No, 8,15 and 16 is not a Pythagorean triplet.
A set of three integers that can be the lengths of the sides of a right triangle is called a Pythagorean triple, it also defines the positive integers a, b, and c which is a right triangle that exists with legs a,b, and hypotenuse c.
By the Pythagorean theorem, this is equivalent to finding positive integers a, b, and c satisfying a²+b²=c²
One of the simplest Pythagorean triples is the set “3,4,5.”
Now, substitute the values in the above equation:
16²=8²+15²
256=64+225
256[tex]\neq[/tex]289
Therefore, (8,15,16) is not a Pythagorean triplet.
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Work with a partner. Every equation that has an unknown variable can be written as a question. Choose the question that represents the equation. Then answer the question.
$x\div5=3$
Responses
Answer:
x + 5 = 10
Step-by-step explanation:
Please hurry its timed
The correct option regarding the high tide and the low tide is given as follows:
B. high tide at 6 a.m. and 6 p.m., depth of 28 ft.
low tide at 12 midnight and 12 noon, depth of 20 ft.
What is the definition of the cosine function?The cosine function is defined as follows:
g(x) = acos(bx+c)+d.
The coefficients have these following roles:
a: amplitude.b: The period is of 2π/B.c: phase shift.d: vertical shift.The amplitude for this problem is of 4, with a vertical shift of 24, hence the low and high tides are given as follows:
Low: -4 + 24 = 20 ft.High: 4 + 24 = 28 ft.The function is reflected over the x-axis, due to the multiplication by the negative number, hence the low tide is at midnight.
The period of the function is given as follows:
2π/(π/6) = 12 hours.
Thus the low tide also happens at noon, meaning that option B is correct.
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On a negatively skewed curve, which is true?
The statistical model is not good, and this is true for a negatively skewed curve.
What means negatively skewed curve?It is a statistical term implies that a curve is skewed at the left side.
In a statistical data for a certain distribution, we can get a negatively skewed curve when most of the data values are located on the right side of the distribution graph. The high concentration of values on the right side of distribution curve forms a long tail in the negative direction.
Which is true for negatively skewed curve?In general, negatively skewed curve is not good because it expresses the tendency of left tail events. Negatively skewed curves indicate a poor return from an investment. That means a person might be earn lower or no profit from his business. In case of an exam scores, negative skewed data value implies the question was too easy to perform better than usual.
In a word, left skewed or negatively skewed curve or data values inform us to be aware about the current statistical model and inspire us to take proper steps for wellbeing.
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There are 6 students at a club meeting. If they make up 40% of the club, how many total students are in the club?
please answer with mostly numbers and please explain well.
Using basic concept of proportion value and percentage from the total, The answer is there are 15 students in the club.
What do you mean by percentage?A percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%". For example, 50% means 50/100 or 0.50. It is commonly used to express rates and proportions. Percentages can be used to express a variety of information, such as discounts, increases, and proportions. For example, if a product is on sale for 20% off, that means the price has been reduced by 20/100 or 0.20 times the original price. If a company's profits have increased by 10%, that means they have gone up by 10/100 or 0.10 times the original amount.
What do you mean by proportion?A proportion is a mathematical relationship between two values that indicates that they are in a specific ratio to each other. Proportions can be expressed in a variety of ways, but one common way is to use the symbol ":" to separate the two values. In statistics, it is common to use proportions to express the relationship between different groups or categories in a population. In physics, proportions can be used to calculate different quantities in systems.
total = x
40% of x =6
40/100 * x =6
x=6*100/40
=15
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5x6+78-12
help please
Answer:
96
Step-by-step explanation:
5 x 6 = 30
78 - 12 = 66
5 x 6 + 78 - 12
= 30 + 66
= 96
Answer:96
Step-by-step explanation:
Keith Martin is the controller for Daniels Printing Service. Keith has been putting in a lot of overtime; therefore, Mr. Daniels has allowed Keith to hire an assistant. Keith’s assistant is a bright, high school graduate, but he has never taken an accounting class. Keith is trying to decide which accounting activities he should delegate to his assistant. Keith is willing to give the assistant a few simple instructions on how to complete each task, but he doesn’t have time to teach the assistant to be an accountant
The tasks that Keith can delegate to the assistant are List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet, Add the Debit and Credit columns of the trial balance and Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet.
