The statement "The arithmetic mean of two numbers is the positive square root of the product of the numbers." is False.
And the true sentence is "The geometric mean of two numbers is the positive square root of the product of the numbers."
Arithmetic Mean:
The arithmetic mean, is also called the average or average value, is the quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables.
Given,
Here they given the sentence, "The arithmetic mean of two numbers is the positive square root of the product of the numbers.".
We need to find this one is true or not and we also need to replace the underlined word or phrase to make a true sentence.
Based on the definition of arithmetic mean, the given statement is false.
And the correct sentence is
"The geometric mean of two numbers is the positive square root of the product of the numbers.".
Because geometric mean is average value or mean which signifies the central tendency of the set of numbers by finding the product of their values.
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Write the equation of the line that is perpendicular to x + 4y = 12 and passes through the point (-8, 5) in slope-intercept form.
y = mx + b
m=
b=
The equation of the line is: y = 4x + 37
m = 4
b = 37
How to Write the Equation of a Line in Slope-intercept Form?The equation of the line that is perpendicular to x + 4y = 12, will have a slope that is the negative reciprocal of the its slope.
Rewrite the equation, x + 4y = 12 in slope-intercept form:
4y = -x + 12
y = -x/4 + 3
The slope is -1/4. Therefore, the slope of the perpendicular line would be 4.
Substitute m = 4 and (a, b) = (-8, 5) into y - b = m(x - a)
y - 5 = 4(x - (-8))
y - 5 = 4x + 32
y = 4x + 32 + 5
y = 4x + 37
The equation of the line is: y = 4x + 37
m = 4
b = 37
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the product of 5 less than x and 7
Answer:
7x - 35
Step-by-step explanation:
This states the product of (5 less than x) and (7). Five less than x can be written as (x - 5), and 7 is just 7. The product of (x-5) and 7 is 7x - 35.
Hope this helped :)
Which expression has a value of -5?
A: (-3) -8
B: (-8) - (-3)
C:(-3) - (-8)
D: 8-(-3)
A city has 73,400 voters. According to a survey, 96% of them will vote to support a local measure. How many people will vote
for this measure?
Answer: 70,464 people
Step-by-step explanation:
We will write an equation to help us solve. Note that a percent divided by 100 becomes a decimal and that "of" means multiplication in mathematics. Let x be the number of people who will support the measure.
96% of 73,400 voters will support the local measure.
(0.96)(73,400) = x
70,464 people = x
From 125 yards away, a marksman hit 55.6 of the targets last year.
From 125 yards, a marksman hit 55.6 of the targets last year, which is equal to (55.6 × 100)% that is 5560%
What is percentage?A percentage (from Latin: per centum, "by a hundred") is a number or ratio stated as a fraction of 100 in mathematics. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A percentage is a dimensionless (pure) number; it does not have a unit of measurement.
A percentage is a fraction or a ratio in which the full number is always 100. For example, if Sam received 30% on his arithmetic test, he received 30 points out of a possible 100. It is written as 30/100 in fraction form and 30:100 in ratio form.
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Full question
Rewrite the decimal in the sentence below as a percentage.
From 125 yards away, a marksman hit 55.6 of the targets last year.
Solve each equation. Check each solution. 2/n + n+2 / n+1 = -2 / n² + n
The solution of given rational equation [tex]\frac{2}{n} +\frac{n+2}{n+1}=\frac{-2}{n^2+n}[/tex] is n = -2
In this question,
We have been given a rational equation.
[tex]\frac{2}{n} +\frac{n+2}{n+1}=\frac{-2}{n^2+n}[/tex]
We need to find the solution of given rational equation.
First we simplify the LHS of given equation.
[tex]\frac{2}{n} +\frac{n+2}{n+1}\\\\=\frac{2(n+1)+n(n+2)}{n(n+1)} \\\\=\frac{2n+2+n^2+2n}{n^2+n}\\\\ =\frac{n^2+4n+2}{n^2+n}[/tex]
So, given equation would be,
[tex]\frac{n^2+4n+2}{n^2+n}=\frac{-2}{n^2+n}[/tex]
Here, the denominator is same on the both sides.
⇒ n² + 4n + 2 = -2
⇒ n² + 4n + 4 = 0
⇒ (n + 2)² = 0
⇒ n + 2 = 0
⇒ n = -2
We need to check above solution.
so, substitute n = -2 in LHS of given equation.
[tex]\frac{2}{-2} +\frac{-2+2}{-2+1}\\\\=-1+0\\\\=-1[/tex]
Now, substitute n = -2 in RHS of given equation.
