So, the point (20,13) is on the same line.
Define line.A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. the trail of a moving point; a continuous length, straight or curved, without breadth or thickness. something lined up in a line, especially one that is straight; a line or sequence: a row of trees a group of people waiting in line after one another to do something or receive something.
Given Data
point (20,13) in this line
On the line y=1/2x+3, the point (20, 13) fits.
By entering the x and y values, this may be demonstrated.
13=[tex]\frac{1}{2}[/tex](20) +3
[tex]\frac{1}{2}[/tex](20)=10
13=10+3
13=13
20 and 13 fit on the line
So, the point (20,13) is on the same line.
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if we subtract 2/4 from 3/4, what isthe difference?
Answer:
-[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Ans:
In Fractional/Exact Form:
1/4
In Decimal Form:
Ans=0.25
Steps to Simplify the expression.
Step 1:Find the least common denominator
Step 2:Multiply the least common denominator
Step 3:Simplify the equation
Step 4:Solve
(3/4)-(2/4)= (3-2)/4
Exact Form:
1/4
Decimal Form:
Ans=0.25
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One brand of cereal sells for $3.15 for 10 ounces. What is the unitprice per pound?a. $.31b. $5.04c. $ 3.49d. $50.40
Answer:
[tex]\begin{gathered} \\ B\colon\text{ \$5.04} \end{gathered}[/tex]Explanation:
Here, we want to get the unit price per pound
From the question, the brand sells for $3.15 per 10 ounces
Mathematically, 1 ounce is 0.0625 pound
Thus $3.15 is the price for 0.625 pounds (10 * 0.0625 pounds)
if $3.15 is for 0.625 pounds
$x will be for 1 pound
Mathematically:
[tex]\begin{gathered} 3.15\times1\text{ = 0.625}\times x \\ x\text{ = }\frac{3.15}{0.625} \\ x\text{ = \$5.04} \end{gathered}[/tex]La suma de tres numeros consecutivos impares es 63
Answer:
19, 21, 23
Step-by-step explanation:
The Matrix Fishing Company does fishing in Toluca Lake the first year of the company's operation it managed to catch a 190,000 fish due to population decreases the number of fish the company was able to catch decreased by 8% each year how many total fish did the company catch over the first 12 years round to the nearest whole number
Solution
For this case we can model the number of fishes with the following equation:
[tex]A=19000(1-0.08t)[/tex]And for this case we want to find the value for t =12 and replacing we got:
[tex]A=190000\cdot(1-0.08\cdot12)=7600[/tex]And then the number of fishes after 12 years would be 7600
so then they catched 182400
Please reference attached image for the problem that requires solving. Thank you so much for taking the time to help.
Explanation:
The number of times the 6-sided number cube will be rolled will is
[tex]750[/tex]Let the numbers greater than 4 be represented below as
[tex]E_1[/tex][tex]\begin{gathered} E_1=\lbrace5,6\rbrace \\ n(E_1)=2 \end{gathered}[/tex]The number of sample space will be
[tex]n(S)=6[/tex]The probability of rolling a number greater than 4 will be calculated below as
[tex]\begin{gathered} Pr(E_1)=\frac{n(E_1)}{n(S)} \\ Pr(E_1)=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]Hence,
To calculate the number of times a number greater than 4 will be rolled will be calculated below as
[tex]\begin{gathered} =Pr(E_1)\times750 \\ =\frac{1}{3}\times750 \\ =250times \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow250\text{ }times[/tex]Question 2 of 1010 PointsWhich inequality below satisfies the solution set graphed on the following number line?
ANSWER
C. x² - x ≥ 6
EXPLANATION
Let's analyze the solution set graphed first. We can see that the values -2 and 3 are included in the set, and all values below -2 and above 3. So, the solution set is (-∞, 2] U [3, ∞).
