The thirty-fifth term in an arithmetic sequence is 1.
The formula for the nth term of an arithmetic sequence is:
[tex]t_{n}[/tex] = a + (n - 1)d
The twenty-third term in an arithmetic sequence is [tex]$\frac{2}{3}[/tex].
a + 22d = [tex]$\frac{2}{3}[/tex] ...... (1)
The fifty-third term in an arithmetic sequence is [tex]$\frac{3}{2}[/tex].
a + 52d = [tex]$\frac{3}{2}[/tex]........(2)
Subtracting both the equations.
Subtract equation (1) from equation (2):
a + 52d - (a + 22d) = [tex]$\frac{3}{2} - \frac{2}{3}[/tex]
a + 52d - a - 22d = [tex]$\frac{9-4}{6}[/tex]
30d = [tex]$\frac{5}{6}[/tex]
d = [tex]$\frac{1}{36}[/tex]
Substitute the value of d in equation (1).
We get:
a + 22[tex]$(\frac{1}{36})[/tex] = [tex]$\frac{2}{3}[/tex]
a + [tex]$\frac{11}{18}[/tex] = [tex]$\frac{2}{3}[/tex]
a = [tex]$\frac{2}{3}[/tex] - [tex]$\frac{11}{18}[/tex]
a = [tex]$\frac{12}{18} - \frac{11}{18}[/tex]
a = [tex]$\frac{1}{18}[/tex]
To find the 35th term substitute the values of a and d in the nth term equation.
The thirty-fifth term in an arithmetic sequence is:
= [tex]$\frac{1}{18}[/tex] + (35 - 1) [tex]$\frac{1}{36}[/tex]
= [tex]$\frac{1}{18}[/tex] + [tex]$\frac{34}{36}[/tex]
= [tex]$\frac{1}{18}[/tex] + [tex]$\frac{17}{18}[/tex]
= [tex]$\frac{18}{18}[/tex]
= 1
Therefore the thirty-fifth term is 1.
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5^2-log(5)5
pls help
Answer:
5
Step-by-step explanation:
log(5)5=1
5^2-1 = 5^1 = 5
What are the coordinates of the point on the directed line segment from (-9, 9) to (7, -7) that partitions the segment into a ratio of 3 to 5?
The coordinates of the point that partitions the segment is given as : (-3, 21)
How to solve for the segmentTo find the coordinates of the point on the directed line segment from (-9, 9) to (7, -7) that partitions the segment into a ratio of 3 to 5, we can use the concept of vector addition.
First, we can represent the directed line segment as a vector, with the initial point (-9, 9) being the tail, and the terminal point (7, -7) being the head. The vector representing the directed line segment is:
V = <7 - (-9), -7 - 9> = <16, -16>
To partition the segment into a ratio of 3 to 5, we can represent the partition point as a scalar multiple of the vector V:
P = (-9, 9) + (3/8)V = (-9, 9) + (3/8)(16, -16)
The scalar multiple 3/8 is used to get the partition point, it's calculated by dividing the desired ratio (3) by the sum of the ratio (3+5)
Then, we can find the x and y coordinates of the point P by applying the scalar multiple to the components of the vector:
P(x, y) = (-9, 9) + (3/8)(16, -16) = (-9, 9) + (3/8)(16, -16) = (-9 + 316/8, 9 - 3-16/8) = (-9 + 6, 9 + 12) = (-3, 21)
So the coordinates of the point on the directed line segment that partitions the segment into a ratio of 3 to 5 are (-3, 21).
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Answer:(−3,3)
Step-by-step explanation:
A bakery offers 10 kinds of cookies, 5 of which are frosted. The baker wants to put 3 different cookies in bags to sell.
From the 10 types of cookies, what is the probability that the baker places 3 frosted cookies into a bag?
A: 4/5
B: 5/126
C: 1/12
D: 3/20
Answer:
I think 3/20 of a chance of putting 3 frosted cookies in bags to sell.
