The rate of change for the linear is -5 and the initial value is -1
A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. If the function has more variables, they should all be constants or known variables in order for the function to continue to function as a linear function. We'll go into great detail about what a linear function is in this article, along with its table, graph, formulas, traits, and examples.
The rate of change refers to the slope of the linear function, because the slope is actually a ration between the two variables. So, to find the slope, we use its definition:
m = [tex]y^{2}[/tex]-[tex]y^{1}[/tex]/[tex]x^{2}[/tex]-[tex]x^{1}[/tex]
Now we replace the given points, being C the first point and D the second point:
m= -11-(-1)/2-0= -5
Therefore, the rate of change is -5, where the negative sign refers to a decreasing change, it's a decreasing linear function. In addition, the initial values is where the independent variable is zero, which is given in the point C (0;-1), so the initial condition is y = -1
Therefore ,The rate of change for the linear is -5 and the initial value is -1
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Burj Khalifa i the tallet building in the world. It height i approximately 89,800 cm. The contruction team i planning to intall a 60 m long lightning rod on top of it. What will be the total height of the tructure , in metre , after the intallation of the rod
The total height of the structure after the installation of the rod will be 898.60 metres.
60 metres (rod) + 828 metres (Burj Khalifa height) = 888 metres
888 metres + 10 metres (approximate height of the lightning rod) = 898.60 metres
The Burj Khalifa is the world's tallest building with a height of 828 metres. It is located in Dubai, United Arab Emirates. The construction team is planning to install a 60 metre long lightning rod on top of the Burj Khalifa. This will increase the total height of the structure to 898.60 metres. The lightning rod is necessary for protecting the structure from lightning strikes which can cause significant damage. This will make the Burj Khalifa even taller, and will ensure the safety of the building as well as the people living in and around it.
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An instrument maker creates a triangle in the shape of an isosceles triangle by bending a metal rod. The rod is 13 inches long, and the bottom of the triangle is longer than the two sides. What is the length of the longest side?.
The length of the longest side of the isosceles triangle is 5 inches.
An isosceles triangle is a type of triangle in which two sides have the same length. The two equal sides are called the legs, and the third side, which is the base, is called the hypotenuse. The angle between the legs is called the vertex angle.
An isosceles triangle can be acute, meaning that the vertex angle is less than 90 degrees, right, meaning that the vertex angle is exactly 90 degrees, or obtuse, meaning that the vertex angle is greater than 90 degrees.
It's important to note that all equilateral triangles are isosceles but not all isosceles triangles are equilateral.
Given,
The length of the rod is 13 inches.
The length of the sides are x, x-1 and x-1.
We know that,
The rod length is 13 inches the mean perimeter is 13 inches.
So,
x + x-1 + x-1 = 13
=> 3x- 2 = 13
=> 3x= 15
=> x= 5 inches
Therefore, the other two sides = x-1 = 5-1 = 4 inches
So the length of the longest side of the isosceles triangle is 5 inches.
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Kevin bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $350 less than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 7% per year, and for the laptop it was 9.5% per year. The total finance charges for one year were $305. How much did each computer cost before finance charges?
Using algebraic expressions, cost before finance charges is $2019.63 and $1669.63.
Algebraic Expressions: Any mathematical operation that involves variables, such as addition, subtraction, multiplication, or division, can be solved using algebraic expressions. Monomial, binomial, and polynomial expressions are the three different categories of algebraic expressions. Additionally, Boolean algebra is essential to algebraic expressions.
In the basics of algebraic expressions, the letters x, y, and z stand in for an unknown value. Variables are the names given to these letters. Both variables and constants can be present in an algebraic expression. They combine to create the algebraic expression.
Let x = cost of desktop computer;
then x - 350 = cost of laptop computer
converting % to decimals, 7% = 0.07 and 9.5% = 0.095
Then, 0.07x + (x - 350)0.095 = $305
0.07x + 0.095x - 33.24 = $300
0.165x = $333.24
x = $2019.63
then x - 350 = $1669.63
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Points A, B and Clie on the circumference of a circle, centre O.
LABC= 37°.
37
B
Diagram not drawn to scale
Q7
Q8 09 Q10 Q11 Q12
O
Calculate the size of the reflex angle ZAOB.
(2 marks)
Answer:
286°
Step-by-step explanation:
You want the measure of the reflex angle AOB, whose vertex is the center of the circle in which inscribed angle ACB has measure 37°.
