Answer:
Hope this helps, Good Luck! :)
Step-by-step explanation:
EV = - + prob(win)*win
= -5 + 1/1000 * 375
= -4.62
The requried, the expected value for a person that buys one ticket is approximately -$4.62. The correct answer is option A. -$4.62.
To calculate the expected value, we need to consider the probability of winning the color television and the corresponding value of the prize. We can then subtract the cost of buying the ticket to find the expected value.
Given:
Cost of one ticket = $5
Value of the color television (prize) = $375
Number of tickets sold = 1000
The probability of winning the color television is 1 out of 1000, as only one ticket will be selected out of the total 1000 tickets sold.
Expected Value (EV) = (Probability of winning * Value of prize) - Cost of the ticket
EV = (1/1000 * $375) - $5
EV = $0.375 - $5
EV = -$4.625
Rounded to two decimal places, the expected value for a person that buys one ticket is approximately -$4.62. The correct answer is option A. -$4.62.
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Julian is older than Nachelle. Their ages are consecutive odd integers. Find Julian's
age if the sum of the square of Julian's age and 2 times Nachelle's age is 139.
The age of Nachelle would be 5 years and the age of Julian would be 7 years.
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Let's suppose the age of Nachelle is 'x' years then Julian's age would be 'x+2'.
x² + [2(x + 2)]² = 139
x² + 4x² + 8x + 16 = 139
5x² + 8x - 123 = 0
Simplifying this, we get
x = 4.22 and x = -5.82
Age cannot be a negative number so
x ≈ 5.
x + 2 = 7 years
Hence the age of Nachelle would be 5 years and the age of Julian would be 7 years.
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Triangle ABC is shown in the xy-coordinate plane. The triangle will be translated 2 units down and 3 units right to create triangle A'B'C'. Indicate whether each of the listed parts of the image will or will not be the same as the corresponding part in the preimage (triangle ABC) by selecting the appropriate box in the table.
The coordinates of A' and C' will not be the same. The perimeter and area of ΔA'B'C' will be the same. The measure of ∠B' and the slope of A'C' will be the same.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
As per the given translation,
2 units down and 3 units right
The coordinate will change as,(x,y) → (x+3,y-2) so it will change.
The transformation consists only of linear transformation no rotation exists thus area and perimeter will remain the same.
The slope and angle are unchanged irrespective of any transformation.
Hence "A' and C' will not have the same coordinates. The boundaries and surface area of ΔA'B'C' will be identical. The slope of A'C' and the measure of ∠B will be equal.".
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A company has a monthly time series that regularly shows sales being higher in the summer months. This is an example of which component?.
Answer: The Seasonal? brainleist if im right
Step-by-step explanation:
What is the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean?.
The relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean is wider than one other.
Confidence interval:
In statistics, confidence interval means the probability that a population parameter will fall between two set values.
Given,
Here we need to find the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean.
According to the given question, the given confidence interval values are 90% and 95 %.
When we convert this percentage value into decimal, then we get the value as,
90% = 0.9
95% = 0.95
Here a 95 percent confidence interval, you have a 5 percent chance of being wrong.
And with a 90 percent confidence interval, you have a 10 percent chance of being wrong.
Therefore, 90 percent confidence interval would be wider than a 95 percent confidence interval.
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TWO PART QUESTION NEED! :)))
You decide to invest $500 into a 4-year CD that pays 2.85% interest
compounded monthly.
Use the compound interest formula:A = P(1 + r/n) ^nt to give:
a. The future value in 4 years.
b. The interest gained in 4 years.
Future value in four years is $1060.30 and Interest gained in four years is 560.30.
Define compound interest.Compound interest is interest that builds up over a set length of time on both principal and interest. The principal is also used to account for the interest that has accrued on a principal over time. Furthermore, the accumulated principal value is used to calculate interest for the subsequent time period. The new way of calculating interest now utilized in all international financial and commercial operations is known as compound interest. When we look at the compound interest values that have built over successive time periods, the power of compounding is clearly apparent.
