The rate of petrol in this case is R9 per liter.
What is rate?
In mathematics, rate is a measure of how one quantity changes in relation to another quantity. It is often expressed as a ratio or fraction, where the numerator represents the amount of change in the first quantity and the denominator represents the amount of change in the second quantity.
The rate of petrol can be expressed as the cost per liter. To find the cost per liter of petrol in this case, we can divide the total cost by the total amount of petrol:
Cost per liter = Total cost / Total amount
For the given scenario, we have 20 litres of petrol for R180. So the rate can be calculated as:
Rate = Total cost / Total amount = R180 / 20 litres
Simplifying the expression, we get:
Rate = R9 per litre
Therefore, the rate of petrol in this case is R9 per liter.
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Arabella wants to buy 42 dresses.
Each dress costs £8.70.
Estimate the cost of Arabella's 42 dresses
Answer:
378 Euros
Step-by-step explanation:
A good way to estimate is to round to the nearest whole number or 10th and then multiply:
8.70 --> 9.00 (since 7 > 5 you round up to the nearest whole number, in this case 9)
then you multiply. A good way to do this in your head is doing:
split 42 into 2 numbers:
40, 2
then multiply by nine:
9 * 4 = 36 (9 * 40 = 360) added a zero since we multiplied by 40, its just easier to multiply by smaller numbers
9 * 2 = 18
then add the two numbers together:
360 + 18 = 378 Euros
The actual answer with a calculator is 365.4 Euros, so for an estimation its fairly close.
Another way you could solve it is to just round 8.70 --> 10 (rounding to the nearest 10th)
then:
10 * 42 = 420 (nice)
I don't recommend it since its way too off from the original value, but could be good for quick estimations.
hope this helped you :)
what is the greatest two-digit prime number with the property that the product of its digits is also a prime number?
The greatest two-digit prime number with the property that the product of its digits is also a prime number is 37, since 3 x 7 = 21.
The greatest two-digit prime number with the property that the product of its digits is also a prime number is 37, since 3 x 7 = 21. Prime numbers are those numbers greater than 1 that are divisible only by 1 and itself. Two-digit prime numbers are those number between 10 and 99. The prime numbers between 10 and 99 are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. The product of the digits of 37 is 3 x 7 = 21, which is also a prime number. Therefore, the greatest two-digit prime number with the property that the product of its digits is also a prime number is 37.
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Light travels at a speed of 3 x 10 8 metres per second
According to the universe in which light only moves at 3x10^8 meters/sec, it would take 3.333 x 10^-6 seconds to go 1 meter.
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
According to the universe in which light only moves at 3x10^8 meters/sec, it would take 3.333 x 10^-6 seconds to go 1 meter.
Given that light travels 3x10^8 m/s. So there . . .
The speed of light is in units of meters/sec.
If it is 3x10^8 meters/sec, we can also write the inverse:
1 sec/3x10^8 meters
Do the division to find seconds per 1 meter:
3.333 x 10^-9 seconds.
For Milky Way inhabitants,
It only requires 3.33 x 10^-9 second.
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The complete question is;
Light travels about 3 x 10^8 metres per second. Find the time it takes to travel 1 metre.
Point A(-3, 5) is first reflected over the line y =x, then reflected over the line with equation y = -4. What are the coordinates of the image of A after the two reflections?
The two coordinate values are simply swapped in the reflection over the line y=x: A'' = (4, 1) (4, 1)
What are the positions of A's reflections after the two?The x-coordinate and y-coordinate of a point change positions when it is reflected across the line y = x.
The x- and y-coordinates shift positions and are negated when a point is mirrored across the line y = -x.
In light of this, the reflection of the point (x, y) across the line y = x is (y, x).
The first reflection's location across the vertical line x=-3 ensures that the y-coordinate is constant.
The point (-3, 4) on the line of reflection will become the halfway point between A and A' thanks to the x-coordinate of A':
(-3, 4) = (A +A')/2
2(-3, 4) (-3, 4)
-A = A' = (-6-(-7), 8 -4) = (1, 4) (1, 4)
The two coordinate values are simply swapped in the reflection over the line y=x: A'' = (4, 1) (4, 1)
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A chemistry class has learned how to read a sensitive high-caliber balance scale (this is not a digital scale). Since most students are very good at reading the scale, the instructor decides it’s time to test their skills. The instructor asks each student to weigh the same 1. 6 ounce bag of Peanut M&Ms, and then records each student’s reading of the balance scale. Which histogram shows the distribution of the students’ balance-scale readings?