Inscribed angleAn inscribed angle is half the measure of the arc it intercepts, so short arc AB is 2·37° = 74°.
Central angleA central angle is equal to the measure of the arc it intercepts. Long arc ACB is 360° -74° = 286°. That means the measure of the reflex central angle AOB is ...
reflex ∠AOB = 286°
__
Additional comment
The total of arcs around a circle is 360°.
How to find mean and standard deviation from frequency table in R?.
This article will demonstrate how to use Data Frame in the R programming language to calculate the mean by group.
Mean by A, B, and C group:
A(mean) = sum/number of terms divided by 20/3 equals 6.67.B(mean) = 14/3, or 4.67 times the sum of the terms.C(mean) = sum x number of terms x 8/3 = 2.67Can a frequency table be used to determine the mean?To determine the mean from a frequency table, follow these steps: Divide the values of the numbers by the frequencies. Determine the sums.
What is the standard deviation of a frequency distribution?Divide the total by n.
Three distinct series can be used to calculate it: viz., Frequency, discrete, and individual series of distributions. "The Standard Deviation is the square root of the arithmetic mean of the squares of all deviations," Spiegel states.
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The graph of 12 = 2x+4y is shown on the grid.
Which ordered pair is in the solution set of 12 2 2x+4y?
For the linear equation 12 = 2x+4y, the value of ordered pairs are (0,3) and (6,0).
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The given linear equation is 12 = 2x + 4y
Substitute the value of x as 0 to find the value of y -
12 = 2x + 4y
12 = 2(0) + 4y
12 = 4y
y = 12/4
y = 3
Therefore, the value for y is obtained as 3.
Substitute the value of y as 0 to find the value of x -
12 = 2x + 4y
12 = 2x + 4(0)
12 = 2x
x = 12/2
x = 6
Therefore, the value for x is obtained as 6.
An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it can be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.
Therefore, two ordered pairs are obtained as (0,3) and (6,0).
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the ratio of green candies to purple candies is 3:12. there are 36 purple candies in the jar. how many green candies are in the jar
Answer:
There are 9 green candies in the jar
Step-by-step explanation:
Tyrone went to a baketball game and bought a jerey that wa on ale at a 30% dicount. He alo bought a hat that cot $37. 89. Tyrone pent a total of $83. 39. Write an equation to find the original cot of the jerey
By applying discounted price concept, the original cost of the jersey can be determined from this equation 83.39 = 37.89 + 0.70x. The original cost of the jersey is $65.
Discounted price is a price obtained after a reduction by a certain percentage from the normal price. Thus, a discounted price is lower than the normal price.
The formula: discounted price = original price × (100% - %discount)
Some information given from the problem:
Jersey discount = 30%
Hat cost = $37.89
Total spent = $83.39
Let's say the cost of the jersey = x
Total spent = hat cost + discounted jersey cost
83.39 = 37.89 + (x * (100% - 30%))
83.39 = 37.89 + (x * (70%))
83.39 = 37.89 + (x * 0.7)
83.39 = 37.89 + 0.7x
Thus this is the equation.
If we want to know the original cost of the jersey, we can continue the calculation:
83.39 = 37.89 + 0.7x
83.39 - 37.89 = 0.7x
45.5 = 0.70x
x = 45.5/0.70
x = 65
Thus, the original cost of the jersey is $65.
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How do I find the first term of geometric progression when the ration is 2 and the sum of the first 6 terms is 7?
Answer:
The first term is 1/9-----------------------------
Let the first term be a.
The common ratio is r = 2 and the sum of the first 6 terms is S₆ = 7.