List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet: Keith should delegate this task to his assistant. This is a relatively straightforward task that does not require a deep understanding of accounting principles. The assistant can be provided with clear instructions on how to pull the account balances from the general ledger and list them in the trial balance columns of the spreadsheet.
Add the Debit and Credit columns of the trial balance: Keith should delegate this task to his assistant. This is a simple arithmetic task that the assistant can perform with clear instructions.
Make the adjusting entries on the spreadsheet: Keith should retain this task. Adjusting entries involve more complex accounting knowledge and require a deeper understanding of accounting principles. It would be difficult for the assistant to complete this task without proper training.
Complete the spreadsheet: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.
Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet: Keith should delegate this task to his assistant. The assistant can be provided with clear instructions on how to organize the data from the spreadsheet into formal financial statements. It does not require a deep understanding of accounting principles.
Journalize and post the adjusting entries: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.
--The question is incomplete, answering to the question below--
"Keith Martin is the controller for Daniels Printing Service. Keith has been putting in a lot of overtime; therefore, Mr. Daniels has allowed Keith to hire an assistant. Keith's assistant is a bright, high school graduate, but he has never taken an accounting class. Keith is trying to decide which accounting activities could be delegated to his assistant. Keith is willing to give the assistant a few simple instructions on how to complete each task, but he doesn't have the time to teach the assistant to be an accountant.
For each task listed, state whether Keith should continue to do the work or delegate the task to his assistant. Explain each answer.
1. List the account balances from the general ledger in the Trial Balance columns of the work sheet.
2. Add the Debit and Credit columns of the trial balance.
3. Make the adjusting entries on the work sheet.
4. Complete the work sheet.
5. Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the work sheet.
6. Journalize and post the adjusting entries."
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1. y=-1
y = 2x - 7
Hello, and I am confused on this question I was wondering if anyone could help!
simply the following
a) 2(y-1)/3-3(y-2)/4=1
b) 3x=44/5=2x+6
The simplified value of x is 44 / 15 or 7 / 5 and value of y is -2
What is simplification?Simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Given that, simply the following
a) 2(y-1)/3-3(y-2)/4=1
b) 3x=44/5=2x+6
1) 2(y-1) / 3 - 3(y-2) / 4 = 1
Multiplying by 12 to both sides,
8(y-1) - 9(y-2) = 12
8y-8 - 9y+18 = 12
-y + 10 = 12
y = -2
2) 3x = 44 / 5 = 2x+6
3x = 44 / 5
Multiplying by 5 to both sides,
15x = 44
x = 44 / 15
or,
44 / 5 = 2x + 6
Multiplying by 5 to both sides,
44 = 10x + 30
14 = 10x
x = 7 / 5
Hence, the simplified value of x is 44 / 15 or 7 / 5 and value of y is -2
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When 10 is substacted from the square of a number the result is 3 times the number find the positive solution
Answer: So the positive solution is:
ANSWER: X = 5
(x = 5 ), (x = - 2 )
Step-by-step explanation:
when 10 is subtracted from the square of a number the result is 3 times the number.
Find the positive solution.
Let: x = number
Let x^2 = square of a number.
x^2 - 10x = 3x transpose
x^2 - 3x - 10 = 0
Apply Factoring: Fractions of 10 are 5 and 2
( - 5)(2) = - 10
- 5 + 2 = - 3
( x - 5 )(x + 2) = 0
x - 5 = 0 x + 2 = 0
x = 5 x = - 2
So the positive solution is:
ANSWER: X = 5
I hope that helps!!!!
Find the domain and range of the graph
A. D: X ≤ 5
R: y ≤ 7
B. D: X ≤ 7
R: y ≤ 5
C. D : X < 5
R: y < 7
D. D: X < 7
R: y < 5
Domain
The set of x-values that can be inputted into function f(x)Range
The set of y-values that are outputted by function f(x)Interval Notation
ApplicationStep 1: DefineLet's organize what is given to us from the problem.
We are given a graph of a function.
Step 2: SolveWe need to analyze the graph to determine the domain and range of the graph.
If we take a look at our x values, we see that our graph starts at x = 3 and continues infinitely.
∴ we can write the graph's x-values as [3, ∞), or x ≥ 3.
⇒ The domain of the graph is equal to x ≥ 3.
If we take a look at our y values, we see that our graph begins at y = 1 and also continues infinitely.