To find which inequality satisfies this solution set we have to solve them. To do so, we will be using the quadratic formula:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \end{gathered}[/tex]A. To solve this one, first, add x to both sides,
[tex]-x^2+x+6\geqslant0[/tex]Now, apply the quadratic formula to find the zeros. For this inequality, a = -1, b = 1, and c = 6
[tex]\begin{gathered} x=\frac{-1\pm\sqrt{1^2-4(-1)6}}{2(-1)}=\frac{-1\pm\sqrt{1+24}}{-2}=\frac{-1\pm\sqrt{25}}{-2} \\ \\ x_1=\frac{-1-5}{-2}=\frac{-6}{-2}=3 \\ \\ x_2=\frac{-1+5}{-2}=\frac{4}{-2}=-2 \end{gathered}[/tex]But in this case, the solution set is [-2, 3] - note that for any value outside this interval the inequality is false.
B. Similarly, apply the quadratic formula for a = -3, b = 3, c = 18,
[tex]\begin{gathered} x=\frac{-3\pm\sqrt{3^2-4(-3)18}}{2(-3)}=\frac{-3\pm\sqrt{9+216}}{2(-3)}=\frac{-3\pm\sqrt{225}}{-6}=\frac{-3\pm15}{-6} \\ \\ x_1=\frac{-3+15}{-6}=\frac{12}{-6}=-2 \\ \\ x_2=\frac{-3-15}{-6}=\frac{-18}{-6}=3 \end{gathered}[/tex]Again, the solution set is [-2, 3] since for any value outside the interval the inequality is not true.
C. Subtract 6 from both sides,
[tex]x^2-x-6\geqslant0[/tex]Apply the quadratic formula, with a = 1, b = -1, and c = -6,
[tex]\begin{gathered} x=\frac{-(-1)\pm\sqrt{(-1)^2-4\cdot1(-6)}}{2\cdot1}=\frac{1\pm\sqrt{1+24}}{2}=\frac{1\pm\sqrt{25}}{2}=\frac{1\pm5}{2} \\ \\ x_1=\frac{1+5}{2}=\frac{6}{2}=3 \\ \\ x_2=\frac{1-5}{2}=\frac{-4}{2}=-2 \end{gathered}[/tex]In this case, if we take any value between -2 and 3, for example 1,
[tex]\begin{gathered} 1^2-1\ge6 \\ \\ 0\ge6 \end{gathered}[/tex]We can see that the inequality is false, while if we take a value greater than 3 or less than -2, for example, -5,
[tex]\begin{gathered} (-5)^2-(-5)\ge6 \\ \\ 25+5\ge6 \\ \\ 30\ge6 \end{gathered}[/tex]We can see that the inequality is true.
Hence, we can conclude that inequality C satisfies the solution set graphed.
Is a triangle whose sides measure 1.25 in ,0.75 in and 1 in, a right triangle?
In a right triangle, the largest side is called the hypotenuse. Furthermore, from the Pythagorean Theorem, the following relation is satisfied:
[tex]c^2=a^2+b^2[/tex]To find if those measures correspond to a right triangle, verify if it satisfies the Pythagorean Theorem:
[tex]\begin{gathered} 1.25^2=1.5625 \\ 1^2+0.75^2=1.5625 \end{gathered}[/tex]Then:
[tex]1.25^2=1^2+0.75^2[/tex]Therefore, the sides of lengths 1.25 in, 1 in and 0.75 in are indeed the sides of a right triangle.
Solve each system of the equation by elimination method. 2x+3y=258x+5y=37
Answer:
x = -1 and y = 9
Explanation:
Given the below system of equations;
[tex]\begin{gathered} 2x+3y=25 \\ 8x+5y=37 \end{gathered}[/tex]To solve by using the elimination method, the 1st step is to multiply the 1st equation by 8 and the 2nd equation by 2, we'll have;
[tex]\begin{gathered} 16x+24y=200 \\ 16x+10y=74 \end{gathered}[/tex]The 2nd will be to subtract the 4th equation from the 3rd equation and solve for y;
[tex]\begin{gathered} 0+14y=126 \\ y=\frac{126}{14} \\ y=9 \end{gathered}[/tex]The 3rd step is to substitute y = 9 into the 1st equation and solve for x;
[tex]\begin{gathered} 2x+3(9)=25 \\ 2x+27=25 \\ 2x=-2 \\ x=\frac{-2}{2}=-1 \end{gathered}[/tex]3 years ago I was 2/3 as old as I will be 8 years from now. How old am I?