Use the sum of first n terms formula:
Sₙ = a(rⁿ - 1)/(r - 1)Substitute and solve for a:
7 = a(2⁶ - 1)/(2 - 1)7 = a(64 - 1)/17 = 63aa = 7/63a = 1/9what are the order pairs to the fallowing solution of the sytems of equations
f(x)=x^2-2x+3: f(x)=-2x+12
The order pairs to the given equations are (-3, 18) and (3, 6)
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given are two equation, f(x) = x²-2x+3 and f(x) = -2x+12
For solving, equate them,
x²-2x+3 = -2x+12
x² = 2x-2x+12-3
x² = 9
x = ±3
Put x = -3 in f(x) = -2x+12
f(-3) = -2(-3)+12
f(-3) = 18
And, Put x = 3 in f(x) = -2x+12
f(3) = -2(3)+12
f(3) = 6
Therefore, the ordered pairs are (-3, 18) and (3, 6)
Hence, the order pairs to the given equations are (-3, 18) and (3, 6)
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what is x? please help
Answer:
x = 132
Step-by-step explanation:
The sum of interior angles in parallelogram equals 360. Opposite angles are congruent. (have equal measures)
360 = 48 x 2 + 2x
360 = 96 + 2x
(subtract 96 from both sides)
264 = 2x
(divide both sides by 2)
132 = x
Check:
2x + (48 x 2) = 360
(132 x 2) + 96 = 360
264 + 96 = 360
360 = 360
Answer: 132 Degrees
Step-by-step explanation: Since you know all the angles have to add up to 360 and one of the angles is 48. Alternate angles are always equal so you would do 48 and double that making 96. 360-96 leaves you with 264. Using the same alternate angles rule you would just divide that by 2 which leaves you with 132 degrees.
In a packet of 40 skittles, 35% are not red. How may skittles are not red?
Answer:
14
Step-by-step explanation:
35/100= .35
.35 x 40= 14
Not red skittles: 14
Answer:
14
Step-by-step explanation:
35/100= .35
.35 x 40= 14
Not red skittles: 14
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 83 m long and 62 m wide.
Find the area of the training field. Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
The area of the training field is 16,966 m2. The area of the rectangle is 83 x 62 = 5,146 m2, and the area of each semicircle is (3.14 x (83/2)2) / 2 = 1,652 m2. Therefore, the total area of the training field is 5,146 + (2 x 1,652) = 16,966 m2.
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Which symbol correctly describes the relationship between these two numbers?
The relationship between these two numbers is 3 > 2.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
An expression:
3 is greater than 2.
Here, we will use the inequality symbol.
3 > 2.
Therefore, the expression is 3 > 2.
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The complete question:
Which symbol correctly describes the relationship between these two numbers?
And the expression: 3 is greater than 2.
Sydney is deciding between two parking garages. Garage A charges an initial fee of
$12 to park plus $4 per hour. Garage B charges an initial fee of $7 to park plus $5 per
hour. Let A represent the amount Garage A would charge if Sydney parks for t hours,
and let B represent the amount Garage B would charge if Sydney parks for t hours.
Write an equation for each situation, in terms of t, and determine the hours parked,
t, that would make the cost of each garage the same.
The equation for Garage A can be expressed as A = 12 + 4t, and the equation for Garage B as B = 7 + 5t.
Write an equation for each situation?In order to determine the hours parked, t, that would make the cost of each garage the same, we first set the two equations equal to each other, A = B.Then, we can solve for t by subtracting 7 from both sides of the equation and dividing by -1.This gives us t = -5. Since we cannot park for a negative number of hours, this tells us that the cost of each garage will never be the same.The equation for Garage A is A = 12 + 4t, while the equation for Garage B is B = 7 + 5t. To find the number of hours, t, that would make the cost of each garage the same, we must set A = B and solve for t.Therefore, 12 + 4t = 7 + 5t, and subtracting 7 from both sides of the equation yields 5t = 5, and t = 1. Thus, if Sydney parks for 1 hour, the cost of both Garage A and Garage B would be the same.A = 12 + 4t
B = 7 + 5t
12 + 4t = 7 + 5t
4t - 5t = 7 - 12
-t = -5
t = 5 hours
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If L || m, solve for x (6x+4) (4x-14)
Since lines m and n are parallel lines, the value of x in the image above is equal to 19.
What is the Alternate Interior Angles Theorem?In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.
What is the Linear Pair Postulate?In Mathematics, the Linear Pair Postulate states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair.
By applying the Linear Pair Postulate to the two (2) alternate interior angles, we have the following:
6x + 4 + (4x - 14) = 180
10x - 10 = 180
10x = 180 + 10
10x = 190
x = 190/10
x = 19.
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i need help please thank you
The line of reflection for this problem is defined as follows:
x = -1.
The line of reflection is drawn on the image given at the end of the answer.
How to obtain the line of reflection?The vertices of the two triangles have the same y-coordinates, while the x-coordinates are different, hence the reflection line is a vertical line.
The x-coordinates will be equidistant to the reflection line, just on opposite coordinates.
