$21,500 this would be cause a person to be indifferent between Fund A and Fund B (i. E. , the EMVs would be the same)
EMV 1 = 0.2*10,000 + 0.3*2,000 + 0.5*-5,000 = $100EMV 2 = 0.2*6,000 + 0.3*4,000 + 0.5*-0 = $2,400.
Comparing both funds based on EMV calculations, Fund B shows a higher EMV. Therefore, to maximize expected value, we should invest in Fund B with an expected value of $2,400. First, his EMV for Fund A is not the same as Fund A's return being higher or lower in good economic conditions. Therefore, the EMC can also be higher or lower. But obviously the economy changes quickly sometimes. You don't always get the same return. So relying solely on returns is risky. Relying heavily on favorable economic conditions makes Fund A vulnerable to change and increases investor risk, so investors need to be more diversified. We can do the calculation:
Fund A return in good economy = Difference between A and B: EMV (Fund A) = EMV (Fund B) 0.2*X + 0.3(2,000) + 0.5(- 5,000) = 2 4,000.2X = 4,300X = $21,500.
Therefore, if the economy is good, Fund A's return should be $21,500 for there to be indifference between Fund A and the fund B.
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HELP!!!
Marta bakes 3 types of cake: chocolate, fruit, and sponge. The recipe for each cake includes flour and sugar and she uses 3.3kg of flour and 3.1kg of sugar in total.
Each chocolate cake uses 225 g of flour and 300g of sugar
Each fruit cake uses 320g of flour and 250g of sugar
Each sponge cake uses 400 g of flour and 325g of sugar
Marta sells chocolate cakes for $12, fruit cakes for $10, and sponge cakes for $8 and makes a total of $114
How many of each cake does she make?
(Answer in the back of the book: 4 chocolate, 5 fruit, 2 sponge cakes)
The three equations for this problem are:
The total amount of flour used: 3.3kg = (225g/cake) * (number of chocolate cakes) + (320g/cake) * (number of fruit cakes) + (400g/cake) * (number of sponge cakes)The total amount of sugar used: 3.1kg = (300g/cake) * (number of chocolate cakes) + (250g/cake) * (number of fruit cakes) + (325g/cake) * (number of sponge cakes)The total revenue from sales: $114 = ($12/cake) * (number of chocolate cakes) + ($10/cake) * (number of fruit cakes) + ($8/cake) * (number of sponge cakes)Let's call the number of chocolate cakes x, the number of fruit cakes y, and the number of sponge cakes z
so the
first equation can be written as 3.31000 = (225x) + (320y) + (400z)second 3.11000 = (300x) + (250y) + (325z)and third one 114 = (12x) + (10y) + (8*z)let's use the third equation to get the value of x,y and z:
x = (114 - 10y - 8z) / 12y = (114 - 12x - 8z) / 10z = (114 - 12x - 10y) / 8If you get the values and substitute, then the answer would be:
4 chocolate cakes, 5 fruit cakes, 2 sponge cakes
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Use the distributive property to rewrite each expression. Then evaluate. 14 (102)
Using the distributive property to rewrite the expression, gives (14 x 10) + ( 14 x 2). When evaluated, the result would be 168.
What is the distributive property?According to the distributive property, it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.
This means that with the formula given, 14 (10 + 2):, the distributive property makes it:
= 14 (10 + 2)
= (14 x 10) + ( 14 x 2)
The evaluation gives :
= (14 x 10) + ( 14 x 2)
= 140 + 28
= 168
In conclusion, using the distributive property gives (14 x 10) + ( 14 x 2).
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What is the slope of this line? (5 points)
Show all work.
Answer:
-2,2
Step-by-step explanation:
Can u please help me...............
Please find attached the graph showing the translation transformation of the triangle ΔABC with vertices A(2, 1), B(-1, 2), and C(-2, -1) using the rule (x, y) → (x - 1, y - 3), to produce triangle ΔA'B'C' with vertices A'(1, -2), B'(-2, -1), and C'(-3, -4), created with MS Excel
What is a translation transformation?A translation transformation is one in which the location of the points on the original figure slides by the same amount and in the same direction to form the image.
