaller factors until only prime numbers are left.
Here are the factor trees for the numbers you provided:
The Factor Trees8:
8
/
2 4
/
2 2
20:
20
/
2 10
/
2 5
27:
27
/
3 9
/
3 3
36:
36
/
2 18
/
2 9
/
3 3
72:
72
/
2 36
/
2 18
/
2 9
/
3 3.
To solve this, I used the process of prime factorization. Prime factorization is the process of finding the prime numbers that multiply together to form a given number.
The steps I followed to solve this problem are:
Starting with the first number, I divided it by 2 until I couldn't divide it anymore.If the result of the division is not a prime number, I divided it again by the smallest possible prime number.I repeated this process until all the factors of the number were prime numbers.I repeated this process for all the numbers provided.I then organized the prime factors in a tree-like structure, with the original number at the top and the prime factors branching off into their own factors, until all the factors were prime numbers.Read more about factor trees here:
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Find the average rate of change of the function f(x)=9/-3x+4, on the interval [3,5]
The average rate of change of the function f(x)=9/-3x+4, on the interval [3,5] is 1.
What is function?A function is a process or set of instructions that takes inputs, performs a specific task, and produces an output. Functions are key components of programming languages, allowing the coder to create complex commands with simple instructions. For example, a function can be used to add two numbers together or to generate a random number. Functions can also be combined to create more complex sequences of instructions.
The average rate of change of the function f(x)=9/-3x+4, on the interval [3,5] can be determined by taking the difference of the output values of the function at the endpoints of the interval, and then dividing it by the difference of the input values of the interval.
The output of the function at x=3 is f(3)=9/-3*3 +4 = -5,
and the output of the function at x=5 is f(5)=9/-3*5 +4 = -3.
Therefore, the difference of the output values is f(5)-f(3) = -3 - (-5) = 2
The difference of the input values is 5-3 = 2
Therefore, the average rate of change of the function on the interval [3,5] is f(5)-f(3) / (5-3) = 2/2 = 1.
Hence, the average rate of change of the function f(x)=9/-3x+4, on the interval [3,5] is 1.
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Find the perimeter of the figure to the right.
Answer: [tex]11a+16[/tex] feet
Step-by-step explanation:
The perimeter is equal to the sum of the lengths of the sides.
[tex]2a+2a+2a+8+5a+8=11a+16[/tex]
Which expressions are equivalent to the one below? Check all that apply.
21x
3*
A.
B. 3x
C. 7* 3*
3*
D. 7
☐ E. 7*
F. (21-3)*
Answer:
[tex]A.\;\; \left(\dfrac{21}{3}\right)^x\\\\\\C. \;\;\dfrac{7^{x}\cdot3^{x}}{3^{x}}\\\\E. \;\;7^x[/tex]
Step-by-step explanation:
[tex]\dfrac{21^x}{3^x} = \left(\dfrac{21}{3}\right)^x[/tex][tex]21 = 7 \cdot 3\\\\So\; \dfrac{21^x}{3^x} = \dfrac{7^x \cdot 3^x}{3^x}[/tex]
So choice A is correct
[tex]------------------------[/tex]
[tex]21 = 7 \cdot 3\\\\So\; \dfrac{21^x}{3^x} \\\\\\= \dfrac{(7\cdot3)^{x}}{3^{x}}=\dfrac{7^{x}\cdot3^{x}}{3^{x}}[/tex]
So Choice C is correct
[tex]------------------[/tex]
[tex]\text{SInce $\dfrac{21}{3} = 7$}\\\\\text{ $\left(\dfrac{21}{3} \right)^x = (7)^x = 7^x$}[/tex]
Therefore choice E is correct
All the other three are incorrect
Explain what is wrong with the following argument - be specific.
lim x→2 x^2 +3x-10/x^2-x-2 = (x-2)(x+5)/(x-2)(x+1) = x+5/x+1 = 2+5/2+1 = 7/3
Step-by-step explanation:
brackets are missing.
it should look like
lim x→2 (x² + 3x - 10)/(x² - x - 2) =
= (x - 2)(x + 5)/((x - 2)(x + 1)) = (x + 5)/(x + 1) =
= (2 + 5)/(2 + 1) = 7/3
content-wise there is nothing wrong with the argument.
left and right limits are the same.
so, the result is correct.