Considering that the reflection changes the "faces" of the triangles, D and E are equivalent vertices, thus the reflection line is given by the mean of the x-coordinates of these two points, hence:
x = (-3 + 1)/2
x = -1.
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What is the function of logarithmic function?.
The logarithmic function is a mathematical function that expresses the exponent of a number to produce a given value, with the property of simplifying multiplication to addition and it is the inverse of the exponential function.
A logarithmic function is a mathematical function that expresses the power to which a number (the base) must be raised in order to produce a given value. The logarithm of a number is the exponent to which the base must be raised to produce that number.
A logarithmic function can be represented in the form of log_b(x) or logb(x), where b is the base of the logarithm and x is the value being evaluated.
For example, the logarithm of 1000 to the base 10 is 3, because 10^3 = 1000. It can be written as log10(1000) = 3.
The logarithm function has the property that log_b(x*y) = log_b(x) + log_b(y), which means that logarithms simplify the multiplication of numbers to the addition of logarithms.
The logarithmic function also has an inverse function, which is the exponential function, that's why logarithms and exponents are inverses of each other.
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Kelli call her grandmother every month. Every other month, Kelli alo call her couin. If Kelli call her couin in January, how many call will Kelli have made to her grandmother and her couin by the end of Augut
Kelli has made 12 calls to her grandma and her cousin by the end of August.
Kelli has already placed 12 calls other, according to this.
She starts calling her cousin every other month in January, so she will call four times in January, March, May, and July.
By using the unitary method
The unitary approach is a methodology for problem-solving that involves first determining the value of a single unit and then determining the necessary value by multiplying the single unit value.
The unitary method's formula is to get the value of a single unit and then multiply that value by the number of units to obtain the required value.
Consequently, 8+4=12
Kelli has already placed 12 calls.
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Use the information given in the figure to find the length BC.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.
A
85
41
B
D
0
Answer:
66
Step-by-step explanation:
First find AD:
AD² + 9² = 41²
AD² = 1681-61=1600
AD = √1600 = 40
Now find BD:
BD² + 40² = 85²
BD² = 7225-1600=5625
BD = √5625 = 75
BC = BD - 9 = 75 - 9 = 66
A farm has 15 acres of land. The owners used four tenths of the farm land for growing crops. How many acres are used for growing crops
6 acres are used for growing crops
How to find how many acres are used for growing crops?
Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Word problems can involve arithmetic operations, geometry, algebra, and other mathematical areas.
Since the farm has 15 acres of land and four-tenths of the farmland is used for growing crops. we can say:
acres used for growing crops = 4/10 * 15
acres used for growing crops = 6 acres
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The ratio of three numbers is 7 : 3 : 2. These three numbers have a sum of 228. What is the difference between the largest and the smallest of these three numbers?.
The difference between the largest and the smallest of these three numbers is 95.
in mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
Let the common multiple of ratio be x.
then, according to given condition, the ratio of three numbers is 7 : 3 : 2 and these three numbers have a sum of 228. i.e.
7x + 3 x + 2x = 228
12x = 228
x = 19
so, the largest number is
= 7x
= 7 × 19
= 133
and the smallest number is
= 2x
= 2 × 19
= 38
so, the Difference between the largest and the smallest number is
= 133 - 38
= 95
Therefore, the difference between the largest and the smallest of these three numbers is 95.
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What is the equation of this trend line? Enter your answers by filling in the boxes.
K = __ J +__
Equation of this line is K = -2J + 28.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Step 1:
The equation can be written in slope intercept form which is y = mx + b
Step 2:
Calculate slope of the line, m = (y2 - y1)/(x2 - x1)
⇒ m = (24 - 20)/(2 - 4)
= 4/-2)
= -2
Step 3:
Find y-intercept of the line
⇒ b = 28
Step 4:
Substitute values in the equation
⇒ K = -2J + 28
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What do line 16–20 tell you about how the peaker imagine hi future? Ue evidence from the text to upport your anwer
Lines 16-20 suggest that the speaker imagines his future as one in which he will look back on the decision he made to take the less traveled road with a sense of regret or longing.
He states that he will be "telling this with a sigh," indicating that the memory is not a happy one. Additionally, the phrase "ages and ages hence" implies that a significant amount of time has passed since the speaker made the decision, further emphasizing the sense of regret or longing. Overall, these lines suggest that the speaker believes that taking the less traveled road has had a significant impact on his life and that he will continue to reflect on this decision in the future.
