The first step that justifies Anne's first step while solving the expression is the commutative law of addition.
The property that best justifies Anne’s first step is the addition property of equality. This allows you to add four on the left side of the equal sign to cancel it out. In order to be fulfill the property, what you do to one side you must do to the other so you add that same amount (4) to the right side of the equal sign.
3x-4 = 5
(3x-4) +4 = 5 + 4
3x = 9
Final Answer: Addition Property of Equality
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What is the nature of roots of quadratic equation 2x² 4x 3 0 *?
The nature of roots of the given quadratic equation is "real and unequal".
Nature of Roots:
Root type simply means the category to which the root belongs. Roots can be imaginary, real, unequal, or equal. If the discriminant is negative, the root is imaginary.
Depending on the value of the discriminant, we discuss the following cases for the nature of the root:
Case 1: D = 0
If the discriminant is zero (b2 – 4ac = 0), a, b, and c are real, and a≠0, the root of the quadratic equation is ax2 + bx + c = 0 is Real and equal. In this case the root is x = -b/2a. A graph of the equation is tangent to the x-axis at a point.
Case 2: D > 0
If the discriminant is greater than zero (b2 – 4ac > 0), then a, b, and c are real and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is real and not equal. The equation graph touches the x-axis at two different points.
Case 3: D < 0
If the discriminant is less than zero (b2 – 4ac < 0), a, b, and c are real, and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is Imaginary and not equal. Roots exist in conjugate pairs. The equation graph does not touch the x-axis.
Case 4: Perfect Square with D > 0
If D > 0 and Perfect Square, the roots of the quadratic equation are real, unequal, and rational.
Case 5: D > 0 and Not Perfect Square
If D > 0 and not perfect square, the roots of the quadratic equation are real, unequal, and irrational.
According to the Question:
The given quadratic equation:
2x²-4x-3 = 0
Here, a = 2, b = - 4 and c = -3
To Find: the nature of roots of the given quadratic equation.
∴ Discriminant, D = b²-4ac
= (-4)² - 4×2×(-3)
= 16 -8(-3)
= 16 + 24
=40
Since,
D = 40 > 0, the roots are real and unequal.
Hence, the nature of roots of the given quadratic equation is "real and unequal".
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Select all the true statements about this graph.
A. The graph is nonlinear
B. The function increases at the same rate
C. The rate decreases after x = 2
D. The graph is a function
E. The graph is increasing in two intervals
(Picture of graph included.)
Answer:
A. The graph is nonlinear.
D. The graph is a function
E. The graph is increasing in two intervals.
Step-by-step explanation:
We will review each answer choice to decide on our answer to this question.
✓ A. The graph is nonlinear.
Since the graph has a change in it's rate of increase, it's nonlinear.
✗ B. The function increases at the same rate.
As stated below, the rate increases after x = 2 so the function is not increasing at the same rate.
✗ C. The rate decreases after x = 2.
No, the rate increases after x = 2.
✓ D. The graph is a function.
Yes, there is only one output for every input, so this is a function.
✓ E. The graph is increasing in two intervals.
The graph is only increasing in two intervals. These intervals change at x = 2.
Which is the standard form of linear equation in two variables y 4?
The standard form of linear equation in two variables is Ax + By = C.
The standard form of linear equation in two variables is Ax + By = C, where A, B and C are constants and A and B are not both zero. This equation can be used to represent a line on a graph, which can be found by plotting any two points that satisfy the equation.
To calculate the equation of a line in standard form, first identify two points on the line. For example, point (x1, y1) and point (x2, y2). Then, calculate the slope of the line using the formula m = (y2 - y1) / (x2 - x1). The slope determines the constants A and B for the equation. A = m and B = -1. Finally, calculate the constant C by substituting one of the two points into the equation. C = Ax1 + By1.
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Tara picks out 4 paint colors (beige, blue, green, and gray) to paint 4 rooms in her house (living room, dining room, main bedroom, and kitchen). The probability that Tara first paints her bedroom green is .
The probability that Tara first paints her bedroom green is 1/16.
What is the probability that Tara first paints her bedroom green?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
In this case, Tara picks out 4 paint colors (beige, blue, green, and gray) to paint 4 rooms in her house (living room, dining room, main bedroom, and kitchen).