Given
You decide to invest $500 into a 4-year CD that pays 2.85% interest compounded monthly
Compound interest
A = P( 1+ r/n)^nt
Interest gained in 4 years
A = 500( 1+ 0.0285/12)^(12)(4)
A = 500( 1 + 0.002375) ^48
A = 560.30
Future value in 4 years = $500 + $560.30
Future value in 4 years = $1060.30
Future value in four years is $1060.30 and Interest gained in four years is 560.30.
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The points in the table lie on a line. Find the slope of the line.
x: 1, 3, 5, 7
y: 2, 10, 18, 26
Answer:
Step-by-step explanation:
(1, 2), (3, 10)
(10 - 2)/(3 - 1) = 8/2 = 4
m = 4
Can you help me thank you so so much Really having trouble in math
Answer:
Step-by-step explanation:
the answer is A
Answer:
A.) [tex]\frac{-343}{27}[/tex]
Step-by-step explanation:
Looking at the available answers, I'm assuming the expression is [tex](-2-\frac{1}{3})^3[/tex].
So,
[tex](-2-\frac{1}{3})^3\\(-\frac{6}{3}-\frac{1}{3})^3\\(\frac{-7}{3})^3[/tex]
Use the exponent rule that states [tex](\frac{a}{b})^m=\frac{a^m}{b^m}[/tex]
So,
[tex](\frac{-7}{3})^3\\\frac{(-7)^3}{3^3}\\\frac{-343}{27}[/tex]
Sarah has a solid wooden cube with a length of centimeter. From each of its 8 corners, she cuts out a smaller cube with a length of centimeter. What is the volume of the block after cutting out the smaller cubes?.
Therefore ,the volume of the block after cutting out the smaller cubes is (8/25 cm^2)
What is volume ?Any three-dimensional solid's volume is just the amount of space it takes up. A cube, cuboid, cone, cylinder, or sphere can be one of these solids.
Volumes vary depending on the shape. We have examined different three-dimensional objects and shapes in geometry, including cubes, cuboids, cylinders, cones, and more. We will learn how to calculate the volume for each of these shapes.
Here,
volume = (8/25 cm2) represents the block's volume after the smaller cubes have been removed.
First, we must determine the volume of a cube with four or five centimeter sides, which is:
V = (4/5 cm)^2 = (16/25 cm^2)
The volume of each of the eight smaller cubes that was removed must now be subtracted.
v = (1/5 cm)^2 = (1/25 cm^2)
After the smaller cubes are removed, the block's volume is:
V - 8v = (16/25 cm^2) - 8*(1/25 cm^2) = (8/25 cm^2)
Therefore ,the volume of the block after cutting out the smaller cubes is (8/25 cm^2)
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Patrick borrows $1400 from a bank with 10% simple interest each year. How much will patrick need to pay back in total in 2 years?.
Amount Patrick has to pay back is $ 1680 and the simple interest is $ 280.
What is Simple Interest?
Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) 100
Given data ,
Let the principal amount be = A
The value of A = $ 1400
Let the rate of interest be = r
The value of r = 10 %
Let the number of years = T
The value of T = 2 years
Now , the simple interest is calculated by the formula
Simple Interest = ( Principal Amount x Rate x Time Period ) 100
Substituting the values in the equation , we get
Simple Interest = ( 1400 x 10 x 2 ) / 100
Simple Interest = 14 x 20
Simple Interest = $ 280
Therefore , the simple interest in 2 years is $ 280
And , the total amount Patrick has to give back to the bank is given by the formula
Amount in 2 years = Principal + Interest
Amount in 2 years = 1400 + 280
Amount in 2 years = $ 1680
Therefore , the amount in 2 years is $ 1680
Hence , Amount Patrick has to pay back is $ 1680 and the simple interest is $ 280
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Rory is writing an introduction paragraph for an argumentative essay about the treatment of egg-laying chickens. Which of the following is an effective
claim?
O Chickens raised for-eggs should be allowed to roam free.
OI like knowing that chickens are descended from dinosaurs, and that their egg colors are based on genetics and feather colors.
