The value of x in this equation (x/2) - (2/x+1) = 1 is -2 and 3.
What is called equation?Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. Since we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
Given the equation is
(x/2) - (2/x+1) = 1
thaking LCM of left side of equation we get,
[x(x+1) - 2*2]/ 2(x+1) = 1
⇒ (x² + x - 4) / (2x +2) = 1
multiply both side by (2x +2) we get,
⇒ (x² + x - 4) = (2x +2)
subtract both side by (2x +2) we get,
⇒ (x² + x - 4) - (2x +2) = 0
⇒ x² - x - 6 = 0
to get the value of x we factorize this equation
⇒ x² - (3-2)x - 6 = 0
⇒ x² - 3x +2x - 6 = 0
⇒ x (x - 3) + 2 (x - 3) = 0
⇒ (x - 3) (x +2) = 0
from x+2 = 0, we get the value of x = -2
and from x-3 = 0, we get the value of x = 3,
So that the value of x in this equation (x/2) - (2/x+1) = 1 is -2 and 3.
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Given the following summary statistics, determine the regression equation used to predict y from x. Sy= 2.33, Sx 2.35, r= 0.25, x- = 22.85, y -=77.34. Round all answers to 2 decimal places. Slope (Please use the exact value of slope.) Intercept
The regression equation used to predict y from x is: y = -2.93x + 95.45. The slope of the regression line is -2.93 and the intercept is 95.45.
Regression analysis is a process used to estimate the relationship between two or more variables. It is used to examine the strength of the relationship between a response variable (y) and one or more predictor variables (x).
The coefficients of the regression equation are estimated by minimizing the sum of squared errors between the predicted and actual values of y. The strength of the relationship is indicated by the coefficient of correlation (r), which is a measure of how closely the data points fit the regression line.
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the regression equation y equals negative 0.414 x plus 106.55 approximates the percent of people in an audience who finish watching a documentary, y, given the length of the film in minutes, x. which percent is the best prediction for the percent of people in an audience who will finish watching a documentary that is 85 minutes long?
According to the regression model, approximately 71.46% of the audience will finish watching a documentary that is 85 minutes long.
Regression is a statistical method used to model the relationship between two variables.
In this case, the regression equation y = -0.414x + 106.55 is used to approximate the percent of people in an audience who finish watching a documentary, y, given the length of the film in minutes, x.
To find the best prediction for the percent of people who will finish watching a documentary that is 85 minutes long, we need to plug in 85 for x in the regression equation:
y = -0.414x + 106.55
y = -0.414(85) + 106.55
y = -35.09 + 106.55
y = 71.46
Therefore, the best prediction for the percent of people who will finish watching a documentary that is 85 minutes long is 71.46%.
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Explain what each point on the least-squares regression line represents.
Choose the correct answer below.
A.Each point on the least-squares regression line represents the y-value of the data set at that corresponding value of x.
B. Each point on the least-squares regression line represents the y-values that would be considered ideal at that corresponding value of x.
C.Each point on the least-squares regression line represents the predicted y-value at the corresponding value of x.
D.Each point on the least-squares regression line represents one of the points in the data set.
(C) The corresponding value of x represents the expected y-value at each location on the least-squares regression line.
What is the least-squares regression line?
A straight line that depicts the relationship between a response variable (y) and an explanatory variable (x) is called a regression line (LSRL, or Least Squares Regression Line).
A mathematical model called the line is used to forecast the value of y given a value for x.
We need an explanatory and a response variable for regression.
The anticipated y-value at each position on the least-squares regression line is represented by the corresponding value of x.
One way to use linear regression is by using least squares. It enables us to identify abnormalities in our data and forecast results based on an existing collection of data.
Values that are either too wonderful or awful to be real or that are unique cases are known as anomalies.
Therefore, (C) the corresponding value of x represents the expected y-value at each location on the least-squares regression line.
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Identify the probability distribution. A spinner with a yellow, blue, red, and green section is shown. The arrow is pointing at the yellow section. The fair spinner shown is spun 1 time. There are four possible outcomes, one for each color. Based on the picture, which statements are true? The probability of each outcome is equal The probability of each outcome is different. The outcomes have a uniform probability distribution. The outcomes have a nonuniform distribution What is the probability of spinning a yellow? 1 /4 What is the probability of spinning a yellow or a green?
The probability of each outcome is equal, and the outcomes have a uniform probability distribution.
The probability of spinning a yellow is 1/4,
The probability of spinning a yellow or green is 1/2.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.