Step-by-step explanation:
Hope it helps! =D
15 foot ladder leaning agaisnt a building touches the wall 12 feet above the ground how far from the building is the bottom of the ladder
The bottom of the ladder is 9 feet from the wall.
Using the Pythagorean Theorem, we can calculate the distance from the wall. The Pythagorean Theorem states that for a right triangle, the sum of the squares of the sides is equal to the square of the hypotenuse. In this case, the hypotenuse is 15 feet and the side adjacent to the wall is 12 feet.
The formula for the Pythagorean Theorem is a^2 + b^2 = c^2.
We can solve for the distance from the wall (a). a^2 = c^2 - b^2, so a^2 = 15^2 - 12^2, which equals a^2 = 225 - 144, so a^2 = 81. Taking the square root of both sides, a = 9 feet.
Therefore, the bottom of the ladder is 9 feet from the wall.
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(01.03 MC)
What is the domain of the rational function f(x)=
x²+x-20 -?
X-4x²-9x+36
The domain of the rational function in this problem is given as follows:
All real values except x = -3, x = 3, x = 4.
How to obtain the domain of the function?The domain of a function is the set composed by all the input values that the function accepts.
The function in this problem is a fraction, meaning that the denominator cannot be zero.
The denominator is given as follows:
x³ - 4x² - 9x + 36.
The roots of the denominator are given as follows:
x = -3, x = 3, x = 4.
Hence the domain is all real values except those, meaning that the second option is the correct option.
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a passenger jet took 3 hours to fly 1800 miles in the direction of the jet stream. The return trip against the jet stream took 4 hours. What was the jets speed in still air and the jet streams speed?
The speed of the jet in still air is 525miles per hour and the speed of the jet stream is 75miles per hour
What is speed ?speed is defined as the rate of change of distance with time. It is measured in meter per second and it is a scalar quantity. It has other units like miles per hour, kilometers per hour e.t.c
The speed of the jet with jet stream = displacement /time = 1800/3 = 600 miles/hour
The speed of the jet against = distance /time = 1800 / 4 = 450 miles per hour
The speed of the jet in still air will be the average speed of the jet to and fro. = (600+450)/2
= 1050/2
= 525 miles per hour
Therefore the speed of the jet in still air = 525 miles per hour
Also, the the jet stream speed = 525- 450 = 75 miles per hour.
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The balance in Jamie's checking account in the month of June was thrice the amount of what it was in the month of May he swiped his card for $69 in the restaurant which caused this account to be overdrawn by nine
The balance of Jamie's checking account in the month of May is given as follows:
$20.
How to obtain the balance?The balance in the month of May is obtained applying the proportions in the context of this problem.
He swiped his card for $69 in the restaurant which caused this account to be overdrawn by nine, hence the June balance is of:
-9 + 69 = $60.
The balance in Jamie's checking account in the month of June was thrice the amount of what it was in the month of May, hence the May's balance is given as follows:
3x = 60
x = $20.
Missing InformationThe problem asks for the balance of the checking account in the month of May.
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Lewis needed to find the difference in lengths between the hypotenuse and the longest leg of this triangle. His work is shown below.
Triangle A B C. Side B C is 16 and side A C is 12. Hypotenuse A B is labeled c.
The difference in lengths between the hypotenuse and the longest leg of the triangle is 4.
What is Pythagoras Theorem?Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.
By Pythagoras Theorem,
Hypotenuse² = (Leg 1)² + (Leg 2)²
(AB)² = (BC)² + (AC)²
c² = 16² + 12²
c² = 256 + 144
c² = 400
c = √400
c = 20
Length of longest leg = 16
Difference = 20 - 16 = 4
Hence 4 is the difference between the length of the hypotenuse and the longest leg.
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4.
What is the constant of proportionality? What does it represent?