Aiden paid $180 in interest for a loan of $2000. what would the loan have been if he had paid $270 in interest instead
Answer: 1730
Step-by-step explanation:
subtract 270 from 2000
Which expression is equivalent to − 3 +t-6
The equivalent expression is t - 9
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
− 3 +t-6
Collect the like terms
So, we have the following representation
t - 3 - 6
Evaluate the like terms
This gives
t - 9
Hence, the expression is t - 9
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Find an angle θ that is coterminal with an angle, in radians, measuring 14π/3, where 0≤θ<2π. Give your answer as an exact answer involving π, if necessary.
The angle θ that is coterminal with angle 14π/3, is 20π/3
What is coterminal angle?Coterminal angles are the angles that have the same initial side and share the terminal sides. These angles occupy the standard position, though their values are different. They are on the same sides, in the same quadrant and their vertices are identical.
Given that, we need to find a coterminal angle of 14π/3,
The formula to find the coterminal angles is, θ ± 2πn where, n is an integer and it denotes the number of rotations around the coordinate plane.
For finding one coterminal angle: n = 1 (anticlockwise)
Then the corresponding coterminal angle is,
= 14π/3 + 2πn
= 14π/3 + 2π(1)
= 14π/3 + 2π
= 20π/3
Hence, the angle θ that is coterminal with angle 14π/3, is 20π/3
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Which point is a solution of the system of linear equations? x − 3y = −2 y = −3x + 4 (1, 1) (1, −1) (−1, 1) (−1, −1)
Answer:
working on a answer one second
Step-by-step explanation:
The lateral height of a cone is 8 inches and the area of the base of the cone is 49π in². It requires 2.5 minutes to paint the cone.
The area of the base is doubled.
How long will it take to paint this cone if it can be painted at the same rate? Use π≈3.14.
Enter your answer, rounded to the nearest tenth, in the box.
The time required to paint the cone when the base area is doubled is determined as 5.0 minutes.
How will it take to paint the cone when the area of the base doubles?
The amount of time requires to paint the entire cone when the area of the base of the cone is doubled is calculated using simple proportion as shown below;
time
Area of base of cone = 49π in². -----------------------> 2.5 minutes
Area of base of cone = 2 (49π in² ) -------------------> ?
49 x = ( 2 x 49 x 2.5 )
x = 2 x 2.5 min
x = 5.0 minutes
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Please help me on the problems below and show work
The correct form of the equation can be written as y = 35/6 x + 2
How do we rewrite the equation?
We have to know that the equation have been given to us in the point that we have as; y - 5/7 = 5x - 6/6. We would then have to multiply both sides with the LCM of the equations and then we have that;
42(y - 5/7) = 42(5x - 6)/6
6(y - 5) = 7(5x - 6)
6y - 30 = 35x - 42
Collecting the like terms we have that;
6y - 35 x = -42 + 30
6y - 35x = -12
6y = 35x + 12
y = 35/6 x + 12/6
y = 35/6 x + 2
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Algebra homework. Help!
(the tail points right on the number line), the mean is higher than the median.
What is median?
The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simples to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the center of a sequence to determine its value.
Every student learns one of the fundamental principles of statistics, which is that in a skewed distribution, the mean is closer to the tail, in around the second week of introductory statistics.
Every student learns one of the fundamental principles of statistics, which is that in a skewed distribution, the mean is closer to the tail, in around the second week of introduction to statistics. Therefore, the mean is greater than the median in a right-skewed distribution (where the tail points directly to the right on the number line).
Hence, (the tail points right on the number line), the mean is higher than the median.
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HELP!!! Compare 5.6 and 5
Answer:
5.6 is greater than 5.
Answer:
5.6>5
Step-by-step explanation:
5.6 is more than 5 :)
Using substitution, what is the solution for the system of equations below..
y = -1x + 6
y = -12x - 5
Answer:
Step-by-step explanation:
Solve the System of Equations
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(−1,7)
Equation Form:
x=−1,y=7
In a survey, the planning value for the population proportion is p*= 0.25. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.06? Round your answer up to the next
whole number.