Given A spinner with yellow, blue, red, and green sections,
total outcomes = 4
and the possibility for occurring of each color is 1,
probability = favorable outcome/total outcome
P(yellow) = 1/4
P(Red) = 1/4
P(blue) = 1/4
P(green) = 1/4
so the probability of each color is equal,
and a probability distribution known as a "uniform distribution" assumes that all possible outcomes are equally likely to occur.
The probability of spinning a yellow or green,
a favorable outcome for a yellow or a green = 2
P( yellow or green) = 2/4 = 1/2
Hence the probability of each outcome is equal and the outcomes have a uniform probability distribution.
and P(yellow) = 1/4, and P( yellow or green) = 1/2.
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the population of a city increases by 2.5% each year. how many years , to the nearest tenth, will it take until the population if the city increases from 120000 people to 180000 people?
To find the number of years it will take for the population of a city to increase from 120000 to 180000, we need to use the formula:
Years = log (target population / starting population) / log (1 + annual growth rate)
Where the annual growth rate is 2.5% or 0.025.
Plugging in the values, we get:
Years = log (180000 / 120000) / log (1 + 0.025)
Years = log (1.5) / log (1.025)
Years = 7.36 years
Rounding to the nearest tenth, we get:
Years = 7.4 years
So it will take approximately 7.4 years for the population of the city to increase from 120000 to 180000 people, assuming a constant annual growth rate of 2.5%.
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6. Rewrite each of the following in simplest form by combining like terms and constants (normal
numbers with no variables attached). Rewrite subtraction as addition when necessary.
(a) 5x+7+6x+2
(b) 7y+4-2y + 10
(c) 6c-2-9c-8
(d) 1lx+2y+4x+8y
(g) 15x+2y+7+6y+4x+2
(e) 3m +2n-5m +11n
(f) -2w+4z +7w-9z
(h) 3a +7b-9+8a-3b+4
The following expressions can be written as 12x+9 , 5y + 14 , -3c-10 and 11a+4b-5
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that consists of one or more variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division. Algebraic expressions can be used to represent a wide range of mathematical situations, such as equations, inequalities, functions, and formulas.
(a) 5x + 7 + 6x + 2 = 11x + 9
(b) 7y + 4 - 2y + 10 = 5y + 14
(c) 6c - 2 - 9c - 8 = -3c - 10 (Rewrote subtraction as addition: 6c - 2 + (-9c) - 8)
(d) 1lx + 2y + 4x + 8y = 5x + 10y (Combined "like terms": lx and x are not the same, so they can't be combined)
(e) 3m + 2n - 5m + 11n = -2m + 13n
(f) -2w + 4z + 7w - 9z = 5w - 5z
(g) 15x + 2y + 7 + 6y + 4x + 2 = 19x + 8y + 9
(h) 3a + 7b - 9 + 8a - 3b + 4 = 11a + 4b - 5
Therefore, The following expressions can be written as 12x+9 , 5y + 14 , -3c-10 and 11a+4b-5
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a measurable characteristic about an entire population is a. an experiment b. a parameter c. a population d. a sample e. a statistic
A measurable characteristic of an entire population is a parameter.
The population data is the real data for a certain attribute in the context of statistics, whereas the sample data is the representative data picked from the population. Metrics like mean, standard deviation, median, and mode are typically used to measure the characteristics of the sample and population.
Option B is the right response to the provided question.
A parameter is a quantity that affects a mathematical object's output or behavior yet is thought of as being held constant. Variables and parameters have a lot in common, and in some cases, the distinction is really one of perspective.
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Find b.
O 35
O 55
O 72.5
O 90
Check the picture below.
so by the "inscribed angle theorem" that means "c" is half of 70°, and by Thales Theorem "a" is a right-angle, btw that can also be derived by the "inscribed angle theorem", that makes angles "b" and "c" complementary angles.
pls i need help asap. just these 2 questions
Appropriate values of equation with standard form:
2.D. A=4, B=0, C=9
3.B.5x-4y=9
System of Linear EquationsA system of linear equations is one of the algebraic equations. This equation has the characteristic that each term contains a constant, or multiplication of a constant with a single variable.
This equation is said to be linear because this mathematical relationship can be described as a straight line in the Cartesian coordinate system, a system that uniquely assigns each point in a plane a series of numerical coordinates.
This system of linear equations generally has two main properties, namely:
For example l is a linear equation, then:
Adding and subtracting numbers in both sides of equation l, does not change the solution of the equation. Multiplication of non-zero numbers in both sides of equation l does not change the solution of the equation.Learn more equation at
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$1,240 at 8% compounded annually for 2 years.
The compound interest on $1240 at 8% for 2 years is $205.8
What is compound interest?Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.
