Answer:
b)
Step-by-step explanation:
If x - 2 is a factor polynomial f(x), then the polynomial can be expressed as f(x) = (x - 2) g(x), where g(x) is another polynomial.
Using this information, we can check each statement to see which one does NOT have to be true:
A) f(2) = 0:
If x - 2 is a factor of f(x), then plugging in x = 2 gives f(2) = (2 - 2) g(2) = 0. This statement has to be true.
B) f(-2) = 0:
If x - 2 is a factor of f(x), then plugging in x = -2 gives f(-2) = (-2 - 2) g(-2) = -4 g(-2). This statement does NOT have to be true. For example, if g(-2) = 1/(-4), then f(-2) would not equal 0.
C) 2 is a root of f(x):
If x - 2 is a factor of f(x), then 2 is a root of f(x), meaning f(2) = 0. This statement has to be true.
D) 2 is a zero of f(x):
The term "zero" can be interpreted in different ways, but if it means the same as a root or a solution, then this statement is the same as statement C and has to be true.
Therefore, the statement that does NOT have to be true is B) f(-2) = 0.
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red. Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow. Determine the theoretical probability of the spinner not landing on red, P. 0.125 0.250 0.675 0.875
The theoretical probability of the spinner not landing on red is 0.875.
How to determine the theoretical probability of the spinner not landing on redThe total number of sections on the spinner is 8, out of which only one section is red. Therefore, the probability of the spinner landing on red is:
P(Red) = 1/8
The probability of the spinner not landing on red would be the probability of landing on any other section, which is:
P(Not Red) = 1 - P(Red) = 1 - 1/8 = 7/8
Therefore, the theoretical probability of the spinner not landing on red is 7/8 or 0.875 in decimal form.
So, the correct answer is: 0.875.
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Answer:
D
Step-by-step explanation:
Subtract the sum of -52 and - 638 from the sum of - 29 and 303 the value is
The solution of the expression is 964.
To start solving this problem, let's find the sum of -29 and 303. The sum of two numbers is the result when you add them together. So,
-29 + 303 = 274
The sum of -29 and 303 is 274.
Now, let's find the sum of -52 and -638. To add two negative numbers, you just add their absolute values and put a negative sign in front of the result. So,
-52 + (-638) = -690
The sum of -52 and -638 is -690.
Finally, the problem asks us to subtract the sum of -52 and -638 from the sum of -29 and 303. To subtract one sum from another, we just subtract the second sum from the first. So,
( -29 + 303 ) - ( -52 + -638 )
We can simplify the expression by rearranging the terms:
274 - (-690)
When we subtract a negative number, it's the same as adding its absolute value. So,
274 + 690 = 964
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Which number is closest to zero on a number line? A. ¯ 3/5 B. ¯ 2/5 C. 1/5 D. 4/5
Answer:
Step-by-step explanation:
To find which number is closest to zero, we must find the number with the lowest absolute value. Luckily to our advantage, all of these numbers have the same denominators, so the number with the lowest numerator is closest to zero.
Out of these numbers, 1/5 is the closest to zero.
What is the Y-intercept of boundary line of y < c + 5 ?
Answer: The given inequality is:
y < c + 5
We can rewrite this inequality in slope-intercept form, y = mx + b, by isolating y:
y < c + 5
y - 5 < c
c > y - 5
In slope-intercept form, this is:
y = 1x + (-5)
The y-intercept of this boundary line is -5.
Step-by-step explanation:
the applet is selecting random samples from the town's population this year. what do we assume is true about this population of babies?
When the applet selects random samples from the town's population of babies, we assume that the population is large enough and diverse enough to accurately represent the characteristics and traits of the entire population.
We assume that the selection of the random samples is unbiased and that every member of the population has an equal chance of being selected for the sample.
