The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex].
What is equation?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
Given Data
Function
8x-5x+21 = 36-6y
6y = 36 - 21 - 8x +5x
6y = -3x + 15
y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]
The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]
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x-y=5 find the x and y intercepts
A flight to Sydney to Auckland takes 3 hours and 12 minutes, Auckland times is 2 hours ahead of Sydney's if the flight departed Sydney at 10:10 am at what time did it arrive at Auckland
Flight will reach Auckland at 11:22 am with respect to Auckland time.
We have the following given information which states as follows
A flight to Sydney to Auckland takes 3 hours and 12 minutes.
∴ Total journey time = 3hr 12min.
Auckland times is 2 hours ahead of Sydney's time.
∴ Change in time will be 2hr
The flight departed Sydney at 10:10 am
∴ Flight will reach Auckland after the journey time
∴ Flight will reach Auckland after 3hr 12min
∴ Flight will reach Auckland at 01:22 pm
But Auckland times is 2 hours ahead of Sydney's time.
∴ Change in time will be 2hr
∴ Flight will reach Auckland 2hr less than the considered reach time with respect to Sydney.
∴ Flight will reach Auckland at 11:22 am.
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what is the simplified form for 3x -(2x-5)
Answer:
1x-5
Step-by-step explanation:
3x-(2x-5) Write equation
3x-2x-5 Open Parentheses
1x-5 Answer; This is how much it can be simplified.
what do i do to create a graph for c=3p
Answer: Graph the line using the slope and y-intercept, or two points.
Slope: 3
y-intercept: (0,0)
Step-by-step explanation: Example graph for c=3p .
what does it mean when we say that the tails of the normal curve are asymptotic to the x axis? multiple choice the tails get closer and closer to the x axis but never touch it. the tails get closer and closer to the x axis and eventually touch it. the tails get closer and closer to the x axis and eventually cross this axis. the tails get closer and closer to the x axis and eventually become this axis.
When we say that the tails of the normal curve are asymptotic to the x axis, it mean the tails get closer and closer to the x axis but never touch it
The tails of normal curve are actually asymptotic. To say they are asymptotic, then it means that they approach the x axis but never quite meet its horizons.
These tails will extends indefinitely in both directions without crossing and touching the x axis or the horizontal axis.
Tails of normal curve or normal curve itself is asymptotic to the x-axis. That is the curve touches the x-axis only at -∞ and +∞. So the curve only approaches nearer and nearer to x-axis but never touches or crosses it.
For this reason, the correct choice is get closer and closer to the x-axis but never touches it.
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I WILL MARK BRAINIEST!!!!!!!!!!!!!!!!!!!!!!!!!!
you have to show your work
the scores 4, 6, x, 8, 10 are written in acsending order. find the value of x if the mean of the set equals the median
Answer:
7
Step-by-step explanation:
(4+6+7+8+10)/5=7
the median is the middle number=7
11.The side length of a square seat cushion is √65 square inches. Determine
whether the side length is rational or irrational. Then explain your
reasoning.
The side length of the square seat cushion which was given as; √65 is an irrational number.
What are rational and irrational numbers?It follows from the task content that the side length of the square seat cushion is to be determined as rational or irrational.
It follows from the definition of rational numbers that they are numbers which can be written as a ratio of quotients (fractions) while irrational numbers are the exact opposite and can not be expressed as a ratio of quotients.
Hence, since the number given √65 is not a perfect square, it follows that the number is an irrational number.
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The length, d, of a violin string varies inversely as the frequency, f, of its vibrations (cycles per second). Suppose it is known that a 16-in.-long violin string vibrates 320 cycles per second.
A. Write an inverse variation equation modeling this information
B. Use your inverse variation equation from Part A to determine the frequency of an 8-inch-long violin string.
An 8-inch violin string has a frequency of 640 cycles per second using the inverse variation equation.
Who defines frequency?The pace of direction changes in current per second is known as frequency. It is expressed in hertz (Hz), a unit of measurement that is used internationally. One hertz is equivalent to one cycle per second. One hertz (Hz) is equivalent to one cycle per second.Given: A 16-inch violin string is known to vibrate at 320 cycles per second.
We know that,
Using the frequency equation where l for the length of the string and f for the frequency.
f = k/l
320 = k/16
k = 5120
So, the equation becomes f = k/l
For l = 8
f = 5120/8
f = 640
Therefore, the frequency of an 8-inch-long violin string is 640 cycles per second.