The sample should be taken to provide a 95% confidence interval is 200.
What is a confidence interval?A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.
Confidence is another name for probability in statistics.
Given the planning value for the population proportion,
probability, p = 0.25
q = 1 - p = 1 - 0.25
q = 0.75
margin of error = E = 0.06
value of z at 95% confidence interval is 1.96,
the formula for a sample is,
n = (z/E)²pq
n = (1.96/0.06)²*0.25*0.75
n = 200.08
n = 200 approx
Hence sample size is 200.
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Six times the difference of a number and two us forty - two less than the number. Find the number.
Six times the difference of a number and two us forty - two less than the number is 6.
What are the arithmetic calculations?
Arithmetic is the branch of mathematics that deals with basic operations such as addition, subtraction, multiplication, and division, and their properties and applications. Arithmetic calculations are mathematical operations that involve one or more numbers and result in a numerical answer. These operations can be performed using mental arithmetic, pencil, and paper, or with the help of a calculator.
Let the number be x. We can write the given expression as:
6(x - 2) = x - 42
Expanding the left side:
6x - 12 = x - 42
Solving for x:
5x = 30
x = 6
Therefore, the number is 6.
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1. Fatima drinks her 12 ounce milkshake at a rate of an ounce per second. Bailey starts with 20 ounce milkshake and drinks at the rate of an ounce per second. Is there a time when they have the same quantity of milkshake? a) Write an equation for Fatima's drinking (y = mx + b):. b) Write an equation for Bailey's drinking (y = mx + b): c) Graph the equations on the grid below. $0.0
Situations with constant rates are represented using linear equations.
The parameters that have been provided are:1 third of an ounce of milkshake every second, 20 ounces at first.
Find linear equation?A linear equation is denoted by the following:
Where:
The rate is shown by m.
The starting value is represented by b.
The equation that summarizes Lin's circumstance is as follows:
The graph is shown in the attachment.
Since the other equation is missing, the solution cannot be found.
Situations with constant rates are represented using linear equations.
The parameters that have been provided are:
1 third of an ounce of milkshake every second
20 ounces at first.
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Find 4th, 9th and 10th term for each of 3, 6, 12, 24. following geometric progress issions
A series of terms is referred to as a geometric progression if each next term is produced by multiplying each previous term by a fixed amount. (GP), whereas the common ratio is the name given to the constant value. In the case of the GP 2, 4, 8, 16, 32, 64, for instance, the common ratio is 2.
What is the GP equation?The phrase that comes after the previous one in the GP, having a common ratio of r = l/[r(n-1)]. S=a/(1 - r), where 0 r 1, is the sum of infinite, or the sum of a GP with infinite terms.
What does GP number mean?A number progression is said to as a geometric progression if any two consecutive terms is always same.
Hence we have a=3,n=9,r=2
Now [tex]t=ar^n^-^![/tex]
=[tex]3*2^9^-^1[/tex]
=[tex]3*2^8[/tex]
=3×256
=768
∴ The ninth term of the G.P. is 768.
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-x² + 1
The expression represents a
The constant term is
coefficient is
polynomial with
the leading term is
terms.
, and the leading
The expression represents a quadratic polynomial.
The constant term is 1.
The leading term is -x².
The coefficient of the leading term is -1.
What is a polynomial?
A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
Given expression is -x² + 1
The variable of the expression is x.
The constant term is 1.
Leading term: The highest power of the variable that occurs in the polynomial is its degree. The term with the highest degree—i.e., the term with the highest power of the variable—is the leading term. The leading coefficient is the leading term's coefficient.
The leading term of the expression is -x² .
The coefficient of -x² is -1.
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Jan made fruit cups. She had 15 apple slices, 20 orange slices and 60 grapes. She put the same amount of each type of fruit into each cup. What is the greatest number of fruit cups she could have made?
Answer:
5
Step-by-step explanation:
The greatest common factor between all 3 fruits is 5. There would be 3 apple slices, 4 oranges, and 12 grapes per cup.
Divide. (40c3+20c2−36c)÷(4c)
Enter your answer in standard form in the box.