Answer:
In Explanation
Step-by-step explanation:
The constant of proportionality is a value that relates two variables that have a proportionate relationship. It is often represented by the letter "k".
For example, if two variables x and y are directly proportional, their relationship can be represented by an equation of the form y = kx, where k is the constant of proportionality. In this equation, the value of k represents the ratio of y to x and it is constant, meaning that it does not change as the values of x or y change.
In physics, the constant of proportionality also appears in many mathematical models of natural phenomena, such as Hooke's law (F = km) which relates the force applied on an object (F) to its displacement (x) with a spring constant (k), and Ohm's law (V = IR) which relates the voltage (V) across a resistor to the current (I) flowing through it with a resistance constant (R).
The constant of proportionality can have different units of measure depending on the context and is used to make quantitative predictions about the relationship between the variables. In some cases, it can be used to determine the behaviour of a system or physical process.
(Please give brainlist)
PLEASE SOMEONE HELP ME!!
I need this turned in by 10:00
The slope-intercept form of the linear function is given as follows:
y = 0.8x + 8.
How to define the linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The graph crosses the y-axis at y = 8, hence the intercept b is given as follows:
b = 8.
When x increases by 10, y increases by 8, hence the slope m is given as follows:
m = 8/10
m = 0.8.
Then the function is defined as follows:
y = 0.8x + 8.
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what is 5g=20 step by step
Answer:
4
Step-by-step explanation:
It says 5g is 20. To figure out the value of g, you need to divide 5g by 5, and 20 by 5, which gives the answer of g=4
coach mac finds a new practice court for the basketball team. if the width of the rectangular lot is 16 feet less than the length, and the perimeter is 160 feet, what are the dimensions of the new practice court?
perimeter of rectangle = 2W + 2L
first complete these equations: 160 = ?W + ? L ; W = L - ?
The dimensions of the new practice court is 45.5 feet by 29.5 feet.
The equations should be completed as 160 = 2W + 2L; W = L - 16
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;
P = 2(L + W) or P = 2L + 2W
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Since the width of the rectangular lot is 16 feet less than the length, we have:
W = L - 16
Substituting the given parameters into the perimeter formula, we have;
160 = 2L + 2W
160 = 2(L - 16) + 2L
160 = 2L - 32 + 2L
160 = 4L - 32
4L = 182
L = 45.5 feet.
For the width, we have:
W = L - 16
W = 45.5 - 16
W = 29.5 feet.
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3) Make the following number 100 times
greater.
6.4
Answer: 640
Step-by-step explanation:
6.4 * 100 = 640
a local ice cream store is analyzing the day's sales. each serving came in either a cup or a cone, but not both, and the ratio of servings to cups was 7:47:47, colon, 4. what was the ratio of servings to cones?
The ratio of servings to cones is 47:4.
In mathematics, a ratio is a way of comparing two or more values. It is usually represented as a fraction, with the values being separated by a colon (:). For example, if you have 7 apples and 4 oranges, the ratio of apples to oranges would be 7:4. This can also be written as 7/4 or 1.75. Ratios can also be written as a decimal or a percentage. Ratios can be used to compare quantities, sizes, or measurements in different units.
If the ratio of servings to cups is 7:47:47:4, that means for every 7 servings, there are 47 cups.
Since the servings came in either a cup or a cone, but not both, the ratio of servings to cones is the remaining portion of servings that are not accounted for in the ratio of servings to cups.
So, it's 7 servings + 47 cups = 47 servings + 4 cups.
Therefore, the ratio of servings to cones is 47:4.
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A number tripled and tripled again is 819. What is the number? Show your work.
3(_____ x)= 819
_____x= 819
The number is ______.
tell what you put in the empty spots pls!!
The number representing the property of tripled a number two times and getting result 819 is equal to 91.
Let us consider a required number be 'x'.
Triple a given number is represented by 3x.