The vertices of the triangle ΔABC are; A(2, 1), B(-1, 2), and C(-2, -1)
The specified transformation is; (x, y) → (x - 1, y - 3)
Applying the specified transformation, we get;
A(2, 1) ⇒ (x, y) → (x - 1, y - 3) ⇒ A'(2 - 1, 1 - 3) = A'(1, -2)
B(-1, 2) ⇒ (x, y) → (x - 1, y - 3) ⇒ B'(-1 - 1, 2 - 3) = B'(-2, -1)
C(-2, -1) ⇒ (x, y) → (x - 1, y - 3) ⇒ C'(-2 - 1, -1 - 3) = C'(-3, -4)
The vertices of the image ΔA'B'C' of the triangle ΔABC following the transformation, (x, y) → (x - 1, y - 3) are therefore;
A'(1, -2), B'(-2, -1), C'(-3, -4)
Please find attached the graph of the triangle ΔABC and its image ΔA'B'C' after the translation (x, y) → (x - 1, y - 3), created with MS Excel
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can someone help me find two true statements!
1. In a triangle line parallel to one side will divides other two sides in the same ratio
2. 8/x = 12/18
x = 12
How do you find a linear equation from two points?Finding the slope between two points on a line and solving for the y-intercept in the slope-intercept equation y=mx+b allows us to formulate an equation for that line.
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).
Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.
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Complete the stemplot for the following data. 34 53 66 52 48 42 41 58 36 50 40 59 49 35 30 40 43 35 61 43 49 39 44 43 34 42 68 46 46 39 Enter the numbers for the last row. Do not enter commas or other symbols, just numbers.
The stem plot for the given data is 3 4 5 6.
A stem and leaf plot, also known as a stem and leaf diagram, is a technique to arrange data such that it is simple to see how frequently certain sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.
Arranging the given data in ascending order,
30, 34, 34, 35, 35, 36, 39, 39, 40, 40, 41, 42, 42, 43, 43, 43, 44, 46, 46, 48, 49, 49, 50, 52, 53, 58, 59, 61, 66, 68
The stem plot = 3 4 5 6
Calculated Statistics:
Minimum:30
Maximum:68
Range:38
Count:30
Sum:1365
Mean:45.5
Median:43
Mode:43
Standard Deviation:9.616
Variance:92.47
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Donovan flips a coin a total of 96 times. How many times should he expect the coin to land on heads? Donovan records the results of the next 50 flips. The results are shown in the table. Heads Tails 32 18 Based on Donovan's results, if he flips the coin an additional 75 times, about how many times should he expect the coin to land on tails?
When Donovan flips a coin a total of 96 times, the number of times he should expect the coin to land on heads will be 48 times.
The times he should expect the coin to land on tail based on the table will be 27 times.
How to illustrate the value?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
When Donovan flips a coin a total of 96 times, the number of times he should expect the coin to land on heads will be:
= 1/2 × 96
= 48
The number of times he should expect the coin to land on tail based on the table will be:
= 18/50 × 75
= 27 times
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Write the coordinates of the vertices after a rotation 90°
counterclockwise around the origin.
Answer:
see explanation
Step-by-step explanation:
under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) , then
C (1, 9 ) → C' (- 9, 1 )
D (4, 9 ) → D' (- 9, 4 )
E (0, 3 ) → E' (- 3, 0 )
A guy wire attached to the top of a radio antenna
is bolted to the ground 48 m from the base of
the tower. If the wire makes an angle of 14°
with the ground. What is the length of the
guy wire? Round your answer to the nearest
hundredth of a meter.
1
The length of the guy wire is 48.87 m.
How to find the length?To find the length of the guy wire, you can use the formula for the length of a side of a right triangle (the Pythagorean theorem): [tex]c = sqrt(a^2 + b^2)[/tex]. In this case, c is the length of the guy wire, a is the distance from the base of the tower to the point where the guy wire is attached to the ground (48 m), and b is the distance from the point where the guy wire is attached to the ground to the top of the antenna.
To find b, you can use the tangent function: [tex]tan(14°) = b / 48.[/tex]
Solving for b gives b = 6.78 m
Then, length of wire can be calculated as
[tex]c = sqrt(48^2 + 6.78^2)[/tex]
[tex]c = 48.87 m (approx)[/tex]
Rounding it to the nearest hundredth of a meter, the length of the guy wire is 48.87 m.
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If lunch cost $15.70, before tip, and you left $3.14, what %
tip did you leave and what was the total cost of lunch?
Answer:
20%
$18.84
Step-by-step explanation:
3.14 is what percent of 15.70?