Considering the definition of an equation and the way to solve it, if 3 years ago I was 2/3 as old as I will be 8 years from now, I am 25 years old.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign. One or more unknown values appear in it, in addition to certain known data.
Solving an equation is determining the value or values of the unknowns that transform the equation into an identity. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.My ageBeing "x" the my age today, and knowing that 3 years ago I was 2/3 as old as I will be 8 years from now, the equation in this case is:
x -3= 2/3×(x +8)
Solving:
x -3= 2/3x +2/3×8
x -3= 2/3x +16/3
x - 2/3x= 16/3 + 3
1/3x= 25/3
x= 25/3 ÷ 1/3
x= 25
Finally, I am 25 years old.
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What is anequation of the line that passes through the points (-6,5) and (6,-7)?
The line that passes through the given point may be stated as
y - y1 = m(x - x1)
where (x1, y1) and (x2, y2) = (-6,5) and (6,-7)
m = (y2 - y1)/(x2 - x1)
= (-7 - 5)/(6 - -6)
= -12/12
= -1
Hence the equation of the line that passes through the given points is
(y - 5) = -1(x - -6)
y - 5 = - x - 6
y = -x - 6 + 5
y = -x - 1
A boy sold $88.50 worth of stationery. If he received a 33 1/3% commission, what was the amount of his commission?
A) $29.50
B) $40
C) $50
D) $62.50
Work Shown:
33 & 1/3% = 0.3333... the '3's go on forever
0.3333*88.50 = 29.49705 which rounds to 29.50
Answer: A. $29.50 is the correct answer.
Determine the CPI for a suit that costs $235 now and cost $90 in 1967.a. 261b. 203c. 219d. 275
Answer:
[tex]A\text{ :261}[/tex]
Explanation:
Here, we want to calculate the CPI for the cost of the suit
To do this,we use the weighted average method
What we will do here is to divide the past price by the current price and convert the value to a percentage
Mathematically, we have this as:
[tex]\frac{\text{Present cost}}{\text{Cost in 1967}}\text{ }\times\text{ 100 \%}[/tex]Substituting the values, we have:
[tex]\frac{235}{90}\text{ }\times\text{ 100 = 261}[/tex]please answer by correcting the math equation asap
The error in the subtraction of the given fraction is that the LCM was not used before subtraction of numerators and as such if correctly answered the final fraction is; -15/4
How to subtract fractions?
We are given the subtraction of fraction expression as;
3/4 - 9/2
Now, the first step in this subtraction is to find the L.C.M of both denominators.
Factors of 2 ; 1, 2
Factors of 4; 1, 2, 4
Thus, the L.C.M of both denominators is; 2 * 2 = 4
Now, the next step is to divide the LCM by the denominator and multiply by the numerator while retaining the LCM as common denominator to get;
[(3 * 4/4) - (9 * 4/2)]/4
= (3 - 18)/4
= -15/4
The method used in the question to subtract the fraction did not take into account finding the LCM.
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There are 3 consecutive even integers that have a sum of 30. What are the integers?
Answer:
8, 10, 12
Step-by-step explanation:
x+x+2+x+4=30
3x+6=30
3x=30-6
3x=24
x=8
M(5,-10) is rotated 270 degrees what is M’?
Problem
M(5,-10) is rotated 270 degrees what is M’?
Solution
For this case we need to remember that is we have any point A =(x,y) when we apply a transformation fo 270° then the new coordinates would be:
M' = (x,-y)
And for this case if we apply this transformation we got:
M'= (5, -(-10))= (5,10)
The hypotenuse of right triangle is 226 miles long. The difference between the other two sides is 194 miles. Find the missing sides. Use exact values.