Tripled a tripled number again is expressed as 3 × ( 3x )
Result of a tripled a tripled number is equal to 819
⇒ 3 × ( 3x ) = 819
⇒ 9x = 819
Divide both the side by 9 we get,
⇒9x /9 = 819 /9
⇒ x = 91
Therefore, the required number having property of tripled and tripled a number again with result 819 is equal to 91.
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a marble is selected at random 3 times from a bag of 2 green marbles, 2 blue marbles, and 2 red marbles. the selected marble is replaced each time. what is the probability that at least 1 of the selections is blue?
The odds of choosing a red and a blue are 6/20 (4/20), or 3/5.
What is meant by probability?The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true.A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability. The likelihood that something will happen is known as probability. The number of possible outcomes is divided by the total number of possible outcomes to determine probability.The balls in the bag are unaware of what was drawn the first time because the two choices are separate.
Six of the 20 pebbles in the bag are red. The odds of selecting a red are 6/20.
Four of the 20 pebbles in the bag are blue. Picking a blue one has a 4/20 chance.
Multiplying the odds of each event will yield the likelihood of two independent events.
The likelihood of selecting a red followed by a blue is 6/20 (4/20), or 3/5.
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need the answer asap ! thank you to anyone who helps <3 !
Answer:
B
Step-by-step explanation:
What you're seeing is a (x,y,z) plane.
At this point, it's just plug and play.
Looking at choice B....
(1) + (2) + (2)(3) = 1 + 2 + 6 which is indeed 9
(2)(1) + (2)(2) + 3(3) = 2 + 4 + 9 which is indeed 15
(1) + (-3) = 1 - 3 which is indeed -2
8×1+3×
1
10
+8×
1
100
+9×
1
1000
=
Answer:
108,138
Step-by-step explanation:
Hope this helps :)
in a room of 60 people. whts the probability that there exist people that share the same birthday? assuming no one was born on feb 29?
The probability that there exists people who share the same birthday is 0.995.
Considering that all the 365 days are equally likely to be the birthday of a person and all the events that a person has birthday on 'y' are independent of others.
Under the said assumptions, let's say that there are n number of people in the room. If we number the people from 1 to n, then the total number of possibilities of birthdays are (365)^n.
Therefore, the possible combinations that all birthdays are different:
365 * 364 * 363 * .... * (365- n+1)
Thus, the probability that all birthdays are different is:
[tex]\frac{365* 364 * 363* .... (365- n+1)}{365^n}[/tex]
To get the probability of at least two people sharing the same birthday is,
[tex]1- \frac{365* 364 * 363* .... (365- n+1)}{365^n}[/tex]
= 1 - 0.0058
= 0.9942
=0.995
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Find the equation of line that passes through the points (2,0) and (5,12). Write the equation in slope-intercept form.
Answer:
y=4x+2
Step-by-step explanation:
slope (12-0)/(5-2)=4
y=4x+b
plug in (2,0)
b=2
y=4x+2
It would help me soooo much if you could solve these two
Answer:
8) 27.75
10) See down below. May be 1.83 OR 123.75, depending on what your problem says
Step-by-step explanation:
Problem 8)
Let's first take apart [tex]2^{3}[/tex], which will be 8. Now, let's plug that back into the equation real quick:
12 + (8 ÷ [tex]\frac{2}{3}[/tex]) + 3.75
Since dividing a fraction can also be equal to multiplying the reciprocal of that same fraction, ÷ [tex]\frac{2}{3}[/tex] can be re-written as: * [tex]\frac{3}{2}[/tex]
Let's put that into the equation now and solve:
12 + (8 * [tex]\frac{3}{2}[/tex]) + 3.75
= 12 + 12 + 3.75
= 27.75
Problem 10) (I'm unsure if the sign after 80 is ÷ or +, but I'll do equations for both)
(If the sign after 80 is ÷, check these steps on how to solve):
Same methods as problem 8. Let's first break down [tex]4^{2}[/tex], which will be 16. Then, let's set the ÷ [tex]\frac{2}{5}[/tex] to * [tex]\frac{5}{2}[/tex] and solve:
80 ÷ (16 * [tex]\frac{5}{2}[/tex]) + 3.75
= 80 ÷ (40) + 3.75
= [tex]\frac{80}{40+3.75}[/tex]
= 1.82857
(If the sign after 80 is +, check these steps):
80 + (16 * [tex]\frac{5}{2}[/tex]) + 3.75
= 123.75
For every pound a company spends on advertising, it spends 49 pence on its website. Express the amount spent on advertising to its website as a ratio in its simplest form.