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A) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over times, x measured in seconds. During what interval(s) of the domain is the water balloon's height staying the same?
A.0 ≤ x ≤ 2
B.2 ≤ x ≤ 5
C.5 ≤ x ≤ 6
D.6 ≤ x ≤ 8
B) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height increasing?
A.0 ≤ x ≤ 2
B.40 ≤ y ≤ 70
C.5 ≤ x ≤ 8
D.40 ≤ y ≤ 10
C) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height decreasing the fastest?
A.5 ≤ x ≤ 9.5
B.8 ≤ x ≤ 9.5
C.6 ≤ x ≤ 8
D.5 ≤ x ≤ 6
D) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Justify your answer from Part C.
A.5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing.
B.8 ≤ x ≤ 9.5 is the interval where the slope is the steepest.
C.6 ≤ x ≤ 8 is the interval where the balloon's height decreases the most.
D.5 ≤ x ≤ 6 is the interval where the slope is the steepest.
Please help as fast as possible <3
As shown in the reference graph attached hereby with the question statement, if the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds, then,
(A) During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.
(B) During (0 ≤ x ≤ 2) seconds, the height of the water balloon is increasing.
(C) During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
(D) From Part (C), it can be justified that 5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing, and, (5 ≤ x ≤ 6) is the interval where the slope is the steepest.
As per the question statement and the reference graph attached alongside, the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds.
We are required to determine the correct time domains for four different situations, by observing the plotted graph.
Part (A) is to determine the correct time domain where the water balloon's height remains the same.
From the graph, it is clear that, the height remains constant at (y = 70), parallel to the x-axis from the 2nd second to the 5th second. Hence, During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.
Part (B) is to determine the correct time domain where the height of the water balloon is increasing.
From the graph, it is clear that, the slope of the concerned graph rises only from [(y = 40) to (y = 70)], starring from the 0th second until the 2nd second. Hence, During (0 ≤ x ≤ 2) seconds in the time domain, , the height of the water balloon is increasing.
Part (C) is to determine the correct time domain where the height of the water balloon decreases the fastest.
From the graph, it is clear that, the graph decreases thrice, first from [(y = 70) to (y = 40)], starting at the 5th second uptil the 6th second, then from [(y = 40) to (y = 10)], starting at the 6th second uptil the 9th second and lastly, from [(y = 10) to (y = 0)], starting at the 9th second till the 9.5th second. Here, we can easily calculate that, the balloon dropped 30ft in 1 sec at the first instance, 30ft in 3 seconds at the second instance and, 10ft in 0.5 seconds.
Since, [(30/1) > (10/0.5) > (30/3)],
Or, [30 > 20 > 10],
Thus, During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
Part (D) is to determine the correct statement mentioned under it's options, with judgement based on Part (C).
Option (i) states that [(5 ≤ x ≤ 9.5) is the interval where the balloon's height is decreasing] which is true, as we can observe from the graph that the slope is decreasing during the time interval of 5 to 9.5th seconds, although at different rates at different intervals.
Option (ii) states that [(8 ≤ x ≤ 9.5) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is false, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
Option (iii) states that, [(6 ≤ x ≤ 8) is the interval where the balloon's height decreases the most] which is false, as balloons height falls the farthest by 30fts in two separate intervals, between (5 ≤ x ≤ 6) seconds and (6 ≤ x ≤ 9) seconds.
Finally, Option (iv) states that [(5 ≤ x ≤ 6) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is true, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the maximum in the shortest time period.
Time Domain: Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to the time interval over which, the function occurs.To learn more about Time Domain, click on the link below.
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What is the slope of the line that passes through the points (-8, -6)(−8,−6) and (-8, 4)(−8,4)? Write your answer in simplest form.
. A swim coach has at most $800 to buy equipment for the swim team. Each
pull buoy costs $5.50 and each kickboard costs $10. Let X represent the
number of pull buoys and y represent the number of kickboards.
a. Write an inequality for the scenario..
5.50x+10y_< 800 I already wrote the inequality now graph the inequality
A mathematical phrase in which the sides are not equal is referred to as being inequal. The point (80, 35) exists in the solution space. The coach could buy 80 pull buoys and 35 kick boards.