Find the value of the short and ling leg.
Answer: short line: 30 miles, ling leg: 224 miles
Step-by-step explanation:
Intro:
We will be using Pythagoras theorm, which states, if we have a 90 degree triangle which has 3 side as H, B and P defined as Hypotenuse, Base and Perpendicular, then H² = B² + P²
In your case, we know that hypotenuse is 226.
We also know that (A + B)² = A² + B² + 2AB
Given:
H = 226
B - P = 194
Solution:
B = 194 + P
So
(226)² = (194 + P)² + P²
51076 = (194)² + P² + (2 x 194 x P) + P²
51076 = 37636 + 2P² + 388P
51076 - 37636 = 2P² + 388P
13440 = 2P² + 388P
6720 = P² + 194P
P² + 194P - 6720 = 0
P² - 30P + 224P - 6720 = 0
P(P - 30) + 224(P - 30) = 0
(P - 30) x (P + 224) = 0
P = 30 or -224
As miles cannot be negative, we will choose answer as 30 miles.
Now we have H = 226 and P = 30
Using Pythagoras theorm:
(226)² = (30)² + B²
51076 = 900 + B²
50176 = B²
B = 224 miles.
So the missing miles are 224 miles and 30 miles
Solve -3(x+2) > 10+5x
What is the slope intercept equation for this line?
the slope for this line is 2
what is slope?The slope or gradient of a line is a number that describe both the direction and the steepness of the line. the steepness of a line is defined as the slope (or gradient). The slope is the ratio of vertical distance to the horizontal distance between any two points on a line. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).The greater the value of the slope, the "steeper" the slope is, and vice versa. So the smallest value of the absolute value of these slopes is 1/2.
So, A.T.Q:-
The formula of slopet intercept is Y2 -Y1 /X2-X1
From the question:
slope = -1-1/0-1
slope = 2
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Hi can you give me the basic answer for 12 please
Given the equation of the line:
[tex]y=-5x-\frac{1}{2}[/tex]• You can identify that it is written in Slope-Intercept Form:
[tex]y=mx+b[/tex]Where "m" is the slope of the line, and "b" is the y-intercept.
Notice that:
[tex]\begin{gathered} m_1=-5 \\ b_1=-\frac{1}{2} \end{gathered}[/tex]• By definition, parallel lines have the same slope, but their y-intercepts are different.
Therefore, you can determine that the slope of the line parallel to the first line is:
[tex]m_2=-5[/tex]You know that this line passes through this point:
[tex](-4,2)[/tex]Therefore, substituting the slope and the coordinates of that point into this equation:
[tex]y=m_2x+b_2[/tex]And solving for the y-intercept, you get:
[tex]\begin{gathered} 2=(-5)(-4)+b_2 \\ \\ 2-20=b_2 \\ \\ b_2=-18\frac{}{} \end{gathered}[/tex]Then, the equation of the line parallel to the first line is:
[tex]y=-5x-18[/tex]• By definition, the slopes of perpendicular lines are opposite reciprocal, therefore, the slope of this line is:
[tex]m_3=\frac{1}{5}[/tex]Using the same procedure used before to find the y-intercept, you get:
[tex]\begin{gathered} 2=(\frac{1}{5})(-4)+b_3 \\ \\ 2+\frac{2}{5}=b_3 \\ \\ b_3=\frac{14}{5} \end{gathered}[/tex]Therefore, its equation is:
[tex]y=\frac{1}{5}x+\frac{14}{5}[/tex]Hence, the answer is:
- Equation for the parallel line:
[tex]y=-5x-18[/tex]- Equation for the perpendicular line:
[tex]y=\frac{1}{5}x+\frac{14}{5}[/tex]Expand and simplify: 3(2a+5) + 5(a-2)
Answer:
11
a
+
5
Step-by-step explanation: you're welcome. Brainlyest?