The Amount on a compound interest is expressed as: A = P(1+r/100)^t
where P is the principal and r is the rate, t is the time
A = 1240( 1+8/100)²
A = 1240(1+0.08) ²
A = 1240(1.08)²
A = 1240× 1.166
A = $1445.8
A = P+I
I = A-P
I = 1445.8-1240
I = $ 205.8
therefore the interest on the $1240 compounded for 2 years is $205.8
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describe different real world situatons include units of x and y that would be consistent with the data provided
A real-world situation consistent with the data provided would be (a) the height of a balloon as it ascends in the air at a constant rate, (b) the speed of a car as it accelerates from a standstill to a constant speed, (c) the height of a soccer ball as it is kicked into the air (d) the velocity of a skydiver as they fall to the ground.
a. A real-world situation consistent with the data provided would be the height of a balloon as it ascends in the air at a constant rate. In this case, x can be the time elapsed in seconds, and y can be the height in meters.
The balloon's height will not change with time (f'(x) = 0), meaning the balloon is not accelerating, and the height remains constant as it moves from 0 to 3 seconds.
b. A real-world situation consistent with the data provided would be the speed of a car as it accelerates from a standstill to a constant speed. In this case, x can be the time elapsed in seconds, and y can be the speed in meters per second.
The speed of the car will increase at a constant rate (f'(x) = 50), meaning the car is accelerating, and the speed increases as it moves from 0 to 3 seconds.
c. A real-world situation consistent with the data provided would be the height of a soccer ball as it is kicked into the air. In this case, x can be the time elapsed in seconds, and y can be the height in meters.
The height of the ball will increase as time goes by (f'(x) is increasing as x increases), meaning the ball is moving upwards, and the height increases as it moves from 0 to 3 seconds.
d. A real-world situation consistent with the data provided would be the velocity of a skydiver as they fall to the ground. In this case, x can be the time elapsed in seconds, and y can be the velocity in meters per second.
The velocity of the skydiver will decrease as time goes by (f'(x) is decreasing as x increases), meaning the skydiver is falling faster and faster, and the velocity decreases as it moves from 0 to 3 seconds.
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--The given question is incomplete; the complete question is
"Describe different real-world situations (include the units of x and y) that would be consistent with the data provided:
a. f'(x)=0, 0 ≤ x ≤ 3
b. f'(x) = 50, 0 ≤ x ≤ 3
C. f'(x) is increasing as x increases, 0 ≤ x ≤ 3
d. f'(x) is decreasing as x increases, 0 ≤ x ≤ 3"--
Find the slope of the line that contains the following points: (17, -12) and (12, 8). Use the slope formula.
PLEASE NEED HELP ASP!
Given: AD, BE and FC intersect at point P. AD⊥FC.
Write at least 6 algebra equations to relate different pairs of angles. Justify your statements with the correct definition or theorem.
The six algebraic equations are given below.
What is an angle addition postulate?According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.
Given:
AD, BE and CF intersect at point P.
And AD⊥CF.
The algebraic equations:
∠APC + ∠CPD = 180° {Supplementary angles}
∠FPA + ∠CPA = 180° {Supplementary angles}
∠EPA + ∠BPA = 180° {Supplementary angles}
∠EPD = ∠BPA {opposite angle theorem}
∠APB + ∠CPB = ∠CPA {Angle addition postulate}
∠EPF + ∠EPD = ∠DPF {Angle addition postulate}
Therefore, 6 equations are given above.
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We have two fractions, 3/4 and 7/6, and we want to rewrite them so that they have a common denominator (and whole number numerators).
What numbers could we use for the denominator?
Choose 2 answers: a) 24 b) 12 c) 18 d) 8 HURRY PLSSS!!!!
Answer:
A & B
Step-by-step explanation:
24 and 12 are both multiples of 4 & 6
How can data displays be used to compare populations?
The data displays be used to compare populations as
(i)they quickly illustrate measures of center
(ii)they show trends in data that can be compared.
Data Display is basically displaying of useful data which has been extracted from bundles of raw data or raw data points. That useful data can be used to compare two different datasets as well.
It says that it quickly illustrate measures of centre. True, because it presents you quick display so that everyone seeing the data in form of charts or tables easily catch the information to be conveyed.
It says, they show trends in data that can be compared. Yes again true. Data displays show you trends of different things in one clear picture and it can be compared with other datasets through the use of data displays.
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What is (gof)(x) if f(x) = 3x - 1 and g(x) = 4x² + 9?