Based on your question, we are discussing random samples taken from a town's population of babies this year. When selecting random samples from this population, we assume the following:
1. The population of babies is well-defined and includes all babies born in the town within the specified year.
2. The random samples are representative of the entire population, meaning that each baby has an equal chance of being selected in the sample.
3. The samples are independent, meaning that the selection of one baby does not influence the selection of another.
These assumptions ensure that the results obtained from the random samples can be generalized to the entire population of babies in the town for this year.
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By assuming these conditions are met, we can perform statistical analyses on the random samples and make valid inferences about the entire population of babies in the town.
When an applet is selecting random samples from a town's population of babies this year, we typically assume the following about the population:
Independence:
Each baby selected in the sample is independent of the others, meaning that the outcome of one selection does not affect the outcome of another selection.
Randomness:
The applet chooses babies from the population in a random manner, ensuring that every baby has an equal chance of being selected.
Representativeness:
The random samples selected are representative of the entire population, meaning that the samples accurately reflect the characteristics of the town's population of babies as a whole.
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an imaginary circle that goes through both retinae and the fixation point is known as
The Vieth-Müller Circle is an imaginary circle that passes between both retinae and the fixation point.
The Vieth-Müller Circle is an ophthalmology concept that depicts an imaginary circle that passes across the foveas (the primary points of the retinae that are responsible for acute, detailed vision) and the fixation point (the point at which the eyes are directed).
The Vieth-Müller Circle is significant because it helps to explain the phenomenon of binocular vision, which is the ability to perceive depth and three-dimensional space using both eyes together. The circle aids in the definition of the equivalent locations on the two retinae, which are sites that receive visual field information and are critical in combining the images from the two eyes into a single, three-dimensional perception.
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The imaginary circle that passes through both retinae and the fixation point is called the horopter. The horopter is important in visual perception as it represents the set of points in space that stimulate corresponding points on each retina, which is necessary for binocular vision and depth perception.
The Horopter is an imaginary circle that passes through both retinae and the fixation point. In this context:
1. "Imaginary" refers to the fact that the Horopter is a theoretical concept rather than a physical object.
2. "Retinae" are the light-sensitive layers at the back of both eyes, which play a crucial role in processing visual information.
3. "Fixation" is the point where both eyes are focused on a single object in the visual field.
In brief, the Horopter represents a collection of points in the 3D space that are perceived as having the same depth or distance as the fixation point. It helps in understanding binocular vision and depth perception, as points on the Horopter contribute to forming a single, fused image from both eyes.
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sally works in hr at a company with 20 full-time employees in one location. what employee census data should sally gather to prepare for a benefits bid? race, gender, and ethnicityage, marital status, and number of childrendisability and veteran statustenure and education levels
To prepare for a benefits bid, Sally should census gather data on the age, marital status, and number of children of the 20 full-time employees.
This information will help Sally determine what types of benefits would be most appealing to the employees and what types of benefits might be necessary to attract and retain talent.
Additionally, Sally should gather data on the tenure and education levels of the employees to help her understand what types of benefits might be necessary to incentivize employees to stay with the company long-term and to attract highly educated candidates.
Finally, Sally should consider gathering data on disability and veteran status to ensure that the company is providing adequate support for those employees who may require additional assistance.
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Factor.
z squared+18z–19
(z - or + ?)(z- or + ?)
Answer:
(z - 1) (z + 19)
Step-by-step explanation:
z² + 18z - 19
Consider the form x² + bx + c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is −19 and whose sum is 18.
-1, 19
Write the factored form using these integers.
(z - 1) (z + 19)
What is the square √ 64?
Step-by-step explanation:
[tex]8 ^{2} [/tex]
is your answer please make me brainalist and keep smiling
8*8=64 then
8 is your answer
Answer: Square root of 64 is 8
Find the area of the shaded region
The area of the shaded region which is a semi-circle is 157ft.
What is semi-circle?
In geometry, a semicircle can be defined as a half of a circle formed by cutting the circle into two halves. It is formed when a line or cut passes through the center and touches the two end positions of the circle and the line is called the diameter of the circle.