A health inspector from the Food and Drug Administration was tasked with oversight of a pharmaceutical company in their development of a new medication. He used a 99% confidence interval to estimate the true mean amount of propionic acid in each 800 mg pill. Propionic acid is an important ingredient in several medications, including ibuprofen. His confidence interval was (3.2 mg, 6.5 mg). Which one of the following is the best interpretation of this confidence interval?
The best interpretation of the confidence interval is given by:
We are 99% sure that the true mean amount of propionic acid in all 800 mg pills of the new medication is between 3.2 mg and 6.5 mg.
What is the interpretation of a x% confidence interval?The x% confidence interval means that it is x% likely that the population parameter(mean/proportion/standard deviation) is between the bounds a and b of the confidence interval
The bounds of the confidence interval are given by the estimate plus/minus the margin of error.
In this problem, the bounds of the problem are already given, as follows:
3.2 mg.6.5 mg.The variable of interest is given by:
Mean amount of propionic acid in all 800 mg pills of the new medication
The level of confidence is of 99%, hence, considering the variable and the bounds, the interpretation of the interval is:
We are 99% sure that the true mean amount of propionic acid in all 800 mg pills of the new medication is between 3.2 mg and 6.5 mg.
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If a woman making $33,000 a year receives a cost-ofliving increase of 2.8%, what will her new salary be?
Answer:
$33,924
Step-by-step explanation:
The amou8nt of the raise is 2.8% of $33,000.
2.8% of $33,000 =
= 2.8% × $33,000
= 0.028 × $33,000
= $924
The amount of the raise is $924.
The new salary is the amount of the raise added to the original salary.
$33,000 + $924 =
= $33,924
Line segment LN has endpoints L-2, -3) and N(3, 7).Which of the following determine the coordinates of point M located at the midpoint of LN?M= - (³2/2/², 2/³) 3-2 7-3M= =(3+2, 7+³)M = (-2-³, -3-7)M = (¹+³, 32)
The line segment LN has coordinates as follows;
[tex]\begin{gathered} L=(-2,-3) \\ N=(3,7) \end{gathered}[/tex]The midpoint of a line is derived with the following coordinates;
[tex]M=\frac{(x_1+x_2)}{2},\frac{y_1+y_2}{2}[/tex]The coordinates are thus;
[tex]\begin{gathered} (x_1,y_1)=(-2,-3) \\ (x_2,y_2)=(3,7) \end{gathered}[/tex]The midpoint, which is M, now becomes;
[tex]\begin{gathered} M=\frac{-2+3}{2},\frac{-3+7}{2} \\ \text{Also, re-written as;} \\ M=\frac{3-2}{2},\frac{7-3}{2} \end{gathered}[/tex]ANSWER:
The first option is the correct answer.
Find the area of the following circles. Leave your answer in terms of pi or round to the nearest 10th.
To find the area of a circle, we use the formula for area
A = pi r^2 where r is the radius
We are given the diameter
d = 2r
8 = 2r
Solving for r
8/2 =r
4= r
A = pi (4)^2
A = 16 pi
The circumference of a circle is 25.2 cm. Find the area of the circle correct to 1 decimal place. Area = cm²
The area of the circle is 12.56 [tex]cm^{2}[/tex].
What is area of circle?
The space occupied by a circle in a two-dimensional plane is defined as its area. A circle is a critical geometric figure found in many fields, including construction, engineering, and many others. Geometry problems involving circles necessitate the ability to calculate the area of a circle. The area of a circle is calculated as A = πr2, where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, in2, and so on.
Here the circumference of the circle is,
=> C = 25.2 cm
=> 2πr = 25.2
=> 2×3.14×r=25.2
=> r = [tex]\frac{25.2}{2*3.14}[/tex]
=> r= 4cm
Now area of the circle A= π[tex]r^2[/tex] [tex]unit^{2}[/tex]
=> A= 3.14*4 = 12.56 [tex]cm^{2}[/tex]
Hence area of the circle is 12.56 [tex]cm^{2}[/tex].