[tex]\frac{-2}{-2^2-2}\\\\=\frac{-2}{4-2}\\\\= \frac{-2}{2} \\\\-1[/tex]
For n = -2, LHS = RHS
Therefore, the solution of given rational equation [tex]\frac{2}{n} +\frac{n+2}{n+1}=\frac{-2}{n^2+n}[/tex] is n = -2
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Michael wants to borrow $12000 for a car loan. Which option would allow him to pay the least amount of interest?
A. A 12-month loan with a 7.25% annual simple interest rate
B. A 18-month loan with a 3.50% annual simple interest rate
C. A 24month loan with a 3.75% annual simple interest rate
D. A 36-month loan with a 2.75% annual simple interest rate
Based on the interest rates available to Michael, the option that would allow him to pay the least interest is B. 18-month loan with a 3.50% annual simple interest rate
How much interest will Michael pay?The interest on the first option is:
= (7.25% x 12,000) x 12/12months in year
= $870
Interest on second loan:
= (3.5% x 12,000) x 18 / 12 months in year
= $630
Interest on third loan:
= (3.75% x 12,000) x 24/12 months in year
= $900
Interest on fourth loan:
= (2.75% x 12,000) x 36/12 months in year
= $990
In conclusion, the 18-month loan with a 3.50% annual simple interest rate gives the lowest rate.
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Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x) = (2/9)x - (9/2) for x=9
f (9) = - 5/2 is the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x)= (2/9)x - (9/2)
Put x = 9 ⇒ (2/9) * 9 - (9/2)
⇒ 2 - 9/2
⇒ -5/2
Therefore f (9) = - 5/2
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Is the distance from the center of a circle to a point in the interior of a circle sometimes, always, or never less than the radius of the circle? Explain.
The distance from the center of a circle to a point in the interior of a circle is always less than radius of the circle.
It is given that there is a point inside the circle.
We have to find that whether its distance from center of circle is sometimes, always, or never less than the radius of the circle.
What is the radius of a circle ?
The distance between the center of a circle and any point on the circle is called the radius of circle.
We know that ;
Radius is the distance between the center of a circle and any point on the circle.
Let's assume three points which are A, B, and C, where A is a point inside circle, B is a point on circle, and C is a point outside circle.
Also ;
O is the center of circle.
So ;
OA = the length of the line from center to point inside the circle.
OB = radius of the circle.
OC = the length of the line from center to the point outside the circle.
So ;
We can conclude that ;
OA<OB<OC.
or
The length of the line from the center of a circle to any point inside the circle will be always less than it's radius.
Thus , the distance from the center of a circle to a point in the interior of a circle is always less than radius of the circle.
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Points that are on the same line are collinear. Use the definition of slope to determine whether the given points are collinear.Prove that the triangle with vertices (3,5),(-2,6) , and (1,3) is a right triangle.
Using the definition of slope, the triangle with vertices (3 , 5), (-2 , 6), and (1 , 3) is a right triangle.
The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.
m = (y2 - y1)/(x2 - x1)
To prove that the triangle with vertices (3 , 5), (-2 , 6), and (1 , 3) is a right triangle, there should be a pair of adjacent lines perpendicular with each other(forms 90 degree angle). The slope of this pair of adjacent lines must be negative reciprocal of one another.
let A = (3 , 5)
B = (-2 , 6)
C = (1 , 3)
Determine the slope of each line of the triangle: AB, BC, AC.
AB : m = (6 - 5)/(-2 - 3) = 1/-5 = -1/5
BC : m = (3 - 6)/(1 - -2) = -3/3 = -1
AC : m = (3 - 5)/(1 - 3) = -2/-2 = 1
-1 is the negative reciprocal of 1. The slope of BC is the negative reciprocal of the slope of AC, hence, side BC is perpendicular with each other.
Therefore, the triangle with vertices (3 , 5), (-2 , 6), and (1 , 3) is a right triangle.
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Determine the distance between each pair of points. Then determine the coordinates of the midpoint M of the segment joining the pair of points.
D(0,0,0) and E(1,5,7)
Distance between the points D and E is [tex]5\sqrt{3}[/tex] and the mid point of the line segment joining D and E is (1/2,5/2,7/2) .
Distance Formula is used to calculate distance between two given points.
the distance between points A(a,b,c) and B(x,y,z) is given by [tex]\sqrt{(x-a)^{2}+(y-b)^{2}+(z-c)^{2} }[/tex]
Mid point formula the mid point M(m₁,m₂,m₃) between the points A(a,b,c) and B(x,y,z) is given by M(m₁=[tex]\frac{a+x}{2}[/tex],m₂=[tex]\frac{b+y}{2}[/tex],m₃=[tex]\frac{c+z}{2}[/tex])
To calculate the distance between the points D(0,0,0) and E(1,5,7) we will use distance formula.