The shaded region is a semi- circle.
The radius is 10 ft.
The formula for the area of semi- circle is π×r²/2 where π= 3.14 and r is the radius.
So, the area of the semi- circle is {3.14× (10)²}/ 2
= 157 ft.
Hence, the area of the shaded region which is a semi-circle is 157ft.
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Mary needs $9000 in 9 years. What amount can she deposit in a sinking fund at the end of each quarter at 4% interest compounded quarterly so she will have her $9000?
Please serious answers only
Mary needs to deposit $282.44 at the end of each quarter into a sinking fund that earns 4% interest compounded quarterly in order to have $9,000 in 9 years.
what is deposit ?
In the context of finance, a "deposit" refers to the act of placing money or funds into a bank account, investment account, or other financial account. A deposit can also refer to the initial payment made to secure or initiate a purchase
In the given question,
To calculate the sinking fund payment that Mary needs to make at the end of each quarter, we can use the formula for the future value of an annuity:
FV = PMT x [(1 + r/n)ⁿᵇ - 1]/(r/n)
Where:
FV = future value (the amount Mary needs to accumulate, which is $9,000 in this case)
PMT = payment per period (what Mary needs to find)
r = annual interest rate (4% in this case)
n = number of compounding periods per year (4, since interest is compounded quarterly)
t = number of years (9 in this case)
Substituting these values into the formula, we get:
$9,000 = PMT x [(1 + 0.04/4)³⁶ - 1]/(0.04/4)
Simplifying and solving for PMT, we get:
PMT = $9,000 / [(1.01³⁶ - 1)/0.01]
PMT = $9,000 / 31.8422
PMT = $282.44 (rounded to the nearest cent)
Therefore, Mary needs to deposit $282.44 at the end of each quarter into a sinking fund that earns 4% interest compounded quarterly in order to have $9,000 in 9 years.
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Please explain how to do this step by step
The correct answer to the fraction expression is: 2²/₂₁
How to solve Fraction Problems?There are different types of fractions such as:
Proper fractions
Improper Fractions
Mixed Fractions
We are given the fraction expression:
²/₃ + 3⁴/₇ ÷ 2¹/₂
Let us convert all to proper or improper fraction to get:
²/₃ + ²⁵/₇ ÷ ⁵/₂
Using PEMDAS order of operations, we will carry out division first to get:
²/₃ + (²⁵/₇ ÷ ⁵/₂)
When dividing fractions, the divisor changes numerator and denominaor and the sign becomes multiplication:
= ²/₃ + (²⁵/₇ * ²/₅)
= ²/₃ + ¹⁰/₇
Using L.C.M, we have:
= (28 + 60)/42
= 88/42 = 44/21
= 2²/₂₁
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You are going grocery shopping and want to spend less than $90. You have already bought $40 worth of
food and are wondering how many cartons of eggs you can get if they are each $4.49 each
Answer:
Total=$90
Used=$40
Left=($90-$40)=$50
1 carton = $4.49
$50÷$4.49
=11.135857 ≈ $11 10¢
survey of small businesses with websites found that the average amount spent on a site was $11,000 per year with a standard deviation of $3,000. given a sample of 40 businesses, what is the margin of error if you are to assume a 95% confidence level? (round your answer to two decimal places.)
The margin of error for the 95% confidence level is approximately $873.15.
To calculate the error bars for the 95% confidence level, we need to find the critical value of the z-score from the standard normal distribution table.
Accepting a 95% certainty level, the importance level (α) is 0.05, which implies the certainty level is 1-α = 0.95.
On the off chance that we see the z-score at the 95% certainty level on the standard typical conveyance table, we get an esteem of 1.96.
Then you can use the formula for Tolerance (E).
error bar (E) = z * (standard deviation / sqrt(n))
where:
z = critical value in the standard normal distribution table
standard deviation = $3,000
n=40
Substitute the obtained value.