Histogram II shows the distribution of the students’ balance-scale readings, so the correct answer is option (b).
It is stated that most students are very good at reading the scale. Thus, most of the students will read the scale accurately around the actual weight (i.e., around 1.6 ounces), and very few will read far below or far above the accurate weight of 1.6 ounces.
As a large portion of the understudy score tremendous and ought to have rough equivalent aptitude; in this manner, the histogram ought to be around symmetrical.
Therefore, histogram II (symmetrical distribution) shows the perfect distribution of the students' balance-scale readings.
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The complete question is:
A chemistry class has learned how to read a sensitive high-caliber balance scale (this is not a digital scale). Since most students are very good at reading the scale, the instructor decides it’s time to test their skills. The instructor asks each student to weigh the same 1. 6 ounce bag of Peanut M&Ms, and then records each student’s reading of the balance scale. Which histogram shows the distribution of the students’ balance-scale readings?
(a) Histogram I
(b) Histogram II
(c) Histogram III
(d) Histogram IV
I need help with this question please and thank you
The type of transformation and scale factor as required are;
16) Rotation
17) Reflection
18) Dilation
19) n = 5
20)P = r = 4
What is the type of transformation?There are different types of transformation as follows;
1) Translation: This type of translation is defined as moving the object in space by keeping its size, shape or orientation constant. In a translation, each point of the shape must be moved in the same direction and for the same distance
2) Dilation: This type of translation expands or contracts the object by keeping its orientation or shape the same. This is also known as resizing.
3) Rotation: This type of transformation has an object about a fixed point without changing its size or shape.
4) Reflection: This type of translation is called reflection because it flips the object across a line by keeping its shape or size constant.
16) This transformation is rotation based on the definitions above.
17) This type of transformation is a reflection as it is like the image was flipped across a line more like a mirror image.
18) This called dilation as the scale factor was adjusted to produce the new image.
19) Scale Factor = 6/3 = 2
Thus;
n = 10/2 = 5
20) Scale factor = 12/9 = 4/3
Thus;
P = r = 3 * 4/3
= 4
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A 6 ft. tall man flies a kite and lets out 100 feet of string. The angle of elevation of the string is 52° . How high off the ground is the kite?
The kite is 84.8 feet off the ground.
What is an angle of elevation?The angle produced whenever an object if viewed above the horizontal plane is termed the angle of elevation.
To determine how high off the ground is the kite, we have;
let the altitude of the kite from the man's head be represented by s,
Sin θ = opposite/ hypotenuse
Sin 52 = s/ 100
s = Sin 52*100
= 0.7880*100
s = 78.8 feet
The height of the kite off the ground = 78.8 + 6
= 84.8
The height of the kite off the ground is 84.8 feet.
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of the 900 students at columbia middle school, there are 324 7th graders. If one student is chosen at random to lead the pledge at a school assembly, what is the probability the person chosen will be a 7th grader? Use prime factorization to reduce the answer.
Answer:
Step-by-step explanation:
im am sorry but i dont understand so i cant answer this question see you later!
please help me find angle m< 4 (geometry)
Assuming the horizontal lines are parallel, we will see that the measure of angle 4 is m∠4 = 39°
How to find the measure of angle 4?First, we assume that the two horizontal lines are parallel, that will mean that the measures of angle 4 and 7 are equal, beacause both of them are on the same quadrant.
Also, notice that angle 7 and 141° should add up to 180° (a plane angle) thus, we will get:
m∠7 + 141° = 180°
m∠7 = 180° - 141°
m∠7 = 39°
The measure of angle 4 is also that, so we conclude that:
m∠4 = 39°
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enter the value of n for the eqation 5 n = 5 11 times 5 3
For the equation 5^n = 5^11 × 5³ the value of n using the exponents rule is obtained as n = 14.
What is an exponent?
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
The given equation is 5^n = 5^11 × 5³
Since, the base of the exponents is same, so apply the operations on the powers of the base.
The value of n can be found by following the exponent rule.
The exponent rule is - a^(b) × a^(c) = a^(b + c)
Write the equation according to the rule -
5^n = 5^(11 + 3)
Use the arithmetic operation of addition -
5^n = 5^(14)
n = 14
Therefore, the value of n is obtained as 14.
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What is the value of f(150)?