The probability of painting bedroom = 1/4
The probability of picking green = 1/4
Therefore, the probability that Tara first paints her bedroom green is:
P(bedroom) × P(green)
= 1/4 × 1/4
= 1/16
The probability is 1/16.
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How do you write 2x 3y 12 in slope intercept form?
The required equation in the slope-intercept form is y = 2/3x - 4.
What is slope intercept form?Y = MX + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form.
We can see that the slope of the line in our equation, y = 6x + 2, is 6.
So, we have the equation:
2x − 3y = 12
To represent the equation in the slope-intercept form:
First, remove 2x from both sides of the equation to move the independent variable (x) to the right side of the equation.
2x − 3y − 2x = 12 − 2x
− 3y = 12 − 2x
The dependent variable is the only component of the left side of the equation, as seen in the generic equation of a line in slope intercept form, whereas the independent variable and constant are both present on the right side of the equation.
The result of multiplying by 1 and dividing by 3 into both sides of the equation is:
-1 * -3y/3 = -1 * (12 - 2x)/3
y = 2/3x - 12/3
y = 2/3x - 4
Therefore, the required equation in the slope-intercept form is y = 2/3x - 4.
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The salaries of the employees at four companies are summarized below. Answer the questions about them
Company A: The range of salaries is $60,000 and the mean salary is $41,000.
Company B: The range of salaries is $53,000 and the mean salary is $39,000.
Company C: The range of salaries is $54,000 and the mean salary is $47,000.
Company D: The range of salaries is $58,000 and the mean salary is $38,000.
(a) Based on the information above, which company's salaries have the most variability?
a: Company A
b:Company B
c:Company C
d:Company D
(b) Based on the information
above, which company has the lowest salaries on average?
a:Company B
b:Company A
c:Company C
d:Company D
Part (a)
Company A has the most variability because it has the m greatest range.
Part (b)
Company B has the lowest salaries on average since they have the smallest mean salary.
The which raito is equivalent to 8/6?
Answer:
Hence, three equivalent ratios of 8: 6 are 16: 12, 24: 18, and 32: 24.
Step-by-step explanation:
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The general solution of the given non homogeneous
equation is
y(t)=c₁[tex]e^{-t}[/tex] +c₂[tex]e^{t}[/tex] - t
A non-homogeneous system of equations is a system in which the vector of constants on the right-hand side of the equal sign is non-zero.
Given:-General solution for the equation: [tex]y^{"} - y^{'} = t[/tex], [tex]y_{p} (t) = - t[/tex]
Explanation:-Consider the equation [tex]y^{"} - y^{'} = t[/tex] . The corresponding homogeneous equation has the associated auxiliary equation [tex]r^{2} -1 =0[/tex] which has [tex]r^{} =-1[/tex] and [tex]r^{} =1[/tex] as solutions.
The solution of an n-order differential equation depends on an algebraic equation of degree n called the characteristic equation (or auxiliary equation) in mathematics.
Hence the general solution for a homogeneous equation is
y(t) = [tex]-t[/tex]+[tex]c[/tex]₁[tex]e^{t}[/tex]+[tex]c[/tex]₂[tex]e^{-t}[/tex]
Combining the general solution [tex]y(t)=c[/tex]₁[tex]e^{t}+c[/tex]₂ [tex]e^{t}[/tex] with the particular solution of [tex]y_{p} (t) =-t[/tex] of [tex]y'-y"=t[/tex], we find that the general solution to[tex]y"-y'=t[/tex] is [tex]y(t)=c[/tex]₁[tex]e^{-t}+c[/tex]₂[tex]e^{t}[/tex]
The general solution of the given non homogeneous equation is
y(t)=c₁[tex]e^{-t}[/tex] +c₂[tex]e^{t}[/tex] - t
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What is square root of 1 called?
Answer:
1
Step-by-step explanation:
The square root of 1 is called 1.
In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 4 is 2, because 2 x 2 = 4. The square root of 9 is 3, because 3 x 3 = 9.
The square root of 1 is 1, because 1 x 1 = 1. Therefore, the square root of 1 is simply called 1.
The figure is made of a rectangle and a half of a circle find the perimeter of the figure to the nearest tenth . Use 3.14 for pi . Also Please show ur work Bc I have too !!
The perimeter of the figure as shown in the diagram is 60.84 m.
What is perimeter?Perimeter is the total distance around an object.
To calculate the perimeter of the figure, we use the formula below.