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3x^2-4x+5-x^2+x
Combine like terms
y=-2/3 3 what is the slope of the equation entered as a fraction
The equation:
[tex]y=-\frac{2}{3}x-1[/tex]has the form:
y = mx + b
with
[tex]\begin{gathered} m=-\frac{2}{3} \\ b=-1 \end{gathered}[/tex]m is known as the slope of the line, then the slope is -2/3
A rectangle is placed around a semicircle as shown below. The width of the rectangle is 6 mm. Find the area of the shaded region.Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
Q) In the picture we have a semi-circle inscribed in a rectangle. We see that the diameter is equal to the width of the rectangle (the horizontal side) of the rectangle (w), so we have:
[tex]d=w=6\operatorname{mm}[/tex]From the fact that the diameter is always two times the radius for every circle, we have:
[tex]r=\frac{d}{2}=\frac{6}{2}\operatorname{mm}=3\operatorname{mm}[/tex]Now, we also see from the picture:
[tex]h=r=3\operatorname{mm}[/tex]The question asks us about the area of the shaded region.
A) The shaded region can be computed in the following way:
1) First, we compute the area of the rectangle (Ar).
[tex]A_r=w\cdot h=6\operatorname{mm}\cdot3\operatorname{mm}=18mm^2[/tex]2) Secondly, we compute the area of the semi-circle (Asc), which is half of the area of the entire circle.
[tex]A_{sc}=\frac{1}{2}\cdot A_c=\frac{1}{2}\cdot\pi\cdot r^2=\frac{1}{2}\cdot3.14\cdot(3\operatorname{mm})^2=14.13mm^2[/tex]3) Finally, we compute the area of the shaded region taking the difference between the area of the rectangle and the area of the semi-circle.
[tex]A_s=A_r-A_{sc}=18mm^2-14.13mm^2=3.87mm^2[/tex]help meeee please !!
thank you
The answers are :
a) The average price of a new home (y) is given by a linear equation which is y = -800x + 294000.
b) The average price of a new home in year 2014 will be $286000.
What is the point slope form of a line ?
Point slope form is used to represent a straight line using its slope and a point on the line.
a)
We know that the two point -slope form of a line is given by :
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex])
where : m is slope and represented by
m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]
As per the questions hint is that two points that is (-2 , 11) and (1 , -4).
These points can be represented by :
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (0 , 294000)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (7 , 288400)
So : the slope will be :
m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{288400-294000}{7 - 0}[/tex]
m = -5600 / 7
m = -800
So , the point -slope form of line will be :
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex])
y - 294000 = -800 ( x - 0)
y - 294000 = - 800 x
or
y = -800x + 294000
So , the average price of a new home (y) is given by a linear equation which is :
y = -800x + 294000
b)
As per the question y is the average price of a new home in year x and is given by :
y = -800x + 294000
It is given that x = 0 meant year 2004. So , for year 2014 value of x will be x =10.
Substituting this value to get the value of y or average price of a new home in year 2014 , we get :
y = -800x + 294000
y = - 800 × 10 + 294000
y = -8000 + 294000
or
y = $ 286000
Therefore , the answers are :
a) The average price of a new home (y) is given by a linear equation which is y = -800x + 294000.
b) The average price of a new home in year 2014 will be $286000.
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what percent of 8,7 is 17.4
The number 17.4 is 200 percent of 8.7
How to determine the percentage?The statement is given as
"what percent of 8.7 is 17.4"
From the above statement, we have the following parameters
Dividend = 17.4
Divisor = 8.7
The percentage is then calculated as
Percentage = Dividend/Divisor x 100%
Substitute the known values in the above equation
So, we have
Percentage = 17.4/8.7 x 100%
Evaluate the quotient
Percentage = 2 x 100%
Evaluate the product
Percentage = 200%
Hence, the percentage is 200%
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