Answer:
Step-by-step explanation:So make sure you learn this in fifth grade so basically whatever your line go to let's say if it lands on 79 I mean 70 and that's like I mean 150 it depends on what you're using
the value of
3(2x+3) when x=5
Answer:
39
Step-by-step explanation:
3(2x + 3) = 6x + 9 = 6(5) + 9 = 39
[tex]3(2x+3)[/tex] when x is 5
Substitute for x with the given value:
[tex]3(2(5)+3)[/tex]
[tex]3(10+3)[/tex]
[tex]3(13)[/tex]
[tex]=\fbox{39}[/tex]
Astronomers often measure large distances using astronomical units (AU) where 1 AU is the average distance from Earth to the Sun. In the image, d
represents the distance from a start to the Sun. Using a technique called "stellar parallax," astronomers determined θ
is 0.00001389 degrees.
b) Write an equation to calculate d
for any star.
(Your response must include an equal sign, and the variables d
and θ.)
The trigonometric function can be used to calculate the distance (4124966.128 AU) between the star and also the sun.
d = 4124966.128
Define the term "stellar parallax"?Astronomers can determine the apparent shift in location of a star by measuring its position once, then again six months later. Stellar parallax refers to the apparent motion of the star.Given:
Astronomers frequently use astronomical units (AU), where 1 AU represents the typical distance between the Earth and the Sun.The graphic depicts the separation between the Sun and a star.Astronomers discovered that using a method known as "stellar parallax," is 0.00001389 degrees.The steps listed below can be used to calculate the astronomical unit distance between star and the Sun:Step 1: To calculate the distance in astronomical units here between star and the Sun, apply the trigonometric function.
The sine function is used to calculate the distance in step two.
sin Ф = P/ H
where H is the hypotenuse and P is the perpendicular.
Step 3: Replace the above expression with the known terms.
sin (0.00001389 ) = 1/d
Step 4: Condense the previous expression.
d = 4124966.128
Thus, the distance of star from the sun is found as d = 4124966.128.
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remember that we don't consider degenerate triangles unless specially instructed otherwise. two side lengths of a triangle are and . what is the longest possible integer length of the third side of the triangle?
The minimum value of the third side is 9 cm, and The maximum value of the third side is 6.7 cm.
The minimum value of the third side is when the triangle is a degenerate triangle, meaning that the third side is a line segment joining the two endpoints of the first two sides, which is equal to 3 cm + 6 cm = 9 cm.
The maximum value of the third side is when the triangle is a right triangle, and the two sides are the legs. According to the Pythagorean theorem, the third side (the hypotenuse) should be equal to the square root of 3² + 6² = 9 + 36 = 45, which is equal to 6.7 cm.
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--The given question is incorrect; the correct question is
"The length of two sides of a triangle are 3cm and 6cm. What could be the minimum and maximum value of its third side?"--
a number increased by 7 given 20
Answer:
13
Step-by-step explanation:
suppose that the student scores on a test follow a bell-shaped distribution with mean 50 and standard deviation 10. using the empirical rule, what percent of students scored scored above 60?
Approximately 99.7% falls within three standard deviations.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
Since the mean score is 50 and the standard deviation is 10, this means that approximately 68% of the students scored between 40 and 60, approximately 95% scored between 30 and 70, and approximately 99.7% scored between 20 and 80. Therefore, approximately 32% of students scored above 60.
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The prom committee is decorating the venue for prom and wants to hang lights above the diagonals of the rectangular room. If DH=44.5 feet, EF=39 feet, and m∠GHF=128° , find m∠HEF .
The measure of the angle m∠HEF = 64°, for the diagonals of rectangular room.
Define the term linear pair?A linear pair is just a pair of neighboring angles created by the intersection of two lines. 1 and 2 create a linear pair in the illustration. The same holds true for pairs 1, 2, 3, and 4. A linear pair's two angles are always supplementary, that means that the sum of their measurements is 180 degrees.The given data:
DH=44.5 feet, EF=39 feet, and m∠GHF=128°As, GE is the straight line.
Thus,
m∠EHF = 180 - 128 (sum of all angles of line is 180, linear pair)
= 52°
Now,
m∠HEF = 180 - 52 / 2 (isosceles triangle)
m∠HEF = 64°
Thus, the measure of the angle m∠HEF = 64°, for the diagonals of rectangular room.
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The diagram for the question is attached.
15. Use the given degree of confidence and sample data to find a confidence interval for the
population standard deviation c. Assume that the population has a normal distribution.