O It's important to note that chickens have great memories, dream when they sleep, and can recognize over 100 faces.
OWe should respect chickens because they can communicate with other chickens through over 30 different sounds, including purring when they're
happy.
An effective claim in the essay is that; Chickens raised for-eggs should be allowed to roam free. Option A
What is an argumentative essay?The entire point of an argumentative essay is that the essay helps us to be able to bee able to make a point. It is the kind of essay in which we may be able to communicate our perspective about a matter.
In the argumentative essay, there could be a claim which is the main point that the essay is trying to address. The claim would thus provide the kernel of the essay. It is the point that the author wants to pass across to the readers.
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Answer: A: Chickens raised for eggs should be allowed to roam free.
Ann has 30% less money than mary, and jessica has 70% more money than mary. If the three of them have a total of $102, how much money does each girl have individually?.
If Ann has 30% less money than mary, and jessica has 70% more money than mary and If the three of them have a total of $102, then Ann has $50.7, Mary has $51 and Jessica has $51.7
What is meant by percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It can be stated as a decimal or a fraction and is frequently represented by the sign "%". 50%, for instance, can be written as 0.5 or 1/2. A component or proportion of an entire is represented using percentages. For instance, if a student receives a 75% on an exam, it indicates that they correctly answered 75 out of 100 questions individually. Percentages are often used in everyday life to represent changes such as a rise or fall in pricing, an increase or reduction in population, or a growth or drop in sales. Percentages may be determined in mathematics using a variety of formulae and ideas including proportions, ratios, and decimals.
How to solve?
Ann has 30/100 * $x = $0.3x less money than Mary
Jessica has 70/100 * $x = $0.7x more money than Mary
Mary, Ann and Jessica have a total of $102
Mary + Ann + Jessica = $102
Mary + (Mary - $0.3x) + (Mary + $0.7x) = $102
3Mary = $102 + $0.3x + $0.7x
3Mary = $102 + $1x
3Mary = $102 + $x
3Mary - $x = $102
2Mary = $102
Mary = $102/2 = $51
Ann = Mary - $0.3x = $51 - $0.3x = $50.7
Jessica = Mary + $0.7x = $51 + $0.7x = $51.7
Ann has $50.7, Mary has $51 and Jessica has $51.7.
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If Ann has 30% less money than mary, and jessica has 70% more money than mary and If the three of them have a total of $102, then Ann has $50.7, Mary has $51 and Jessica has $51.7
What is meant by percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It can be stated as a decimal or a fraction and is frequently represented by the sign "%". 50%, for instance, can be written as 0.5 or 1/2. A component or proportion of an entire is represented using percentages. For instance, if a student receives a 75% on an exam, it indicates that they correctly answered 75 out of 100 questions individually. Percentages are often used in everyday life to represent changes such as a rise or fall in pricing, an increase or reduction in population, or a growth or drop in sales. Percentages may be determined in mathematics using a variety of formulae and ideas including proportions, ratios, and decimals.
Ann has 30/100 * $x = $0.3x less money than Mary
Jessica has 70/100 * $x = $0.7x more money than Mary
Mary, Ann and Jessica have a total of $102
Mary + Ann + Jessica = $102
Mary + (Mary - $0.3x) + (Mary + $0.7x) = $102
3Mary = $102 + $0.3x + $0.7x
3Mary = $102 + $1x
3Mary = $102 + $x
3Mary - $x = $102
2Mary = $102
Mary = $102/2 = $51
Ann = Mary - $0.3x = $51 - $0.3x = $50.7
Jessica = Mary + $0.7x = $51 + $0.7x = $51.7
Ann has $50.7, Mary has $51 and Jessica has $51.7.
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Determine whether the Law of Sines or Law of Cosines is the best choice to solve for
the missing dimension for the given figure. Substitute the values into the appropriate
formula and solve for x.
X
26.43
21.35
82.42
49.09
Answer:
Hi use the sine rule: answer: 26.43
Step-by-step explanation:
a confidence interval for a proportion ranges from 0.45 to 0.74. what is the margin of error for this confidence interval?