Error Bar (E) = 1.96 * ($3,000 / sqrt(40))
≈ $873.15
Therefore, the margin of error for the 95% confidence level is approximately $873.15.
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0.000309 in scientific
Answer:
0.000309 in scientific notation is 3.09 x 10^(-4)
Answer:
0.309x10 to the -4 power
Step-by-step explanation:
just move the decimal place back till its a whole number and do that number to the power of ten if that makes sense
PLS give brainlist mean the world
have a good day
How does the structure of each poem help to convey different feelings
The fraction of the total vote he should expect to get is 23/75.
What are fractions?A fraction is a mathematical unit used to represent a portion of a whole or a ratio of two integers. They are shown as the top number, or numerator, and the bottom number, or denominator, separated by a line. The denominator is the total number of pieces that make up the whole, whereas the numerator is the number of shares or parts.
For instance, you may write 3/8 for the portion of pizza you consumed if there were 8 pieces and you only ate 3. This indicates that you consumed three of the pizza's eight equally sized portions.
From the given table we can determine the total number of votes are:
13 + 9 + 10 + 8 + 10 + 14 + 5 + 6 = 75.
Now, Jamal received 13 + 10 = 23 votes.
Thus, the fraction of the total vote he should expect to get is 23/75.
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Steven read that the actual distance between Memphis and Chicago is about 525 miles. On a map, the distance between the two cities is about 10 inches. Which is most likely the scale used to make the map?
Answer:About 1,012 Inches
Step-by-step explanation:
your laundry basket contains 4 plain socks: a red one, a blue one, a yellow one and a green one. the basket also contains 4 striped socks: a red striped one, a blue striped one, a yellow stripped one and a green stripped one. if you want to wear a plain sock on your left foot and a stripped sock on your right foot, how many options do you have?
The total number of probability options will be 8 options.
1. Red plain and Red striped.
2. Blue plain and Blue striped.
3. Yellow plain and Yellow striped.
4. Green plain and Green striped.
5. Red plain and Blue striped.
6. Blue plain and Yellow striped.
7. Yellow plain and Green striped.
8. Green plain and Red striped.
There are 8 socks in the basket, and you can choose 1 plain sock and 1 striped sock.
This means that there are 8 possible combinations of socks you could choose.
Count the number of socks in the basket. There are 8 total socks (4 plain and 4 striped).
The number of options: There are 8 possible combinations of socks you could choose, so you have 8 options for wearing a plain sock on your left foot and a striped sock on your right foot.
Therefore,
You have 8 options for wearing a plain sock on your left foot and a striped sock on your right foot.
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The following data set represents the population growth or decay in the past 5 years.
Year Population
2001 6,169,683,257
2002 6,248,055,839
2003 6,325,991,838
2004 6,403,480,654
2005 6,480,500,311
Determine which value is the independent value and the dependant value. Create a set of ordered pairs for the
relation. Graph the relation on a scatter plot, and make sure to label each axis.
In this data set, the year is the independent variable, and the population is the dependent variable. The population depends on the year in which it is measured.
How to create the ordered pairsThe set of ordered pairs for the relation between year and population is:
{(2001, 6,169,683,257), (2002, 6,248,055,839), (2003, 6,325,991,838), (2004, 6,403,480,654), (2005, 6,480,500,311)}
To graph this relation on a scatter plot, we can plot the year on the x-axis and the population on the y-axis. We can label the x-axis as "Year" and the y-axis as "Population (in billions)".
Here is the scatter plot of the relation:
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A peice of art is in the shape of a rectangular pyramid like a the figure shown below.
how much glass is needed to cover the entire pyramid?
The closest possible choice is 198.06 ft².
Option C is correct.
How do we calculate?The area of the base is gotten as :
length x width = 8 ft x 7 ft = 56 ft².
The length of the pyramid's slant height (s) must be determined in order to determine the area of each triangle face.