What is meant by inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
A mathematical phrase in which the sides are not equal exists directed to as being inequal. In essence, a comparison of any two values reveals whether one exists less than, larger than, or equivalent to the value on the opposite side of the equation.
A) The sum of costs must not exceed the budget:
5.50x +10.00y ≤ 800
B) Let the inequality be 5.50(0) +10.00(50) = 500 ≤ 800
Yes, the coach could buy these
C) Let the inequality be 5.50(125) +10.00(25) = 937.50 > 800
No, they cost too much
D) The point (80, 35) exists in the solution space. The coach could buy 80 pull buoys and 35 kick boards.
The complete question is:
A swim coach has at most $800 to buy equipment for the swim team. Each pull buoy costs $5.50 and each kickboard costs $10. Let x represent the number of pull buoys and y represent the number of kickboards.
A) Write an inequality for the scenario
B) could the coach purchase zeros pull buoys and 50 kickboards?
C) could the coach purchase 125 pull buoys and 25 kickboards?
D) What other combination of pull buoys and kickboards works for your inequality?
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A person randomly selects one of six envelopes Each envelope contains a check that the person gets to keep. Determine the person's expectation if three envelopes contain a 491 check and three envelopes contain a 51003 checkThe expected value is $(Simplify your anwwer Type an integer or a decimal)
The probability formula is given by:
[tex]\text{ P(E) =}\frac{\text{ N(Required outcome)}}{\text{ N(Total outcome)}}[/tex]The person selects one of six envelopes.
There is a probability that the person selects an envelope that contains a $491 of 3 envelopes OR an envelope that contains a $1003 check of 3 envelopes
[tex]\begin{gathered} \text{ P(select one containing \$491 check) =}\frac{3}{6}=\frac{1}{2} \\ \text{ P(select one containing \$1003 check) =}\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex]Then, the expected value is given by
[tex]\begin{gathered} \text{ P(Expected Value) =(}\frac{1}{2}\times491)\text{ +(}\frac{1}{2}\times1003) \\ =245.5+501.5 \\ =747.0 \end{gathered}[/tex]
Selena is 2 years older than Maria, and Sofia is 3 years younger than Maria. If the sum of their ages is 44, then how old is each girl? (Let Maria’s age =
x
.)
forty-two thousand, six hundred eighty-three times seven equals blank
296,702
296,576
298,781
299,852
Step-by-step explanation:
forty-two thousand, six hundred eighty-three times seven equals blank
42683 × 7 = _____
42683 × 7 = 298781
write 70 1/3% as a fraction in simplest form.
How to get the answer is the main question for me. I got it wrong on the assignment.
The fraction 70 1/3% in simplest form is 24.67%.
Firstly converting mixed fraction to fraction. For conversion to fraction rewriting the fraction -
Fraction = (3×70 + 1)/3%
Then performing the multiplication in numerator of the fraction to find the fraction in simplest form
Fraction = (73 + 1)/3%
Performing addition in numerator of the fraction to find the fraction in simplest form
Fraction = 74/3 %
We have got the improper fraction as numerator is greater than denominator. Now performing division to find the fraction in simplest form
Fraction = 24.67%
Thus, the fraction in simplest form is 24.67%
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Apple Picking
Name
josiph
Linda and Robin went apple picking. After picking all day, Linda had 15 more
apples than Robin. Together, they gathered 105 apples. Figure out how many
apples Linda got and how many Robin got. Linda got 1/3 of all her apples from
the first tree and % of all her apples from the second tree. She got the rest of her
apples from the third tree. Robin got 1/3 of all her apples from the first tree and
5/9 of all her apples from the second tree. She got the rest of her apples from
the third tree. Who got more apples from the third tree? How many more?
We can write the system of equations:
x = y + 15
x + y = 105
Solving the system, we will see that Robin has 45 apples and Linda 60 apples.
How many apples do Robin and Linda got?Here we can only solve the first part, as the second is incomplete.
Let's define the variables:
x = apples that Linda has.
y = apples that Robin has.
We know that Linda has 15 more apples than Robin, and that between the two there are 105 apples, so we can write the system of equations:
x = y + 15
x + y = 105
To solve this, we can replace the first equation into the second one, so we get:
(y + 15) + y = 105
2y + 15 = 105
2y = 105 - 15 = 90
y = 90/2 = 45
So Robin has 45 apples, and Linda has 15 more, so she has:
x = 45 + 15 = 60
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On a coordinate plane, a graph decreases between (2.5, 2) and (4.5, 0.25).