The value of the given number after division is 10c² + 5c - 9.
What is division?Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.
Given to divide (40c³ +20c² −36c) ÷ (4c)
dividing each term separately,
40c³/4c + 20c²/4c - 36c/4c
dividing constant by constant and variables by variable,
10c² + 5c - 9
Hence the division is 10c² + 5c - 9.
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Penny paid off a loan with a simple interest rate of 11% in 6 months. What was the APR?
Answer:
The solution is Option C.
The annual percentage rate of Penny is 22.4 %
Step-by-step explanation:
52) If a computer prints 108.0 lines in 4.00 seconds, how many lines can it print per minute?
Answer:
1620 lines / minute.
Step-by-step explanation:
Proportions:
1 minute = 60 seconds
Then:
108 lines ⇒ 4 seconds
A lines ⇒ 60 seconds
A = 108 lines * 60 seconds / 4 seconds
A = 1620 Lines
The distance versus time graph for Object A and Object B are shown.
A graph titles Distance vs Time. A curved line is drawn through point 10 on y axis and this line is labeled Object A. The graph for Object B is a straight slanting line passing through the origin
Which statement best describes the motion of Object A and Object B?
Both objects move with variable speed.
Both objects move with constant speed.
Object A moves with constant speed and Object B moves with variable speed.
Object A moves with variable speed and Object B moves with constant speed.
Object A moves with variable speed and Object B moves with constant speed.
The correct option is D.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
A graph titles Distance vs time.
A curved line is drawn through point 10 on y-axis and this line is labeled Object A.
The graph of the object A is shown as a curved line.
The graph for Object B is a straight slanting line passing through the origin.
The graph for Object B is a linear proportional relationship.
So, Object A moves with variable speed and Object B moves with constant speed.
Therefore, object A moves with variable speed and Object B moves with constant speed.
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Initial Knowledge Check
Question 3
Christine publishes a blog on bird-watching, with field notes and pictures of her trips around the country. Recently she decided to conduct a poll among 600 of
her subscribers, and found that 71% of those polled have liked at least one of her blogs, they have posted an average of 1.8 comments per blog, and 128 have
liked all of her blogs. Later she found out that her website already has this information for all of her subscribers. According to her website, she has a total of
12,683 subscribers, of whom 68% have liked at least one of her blogs, they have posted an average of 1.5 comments per blog, and 3781 have liked all of her
blogs.
(a) For Christine's blog poll, identify the population and the sample.
Population:
(Choose one)
Sample: (Choose one)
(b) Choose whether each number described below is a parameter or a statistic for Christine's blog poll.
Number
The average of 1.8 comments per blog that the 600 subscribers polled have posted
The 3781 subscribers among all the subscribers to Christine's blog who like all of her blogs
The 68% of all the subscribers to Christine's blog who like at least one blog?
a) The sample and the population are given as follows:
Sample: 600 subscribers.Population: Total of 12683 subscribers.b) The numbers are classified as follows:
The average of 1.8 comments per blog that the 600 subscribers polled have posted: statistic.The 3781 subscribers among all the subscribers to Christine's blog who like all of her blogs: parameter.The 68% of all the subscribers to Christine's blog who like at least one blog: parameter.What is population and sample?Population: Collection or set of individuals or objects or events whose properties will be studied.
Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.
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solve the system of equations (how many solutions are there
1. x + y = 3
x - y = -3
2. 5x + y = 7
10x + 2y = 16
1: Unique solution: the solution: (0, 3)
2: The system have no solution.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
Two system of equations,
1. x + y = 3
x - y = -3
Adding both the equations,
2x = 0,
x = 0
And y = 3.
The solution: (0, 3)
And 2. 5x + y = 7
10x + 2y = 16
The system have no solution.
Because lines are parallel.
Therefore, all the required solutions are given above.