Use the percent-to-dollar conversion (100: 15.70) :
3.14 * 100% / 15.70 =
3.14 / 15.70 * 100% =
1/5 * 100% =
100% / 5 = 20% ==> percent tip
$15.70 + $3.14 = $18.84 ==> Total cost
which line is LR NOT a transversal to?
Answer: It is not possible for me to determine which line LR is not a transversal to without more context. A transversal is a line that intersects two or more other lines at different points. In order to determine which line LR is not a transversal to, I would need to know the other lines that are involved and the points at which they intersect.
Step-by-step explanation:
Determine if the triangles can be proved congruent by SSS, SAS, ASA, AAS, or HL.
The triangle in the figure can be proved by ASA, SAS, and AAS
What is congruency of triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSS
Side - Angle - Side = SAS
Angle - Side - Angle = ASA
Angle - Angle - Side = AAS
Hypotenuse and one leg = HL
The problem requires the prove by ASA, SAS, and AAS to ensure that the the triangles are congruent.
Alternate angles in the figure are also equal
According to the ASA rule, two triangles are said to be congruent if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.
The Angle-Angle-Side (AAS) Congruence Theorem states that two angles and a non-included side in one triangle must be congruent with two angles and the equivalent non-included side in another triangle for the triangles to be congruent.
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How many 1/9s can go into 2?
i do not understand how proportionality works
Answer:
3.5
Step-by-step explanation:
In this problem, the line's constant of proportionality is the same as its slope.
Slope is defined as rise / run (also notated as change in y / change in x).
Using the given point, we can deduce that the line's rise (change in y) is 3.5, and its run (change in x) is 1. Putting these values into the slope formula:
3.5 / 1 = 3.5
So, the constant of proportionality of this line is 3.5.
DEFG is a square with vertices at D(1, 1), E(1,6), F(6, 6), and G(6, 1). DEFG is reflected in the line x = 1. Find the coordinates of
D',E,F, and G'.
By considering the reflection, the coordinates of the reflected square D'E'F'G' are:
D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)
What is square?A square is a two-dimensional geometric shape that has four equal sides and four right angles. It is a type of rectangle, but with all sides equal. The opposite sides of a square are parallel and of equal length. A square can be defined by its side length or by the coordinates of its vertices.
What is reflection?Reflection is a type of transformation in geometry in which a shape is flipped over a given line, called the line of reflection. The image that is created is a mirror image of the original shape. The line of reflection can be a horizontal line, a vertical line, or any line that is not parallel to the axes. Reflecting a shape over a line involves taking the coordinates of each point of the shape and applying a specific rule (such as multiplying or adding a constant) to the x or y coordinate, depending on the line of reflection. This rule is often simple and easy to apply, such as reflecting over x = 1. The reflected shape will be in the same plane as the original shape but with a different orientation or position.
When a square is reflected in the line x=1, each of the points on the square will have their x-coordinate replaced by 1 subtracted from their original x-coordinate.
The coordinates of the reflected square D'E'F'G' can be found by applying this rule to the original coordinates of square DEFG:
D(1,1) => D'(1-1,1) => D'(0,1)
E(1,6) => E'(1-1,6) => E'(0,6)
F(6,6) => F'(6-1,6) => F'(5,6)
G(6,1) => G'(6-1,1) => G'(5,1)
So the coordinates of the reflected square D'E'F'G' are:
D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)
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There are 18 counters divided equally among 3 groups. How many counters are in each group?
pleaseeeeeee someone help me asappp i need help so bad.
The slope of the linear equation that passes through the points (-6, -2) and (3, -2) is 0.
How to find the slope with the two known points?We can write a linear equation using the sope-intercept form as:
y = m*x + b
Where m is the slope and b is the y-intercept.
For any linear equation, if we know that the line passes through two known points (x₁, y₁) and (x₂, y₂), then the slope is given by:
m = (y₂ - y₁)/(x₂ - x₁).
In this case we know that the line passes through the points (-6, -2) and (3, -2).
Then the slope will be:
m = (-2 + 2)/(3 + 6) = 0
m = 0
The slope is zero, meaning that this is an horizontal line.
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1.
The table below shows the number of animals at a local petting zoo.
Animal
Ponies
Goats
Number
3
3
Rabbits
8
Type a response
Sheep
6
Write the ratio of ponies to sheep.
You may write the ratio in ANY of the three forms. Remember to REDUCE the ratio, it
possible.