The margin of error for this confidence interval is 0.145.
Given :
a confidence interval for a proportion ranges from 0.45 to 0.74.
Confidence interval :
A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times
Margin of error :
Margin of error, also called confidence interval, tells you how much you can expect your survey results to reflect the views from the overall population.
Length of confidence interval = 0.74 - 0.45
= 0.29
we know that,
Margin of error = 1/2 * length of confidence interval.
= 1/2 * 0.29
= 0.29/2
= 0.145
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Which of the correlation values represent a perfect linear relationship between x and y?
A) .05
B) 1
C) 100
D) -1
E) 0
The correlation values for the perfect linear relationship is option (b) 1 and (d) -1.
Correlation:
Correlation refers the measure that determines the degree to which the movement of two different variables is associated.
Given,
Here we need to find the perfect correlation values that represent the perfect linear relationship between x and y.
Here we know that the perfect linear relationship is indicated by a correlation with a magnitude of 1.
Then the sign of the correlation coefficient is the sign of the slope of the line describing the relationship. And it may be positive or negative.
Therefore, the value -1 and 1 are the perfect values for this one.
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What is the LCM of 10, 20 and 35
What is the lcm
if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?
If q is an odd number and the median of q consecutive integers is 120, then the largest of these integers is option (A) (q-1) / 2 + 120
The number q is an odd number
The median of q consecutive integers = 120
Consider the q = 3
Then three consecutive integers will be 119, 120, 121
The largest number = 121
Substitute the value of q in each options
Option A
(q-1) / 2 + 120
Substitute the value of q
(3-1)/2 + 120
Subtract the terms
=2/2 + 120
Divide the terms
= 1 + 120
= 121
Therefore, largest of these integers is (q-1) / 2 + 120
I have answered the question in general, as the given question is incomplete
The complete question is
if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?
a) (q-1) / 2 + 120
b) q/2 + 119
c) q/2 + 120
d) (q+119)/2
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x-5/2 + x-1/8 = x-3/4 +x-4/3 GIVING BRAINLIEST!
Answer:
There are no values of x
that make the equation true.
No solution
Step-by-step explanation:
Two trains leave stations 480 miles apart at the same time and travel toward each other. One train travels at 90 miles per hour while the other travels at 110 miles per hour. How long will it take for the two trains to meet?
It will take 2 hours 24 minutes time to two trains to meet.
Let a train starts from A towards to B with velocity v1 = 90 miles/hour
and another train starts it's journey from B towars A with velocity v2 = 110 miles/hour
Let after time t hour they meet at C.
Hence, we get AC + CB = AB
⇒ v1t + v2t = 480
⇒ (v1 + v2) t = 480
⇒ (90 + 110) t = 480
⇒ t = 480/200 = 48/20 = 12/5 hours
∴ t = [tex]2\frac{2}{5}[/tex] hours
= 2 hour (2/5 × 60) mins
∴ t = 2 hours 24 minutes time
So, after 2 hours 24 minutes time they meet each otherv at C, where AC = v1t = 90 × 12/5 = 216 miles.
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If a boundary line is dashed, what does that mean about the ordered pairs that lie along that line?
The ordered pairs are never part of the solutions of the inequality.
The ordered pairs are sometimes part of the solutions of the inequality.
The ordered pairs are occasionally part of the solutions of the inequality.
The ordered pairs are always part of the solutions of the inequality.
If a boundary line is dashed, The ordered pairs are never part of the solutions of the inequality
What is inequality in math?
Inequality, is a mathematical statement expressing an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
Solid line and dashed line in inequality
A region on one side of a line can be used to graphically show an inequality.
For the purpose of indicating that a line is not a part of the region, inequality plots that employ the < or > symbols have a dashed line.
Plotting a solid line indicates that an inequality that uses the symbol ≤ or ≥ is included in the region.
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if a:3=12:a, calculate the positive of a
When a:3=12:a, then the positive of a will be 6.