∴ we can write the graph's y-values as [1, ∞), or y ≥ 1.
⇒ The range of the graph is equal to y ≥ 1.
Answer∴ the answer to the question is equal to:
A. D: x ≥ 3
R: y ≥ 1
___
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Topic: Algebra I
Unit: Functions
Mitchell made a scale drawing of a house. A rug in the hallway is 5 inches wide in the drawing. The actual rug is 3 feet wide. What is the drawing's scale factor?
Simplify your answer and write it as a ratio, using a colon.
Answer:
Step-by-step explanation:
a.Scale factor = distance on the plot / actual distance
b.3 feet = 12 inchs.
so scale factor = 5/12
FOR 50 POINTS + BRAINLIEST! (NEED ASAP)
Answer:
If Lola wants, then Lola gets
Hypothesis - She is a spoiled brat who has rich parents. But where did they get their wealth?
Conclusion - Her parents are hard workers who have made it up the ladder of wealth.
2. If the measure of an angle is 58*, then the angle is acute
Hypothesis - acute angles are from 1* to 89* which makes it the smallest angle. But why when the word acute means severe?
Conclusion - We know that anything below 90* is an acute angle.
This should be a start. I will finish in a sec...
Answer:
1. Hypothesis: Lola wants.
Conclusion: Lola gets.
2. Hypothesis: The measure of an angle is 58°.
Conclusion: The angle is acute.
3. Hypothesis: The segments are diagonals of a rectangle
Conclusion: The segments are congruent.
4. Hypothesis: You are a Filipino.
Conclusion: You are a God-fearing person.
5. Hypothesis: You are a good citizen.
Conclusion: You will obey rules and regulations.
Step-by-step explanation:
In a statement, the Hypothesis is the part after the "if", and the Conclusion is the part after the "then".
1. If Lola wants, then Lola gets.
Hypothesis: Lola wants.Conclusion: Lola gets.2. If the measure of an angle is 58°, then the angle is acute.
Hypothesis: The measure of an angle is 58°.Conclusion: The angle is acute.3. If the segments are diagonals of a rectangle, then the segments are congruent.
Hypothesis: The segments are diagonals of a rectangleConclusion: The segments are congruent.4. If you are a Filipino, then you are a God-fearing person.
Hypothesis: You are a Filipino.Conclusion: You are a God-fearing person.5. If you are a good citizen, then you will obey rules and regulations.
Hypothesis: You are a good citizen.Conclusion: You will obey rules and regulations.A car moving on a road with velocity 30 m/ ,
when brake are applied it velocity decreae at a rate
of 6 meter per econd. Find the ditance it will cover before coming to ret
the distance it will cover before coming to rest is 75m. Solved using the concept of velocity.
What is velocity?Simply said, velocity is the rate of movement in a certain direction. such as the speed of a car driving north on a highway or the pace at which a rocket takes off.
Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. Since acceleration is only the rate at which velocity changes, acceleration is likewise a vector quantity.
Given that,
initial velocity (u) = 30 m/s
acceleration (a) = - 6 m/s²
As we know,
v² = u² + 2as
or, 0 = (30)² + 2 × (-6) × s
or, s = 75 m
Hence, the distance it will cover before coming to rest is 75m
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which postulate proves the two triangles are congruent
Answer:
SSS
Step-by-step explanation:
If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle it is known was SSS congruence
Two piecewise functions are shown below. What is the value of 3h(2) + 4g(1)?
Answer: In order to calculate the value of 3h(2) + 4g(1), we would need to know the specific functions h(x) and g(x) that you are referring to. Without more information, it is not possible to determine the value of the expression.
Typically, piecewise functions are defined by several different expressions, each defined over a different interval of the input variable x. To evaluate a piecewise function at a specific value of x, we must first determine which interval that value of x falls into, and then use the corresponding expression for that interval to find the output value.
Are you able to provide the piecewise functions, or are you just using them as an example?
Also, in case if you want to describe the functions in words, please let me know.
Step-by-step explanation:
Ramona used the regression equation y =. 444x – 21. 29, where x represents height and y represents shoe size, to predict the approximate height of a man who wears a size 8. 5 shoe. 1. Y =. 444 (8. 5) minus 21. 29. 2. Y = 3. 774 minus 21. 29. 3. Y = negative 17. 52. Ramona determined that her answer was incorrect because a man who is –17. 52 inches tall does not make any sense. What was Ramona’s mistake? She substituted the 8. 5 for the wrong variable. She should have added. 444 and 8. 5. The value for y should be positive. The solution of –17. 52 should be the shoe size
Ramona’s mistake was she just substituted the 8.5 for the wrong variable.