Step-by-step explanation:
(gof)(x) is basically g(f(x))
= 4 × (3x - 1)² + 9
= 4 × (9x² - 6x + 1) + 9
= 36x² - 24x + 4 + 9
= 36x² - 24x + 13
Any question is fine
The duration it takes a teacher and the duration it takes a student to each paint the mural found using the combined work formula are;
One teacher takes 79[tex]\frac{3}{23}[/tex] hours to paint the muralOne student takes -1820 hours to paint the muralThe number of brushes and tubes of paints purchased are;
40 tubes of paint and 80 paintbrushesWhat is the combined work formula?The time, Tₙ, it takes to do a work by two people combined, where the time it takes one person to do the work is T₁ and the time it takes the second person to do the same work is T₂, can be expressed as in the following combined work or rate of work formula equation;
[tex]\frac{1}{T_1}+\frac{1}{T_2} = \frac{1}{T_n}[/tex]
Let T represent the time it takes one teacher to paint the large mural, and let S represent the time it takes a student to paint the large mural, we get;
[tex]\frac{8}{T}+\frac{2}{S} = \frac{1}{10}[/tex]...(1)
[tex]\frac{6}{T}+\frac{8}{S} = \frac{1}{14}[/tex]...(2)
Multiplying equation (1) by 4 and subtracting equation (2) from the result, we get;
[tex]4\times \frac{8}{T}+\frac{2}{S} = \frac{32}{T}+\frac{8}{S} = \frac{4}{10} = \frac{2}{5}[/tex]
[tex]\frac{32}{T}+\frac{8}{S} = \frac{2}{5}[/tex]
[tex]\frac{32}{T}+\frac{8}{S} -\left(\frac{6}{T}+\frac{8}{S}\right) = \frac{2}{5} - \frac{1}{14} = \frac{23}{70}[/tex]
[tex]\frac{26}{T}+0 = \frac{23}{70}[/tex]
T = (70/23) × 26 = 1820/23 = 79 3/23
The time it will take one teacher to paint the mural is; T = 79 3/23 hours[tex]\frac{8}{T}+\frac{2}{S} = \frac{1}{10}[/tex], therefore;
[tex]\frac{2}{S} = \frac{1}{10} - \frac{8}{T}[/tex]
[tex]\frac{2}{S} = \frac{1}{10} - \frac{8\times 23}{1820} = -\frac{1}{910}[/tex]
S = -910 × 2 = -1820
The time it would take a student to paint the mural is -1820 hoursSecond question
The budget on tubes of paint and paintbrushes = $200
The cost of a tube = $4.00 and the cost of a paintbrush = $0.5
Number of brushes purchased = 2 × The number of tubes of paint purchased
Let x represent the number of paintbrushes purchased and let y represent the number of tubes of paint purchased, we get;
0.5·x + 4·y = 200
x = 2·y
Therefore; 0.5 × (2·y) + 4·y = 200
y + 4·y = 5·y = 200
y = 200/5 = 40
The number of tubes of paint purchased, y = 40
x = 2·y, therefore;
x = 2 × 40 = 80
The number of paintbrushes purchased, x = 80
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Anand bought snacks for his team's practice. He bought a bag of popcorn for $2.65 and a 15-pack of juice bottles. The total cost before tax was $34.45. How much was each bottle of juice?
Answer: $2.12
Step-by-step explanation: Subtract $2.65 from 34.45 and then divide that number by 15.
A gardener wants to fence a circular garden of diameter 35 m. Find the length of the rope he needs to purchase, if he makes 5 rounds of fence. Find the cost of the rope if it costs 20 per metre. (==)
Answer:
Below
Step-by-step explanation:
Circumference (distance around) a circle = pi * diameter
= 3.14 * 35 m = 109.9 m
FIVE of these would be 109.9 * 5 = 549.5 meters
at 20 per meter would be 549.5 * 20 = 10 990 (units)
when data are collected in a statistical study for only a portion or subset of all elements of interest we are using a:
When data is collected in a statistical study for only portion or subset of all element of interest we are using a sample.
We frequently collect data from samples, or smaller subsets of the population, as opposed to the entire population as a whole.
A sample is a subset of units chosen to represent all the individuals in the population. Because just a portion of the population was counted, it is only a partial enumeration. To estimate the characteristics for the total population of interest, data from the sampled units is used.
For instance, a medical study looks at how a certain disease spreads among city's stray canines. The population of interest in this case are the city's street dogs. This sample or population of interest corresponds to the overall population on which you want to draw conclusions.