Formula:
P = 2L+W+Wπ/2.............. Equation 1Where:
P = Perimeter of the figureL = Length of the figureW = Width of the figureFrom the question,
Given:
L = 15 mW = 12 mπ = 3.14Substitute these values into equation 1
P = (15×2)+12+(12×3.14/2)P = 30+12+18.84P = 60.84 mHence, the perimeter of the figure is 60.84 m.
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What is the meaning of asymptote of a function?
An asymptote of a function is a line that the graph of the function gets closer and closer to, but never touches. It is an approaching line that has a fixed slope.
An asymptote of a function is a line that the graph of the function gets closer and closer to, but never touches. It is an approaching line that has a fixed slope. Asymptotes are used to determine the behavior of a function as it approaches infinity or negative infinity. They can be used to help visualize the behavior of the function in the large and small limits. Asymptotes can be either horizontal or vertical. A horizontal asymptote is a line that the graph of the function approaches as it approaches positive or negative infinity, and a vertical asymptote is a line that the graph of the function approaches as it approaches either the positive or negative x-axis. Asymptotes can also be used to describe the behavior of a function near a local minimum or maximum. Asymptotes can be found by looking at the degree and leading coefficient of a polynomial, or by analyzing the behavior of the function at different points.
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LO. Gabe has 60 coins consisting of quarters and dimes.
The combined value of the coins is $9.45.
How many
quarters and dimes does Gabe have?
Why is it called an asymptote?
An asymptote function is called such because it is a line that a curve approaches but never touches, or "asymptotically" approaches.
An asymptote is a line that a curve approaches but never actually touches. It is called an asymptote because the word comes from the Greek asymptōtos, which means "not falling together." Asymptotes are used in mathematics to describe curves that approach a particular line without ever intersecting it. For example, in a graph of a function, an asymptote is a line that the graph of the function approaches, but never intersects with, as it approaches infinity. Asymptotes are also used to describe straight lines in a plane that approach each other at a certain angle, but never meet. In both cases, the idea is that the line or curve approaches the asymptote, but never actually touches it, thus the name asymptaote.
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What type of function is f/x )= x?
The domain and scope of the identity function are the same. Equation for the identity function is f(x) = x, or y = x.
What is function?An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.
identity function are the same.
Equation for the identity function is
f(x) = x, or y = x.
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1) Which number is irrational? A) √144 B) √60 C) 2/5 D) 5/6
Answer:
B
Step-by-step explanation:
Answer: B, √60 .
Step-by-step explanation: Irrational numbers are numbers that can not be written in the form of a/b. To further explain, this includes any decimals that go on forever and are non-repeating, such as pi 3.14159... Numbers that have repeating numbers like 5.5555555 are rational, so don't get confused between the two! The square root of 60 is 7.74596669 making it the only irrational number here.
5/3X + 1/3X = 13 1/3+8/3X
The value of x in the equation 5/3x + 1/3x = 13⅓ + 8/3x is calculated as: x = -20.
How to Solve an Equation?To solve an equation is to find the value of the variable by isolating it in such a way that it is moved to one side of the equation.
Given the equation, 5/3x + 1/3x = 13⅓ + 8/3x, to solve this equation, we need to find the value of x by isolating the variable x to one side.
Follow the steps below:
5/3x + 1/3x = 40/3 + 8/3x
2x = 40/3 + 8/3x
Substract both sides by 8/3x:
2x - 8/3x = 40/3 + 8/3x - 8/3x
-2/3x = 40/3
Multiply both sides by -3/2:
-2/3x × -3/2 = 40/3 × -3/2
x = -120/6
x = -20
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What is the slope of the function 4x 2y =- 10?
The slope of the given function 4x + 2y = -10 is equal to -2.
As given in the question,
Given function is equal to 4x + 2y = -10
Standard form of the equation in slope intercept form is given by :
y = mx + c
'm' is the slope of the function
'c' is the value of y-intercept.
Now simplify the given function in standard form we have,
4x + 2y = -10
⇒2y = -4x -10
⇒ y = (-4x -10 ) / 2
⇒ y = -2x - 5
Compare with the standard form we get,
Slope of the function m = -2.
Therefore, the slope of the given function 4x + 2y = -10 is given by m = -2.
The given question is incomplete , the complete question is:
What is the slope of the function 4x + 2y =- 10?