NEED ANSWER ASAP
The ratio of the the total amount spent on advertising to the amount spent on its website is 100: 49.
Now, According to the question:
There are 100 pence in one pound. Money can be written as, for example, £5.50, which means five pounds and fifty pence. The decimal point separates the pounds from the pence.
"Information available from the question"
For every pound a company spends on advertising, it spends £0.49 pence on its website.
Ratio of the the total amount spent on advertising to the amount spent on its website is,
= 1/0.49
[tex]= \frac{1*100}{0.49*100}[/tex]
= 100/49
= 100 : 49
Therefore, the ratio of the the total amount spent on advertising to the amount spent on its website is 100: 49.
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If the price of gas increases by 5% again next week, will the price be 10% higher than it was
originally? Explain your reasoning.
If the price of gas increases by 5% again next week, then the price be approx 10% higher than it was originally because again shows that their is two times increment of 5%.
Let the price of gas is x.
The price of gas is increased by 5% in a week. So after increment the price of gas = x + x × 5%
After increment the price of gas = x + 5x/100
After increment the price of gas = (100x + 5x)/100
After increment the price of gas = 105x/100
After increment the price of gas = 1.05x
The gas price again increase by 5%.
Now the price of gas after again increment = 105x/100 × 105%
The price of gas after again increment = 105x/100 × 105/100
The price of gas after again increment = 11025x/10000
The price of gas after again increment = 1.1025x
Now we find the total increment in two weeks
Percent Increment = (1.1025x - x)/x × 100
Percent Increment = 0.1025x/x × 100
Percent Increment = 0.1025 × 100
Percent Increment = 10.25%
Then we can say that approx 10% the cost of oil increased then originally.
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what are the dimensions of a rectangular tract of land when it’s perimeter is 44 kilometers and it’s area is 120 square kilometers
Answer:
The dimensions of the rectangular tract of land with a perimeter of 44 kilometers and an area of 120 square kilometers are:
Length = 10 kilometers
Width = 12 kilometers
Explanation: To find the dimensions of a rectangular tract of land when its perimeter and area are known, you can use the formulas:
Perimeter = 2(length + width)
Area = length * width
We know that:
Perimeter = 44 kilometers
Area = 120 square kilometers
So, we can use these values to set up the following equation:
44 = 2(length + width)
And we can solve for length and width.
44 = 2(length + width)
22 = length + width
And now we know that the sum of the length and width of the rectangular tract is 22 kilometers.
Now we have to use the area formula:
Area = length * width
120 = length * width
We can use the value we have for the sum of the length and width to find either the length or the width of the rectangular tract.
For example, we can use the equation:
length = 22 - width
And substitute it into the area equation:
120 = (22 - width) * width
And then we can solve for width:
120 = 22 * width - width^2
width^2 - 22 * width + 120 = 0
We can use the quadratic formula to solve for width.
width = (22 +/- sqrt(22^2 - 4 * 1 * 120))/ 2
So,
width = (22 +/- sqrt(484 - 480))/ 2
width = (22 +/- sqrt(4))/ 2
width = (22 +/- 2)/ 2
width = (24)/ 2
width = 12
So, the width of the rectangular tract is 12 kilometers.