1/2
If there are 3 ponies, and 6 sheep,
the original ratio is 3/6.
However, it must be simplified down to 1/2.
In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
The population of the city grew from 2010 to 2020 by 13.37 %
What is percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
Given that, In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.
The population in 2015 =
A = P (1+r)ⁿ
A = final population.
P = Initial population.
r = rate
n = time
The population in 2015 =
A = 237,000(1+0.076)⁵
A = 341829.629
The population in 2020 =
A = P (1-r)ⁿ
A = 341829.629(1-0.047)⁵
A = 268704.047
Percent grow = 268704.047 - 237,000 / 237,000 × 100
= 31704.047 / 237,000 × 100
= 13.37 %
Hence, the population of the city grew from 2010 to 2020 by 13.37 %
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How the addition of 2 and 2 become 5?
In the late 19th century, the Russian press used the phrase 2 + 2 = 5 to describe the moral confusion of social decline at the turn of a century, because political violence characterised much of the ideological conflict among proponents of humanist democracy and defenders of tsarist autocracy in Russia
Solve the system.
6x - y = -15
x+2y = 17
Enter your answer as a coordinate pair in the blank.
The coordinate pair of the given system is (-1,9)
What are coordinate pairs?An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Multiply the first equation by 2 and add the equation 2(6x - y) = 2(-15)
Add the new equation 12x - 2y = -30 to the second equation
12x - 2y = -30, x+2y = 17, add the two equations to eliminate y
13x = -13
x = -1
Substitute -1 back into the equation x+2y = 17.
-1 + 2y = 17
2y = 18
y = 9
So the solution of the system is x = -1, y = 9
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How do you find the midpoint answer?
To find the midpoint of two points in a coordinate plane, you can use the midpoint formula.
The midpoint formula is the average of the x-coordinates and the average of the y-coordinates of the two given points.
The midpoint formula is:
((x1 + x2)/2 , (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
For example, if the two points are (3, 4) and (5, 8), the midpoint would be:
((3 + 5)/2 , (4 + 8)/2) = (4, 6)
So the midpoint between (3, 4) and (5, 8) is (4, 6).
It's important to note that this formula is valid for any dimension, not just 2D, and it can be used to find the midpoint of any two points in space, whether it's in 2D, 3D, 4D and so on.
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I don't know HOW TO DO THIS
Answer:
sorry, I forget how to do the other ones and I'm just as confused but for 4. AD is 20 and 5. GJ is 17
Step-by-step explanation:
4. side AD is equal to side CD so therefore its 20.
5. side are equal again so make
4x+5 = 2x+11
-5 -5
4x = 2x+6
-2x -2x
2x = 6
/3 /3
x = 3
2(3)+11
6+11
17
Solve the given differential equation. 3x^2y'' + 6xy' + y = 0
The solution for given differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)
This is a second-order linear differential equation with constant coefficients. To solve this equation, we can use the method of an auxiliary equation, which is 3r^2 + 6r + 1 = 0. This equation has two complex conjugate roots, r = -3 ± i√3. Therefore, the solution of the differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)cos(√3x^2/2) + c3xe^(-x^3/3)sin(√3x^2/2), where c1, c2, and c3 are arbitrary constants.
The method of an auxiliary equation is a popular way to solve second-order linear differential equations with constant coefficients. It involves finding the roots of an auxiliary equation, which is found by setting the coefficient of the second derivative equal to zero.
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a A trader opens a bank account with #250 000. In one month, she pays out two cheques for #49 000 and 34 000 and pays in one cheque for N14000. How much money does she have in her account after one month?
Answer: #181000
Step-by-step explanation:
So, to solve the problem, recall these definitions:
payout - withdrawal
pay in - deposits.
Normally, deposits add money to your balance, and withdrawals take out money.
So, there is one cheque for paying in 14,000, and two cheques for paying out 49,000 and 34,000
So, the balance is 250000 + 14000 - (49000+34000)
The balance is 181,000
The times taken by 25 people to complete a puzzle are shown. Draw a frequency polygon for data.
To create a frequency polygon calculate the midpoint, locate the midpoints and connect them with lines.
What is a frequency polygon?A frequency polygon is a form of graph that shows how frequently a particular variable—in this case, the amount of time it takes for people to finish a puzzle—occurs.
So, we must determine the midpoint or average of the range for each category.