We may determine that s = (h2 + (w/2)2) = (62 + (7/2)2) = (36 + 24.5) = 60.5 7.78 ft using the Pythagorean theorem.
The area of each triangular face is
(1/2) x base x height = (1/2) x 8 ft x 7.78 ft
= 31.12 ft².
Hence, the total surface area of the pyramid :
56 ft² + 4 x 31.12 ft² = 192.48 ft².
In conclusion, the closest possible choice is 198.06 ft².
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PLEASE HELP DUE TODAY
Answer:
y=-1/12x+61/12
Step-by-step explanation:
y=-1/12x+61/12
Solve for x. -7.6 -1.2 + X 0.5
A colored pencil is a wood hexagonal prism with a column of colored lead running through its center. The typical length of the usable lead is 19 centimeters, and the lead core has a diameter of 3 millimeters. A cross section of the pencil has an area of 89.25 square millimeters. What percentage of a colored pencil is wood?
Answer:
i guess 97 %
Step-by-step explanation: see fist of all
most colour pencils ARE made of wood so yeah sorry dont know im still in 6th
4 times the sum of a number and 4 is 8 less than 40
The unknown number is -8.
Define fractionA fraction is an expression representing a subset of a whole. The numerator and the denominator, which are separated by a horizontal line, are expressed as a ratio. The denominator is the total number of equally sized components that make up the whole, whereas the numerator is the number of parts that are being taken into account.
Call the unidentified number "x" for now. The following equation may then be created from the provided sentence:
3(x + 4) = (1/2)x - 8
Now, we can solve for x by simplifying and rearranging the equation:
3x + 12 = (1/2)x - 8
dividing both sides by two to get rid of the fraction
6x + 24 = x - 16
Subtracting x from both sides:
5x + 24 = -16
Subtracting 24 from both sides:
5x = -40
Dividing both sides by 5:
x = -8
Therefore, the unknown number is -8.
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the complete question is:
Three times the sum of a number and 4 is 8 less than one-half the number. What is the number?
the profit p (in dollars) generated by selling x units of a certain commodity is given by the function p ( x ) = - 1500 + 12 x - 0.004 x ^ 2 What is the maximum profit, and how many units must be sold to generate it?
The profit (p) is $7500 generated by selling 1500 units of a certain commodity is given by the function p ( x ) = - 1500 + 12 x - 0.004 x²
To maximize our profit, we must locate the vertex of the parabola represented by this function. The x-value of the vertex indicates the number of units that must be sold to maximize profit.
We may use the formula for the x-coordinate of a parabola's vertex:
x = -b/2a
where a and b represent the coefficients of the quadratic function ax² + bx + c. In this situation, a = -0.004 and b = 12, resulting in:
x = -12 / 2(-0.004) = 1500
This indicates that when 1,500 units are sold, the profit is maximized.
To calculate the greatest profit, enter x = 1500 into the profit function:
P(1500) = -1500 + 12(1500) - 0.004(1500)^2
P(1500) = -1500 + 18000 - 9000
P(1500) = $7500
Therefore, the maximum possible profit is $7,500 and it is generated when 1,500 units are sold.
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To achieve this maximum profit, exactly 1500 units must be sold.
To find the maximum profit and the number of units needed to generate it, we can use the given profit function p(x) = -1500 + 12x - 0.004x^2. We need to find the vertex of the parabola represented by this quadratic function, as the vertex will give us the maximum profit and the corresponding number of units.
Step 1: Identify the coefficients a, b, and c in the quadratic function.
In p(x) = -1500 + 12x - 0.004x^2, the coefficients are:
a = -0.004
b = 12
c = -1500
Step 2: Find the x-coordinate of the vertex using the formula x = -b / (2a).
x = -12 / (2 * -0.004) = -12 / -0.008 = 1500
Step 3: Find the maximum profit by substituting the x-coordinate into the profit function p(x).
p(1500) = -1500 + 12 * 1500 - 0.004 * 1500^2
p(1500) = -1500 + 18000 - 0.004 * 2250000
p(1500) = -1500 + 18000 - 9000
p(1500) = 7500
So, the maximum profit is $7,500, and 1,500 units must be sold to generate it.