Substituting the values in Distance formula we get
d=[tex]\sqrt{(1-0)^{2}+(5-0)^{2}+(7-0)^{2} }[/tex]
=[tex]\sqrt{1^{2} +5^{2} +7^{2} }[/tex]
=[tex]\sqrt{1+25+49}[/tex]
=[tex]=\sqrt{75} \\ 5\sqrt{3}[/tex]
to determine the midpoint M we will use mid point formula.
Substituting the values of the given points in the mid point formula we get
mid point = [tex](\frac{0+1}{2} ,\frac{0+5}{2} ,\frac{0+7}{2} )[/tex]=(1/2,5/2,7/2)
Therefore , Distance between the points D and E is [tex]5\sqrt{3}[/tex] and the mid point of the line segment joining D and E is (1/2,5/2,7/2) .
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please help!!!!!!!!!!!!!! show your work and try to have the right answer
Answer:
Step-by-step explanation:
f(x)=x²-3x + 20
Find f(5)
[tex]f(x)=x^2-3x+20\\\\f(5)=(5)^2-3(5)+20\\\\f(5) = 25-15+20\\\\f(5)=\boxed{30}[/tex]
a. What sampling method could you use to find the percent of adults in your community who support building more nuclear power plants?
Answer:
One way you could do it is to do a Systematic Sample \textbf{Systematic Sample} Systematic Sample and go to every other house in the neighborhood and ask their opinion.
Step-by-step explanation:
Determine whether each infinite geometric series diverges or converges.
If the series converges, state the sum. 4+2+1+ . . . .
Determine whether each infinite geometric series diverges or converges.
The series converges.
If the series converges, state the sum. 4+2+1+ . . .
The sum of the infinite series is 8
What is the sum of the infinite series?
Given:
[tex]a(\text{ the first term})=4\\\\r(\text{ the common ratio})= \frac{a_2}{a_1} = \frac{2}{4}=\frac{1}{2}[/tex]
Since , [tex]\vert r\vert < 1[/tex] , the infinite series converges.
The sum of infinite geometric series is:
[tex]S_\infty=\frac{a}{1-r} ; -1 < r < 1\\\\S_\infty=\frac{4}{1-\frac{1}{2} } =\frac{4}{\frac{1}{2} }=8[/tex]
The sum of the infinite series is 8
What is an infinite geometric series?
The result of an endless geometric sequence is an infinite geometric series.There would be no conclusion to this series.The total of all finite geometric series can be determined.However, if the common ratio of an infinite geometric series is bigger than one, the terms in the sequence will grow steadily larger, and adding the larger numbers together will not yield a solution.To learn more about infinite geometric series, refer:
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Use your results from Exercise 13 to determine whether the given measures define 0,1, 2, or infinitely many obtuse triangles. Justify your answers.
a=13, b=17, m
When two sides are provided without an angle measurement, such as a = 13m and b = 17m , we can create an infinite number of obtuse triangles.
As an example:
How many different obtuse triangles can we make if our side lengths are 13m and 17m, and our angle value ranges from 90 to 360 degrees?
Make a triangle with sides of 13m and 17m metres, a 120 degree angle, and a third side that can be protractored to the length you desire. You've constructed a triangle.
We may create a whole different triangle that is identical to this one by altering the third side's length and angle.
You must always remember to select the side lengths and angles. It's hinted that you could choose another course of action. There are an infinite amount of distinct triangles that can be created by using the same angles.
Thus, we can make an infinite number of triangles by employing a single angle and a single side length.
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Find the slope of the line.
c. the line containing (4,2) and (4,-3)
The slope of the line containing (4,2) and (4,-3) is Infinity.
The slope of a straight line can be written as follows,
m = [tex](y_{2} -y_{1} ) / (x_{2} -x_{1} )[/tex] equation1
The line is containing the points (4,2) and (4,-3). So, we can write
[tex]y_{2}[/tex] = -3 , [tex]y_{1}[/tex] = 2 , [tex]x_{2}[/tex] = 4 , and [tex]x_{1}[/tex] = 4 .
On substituting the values of variables in equation1, we will get
m = ( (-3)-(2) ) / ( (4)-(4) ) = (-6/0) = Infinity
As the slope of a line is Infinity, so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (4,2) and (4,-3) is Infinity.