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What kind of line is Y =- 3?
What kind of line is Y =- 3?
Answer:
This is a horizontal line occurring at y = -3 meaning there is no slope.
a suburban specialty restaurant has developed a single drive-thru window. customers order, pay, and pick up their food at the same window. arrivals follow a poisson distribution while service times follow an exponential distribution. if the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, what is the average number of customers waiting in line behind the person being served? a. 3.00 b. 0.5 c. 2.25 d. 30.0 e. 0.75
Using the Poisson distribution and the exponential distribution, on average, there are (C) 2.25 consumers in line behind the person serving.
What is exponential distribution?The Poisson point process, or a process in which events occur continuously and independently at a constant average rate, uses an exponential distribution to represent the probability distribution of the time between occurrences.
Statistics and probability theory both make use of this distribution.
So, we know that:
6 arrivals on average are made per hour (Poisson distribution).
It provides two services every fifteen minutes (exponential distribution).
Waiting line behind the person being served:
(15 / 6 * 2) + 1
(15 / 12) + 1
1.25 + 1
2.25
Therefore, using the Poisson distribution and the exponential distribution, on average, there are (C) 2.25 consumers in line behind the person serving.
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There are 52800 fans at a football match between Rovers and City. 37% of the fans support Rovers. How many fans at the match support City?
Total Fans = 52800
Total fans supporting Rovers = 37%
Answer: City fans = 33,264 fans
because City fans percentage = 100% - 37% = 63%
Multiplier = 0.63 (63/100)
So City fans = 0.63 x 52800 = 33,264
Hope this helps!
Answer:
Step-by-step explanation:
To find out how many fans at the match support City, we first need to find out how many fans support Rovers. We can do this by multiplying the total number of fans by the percentage of fans who support Rovers:
Total fans supporting Rovers = 52800 fans * 37% = 19296 fans
Since the total number of fans at the match is 52800, and 19296 of those fans support Rovers, then the number of fans who support City is:
Total fans supporting City = 52800 fans - 19296 fans = 33504 fans
Therefore, there are 33504 fans at the match who support City.
How do you find when a function is increasing at the greatest rate?
The slope of the function may be found by differentiating it. Finding the derivative's maxima will show where the function is rising at the fastest pace as slope is defined as the rate of change.
What is Maxima and Minima ?The slope of the function may be found by differentiating it. Finding the derivative's maxima will show where the function is rising at the fastest pace as slope is defined as the rate of change.
The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.
The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.
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How do you know if the graph has a hole or vertical asymptote?
A hole in a graph appears as a break in the graph line, while a vertical asymptote appears as a line segment that the graph approaches but never crosses.
A hole in a graph appears as a break in the graph line; it's the point where the graph does not exist. Typically, the x-value of this point is the x-coordinate of the hole. To find out if there is a hole, you need to see if the graph is continuous and check to see if there is a break in the graph line.A vertical asymptote appears as a line segment that the graph approaches but never crosses. This occurs when the function value approaches positive or negative infinity. To find out if there is a vertical asymptote, you need to look at the function and see if it is undefined at any particular x-value. If it is, then there is a vertical asymptote.
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-3(-4x + 5) = [?]x -[ ]
rewrite using the distributive property
Answer:
12x -15
Step-by-step explanation:
-3(-4x + 5)
Distribute the -3 to each term inside the parentheses
-3 * -4x + -3 *5
12x -15
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Which statement describes how to determine if a relation given in a table is a function?
If none of the output values are repeated, the relation is a function.
If none of the input values are repeated, the relation is a function.
If any of the input values are equal to the output values, the relation is a function.
If all the output values are paired with the same input value, the relation is a function.
Answer:
“If none of the input values are repeated, the relation is a function” because one input must have one output.
How do you graph an inequality example?
The graph of an inequality is shown below -
What is an inequality equation?The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.
It's a line with a shaded side on one side to show which x-y pairings are the inequality's solutions.
Example -
Let us take a equation, 4x + 8y ≤ -24
Now, solve the above equation in the form of slope-intercept.
4x + 8y ≤ -24
or, 8y ≤ - 4x - 24
or, y ≤ -(1/2)x - 3
Now, the graph becomes according to the slope-intercept form is:
Here we noticed that,
This side of the inequality is shaded below (instead of above) because y is lower than (or equal to) the other side.