From given conditions:
Ramona used the regression equation y = 444x - 21.29,
where x represents height and y represents shoe size,
According to Romana her answer is incorrect as a man who is -17.52 inches tall does not predict the approximate height of a man.
The 8.5 refer to shoes size, not height.
So substituting 8.5 for the x-variable is wrong, because x refers to height and y represents shoe size.
Therefore, Ramon just substituted the 8.5 for the wrong variable. She must replace 8.5 for y-variable, because that's the right one for shoe size.
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How to find the height of an isosceles triangle when only base is given?
It is not possible to find the height of an isosceles triangle when only the base is given. To find the height, you would need to know at least one other side length, in addition to the base.
The height of an isosceles triangle can be found using the Pythagorean Theorem, which states that the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the two shorter sides. To use the Pythagorean Theorem, you must first know the length of at least two sides of the triangle. Since only the base is given, it is not possible to calculate the height of the isosceles triangle. In order to find the height, you would need to know either the length of the other two sides, or the angle of one of the two equal sides. Once you have this information, you can use the Pythagorean Theorem to calculate the height of the triangle.
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A traffic study has shown that the probability that 5 cars will pass over a small bridge in a 4-minute period is 0.16.
What are the odds against exactly 5 cars passing over the bridge in that time?
Answer: The odds against an event occurring are the ratio of the probability that the event will not occur to the probability that the event will occur. To find the odds against an event, you can use the formula:
Odds against = (1 - probability of event occurring) / probability of event occurring
In this case, the event is that exactly 5 cars will pass over the bridge in a 4-minute period. The probability that this event will occur is 0.16. Therefore, the odds against this event occurring are:
Odds against = (1 - 0.16) / 0.16
= 0.84 / 0.16
= 5.25
So, the odds against exactly 5 cars passing over the bridge in a 4-minute period are 5.25 to 1.
It means that there are 5.25 times more likely that it will not happen compare to happen.
Step-by-step explanation:
Notice the number of edge tiles (column 3) is equal to two less than the number of tiles on one side (column 1) multiplied by four. Knowing this relationship, if we built a 10 by 10 square mirror, write a numerical expression that would help us calculate the number of edge tiles we would need.
A numerical equation using addition as the only operator, for instance, is 2 + 17.
What is meant by numerical expression?An expression that uses only numbers and one or more operation symbols is referred to as a numerical expression. Operations like addition, subtraction, multiplication, and division are represented by symbols. Additionally, the square root sign or the absolute value symbol can be used to represent it. A numerical equation using addition as the only operator, for instance, is 2 + 17. An equation with three operators, 11 + 43 x (-4), starts with addition and moves through multiplication and subtraction. Operations are applied to numbers in numerical expressions. Numerical expressions include things like 2(3 + 8). At least one variable and one operation are included in algebraic expressions (addition, subtraction, multiplication, division). An algebraic expression is, for instance, 2(x + 8y).To learn more about numerical expression, refer to:
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Points E and Flie on a circle, centre O.
The radius of the circle is 10 cm.
The area of the shaded sector is 65cm².
Diagram not drawn to scale
Calculate the size of angle EOF
(3 marks)
The measure of the angle of the shaded sector with an area of 65 cm² is 74.5°
What is an equation?An equation is used to show the relationship between numbers and variables.
The area of a two dimensional shape is the amount of space it occupies.
The area of a sector in a circle is given by:
Area = (Ф/360) * π * radius²
Where Ф is the sector angle
Given that sector area is 65 cm², radius is 10 cm, hence:
Area = (Ф/360) * π * radius²
Substituting gives:
65 = (Ф/360) * π * 10²
Ф = 74.5°
The measure of the angle is 74.5°
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Tara placed the numbers -2 1/6, 3/11 and 2 2/9 on the number line below. Which letters
represent the correct location for each number?
-2 1/6 is A, 3/11 is C, and 2 2/9 is E
or
-2 1/6 is A, 3/11 is D, and 2 2/9 is E
or
-2 1/6 is A, 3/11 is D, and 2 2/9 is F
or
-2 1/6 is B, 3/11 is D, and 2 2/9 is F
Answer:
sorry beacuse I don't know anything
12[6.3+3(1.9)] what comes first
The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The numerical expression is given below.