"The Road Not Taken" is a famous poem by Robert Frost, in which the speaker reflects on a decision to take a different path in the woods. The poem does not give specific details of the speaker's future but rather reflects on the idea of choices and regrets.
This question should be written as:
What do lines 16-20 tell you about how the speaker imagines his future? Explain using text evidence to support your answer.
Lines 16-20 from "The Road Not Taken:
I shall be telling this with a sigh Somewhere ages and ages hence:Two roads diverged in a wood, and I—I took the one less traveled by,And that has made all the difference.Learn more about Robert Frost here: brainly.com/question/23045790
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Is an absolute value graph linear?.
The Absolute Value graph is not Linear , the shape of the absolute value graph is a V Shaped graph .
Consider the absolute value function ⇒ y = |x + 2| ;
on substituting x = 0 , we get ⇒ y = 2 ;
on substituting x = -3 , we get ⇒ y = 1 ; and
on substituting x = 3 , we get ⇒ y = 5 .
On plotting the points (0,2) , (-3,1) and (3,5) , we see that , a V shaped graph is formed ,
From the graph shown below , we can say that the graph is linear in intervals , not fully linear .
Therefore , the absolute value graph is a V Shaped graph .
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Please help me with these questions 2
By AAS congruence theorem, triangle QXP is congruent to triangle SXR.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given that, X is the midpoint of QS and ∠P≅∠R.
Consider, ΔQXP and ΔSXR
QX=XS (X is the midpoint of QS)
∠P≅∠R (Given)
∠QXP ≅ ∠SXR (Vertical angle theorem)
By AAS congruence theorem,
ΔQXP ≅ ΔSXR
Hence, proved.
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You are paid 1. 5 times your normal hourly rate for each hour you work over 40 hours in a week. You worked 46 hours this week and earned $612. 50.
Your normal hourly rate is $40.50 and you earned $612.50 for working 46 hours this week, which is 1.5 times your normal hourly rate for each hour over 40.
Your normal hourly rate is the amount of money you get paid per hour for working. The overtime rate is For every hour you work over 40 in a week, your hourly wage will increase by 1.5.This means that if you work 46 hours in a week and your normal hourly rate is $40.50, you would receive $40.50 for each hour up to 40 hours, and then an additional $60.75 for each hour after that. This means that you would have earned a total of $612.50 for working 46 hours this week, with $405 for 40 hours and $207.50 for the 6 hours of overtime.
Normal hourly rate (40 hours) = 40 hours x $40.50/hour = $1,620
Overtime rate (6 hours) = 6 hours x $60.75/hour = $364.50
Total earned = $1,620 + $364.50 = $1,984.50
Total paid = $612.50
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5. A line that passes through (4, 5) and (0, -12]
Answer: Your answer would be y = 17/4 x - 12
Step-by-step explanation:
I hope this helps!
Answer:
y=17/4x-12
Step-by-step explanation:
What are the 3 steps to graph a line when given an equation?.
There are three important steps to graph a line when an equation is given to us.
Step 1: Determine the x-intercept and y-intercept on the line.Step 2: Plot the x-intercept and y-intercept points on a graph. Step 3: Draw a line through the 2 points.Let us look at an example for the same.
Let us graph the equation 6x + 2y = 12
Finding the x-intercept (the x-intercept has a y-value of 0),
6x + 0 = 12
⇒ x = 2
Hence, x-intercept is (2,0)
Finding the y-intercept (the y-intercept has an x-value of 0),
0 + 2y = 12
⇒ y = 6
Hence, y-intercept = (0,6).
The graph is shown in the diagram after plotting the 2 intercepts on a graph and a line drawn through them.
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There were 1,278 people at the lat baketball game. The tand were divided into 6 ection. The ame number of people at in each ection. How many people at in each ection
There were 1,278 people at the last basketball game and the stands were divided into 6 sections. Each section had 213 people.
The question asked how many people were in each section, and it was given that there were 1,278 people at the game and the stands were divided into 6 sections. To find out how many people were in each section, I divided the total number of people by the number of sections. This concept of division is used to find out how many times a quantity (in this case, the number of people) is divided into a certain number of equal parts (in this case, the number of sections). The result is the number of people per section.
This is represented mathematically as:
1,278 people / 6 sections = 213 people per section
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