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The perimeter of the rectangle below is 128 units. Find the length of side CD. Write your answer without variables. 3x + 3 C 4x - 2 B CD =
The length CD of the rectangle is 34 units
How to determine the length CDFrom the question, we have the following parametes that can be used in our computation:
The perimeter of the rectangle below is 128 units
This means that
2 * (3x + 3 + 4x - 2) = 128
So, we have
7x + 1 = 64
Evaluate the like terms
7x = 63
This gives
x = 9
Recall that
CD = 4x - 2
So, we have
CD =4 * 9 - 2
CD = 34
Hence, the length is 34 units
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ians car can go 224 miles on 7 gallons of gas. During a drive last weekend, ian used 4 gallons of gas. How far did drive? Use pencil and paper. Explain how the problem changes if you were given the distance drove last weekend instead of how much gas used.
Answer:
see below
Step-by-step explanation:
4/7*224 = 128
224 miles / 7 gallons = 32 miles per gallon
so given either factors, you'll be able to solve the other.
the problem will become how many gallons used to drive xxx miles.
Help!! Question in pic
The statement W ⊂ J is true.
What is a set?A set is a collection of items where there are operations such as:
Union of sets, the intersection of sets, and the complement of sets.
We have,
From the given information,
R ⊂ J
D ⊂ J
M ⊂ D ⊂ J
W ⊂ D ⊂ J _____(1)
Now,
⊂ means subset.
Example:
A = {1, 2, 3}
B = {1, 2, 3, 4}
So,
A ⊂ B since the element in A is also in B and B has one extra element.
So,
From (1),
W ⊂ J
Thus,
W is a subset of J.
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what is three minus 1third
Answer: 1/9
Step-by-step explanation:
Answer:
3 - 1/3 = 2 2/3
if you take 1/3, then you can just take 1 from 3 for a moment, and then add it back, as shown:
1 - 1/3 = 2/3
Then just add it back:
2/3 + 2 = 2 2/3
Step-by-step explanation:
Hope it helps! =D
a jar contains 4 white, 10 blue, and 16 red marbles. if one marble is drawn at random from the jar, find the probability that:
The probability of drawing a white marble is 2/15
How to determine the probability that a white marble is selectedFrom the question, we have the following parameters that can be used in our computation:
4 white, 10 blue, and 16 red marbles
This means that
Total = 4 + 10 + 16
Total = 30
So, the probability of drawing a white marble is
P = White/Total
Substitute the known values in the above equation, so, we have the following representation
P = 4 / 30 = 2/15.
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Complete question
a jar contains 4 white, 10 blue, and 16 red marbles. if one marble is drawn at random from the jar, find the probability that a white marble is selected
Pls help its for a grade and I really need it bc I have a d
Answer:
232 and 58
Step-by-step explanation:
bro just use a calc
Answer:
Part A: C, 129 & Part B: A, 58
Step-by-step explanation:
Part A:
36+ 51 + 42= 129
Part B:
152- 49 - 45= 58
To double check part B:
58 + 49 + 45 = 152
The ratio of c:d is 1:3. The ratio of d:e is 2:3. What is the ratio of c:d:e?
The ratio of c:d:e is 1:3:2.
How The answer was obtainedTo find the ratio, you can multiply the first ratio by the second ratio: 1 * 2 = 2 and 3 * 3 = 9, so the ratio becomes 2:9:6, which can be simplified to 1:3:2.
A ratio is a comparison between two values. To calculate a ratio, divide the first value by the second value. For example, if you have three apples and seven bananas, the ratio of apples to bananas would be 3/7.
You can also simplify a ratio by dividing both values by their greatest common divisor. For example, if the ratio of apples to bananas is 6/14, you could simplify it to 3/7.
It's also possible to express a ratio as a fraction, decimal, or percentage. To convert a ratio to a fraction, simply divide the two values. To convert a ratio to a decimal, divide the numerator by the denominator. To convert a ratio to a percentage, multiply the ratio by 100.
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At hockey practice, Ajay saved 73 out of the 126 shots on goal. At this pace, how many saves would he make out of 200 shots on goal?
LCD of 11/15 and 9/10
Answer:
LCD = 30
Step-by-step explanation:
11/15 = 11/15 × 2/2 = 22/30
9/10 = 9/10 × 3/3 = 27/30
Finding the Error
A 2-column table with 4 rows. Column 1 is labeled Tons with entries 2, 4, 10, 12. Column 2 is labeled Pounds with entries 4,000, 8,000, 20,000, 40,000. 40,000 is crossed out. An arrow goes from 2 to 12 and a second arrow goes from 4,000 to 40,000.
What error did the student most likely make?
The student multiplied by 6 instead of 10.
The student multiplied by 10 instead of 6.
The student used the ratio of 1:4,000 instead of 2:4,000.
The student used the ratio of 2:2,000 instead of 1:2,000.