⇒ 12 × [6.3 + 3 × (1.9)]
Simplify the numerical expression, then we have
⇒ 12 × [6.3 + 3 × (1.9)]
⇒ 12 × [6.3 + 5.7]
⇒ 12 × 12
⇒ 144
The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.
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Simplify: [tex]\frac{32a^2bc^3}{20abc}[/tex]
The fractions is simplified to 8ac²/ 5
What is a fraction?A fraction can be described as the part of a whole element, number or variable.
There are different types of fractions, which includes;
Improper fractionsProper fractionsMixed fractionsComplex fractionsSimple fractionsExamples of improper fractions; 5/3, 7/5
Examples of proper fractions; 3/4, 5/6
Examples of mixed fractions; 3 1/2, 4 5/6
Examples of simple fractions; 1/2 , 1/ 4
From the information given, we have that;
[tex]\frac{32a^2bc^3}{20abc}[/tex]
This is simplified to;
32 × a × a × b × c × c × c/ 20 × a × b × c
Divide the common terms
8ac²/ 5
Hence, the fractions is 8ac²/ 5
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(−2x+10)+(−8x−1)(-2x+10)+(-8x-1) .
Answer:I know why your father never came back
Step-by-step explanation: So when he got the milk he got stuck in traffic for a long time which caused the milk to expire and so he went back to grab new milk and on his way home he was stuck in traffic again and the milk got expired so he repeats the process and the same thing happens over and over and over, so hes stuck in an infinite loop until he passes away.
The pairs of polygons below are similar. Give the scale factor of figure A to figure B.
3/5
2/5
25/18
5/2
5/3
18/25
In the given pairs of polygons the scale factor of figure A to figure B is 2:4.
How is scale factor calculated?The scale factor is calculated using the following fundamental formula: Scale factor = Dimension of the new shape Dimension of the old shape. The formula for calculating the scale factor is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is magnified.
The ratio of a smaller figure's side to its corresponding side in the bigger figure is the scale factor between the two figures.
As a result, the smaller figure's side length of 4 units and its side length of 10 units are equivalent.
Therefore:
Scale factor = 4:10
i.e. 2:5
Simplify
Scale of the smaller figure to the larger is equal to 2:4.
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The 19th and 15th term of an AP are -5 and -7 1/2 repectively. What i the um of the firt 20 term
The sum of first 20 terms of the AP will be -206.25
As in AP, let us assume that the "a" be the first term and 'd' be the common difference.
So, the value of nth term can be determined by using formula: a_n=a+(n-1)d, where, n = number of terms, and d = common difference.
So, the value of 19th terms = a+(19-1)d = a+18d = -5 -----(i)
And the value of 15th term = a+(15-1)d = a+14d = -7(1/2) ----(ii)
Now subtracting (ii) from (i),
We will get,
4d = 2(1/2)
=>4d = 2.5
=>d = (2.5/4) = 0.625
Now putting value of "d" in (i)
We will get,
a+(18*0.625) = -5
a=-5-11.25 = -16.25
We have, the formula for finding the sum of terms:
Sum of terms can be determined by using formula:
Sum = (n/2) × [2a + (n-1)d]
Here, n = 20, a = -16.25, d = 0.625
We will get sum of first 20 terms as:
[tex](n/2)\times [2a + (n-1)d]\\(20/2) \times [2 \times -16.25+(20-1)0.625]\\[/tex]
10[-32.5+11.875]
=10(-20.625) =-206.25
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Which act of congress set the line of latitude at 36 degrees 30 minutes north, as the northernmost limit for slavery? dred scott v. sandford missouri compromise compromise of 1850 kansas-nebraska act
Latitude 36°30′ was designated by the Missouri Compromise of 1820 as the northern limit for the legalization of slavery in the western territories.
What did the Missouri Compromise, the Compromise of 1850, and "Bleeding Kansas" have in common?By Stephen A. Douglas's Kansas-Nebraska Act of 1854, the Missouri Compromise's prohibition on slavery in the former Louisiana Territory north of the parallel 36°30′ north had been essentially removed. Latitude 36°30′ was designated by the Missouri Compromise of 1820 as the northern limit for the legalization of slavery in the western territories.