Because working with a "or equal to" inequality, draw a solid line rather than a dashed one. Points on the solid line denote locations where the inequality has been solved.
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The number of y of Salmonella cells on an egg after t minutes is y=a(4.7)^t/45 , where a is the initial number of cells. By what percent does the number of Salmonella cells increase each minute?
3.5% percent does the number of Salmonella cells increase each minutes when y = a(4.7[tex])^{t/45}[/tex].
Given that,
The number of y of Salmonella cells on an egg after t minutes is
y = a(4.7[tex])^{t/45}[/tex]
Here,
y is the number of salmonella cells.
a is the initial number of cells.
t is the time in minutes.
We have to find what percent does the number of Salmonella cells increase each minutes.
We know that,
Take the original function,
y = a(4.7[tex])^{t/45}[/tex]
Take the power of proportionality
y = [a(4.7[tex])^{1/45}]^{t}[/tex]
Evaluating the power
y = [a(4.7[tex])^{1/45}]^{t}[/tex]
y = a(1.035[tex])^{t}[/tex]
y = a(1-0.035[tex])^{t}[/tex]
Therefore, 3.5% percent does the number of Salmonella cells increase each minutes when y = a(4.7[tex])^{t/45}[/tex].
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The following table shows the values of y for different values of x:
x
y
0
0
1
0
2
4
Which statement best explains whether the table represents a linear function or a nonlinear function?
Group of answer choices
It represents a linear function because its points are not on a straight line.
It represents a nonlinear function because its points are not on a straight line.
It represents a linear function because its points are on a straight line.
It represents a nonlinear function because its points are on a straight line.
Option B. It represents a nonlinear function because its points are not on a straight line.
What is linear and non-linear functions?
When plotted on a graph, a linear function produces a straight line. Therefore, any non-linear functions are those that are functions. The quickest way to tell if a function is linear or non-linear is probably by graphing it, but we can also tell if a function is linear by looking at its input/output table or equation.
If A(0, 0), B(1, 0) and C(2, 4).
We know that,
If point A,B and C are on a straight line then the slope of AB must be equal to the slope of AC
The formula to calculate the slope between two points is equal to
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Find the slope AB
A(0, 0) and B(1, 0)
[tex]m = \frac{0-0}{1-0} = 0[/tex]
Find the slope AC
A(0, 0) and C(2, 4)
[tex]m = \frac{2-0}{4-0} = \frac{1}{2}[/tex]
Slope of AB ≠ Slope of AC
Points A, B and C are not on a straight line.
Hence, it represents a nonlinear function because its points are not on a straight line.
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a 30 gram fishing weight is dropped from a fishing pier. how long does it take for the weight to hit the water 6.0 meters below?
Answer:
1.1 s
Step-by-step explanation:
The mass ( 30 g ) is not needed for this
d = 1/2 at^2
6 = 1/2 ( 9.8)(t^2
t= 1.1 s
14x-20y=-13
write in slope intercept form
In slope intercept form, Equation 14x-20y=-13 can be written as 13 + 4y/20 = y.
Define slope intercept form.The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.
Given,
Equation
14x-20y=-13
In slope intercept form
13 + 4x = 20y
13 + 4y/20 = y
In slope intercept form, Equation 14x-20y=-13 can be written as 13 + 4y/20 = y.
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i have no clue what i’m supposed to do
A baseball player hit 63 home runs in a season. Of the 63 home runs, 18 went to right field, 25 went to right center field, 9 went to center field, 9 went to left center field, and 2 went to left field. (a) What is the probability that a randomly selected home run was hit to right field? (b) What is the probability that a randomly selected home run was hit to left field? (c) Was it unusual for this player to hit a home run to left field? Explain.
a. The probability that a randomly selected home run was hit to right field is 0.286.
b. The probability that a randomly selected home run was hit to left field is 0.031.
c. Yes it was unusual for this player to hit a home run to left field.
How to calculate the probability?From the information, the baseball player hit 63 home runs in a season. Of the 63 home runs, 18 went to right field, 25 went to right center field, 9 went to center field, 9 went to left center field, and 2 went to left field.
The probability that a randomly selected home run was hit to right field is:
= 18 / 63
= 0.286.
The probability that a randomly selected home run was hit to left field is:
= 2 / 63
= 0.031.
It was unusual for this player to hit a home run to left field as the chance is 3%.
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