How does this graph change between (2.5, 2) and (4.5, 0.25)?
The graph of the coordinate plane is attached below.
Any point on a plane can be uniquely identified by a pair of numerical coordinates using a cartesian coordinate system, which employs signed distances between two fixed perpendicular oriented lines and the point measured in the same unit of length.
The intersection of the ordered pairs serves as the origin of each reference coordinate line, sometimes referred to as an axis of the system or simply an axis (plural axes) (0, 0).The locations of the perpendicular projections of the point onto the two axes, which are displayed as signed distances from the origin, can also be used to derive the coordinates.The graph of the line decreases between (2.5, 2) and (4.5, 0.25) and the graph increases between (2.5, 2) and (4.5, 0.25)
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2 Simplity
A) x² - 2x /x² - 4
Answer:
x/x+2
Step-by-step explanation:
from numerator factor out an x to get x(x-2), in the denominator you can factor it because its a perfect square to get (x+2)(x-2)
cause there are no more add or subtract, you can cancel out x-2 to get x/x+2
Answer:
X³ -4x-2
--------------
x
Write down the sequence then solve
the problem.
On Monday I had 1 cup of tea, Tuesday I had 3
cups, on Wednesday I have 6 cups and on
Thursday I have 11 cups.
How many cups of tea did I have on Sunday?
1,3
38
Answer:
48.
Step-by-step explanation:
The sequence is
1, 3, 6, 11,
The differences are 2, 3, 5, 8, 12, 17
2nd difference 1 2 3 4 5
So, the next difference is 5+3 = 8 (Friday) so on that day you had 11+8 = 19 cups.
The next 2 differences are 8+4 = 12 and 12 + 5 = 17.
Saturday you had 19+12 = 31.
Sunday you had 31 + 17 = 48.
How much greater is the average temperature on Earth than the average temperature on Jupiter? According to the picture.
The average temperature on Earth than the average temperature on Jupiter is greater by
225°F.
What is temperature?Temperature simply means the degree of hotness and coldness that can be found in a body.
Average temperature on Earth = 59°F
Average temperature on Jupiter = -166°F
Therefore, the increase will be illustrated as:
= 59 - (-166)
= 59 + 166
= 225°F
The correct option is 225°F
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Please Help, Urgent and in detail
z = [tex]\frac{13}{20}+\frac{19}{20}i[/tex] is in the form z = a+ ib, where a = 13/20 and b = 19/20
Exact value of |z| = 1.151
Argument of z = 55.6197
Consider the complex number z = (2+7i)/(6+2i)
6a. Here z is in a rational form and we need to simplify it to represent it in the form a+ ib.
Multiplying and dividing the conjugate of the denominator to z, we get,
z = [tex]\frac{2+7i}{6+2i} \times \frac{6-2i}{6-2i}[/tex]
⇒ z = [tex]\frac{12 +38i +14}{6^2+2^2}[/tex]
⇒ z = [tex]\frac{26+38i}{40}[/tex]
⇒ z = [tex]\frac{13}{20}+\frac{19}{20}i[/tex]
is in the form z = a+ ib, where a = 13/20 and b = 19/20
6b.modulus of z = |z| = √(a²+b²)
= [tex]\sqrt{\frac{13^2}{20^2} +\frac{19^2}{20^2} }[/tex]
= [tex]\sqrt{\frac{530}{400}}[/tex]
= √(53/40)
= 1.151
6c. Argument of z = tan⁻¹(b/a)
= tan⁻¹((19/20)/(13/20))
= tan⁻¹(19/13)
= 55.6197
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Eugene bought magazines for $6 each and paperback books for $3 each for a total of $54. Define your variable and write an equation in standard form to represent the situation
The standard form of the equation representing magazines and paperback books bought is is 6x + 3y = 54
How to find the equation in standard formInformation given in the question include:
Eugene bought magazines for $6 each and paperback books for $3 each total of $54
Definition of variables
let the number of magazines bought be x
let the number of paperback books bought be y
The total amount paid for the magazines = $5 * x = 6x
The total amount paid for the paperback books = $3 * y = 3y
Finding the equation
Summing the amounts paid to be equal to the total amount spent which is $54 is given in the equation as written below
6x + 3y = 54
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100pts!!! PLS SHOW WORK!!