Given, the following quadratic equation
a : 3 = 12 : a
That is,
a/3 = 12/a
By cross- multiplication of the values, we will get
a * a = 12 *3
a ^ 2 = 36
From the above equation, we calculate the square root for the value a.
Therefore, we get the square root of,
a ^ 2 = 36
a = 6 ( as the square root of 36 is 6)
So, we can say that when a : 3 = 12: a the positive of a will be 6
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Complete the table below to represent the function: f(x)=x+4
Answer:
x 0 1 2 3 4
f(x) 4 5 6 7 8
Step-by-step explanation:
f(x) = x + 4
f(0) = 0 + 4 = 4
f(1) = 1 + 4 = 5
f(2) = 2 + 4 = 6
f(3) = 3 + 4 = 7
f(4) = 4 + 4 = 8
x 0 1 2 3 4
f(x) 4 5 6 7 8
The ratio of yellow cars to purple cars in a
car park is 97: 63.
Rewrite this as an equivalent ratio of the
form n : 1.
Give any decimals in your answer to
2 d.p.
Answer:
1.54 : 1
Step-by-step explanation:
See photo attached. Hope this helps
The equivalent ratio of yellow cars to purple cars in the form n:1 is 1.54:1.
What is Ratio?A ratio is a mathematical comparison between two or more quantities or values. It expresses the relative sizes or amounts of different quantities and is typically represented in the form of a fraction or a colon (:).
The greatest common divisor (GCD) of 97 and 63 is 1, which means they have no common factors other than 1.
Therefore, we can write the ratio of yellow cars to purple cars as: 97:63
Since we need to write it in the form of n:1, we can divide both sides of the ratio by 63 (the smaller number in the ratio):
= 97/63 : 63/63
= 97/63 : 1
= 1.54 : 1
So, the equivalent ratio of yellow cars to purple cars in the form n:1 is 1.54:1.
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Help me solve this two column proof!
The two column proof is written as follows
Statement Reason
AD ≅ BD ≅ CD given
ΔADB and ΔCDB are isosceles Base angles are equal
< A = < C = < ABD = < CBD = x Definition of isosceles triangle.
< ABC = < ABD + < CBD Adjacent angles
< ABC = x + x = 2x Substitution property of equality
< ABC + < A + < C = 180 Sum of angels of a triangle
2x + x + x = 180 Substitution property of equality
4x = 180 Addition property of equality
x = 45 degrees Division property of equality
< ABC = 2x = 2 * 45 Substitution property of equality
< ABC = 90 Definition of right triangle
What is a right triangle?A triangle is said to be a right triangle if one of the angles is 90 degrees. Right angles are angles that are 90 degrees.
The proof required to proof that < B is 90
With the isosceles triangle giving and the equal sides the equation is written as
4x = 180
x = 45
< B has 2x (< ABD + < CBD) these are adjacent angles
< B = 2 * 45
< B = 90
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Which of the following choices is not a name for the given figure?
The name [tex]\overline{B}[/tex] does not represent a name of the given figure.
What is a line?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
In the figure A and B are two points on the line m.
The line can represent by the symbol [tex]\overline{BA}[/tex].
The line can represent by the name line m.
The line extended on both side of the points A and B.
The given figure can be represented by the symbol [tex]\overleftrightarrow{AB}[/tex].
But B is a point on the line. Using the point B, the line can not represent.
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Add. Write the answer in standard form (6-1)+(7+3t)
Answer:
Step-by-step explanation:
12 + 3t
Dominic is a server at a restaurant. Each dish at the restaurant costs $8. A sales tax of 8% is charged. The total bill amount includes the sales tax of the meal. Dominic earns tips left by customers. The amount of money tipped can be represented by a percentage of the total bill. Order the tip amounts from least to greatest tip, in dollars. 4 dishes 20% tip 6 dishes 14% tip 7 dishes 11% tip
Answer: To find the tip amount in dollars for each order, you need to multiply the total bill amount by the tip percentage.
For the first order of 4 dishes, the total bill amount is $8 per dish * 4 dishes = $<<8*4=32>>32.