0 < t < 10 = 5
10 < t < 20 = 15
20 < t < 30 = 25
30 < t < 40 = 35
2. Add a point where the data of the axis Y and X form an intersection.
3. Connect the points.
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i need help with this
*im second guessing*
Answer:
A) 5
B) X-3
C) 2X+Y
step by step:
base x height = area
A Height= (5x+20) ÷ (x+4)= 5
B Base= (8x-24) ÷ 8 = x-3
C Height= (12x+6y) ÷ 6 = 2x+y
The solution is
Parallelogram A : Base = x + 4 ; Height = 5
Parallelogram B : Base = x - 3 ; Height = 8
Parallelogram C : Base = 6 ; Height = 2x + y
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the area of the parallelogram be A = Base x Height
So , Substituting the values in the equation , we get
a)
Let the parallelogram be A
Now , Area = 5x + 20
Base = x + 4
So , the height = Area / Base
Height = 5
b)
Let the parallelogram be B
Now , Area = 8x - 24
Height = 8
So , the Base = Area / Height
Height = x - 3
c)
Let the parallelogram be C
Now , Area = 12x + 6y
Base = 6
So , the height = Area / Base
Height = 2x + y
Hence , the equations are solved
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I need this ASAP!
( Fractions and whole numbers)
Answer:
C. [tex]4\frac{2}{3}[/tex]
Step-by-step explanation:
One way of approaching this problem is to multiply the numbers the numerators together and then divide by the denominator to receive the quotient and the remainder.
Firstly 6 can be written as a fraction like so: [tex]\frac{6}{1}[/tex] because 6 divided by 1 is equal to 6.
To multiply two fractions together, we simply multiply the numerators and multiply the denominators:
[tex]\frac{7}{9}* \frac{6}{1} =\frac{7*6}{9*1}[/tex]
Which gives us the improper fraction of: [tex]\frac{42}{9}[/tex]
Next, we find the highest multiple of 9 which is smaller than 42. If we write out the multiples of 9 we will find that it is 36:
1x9=9, 2x9=18, 3x9=27, 4x9=36, 5x9=45
Since we know that at least 4 whole 9s go into 42 we can conclude that the coefficient of the fraction will be 4.
To find the fraction itself, we must find the remainder which we can do by subtracting 36 from 42: 42-36 = 6
The remainder is the numerator of the fraction as there are 6 ninths left over after we have divided 42 by 9.
Therefore our answer is [tex]4\frac{6}{9}[/tex]
If we divide 6 and 9 by 3 we will find that 6/9 is equivalent to 2/3 therefore our final answer is [tex]4\frac{2}{3}[/tex].
Option C is correct.
You have 3 3/4 cups of nuts to divide evenly among 5 people. How many cups of nuts will each person get
Each will get 3/5 cups of nuts by ratio and proportion concepts.
What does ratio explain mean?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
We have to divide total nuts within 5 people.
so,
3 3/5 : 5
but first convert,
3 3/5 = 15/4
substitute,
15/4 : 5 = 15/20cups of nuts
simplify,
3/5 cups
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4. Automotive Trades At the beginning of the day on Monday, the parts
department has on hand 520 spark plugs. Mechanics in the service depart-
ment estimate they will need about 48 plugs per day. A new shipment of
300 will arrive on Thursday. Write out a mathematical statement that gives
the number of spark plugs on hand at the end of the day on Friday. Calcu-
late this total.
StS estimate
Therefore , the solution of the given problem of equation comes out to be 580 spark plugs will be left.
Describe the equation.Using the equals symbol (=), a mathematical equation appears to be a formula that connects two statements and denotes equality. A scientific assertion that supports the equality of two mathematical abstraction is known as an equation in algebra. For instance, the equal sign is present between the variables ptdc + 6 and 12 in the output obd + 6 = 12. The link between the syllable on either side of either a letter is described by a mathematical formula. In many cases, the logo and the say — are identical.
Here,
Given: A new supply of 300 spark plugs will come on Thursday,
and 520 spark plugs require 48 plugs per day.
To determine an equation to determine however many plugs will just be left at the end of Friday:
So,
where n is the no of days
=> 520 - 48*n + 300
=> 520 - 48*5 + 300
=> 520 - 240 + 300
=> 520 + 60
=> 580
Therefore , the solution of the given problem of equation comes out to be 580 spark plugs will be left.
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