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Solve by completing the square. Express answer in a simplified radical form when possible. When not possible, round to nearest hundredth.
x^2+6x+2=0
Answer:
[tex]{ \tt{ {x}^{2} + 6x + 2 = 0}} \\ { \tt{ {x}^{2} + 6x = - 2 }}[/tex]
- Add the square of the half of the sum on either sides:
[tex]{ \tt{ {x}^{2} + 6x + ( { \frac{6}{2}) }^{2} = - 2 + {( \frac{6}{2}) }^{2} }} \\ \\ { \tt{ {x}^{2} + 6x + 9 = - 2 + 9}} \\ { \tt{ {(x + 3)}^{2} = 7}} \\ { \tt{x + 3 = \sqrt{7} }} \\ { \tt{x = - 3 \pm2.648}} \\ { \tt{x = ( - 3 \pm \sqrt{7} )}}[/tex]
help please
The cost of having a window fixed is $125 plus $25 per hour of labor. Using h for the number of hours of labor, write an expression that represents the total cost.
25 + 125h
125 + 25h
150h
125+25 over h
I believe the answer would be Y=125+25(h
Answer: 125 + 25h
Step-by-step explanation:
The total amount of money is the cost of the window plus the amount of hours.
The length of a bacterial cell is about 4 x 10−6 m, and the length of an amoeba cell is about 2.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.
6.25 x 102
2 x 102
6 x 101
16 x 101
the bacterial cell is 6.25*10 times smaller than the amoeba cell.
How many times smaller is the bacterial cell than the amoeba cell?
To find how many times smaller is the bacterial cell than the amoeba cell, we need to take the quotient between the amoeba cell's length and the bacterial cell's length
We know that:
bacterial cell's length = 4*10^(-6) m
amoebas cell's length. = 2.5*10^(-4) m
The quotient gives:
Q = ( 2.5*10^(-4) m)/(4*10^(-6) m) = (2.5/4)*(10^(-4)*10^6) = 0.625*10^(-4 + 6)
Q = 0.625*10^2
Now we want this in scientific notation, so we need to have a digit in the left fo the decimal point, so we can rewrite this as:
Q = 0.625*10^2 = 6.25*10^1 = 6.25*10
Then the bacterial cell is 6.25*10 times smaller than the amoeba cell.
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Zachary purchased a computer for $1,900 on a payment plan. months after he purchased the computer, his balance was $1,510 months after he purchased the computer, his balance was $1,250 What is an equation that models the balance y after x months?
An equation that models the balance y after x months is; y = -130x + 1900
What is the equation in slope intercept form?From the given parameters, we can form a table of values as;
Month Balance
0 1900
3 1510
5 1250
Now, the formula for slope between two coordinates is;
m = (y2 - y1)/(x2 - x1)
At first coordinate, we have;
m = (1510 - 1900)/(3 - 0)
m = -390/3 = -130
At second coordinate;
m = (1250 - 1510)/(5 - 3)
m = -260/2
m = -130
Now, the formula for equation in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, equation is;
y = -130x + 1900
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Complete question is;
Zachary purchased a computer for $1,900 on a payment plan. 3 months after he purchased the computer, his balance was $1,510. 5 months after he purchased the computer, his balance was $1,250 What is an equation that models the balance y after x months?
find the value of each expression
16.2 + (-8.4) =
2/5 - 3/5 =
-9.2 - 7 =
(-4 3/8) - (-1 1/4) =
WILL GIVE OUT BRAINLIEST !
Answer:
1. 7.8
2. -1/5
3. -16.2
4. -25/8
Step-by-step explanation:
-
Answer:
7.8
-0.2
-16.2
-3.125
I really hope it helps
ps: from ultra instinct Giga Chad
Jared has completed a controlled scientific experiment in which he found a strong
positive correlation between hours of daylight and pea plant growth. He calculates that
the correlation coefficient is 0.93. Does Jared's experiment suggest that sunlight causes
pea plant growth? Why or why not?
OYes; if the correlation coefficient is close to 1, then there is a cause-and-effect relationship.
Yes; finding a strong correlation in a controlled scientific experiment suggests a cause-and-effect
relationship.
O No; cause-and-effect relationships always have a correlation coefficient of 1 or -1.
No; cause-and-effect relationships can be established only by collecting observations from
nature, not from a controlled experiment.
In Jared's experiment, we can conclude that; No, cause-and-effect relationships can be established only by collecting observations from
nature, not from a controlled experiment.
How to Interpret Correlation Coefficient?
The correlation coefficient is simply the specific measure that quantifies the strength of the linear relationship between two variables in a correlation analysis. It varies from -1 to 1.