The tip amount is $32 * 20% = $6.40.
For the second order of 6 dishes, the total bill amount is $8 per dish * 6 dishes = $<<8*6=48>>48.
The tip amount is $48 * 14% = $6.72.
For the third order of 7 dishes, the total bill amount is $8 per dish * 7 dishes = $<<8*7=56>>56.
The tip amount is $56 * 11% = $6.16.
So, the tip amounts from least to greatest are $6.16, $6.40, and $6.72.
In one corner of the drawing room a flower basket is kept inside the glass lies on the table the basket is designed in such a way that every one please to see it
A cylindrical vase with a curved surface area of 6.79 square metres will cost Rs. 8.14 to paint.
What is curved surface area?The area with just curved surfaces, leaving the circular top and base, is referred to as the curved surface area. Curved surface area is the amount of space left over after subtracting the cylinder's total circular area. The formula for curved surface area is 2 * pi * r * h.
Here,
We have to calculate the curved surface area of glass in which the flower basket is placed.
Glass is cylindrical,
Height of cylinder = 180cm = 1.8m
Radius of cylinder = 60cm = 0.6m
The curved surface area of the cylinder = 2πrh
The curved surface area of the cylinder = 2*22/7*0.6*1.8
The curved surface area of the cylinder = 6.78584 m²
Cost of painting the glass per m² = Rs. 1.2
Cost of painting 6.78584= 6.78584*1.2
Cost of painting 6.78584= Rs. 8.143
The cost of painting an cylindrical vase of curved surface area 6.79 m² will be Rs. 8.14.
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The urface area of a three-dimenional object i the um of the area of the face. If repreent the length of the ide of a cube, write a formula for the urface area S of the cube
A Formula for the Surface area of the cube is 6a².
A cube is a three-dimensional solid with six square faces, facets, or sides, three of which meet at each vertex in geometry. It looks like a hexagon from the corner, and its net usually looks like a cross. One of the five Platonic solids, the cube is the only regular hexahedron.
The sum of the areas on each face of the cube that covers it is the cube's surface area. The formula for surface area is six times the cube's length divided by the square of that number. It is denoted by 6a², where a is the cube's side length. It basically refers to the entire surface area.
area of one face = a² [By area of square formula]
There are six faces altogether. Therefore,
TSA (total surface area) of cube = S = a² + a²+ a² + a² + a² +a²
S = 6a²
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(complete question)
The surface area of a three-dimensional object is the sum of the area of the faces. If a represent the length of the side of a cube, write a formula for the surface area S of the cube.
If you rent a car from Caleb's Cars, you'll pay a $61 fee
and $24 per day. At Vinny's Vehicles, you'll pay a $105 fee and $20 per day. Determine the number of days you can rent a car from either place and pay the same amount. Use substitution or elimination.
Answer:
11 days
Step-by-step explanation:
y=24x+61
y=20x+105
(don't think I can solve this with elimination because there is no coefficient with a y-value.)
When looking for the interception you look for the point where both lines intercept. I graphed both equations online and looked for the point where they intercept, which is (11,325) meaning that in 11 days, both places will cost 325 dollars when you rent a car.
( I also looked for a calculator online that is especially used to find the interception between two points and it gave the same point, if wrong...I'm sorry)
The perimeter of a rectangle is 66cm.
Its longest side has a length of 17cm.
State the length of the shortest side.
[tex]{ \red{\boxed{ \tt{Step-by-step-explaination}}}}[/tex]
Perimeter of a rectangle : [tex]{ \purple{ \tt{2(l+b)}}}[/tex]
length = [tex]{ \red{ \tt{17cm}}}[/tex]
breadth= [tex]{ \red{ \tt{?}}}[/tex]
now,
according to the rule.
perimeter = 2(l+b)
66 = 2(17+b)
66 = 34 + 2b
66 - 34 = 2b
32 = 2b
32/2 = b
16 cm = b
hence b = [tex]{ \pink{ \sf{16cm}}}[/tex]