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Nadia is on a 3-ft ladder and sling shots a rubber band toward her friend. The
rubber band, f(x), can be represented by f(x) = -x² + 4x + 3 where x represents the horizontal distance traveled by the rubber band in feet. Write and solve an equation to find the horizontal distance traveled by the rubber band if its height is 0.75 feet.
The horizontal distance traveled by the rubber band is 4.5 feet
How to write and solve an equation to find the horizontal distance traveled by the rubber band?To write and solve an equation to find the horizontal distance traveled by the rubber band if its height is 0.75 feet, substitute f(x) = 0.75 feet into the equation representing the rubber band and solve for x. That is:
f(x) = -x² + 4x + 3
0.75 = -x² + 4x + 3
x² - 4x - 3 + 0.75 = 0
x² - 4x - 2.25 = 0
(x - 9/2)(x + 1/2) = 0 (factorize)
x = 9/2 or x = -1/2
x = 4.5 or x = -0.5
Since distance cannot be negative.
Thus, x = 4.5 feet
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Phil is baking a pie with cranberries and apples. Apples cost $0.60/cup and cranberries cost $0.40/cup. Phil wants to spend no more than $4.20 on the fruit for his pie.
Question
What is an inequality that represents the combinations he can use?
A rug is 1/2 yard by 2 5/6 yards.
Keith solves 1/2 times 2 5/6 to find the area of the rug in square yards.
Enter numbers to complete Keith's calculation for the area of the rug
The area of the rugs in square yards with given dimensions 1/2 yard by 2 5/6 yards is equal to 1 5 /12 square yards.
Dimensions of the rug are,
1/2 yard by 2 5/6 yards
Area of the rug in square yards solved by Keith is equal to
= 1/2 times 2 5/6
= ( 1/ 2 ) × ( 2 5/6 )
Convert mixed fraction into proper fraction we get,
2 5/6 = ( 6 × 2 + 5 ) / 6
⇒ 2 5/6 = 17 / 6
⇒ Area of the rug in square yards solved by Keith = ( 1 / 2 ) × ( 17 / 6 )
⇒ Area of the rug in square yards solved by Keith = ( 17 / 12 )
⇒ Area of the rug in square yards solved by Keith = 1 5 /12 square yards.
Therefore, the area of the rugs is equal to 1 5 /12 square yards.
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simply answer
f(-6) = ?
The output value of f(-6) in the given function f(x) = 2x² + 5x - x/3 is 44.
What is the output value of f(-6) in the given function?
A function is simply a relationship that maps one input to one output.
Given the function in the question;
f(x) = 2x² + 5x - x/3
f( -6 ) = ?
To find f(-6), we need to substitute -6 for x in the function f(x) and simplify:
f(x) = 2x² + 5x - x/3
Plug in f = -6
[Replace x with -6]
f(-6) = 2(-6)² + 5(-6) - (-6)/3
Simplify using order of operations
f(-6) = 2(36) - 30 + 2
f(-6) = 72 - 30 + 2
f(-6) = 72 - 28
f(-6) = 44
Therefore, the output value of f(-6) is 44.
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Given this snippet of code, what is the value of x after executing the last statement? int x = 10, *y; y = &x; y = y + 1; *y = 100;
The value of x after executing the last statement is still 10.
After executing the last statement, the value of x is still 10. The snippet of code declares an integer variable x and a pointer variable y that points to the address of x. Then, y is incremented by 1 (which means it now points to the next memory location after x). Finally, the value 100 is assigned to the memory location pointed to by y, which is actually beyond the memory allocated for variable x. This can lead to unexpected behavior, but since the value of x is never modified directly, its value remains unchanged at 10.
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