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Imagine you start with $1.00 in a bank account that pays 100% interest per year. If the interest is credited once (annually) at the end of the year, the value of the account at year end will be $2.00. If the interest is credited twice in the year (semi-annually), the interest rate for each 6 months will be 50% (100%/2), so the initial $1 is multiplied by 1.5 twice (1 to include the original principal and .5 to add 50% more), yielding $1.00×1.52= $2.25 at the end of the year. Compounding quarterly yields $1.00×1.254= $2.4414. This formula can be written as: Where n is the number of times that interest is credited or compounded per year. 1. Calculate the value of the $1 investment if the interest is compounded (round to 3 decimal places). Show all work. a. Monthly b. Weekly c. Daily d. 1000 times in a year 2. Is there a big difference between compounding monthly and 1000 times/year? Is this a surprising result to you? Use complete sentences.
The result is the same, $2.7048. This result is not surprising because as the number of compounding periods increases, the difference between the amount after each compounding period becomes smaller and smaller. Eventually, the amount after compounding reaches a limit, which is $2.7048 in this case.
How solve the problem?a. To calculate the value of the investment compounded monthly, the formula to use is:
A = P * (1 + r/m)^(mt)
where P is the principal, r is the annual interest rate (100% in this case), t is the time in years (1 in this case), m is the number of times compounded in a year (12 in this case), and A is the amount after compounding.
A = $1.00 * (1 + 100% / 12)^(12 * 1)
A = $1.00 * (1 + 100% / 12)^12
A = $1.00 * (1.0083)^12
A = $1.0083^12
A = $2.682
b. To calculate the value of the investment compounded weekly, the formula to use is:
A = P * (1 + r/m)^(mt)
where P is the principal, r is the annual interest rate (100% in this case), t is the time in years (1 in this case), m is the number of times compounded in a year (52 in this case), and A is the amount after compounding.
A = $1.00 * (1 + 100% / 52)^(52 * 1)
A = $1.00 * (1 + 100% / 52)^52
A = $1.00 * (1.00192)^52
A = $1.00192^52
A = $2.7005
c. To calculate the value of the investment compounded daily, the formula to use is:
A = P * (1 + r/m)^(mt)
where P is the principal, r is the annual interest rate (100% in this case), t is the time in years (1 in this case), m is the number of times compounded in a year (365 in this case), and A is the amount after compounding.
A = $1.00 * (1 + 100% / 365)^(365 * 1)
A = $1.00 * (1 + 100% / 365)^365
A = $1.00 * (1.00027)^365
A = $1.00027^365
A = $2.7048
d. To calculate the value of the investment compounded 1000 times in a year, the formula to use is:
A = P * (1 + r/m)^(mt)
where P is the principal, r is the annual interest rate (100% in this case), t is the time in years (1 in this case), m is the number of times compounded in a year (1000 in this case), and A is the amount after compounding.
A = $1.00 * (1 + 100% / 1000)^(1000 * 1)
A = $1.00 * (1 + 100% / 1000)^1000
A = $1.00 * (1.001)^1000
A = $1.001^1000
A = $2.7048
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please help me i do not quite understand
Answer:
Represent Wilbur with W and Orville with O
The equation connecting both flights is
W - 120 = O
W = 364 feet
364 - 120 = 246
O = 246
Step-by-step explanation:
wish you best of luck
Stephen and Natasha have played 27 tennis matches. Stephen has won 11 times. Natasha won the rest. a) Estimate the probability that Stephen wins. b) Estimate the probability that Natasha wins.
Step-by-step explanation:
a) The probability that Stephen wins can be estimated by dividing the number of times he wins by the total number of matches:
P(Stephen wins) = 11/27 = 0.407 (or 40.7%)
b) The probability that Natasha wins can be estimated by subtracting the probability of Stephen winning from 1:
P(Natasha wins) = 1 - P(Stephen wins) = 1 - 0.407 = 0.593 (or 59.3%)
What is the y-value of the absolute minimum of the graph?
Step-by-step explanation:
we only have the graph.
it looks like the y-value from the lowest point (= the absolute minimum) is -16.
Write in the missing angle measures of WXYZ and then find the sum of the interior angles.
Answer:
X = 50
Z = 50
W = 130
Y = 130
Sum of Interior Angles: 360 degrees
Step-by-step explanation:
We can infer from the diagram, X = 50, therefore Z must be as well. W is congruent to Y, so 260 / 2 = 130. Quadrilateral is equal to 360 degrees.