Round the confidence interval limits to the same number of decimal places as the sample
standard deviation.
College students' annual earnings: 98% confidence; n = 9, x = $3959, s = $886
Confidence interval will be between $831.57 and $1040.67.
To find a confidence interval for the population standard deviation, we can use the formula:
(sample standard deviation / square root of sample size) x t-multiplier
where t-multiplier is based on the degree of confidence and the sample size.
For a 98% confidence interval and a sample size of 9, the t-multiplier is 2.821 (from a t-table or a calculator with a t-distribution function).
So the confidence interval for the population standard deviation is:
(886 / sqrt(9)) x 2.821 = (886 / 3) x 2.821 = 295.33 x 2.821
= 831.57 to 1040.67
Therefore, we can be 98% confident that the population standard deviation of the annual earnings of college students falls between $831.57 and $1040.67.
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The polygons are similar, but not necessarily drawn to scale. Find the value of x.
The value of x is 5.5
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
Given;
The two polygons are similar
So,
x-1/6=16/21
x/6-1/6=16/21
x/6=16/21+1/6
x=5.5
y+1/32=21/24
y/32+1/32=7/8
y=3
Therefore, the value of x in polygon will be 5.5
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a numerical measure of linear association between two variables is the . a. standard deviation b. covariance c. coefficient of variation d. variance
option b is correct - covariance
The correlation coefficient (r ) is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables.
Covariance
A numerical measure of linear association between two variables.
Covariance is a measure of how changes in one variable are associated with changes in a second variable. Specifically, covariance measures the degree to which two variables are linearly associated. However, it is also often used informally as a general measure of how monotonically related two variables are. It is similar to variance, but where variance tells you how a single variable varies, covariance tells you how two variables vary together.
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Can someone please help me on this?
A linear function is plotted on the coordinate plane with the following points: (0, 3) and (2, 7). What is the rate of change (slope) and the initial value (y-intercept) for the linear function?
The rate of change for the linear function is 2.
The initial value for the linear function is 3.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The points on the coordinate plane:
(0, 3) and (2, 7)
Now,
The equation of the line.
y = mx + c
Slope = m
m = (7 - 3) / (2 - 0)
m = 4/2
m = 2
Now,
(0, 3) = (x, y)
3 = 2 x 0 + c
3 = 0 + c
c = 3
The y-intercept is 3.
Thus,
The rate of change is 2.
The initial value is 3.
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Shane invested $3,500 in a savings account that pays 4% interest
semiannually (every 6 months). How much money will he have in his
account in 5 years?
The money in Shane's account after five years will be $4900.
The formula for simple interest is -
S.I. = PRT/100, where P is principal, R is rate of interest, T is time and SI is simple interest. Interest is calculated semi-annually then t will be 5×2 years.
Keep the values in formula -
S.I. = 3500 × 4 × 5 × 2/100
Performing multiplication in numerator on Right Hand Side of the equation
S.I. = 1,40,000/100
Cancelling common zero on Right Hand Side of the equation
S.I. = $1400
Total amount = Principal + Interest
Keep the values in formula -
Total amount = 3500 + 1400
Performing addition
Total amount = $4900
The total money in account will be $4900.
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Help me please thhhannkkk youuu
Answer:
25 . 3 %
Step-by-step explanation:
it has the circuits of the brain
2x^2-5x-2=0 quadratic formula
Step-by-step explanation:
First add you two numbers in parethese and then subtract thhat and dit =0
A company produces a range of 5 computers models which bring in high volume
Assuming that the factory works equally to produce models for 9 hours days 7 days per week, which monitor bring in the highest revenue
The model with the highest revenue is model D
How to determine the model with the highest revenueFrom the question, we have the following parameters that can be used in our computation:
Model A Model B Model C Model D Model E
Time to manufacture (mins) (t) 15 18 13 20 17
% Of monitors sold (s) 75% 73% 84% 95% 81%
Cost per monitor (c) $175 $188 $145 $198 $170
The factor works 9 hours for 7 days
So, the total duration per unit time is
D = 9 hours * 7/t
D = 63/t
Convert t to hours
D = 63 * 60/t
D = 3780/t
The total revenue is then calculated as
R = c * D * s
So, we have
Model A = 175 * 3780/15 * 75% = 33075
Model B = 188 * 3780/18 * 73% = 28820
Model C = 145 * 3780/13 * 84% = 35444
Model D = 198 * 3780/20 * 95% = 35551
Model E = 170 * 3780/17 * 81% = 30569
The highest value above is 35551
Hence, the model is model D
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Complete question
Model A Model B Model C Model D Model E
Time to manufacture 15 minutes 18 minutes 13 minutes 20 minutes 17 minutes
% Of monitors sold per total products 75% 73% 84% 95% 81%
Cost per monitor $175 $188 $145 $198 $170
A company manufactures computer monitors. Among the various models are top
products, which bring high revenue.