And we can use the equation:
length = 22 - width
to find the length
length = 22 - 12 = 10
So, the dimensions of the rectangular tract of land with a perimeter of 44 kilometers and an area of 120 square kilometers are:
Length = 10 kilometers
Width = 12 kilometers
what language used orthogonality as a primary design criterion and more orthogonal than other languages?
ALGOL 68 is a language that prioritized orthogonality as a key design requirement. ALGOL 68's primary objectives and design tenets are as follows:
1. a thorough and clear design;
2. an orthogonal design
3. Safety
4. Efficiency: Mode-independent parsing, independent compilation, loop optimization, representations in small and big character sets, static mode verification, etc.
As a programming language, Algol 68 offers certain unique and practical concepts that were ground-breaking at the time and have appeared, in varying degrees, in various languages afterwards.
Orthogonal design, which means that core concepts stated in the language can be used anyplace that usage can be said to "make sense." Completeness and clarity of explanation (as facilitated by the adoption of two-level grammar, which sparked many critical reactions).
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Jorge’s family has visited 38 of the 50 states in America. What fraction of the states
have they visited?
To find the fraction of the states that Jorge's family has visited, we can use the formula:
visited states / total states
In this case, Jorge's family has visited 38 states out of a total of 50 states, so the fraction of states they have visited is:
38 / 50
You can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor of 38 and 50 which is 2, so the fraction is
19/25
So, Jorge's family has visited 19/25 of the states in America.
Jorge's family has visited 19/25 of the states in America.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
In this case, Jorge's family has visited 38 states out of a total of 50 states, so the fraction of states they have visited is:
38 / 50
You can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor of 38 and 50 which is 2, so the fraction is
19/25
19 out of the 25 American states have been visited by the Jorge family.
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-2(x + 5)² = 20
solve by square root!
I need help with this!
Use your formula 1/2(a+b)h, to determine the height of a trapezoid with an area of 24 cubic centimeters and base lengths of 9 cm and 7 cm.
Answer:
H (Height) = 3
Step-by-step explanation:
We have the formula A = 1/2(a+b)h
Let's identify all variables
A = 24
a = 9
b = 7
h = ?
Lets plug all that in:
24 = 1/2(9+7)h
9+7 = 16
24 = 1/2(16)h
Half of 16 is 8 so to simplify the rest...
24 = 8h
To get h alone we will divide both sides of the equation by 8
24/8 = h
24/8 = 3
Making H = 3
A 4-kilogram bag of apples costs $8.80. What is the unit price?
Answer: 0.455
Step-by-step explanation:
I figured how to get $1? (The unit price?) so I did 4 divided by 8.8
Answer: The unit price is $2.20 per kilogram of apples
Step-by-step explanation:
Divide $8.80 with 4
8.80/4 = 2.20 per kilogram
Rank the four math operations (+, -, x, LaTeX: \div÷) in order of importance. Defend your ranking with real world examples using math vocabulary and skills we have learned this year
We can see here that ranking the four math operations in order of importance, we have:
AdditionMultiplicationSubtractionDivisionWhat is a math operation?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.
Addition (+) is the most important of the four operations because it is the foundation of all arithmetic. It is used in everyday life for basic calculations such as adding up a grocery bill or calculating the total cost of a purchase with tax. It is also used in more advanced mathematical concepts such as algebra and calculus.
Multiplication (x) is the second most important operation because it is used to find the total number of items in a group or the total area of a shape. It is also used in more advanced mathematical concepts such as solving equations and finding derivatives.
Subtraction (-) is the third most important operation because it is used to find the difference between two numbers. It is also used in more advanced mathematical concepts such as algebra and calculus.
Division (÷) is the least important of the four operations because it is a reverse operation of multiplication, which is more important and more frequently used. It is used to find the number of times one number is contained within another or the size of a group when the total size and number of groups is known.
All four math operations are important and useful in different ways, but the order of importance is based on how frequently they are used and how foundational they are to other mathematical concepts.
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