Now, we are told that the correlation coefficient is 0.93. This means that it is close to 1. Now, we know that when the correlation coefficient is near 1 or −1, the linear relationship is strong; when it is near 0, the linear relationship is weak.
We also know that correlational studies allow researchers to detect the presence and strength of a relationship between variables, while experimental studies allow researchers to look for cause and effect relationships.
Thus, in Jared's experiment, we can conclude that; No, sunlight doesn't cause pea plant growth because cause-and-effect relationships can be established only by collecting observations from
nature, not from a controlled experiment.
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does someone mind helping me with this? Thank you!
Answer:
32
Step-by-step explanation:
Sorry for not neat explanation but i hope u understand
Answer:
32?
Step-by-step explanation:
when i did it with a Pythagorean theorem calculator i got 32
Ana has 8 stamps. Together, Ricky and ana have 23 stamps. The equation 23 = r + 8 represents this situation,where r is the number of stamps Ricky has. Solve the equation to find the number of stamps ricky has
Ricky has the number of stamps in the number of 15 stamps.
According to the question, the given parameters can be used to form the expression by using simplification method and the parameters are as follows:
Stamps for Ana: 8
Stamps for Ricky and Ana: 23
Given equation: 23 = r + 8
The equation formed by the simplification method is: r + a = 23
Solving above two equations, we get a = 8 stamps and r = 15 stamps.
Hence, Ricky has the number of stamps in the number of 15 stamps.
What is simplification?
The word simplification is the procedure in which complicated expression can be written in a simpler form to make the calculation easy. This method is used to calculated the answers for the unknown quantity.
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Can someone help me please!!
The perimeter of a circle with an area of 36 square units is 21.29 units.
How to find the perimeter of a circle with a known area?
For a circle with a radius R, the area is given by the formula:
A = pi*R^2
And the perimeter is given by:
P = 2*pi*R
Where pi = 3.14
In this case the area is A = 36 square units, then the radius is given by:
36 = 3.14*R^2
R = √(36/3.14) = 3.39 units.
Replacing that in the perimeter equation we get:
P = 2*3.14*3.39 units = 21.29 units.
The perimeter of a circle with an area of 36 square units is 21.29 units.
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Find the volume of this cone. Use 3 for pi.
The volume of the cone as shown in the diagram is 192 cm²
Diameter in the question is given as 16cm
We need to find the radius of the cone to find the volume of cone which is half of the diameter = 16/2 = 8 cm
The height of the cone as given in the question is 3cm
The volume of the cone =1/3 (πr²h)
We are told to use the value of pi as 3 so we are not using 3.14 or 22/7 as the value of pie
Volume = 1/3 ( 3 × 8² × 3)
= 1/3 ( 9× 64)
= 1/3 (576)
= 192 cm²
Hence, the volume of the cone as shown in the diagram is 192 cm²
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when slolved please show steps.
The expression for h in the information illustrated will be h = 2r.
How to illustrate the information?It should be noted that the expression is given as:
2πr³ = πr²h
In this situation, the information is that we should make h the subject of the formula.
This will be:
2πr³ = πr²h
Divide both side by πr²
2πr³/πr² = πr²h/πr²
2r = h
Therefore h = 2r
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Help ASAP! 30 points!
Is the mean greater than, less than, or equal to the median? Explain your reasoning.
Since the distribution is symmetric, the mean and the median of the distribution are equal.
What are the mean and the median of a distribution?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.The median of a distribution is the value that separates the bottom 50% of the distribution from the upper 50%, that is, the middle value of the distribution.When a distribution is symmetric, the mean and the median are equal. From the dot plot in this problem, the distribution is uniform(as all outcomes are equally as likely, that is, they have the same frequency in the dot plot), and symmetric, hence the the mean and the median of the distribution are equal.
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Stock Market At the beginning of the day the stock market goes down 30
1
2 points and stays at this level for most of the day. At the end of the day the stock market goes up 120
1
4 points from the low at the beginning of the day. What is the total change in the stock market from the beginning of the day to the end of the day?
The total change in the stock market from the beginning of the day to the end of the day is 89.75 points.
Here, we are given that the stock market goes down 30 1/2 points at the beginning of the day.
30 1/2 can be written as-
{(30*2) + 1}/2 = 61/2
Further it is given that the stock market goes up by 120 1/4 points at the end of the day.
120 1/4 can be written as-
{(120*4) + 1}/4 = 481/4
Thus, the total change in the stock market will be-
481/4 - 61/2
= 481/4 - 122/4
= 359/4
or 89.75
Thus, the total change in the stock market from the beginning of the day to the end of the day is 89.75 points.
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