Answer:
it says 50 points
Step-by-step explanation:
Answer:
can u give me a hint?
Step-by-step explanation:
Spaceship model kids originally cost d dollars online. You buy each kit on sale for 30% of the original price, plus a shipping fee of $3.50 per kit. After assembly, you sell each model online for (2.5d + 5) dollars. What is your profit on each model spaceship sold?
Your profit on each model spaceship sold is; (1.2d + 1.5) dollars
How to solve Algebra Word problems?
We are told that the original cost of the spaceship model was d dollars. Now, you buy each kit on sale at 30% of the original price.
Thus;
Amount of each kit with the 30% of original price = 30%d = $0.3d
Total cost of each kit with shipping fee = (0.3d + 3.5) dollars
Now, he sells each model at (2.5d + 5) dollars.
Now, formula for profit is;
Profit = Selling Price - Cost Price
Profit = (2.5d + 5) - (0.3d + 3.5)
Profit = (1.2d + 1.5) dollars
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if 180 is 37.5% of the whole what would be the whole
(24÷ 3) x 4-(30 ÷ 3)
Answer:
22
Step-by-step explanation:
Betsie tried to solve an equation step by step. \qquad\begin{aligned} 3(a+7)&=-33\\\\ \\ a+7&=-11&\green{\text{Step } 1}\\\\ \\ a&=-4&\blue{\text{Step } 2}\\\\ \end{aligned} 3(a+7) a+7 a =−33 =−11 =−4 Step 1 Step 2 Find Betsie's mistake.
The mistake is at a + 7 = -11 ⇒ a = -18 and not -4.
Betsie made a mistake while solving the equation 3(a+7) = -33
We try to solve this equation step-by-step and will identify her mistake on the way.
3(a+7) = -33
Dividing by 3 on both sides,
⇒ (a+7) = -11
Subtracting 7 from both sides,
⇒ a = -11 -7
⇒ a = -18 is the solution.
Betsie made the mistake at the step where we have to subtract 7 from both sides. Instead of subtracting 7 from the right side, she added 7 on the next step.
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The point (-2, K) lies on the circle x^2 +y^2. Find the values of k. Show all the steps
Answer:
Should be 0
Step-by-step explanation:
At a local mini-mart, the cost of a bottle of
soda at the corner store is $1.40, and the
cost of a bag of chips is $0.85. What
would it cost to get 3 bottles of soda and 8
bags of chips? What would it cost to get x
bottles of soda and y bags of chips?
Total cost, 3 bottles of soda and 8 bags
of chips:
Total cost, x bottles of soda and y bags
of chips:
Total cost, 3 bottles of soda and 8 bags of chips: 9.15, Total cost, x bottles of soda and y bags of chips: 1.25x + 0.9y as calculated from the provided material through mathematical concepts.
What are general mathematical concepts?These basic mathematics skills are addition, subtraction, multiplication, and division. Concepts included in basic math include learning shapes, patterns, fractions, decimals, percentages, exponents, ratios, scientific notation, and formulas.
What are 5 concepts of mathematics?The five fundamental concepts which we aim to consider briefly are those of natural number, unknown, postulate, function and group
What are the 4 basic concepts of mathematics?These functions such as addition, subtraction, multiplication, and division have their application present even in the most advanced mathematical theories.
The total price can be calculated as it is equal to the unit price multiplied by the quantity.
3*1.25 + 6*0.9
= 3.75 + 5.4
= 9.15
Then if we take it as x and y, we get the equation
1.25x + 0.9y
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PLEASe HELP I NEED NUMBER 1 there is an ex sample I need the answer and work to it that looks like the ex sample
a) 20% 60 of is 12
b) 25% of 24 is 6
c) 4% of 600 is 24
Here the problem we are dealing with is related to percentage, which could be a division or a proportion in which the value of the entire is continuously 100. is represented by the symbol "%".
a) let us consider the missing number to be x
so, the problem will be 20% of x= 12
=> 20/1000* x= 12
=>20x= 12*100
=> x= 12*100/20 = 60
b) let the percentage be x
so, the problem will be x% of 24 =6
=>x/100* 24= 6
=>24x=600
=>x=600/24 =25
c) here, we are given 4% of 600=?
=4/100* 600
=24
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