Assuming the manufacturing lines are running for 9 hours a day for 7 days a week,
which model brings in the highest revenue?
Solve for x. Express your answer in simplest radical form if necessary.
81 = x²
Answer:
Step-by-step explanation:√81 = √x²
9 = square root cancel square = x
9=
x=
Systems of Equations and Inequalities 2020-2021 / 5 of 18
Two students were shopping for school supplies. They need spirals which cost x dollars and pens which cost y dollars. One student bought
2 spirals and 3 pens for $8. 66. Another student bought 4 spirals and 5 pens for $15. 20. Find the unit cost of a spiral.
1
Each notebook is $5 and each thumb drive is $12.
To Locate:
The price per notebook and per flash drive
Explain x and y:
Let's say a notebook costs x dollars.
I'll pay whatever a thumb drive costs.
Form equations:
4x + y = 32 ------------------------ [ 1 ]
3x + 2y = 39 ---------------------- [ 2 ]
Equation [ 1 ] x 2:
8x + 2y = 64 ---------------------- [ 3 ]
[ 3 ] - [ 2 ] :
5x = 25
x = 5
Substitute x = 5 into [ 1 ]:
4(5) + y = 32
20 + y = 32
y = 32 - 20
y = 12
Find the cost of each notebook and each thumb drive:
notebook = x
notebook = $5
thumb-drive = y
thumb-drive = $12
Each notebook is $5 and each thumb drive is $12.
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to classify fossils of an insect, archeologists measure the length of the body. the body length of a type a insect is distributed as and the body length of a type b insect is distributed as (in millimeters). the fossil is classified as type a if the length is less than millimeters and classified as type b if the length is larger than or equal to millimeters. find the value of that the probability of correctly classifying a type a insect equals the probability of correctly classifying a type b insect (round off to first decimal place).
The value that the probability of correctly classifying a type an insect equals the probability of correctly classifying a type b insect is 4.5 millimeters.
To find the value that the probability of correctly classifying a type A insect equals the probability of correctly classifying a type B insect, we need to find the point where the probability density functions of the two types of insects intersect.
For type A insects, the probability density function is given as -
f(x) = [tex](1/2)e^{-{x-3}^{2/2}}[/tex]
For type B insects, the probability density function is given as-
f(x) = [tex](1/4)e^{-{x-5}^{2/2}}[/tex]
We can set these two probability density functions equal to each other and solve for x as follows -
[tex](1/2)e^{-{x-3}^{2/2}}[/tex] = [tex](1/4)e^{-{x-5}^{2/2}}[/tex]
Solving for x, we get:
x = 4.5
So the value that the probability of correctly classifying a type A insect equals the probability of correctly classifying a type B insect and is 4.5 millimeters. This means that if the length of the insect is 4.5 millimeters or less, it will be classified as type A, and if it is greater than 4.5 millimeters, it will be classified as type B.
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help me pls , thanks :)
its about funtions and i rlly need help on this
The given relations are:
1) It is a function.
2) not a function.
3)it is a function.
4) not a function.
Are the relations functions or not?A function is a relation that maps inputs into outputs, such that each output needs to be mapped into a single input.
1) For example, the first relation each input (left row) is mapped into a single output, thus, it is a function.
2) Here theinput 9 is mapped into two different outputs, then it is not a function.
3) The notation used here is (input, output), so we can see that no input is repeated,so it is a functon.
4) The input 9 is mapped into 3 different outputs, then it is not a function.
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Sixty three is the product of nine and a number
Sixty three is the product of nine and a number which is seven
What is multiplication?Multiplying in math is the same as adding equal groups.
The number of items in the group grows as we multiply. Parts of a multiplication problem include the product, the two components, and the answer.
In the multiplication problem involving 63 as the product of 9 and another number
let the number be x
9 * x = 63
9x = 63
isolating x by dividing both sides by 9
9x / 9 = 63 / 9
x = 7
the number is 7
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