The expansion of slavery into the western lands was addressed by the Missouri Compromise, the Compromise of 1850, and "Bleeding Kansas." The balance between "free" and "slave" states in the Union was a factor in each of them.
Slavery was proposed to be outlawed in the remaining Louisiana Territory above the 36° 30' latitude line in the Missouri Compromise. The Kansas-Nebraska Act of 1854 abolished this clause after it had been in effect for 34 years.
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The Missouri Compromise of 1820 established latitude 36°30′ as the northern boundary for the legalisation of slavery in the western territories.
What were the similarities between the Missouri Compromise, the Compromise of 1850, and "Bleeding Kansas"?The Missouri Compromise's ban on slavery in the former Louisiana Territory north of the parallel 36°30′ north had been largely lifted by Stephen A. Douglas's Kansas-Nebraska Act of 1854. The Missouri Compromise of 1820 established latitude 36°30′ as the northern boundary for the legalisation of slavery in the western territories.The Missouri Compromise, the Compromise of 1850, and "Bleeding Kansas" all addressed the spread of slavery into the western areas. Each of them was influenced by the proportion of "free" and "slave" states in the Union.In the Missouri Compromise, slavery was suggested to be prohibited in the remaining Louisiana Territory above the 36° 30' latitude line. This provision was removed by the Kansas-Nebraska Act of 1854 after it had been in place for 34 years.To learn more about Bleeding Kansas, visit:
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A cone whose apex lies along its center axis and whose axis is perpendicular to its base is called a __________ cone.
A right cone is a cone whose apex is located along its center axis and whose axis is perpendicular to its base.
What is meant by right cone?When the line connecting the vertex to the circular base's midpoint forms the cone's axis, the cone is said to be right circular. In other words, the apex of the cone and the centre point of the circular base meet and form a right angle. Having a circular base and an apex or vertex, a cone is a three-dimensional solid. The cone whose axis line is parallel to the base is referred to as the right circular cone. In mathematics, a cone is a recognizable three-dimensional geometric shape having a smooth and curving surface pointing upward. The word "cone" comes from the Greek word "konos," which denotes a peak or a wedge.To learn more about right cone, refer to:
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The tape diagram shows that Shanice spent 120 minutes researching for debate club last week, what percentage would 110% be out of 120mins ??
Answer: 110% of 120 minutes is equal to 132 minutes.
Step-by-step explanation:
To calculate percentiles:
Put in the number that you are trying to find the percentage of (120 in this case) in the calculator.Take the percentile (110% in this case) and divide it by 100.Take your new percentile number and multiply your decimal numberThe answer in the calculator is the answer to your percentile question.
The least common multiple of $1! 2!$, $2! 3!$, $3! 4!$, $4! 5!$, $5! 6!$, $6! 7!$, $7! 8!$, and $8! 9!$ can be expressed in the form $a\cdot b!$, where $a$ and $b$ are integers and $b$ is as large as possible. What is $a b$
By solving the given factorial question we get a+b=2538.
How does factorial work?In mathematics, the term "factorial" refers to the sum of all positive integers that are less than or equal to a specific positive integer, which is followed by an exclamation point. Thus, factorial seven is denoted by the symbol 7!, which stands for 1 2 3 4 5 6 7. Factorial 0 is equal to 1 by definition.
Solution:-
We can factor each of these numbers.1! + 2! = 1! ( 1 + 2 )
2! + 3! = 2! ( 1+ 3 )
3! + 4! = 3! ( 1 + 4 )
4! + 5! = 4! ( 1 + 5 )
5! + 6! = 5! ( 1 + 6 )
6! + 7! = 6! ( 1 + 7 )
7! + 8! = 7! ( 1 + 8 )
8! + 9! = 8! ( 1 + 9 )
Once again:
1! + 2! = 1! ( 3 )
2! + 3! = 2! ( 4 )
3! + 4! = 3! ( 5 )
4! + 5! = 4! ( 6 )
5! + 6! = 5! ( 7 )
6! + 7! = 6! ( 8 )
7! + 8! = 7! ( 9 )
8! + 9! = 8! ( 10 )
We can split the number into two parts, a! * bThe LCM of 1!, 2!, 3!, ... , 8! is 8!
The LCM of 3, 4, 5, ... , 10 is 2520
The LCM is 2520 * 8!
a = 2520
b = 8
a + b = 2528
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