Mathematics College
Answers
Answer 1
For this problem, we are provided with the image of a beam and its dimensions, we are then informed that the beam was cut in half, and we need to compare the surface area and volume of the beam before and after the cut.
The surface area of a rectangular prism can be calculated with the following expression:
[tex]A_{\text{surface}}=2\cdot(\text{width}\cdot\text{height}+\text{width}\cdot\text{length}+\text{height}\cdot\text{length)}[/tex]
The volume of a rectangular prism can be calculated with the following expression:
[tex]V=\text{width}\cdot\text{height}\cdot\text{length}[/tex]
We can use these formulas to calculate the characteristics of the beam before the cut:
[tex]\begin{gathered} A_{\text{surface}}=2\cdot(10\cdot1+1\cdot1+1\cdot10)=42\text{ square ft} \\ V=10\cdot1\cdot1=10_{}\text{ cubic ft} \end{gathered}[/tex]
Now we can calculate the characteristics of the beam after the cut:
[tex]\begin{gathered} A_{\text{surface}}=2\cdot(5\cdot1+1\cdot1+1\cdot5)=22\text{ square ft} \\ V=5\cdot1\cdot1=5\text{ cubic ft} \end{gathered}[/tex]
With this, we can conclude that:
The surface area of the cut beam is 20 sq ft smaller than the original beam.
The volume of the cut beam is half the volume of the original beam.
Related Questions
For each row of the table, choose the equivalent expression
Answers
Ok, so:
Let's make all operations and then choose the equivalent expression for each one.
Let's start in order:
a. 4/12 + 4/12 = 8/12
b. 1/12 + (3/12 + 3/12) = 7/12
c. 4/12 + 5/12 = 9/12
d. 2/12 + 2/12 + 2/12 = 6/12.
Notice that the last operations are the columns of the table.
So, let's do it the same with the upper rows:
e. 5/12 + 4/12 = 9/12
f. (1/12 + 3/12) + 3/12 = 7/12
g. 1/12 + 2/12 + 3/12 = 6/12
h. 15/12 - 7/12 = 8/12.
Now, let me draw the table to make this problem more understandable.
This is the order you have to put the answer:
A bowl has 4 green marbles 3 red marbles and 2yellow marbles what is the probability that you are going to select a red marble and a yellow marble. You replace the marble before another marble is selected
Answers
ANSWER
2/27
EXPLANATION
There are a total of 9 marbles in the bowl. The probability of drawing a red marble is,
[tex]P(red)=\frac{\#red.marbles}{\#total.marbles}=\frac{3}{9}=\frac{1}{3}[/tex]
Then you draw another marble, but you put the first back in the bowl, so the total number of marbles is the same. The probability of drawing a yellow marble is,
[tex]P(yellow)=\frac{\#yellow.marbles}{\#total.marbles}=\frac{2}{9}[/tex]
The probability of drawing a red marble and a yellow marble is,
[tex]P(red.and.yellow)=P(red)\cdot P(yellow)=\frac{1}{3}\cdot\frac{2}{9}=\frac{2}{27}[/tex]
The male and female guests attending Patricia's party were surveyed to see if they drove to the party or did not drive. The data is displayed in the table below: MaleFemale 26 24 drove to the party 34 116 did not drive to the partyIf a guest is chosen at random from this group, what are the chances of choosing a guest who is male and did not drive to the party? 12%13%17%58%
Answers
The given table is
Male Female Total
Drive 26 24 50
Did not drive 34 116 150
Total 60 140 200
From the table, total number of males and females = 200
number of guests that are males and did not drive = 34
Recall, Probability is expressed as
number of favorable outcomes/number of total outcomes
Therefore, the chances of choosing a guest who is male and did not drive to the party is
34/200 = 0.17
By converting to percentage, it is
0.17 x 100 = 17%
To find the missing length below, would you use Law of Sines or Law of Cosines?Find the missing length. There are 2 answers, Law of _____ and missing side length.
Answers
[tex]\begin{gathered} To\text{ find the missing length, we will use law of cosines.} \\ Co\sin es\text{ rule is-} \\ (L)^2=38^2+42^2-2\times38\times42\times\cos 39^{\circ} \\ L^2=727.35 \\ L=\sqrt[]{727.35} \\ L=26.96 \end{gathered}[/tex]
the u.s senate has 100 members. after a certain election, there were 6 more democrats than republicans, with no other parties represented. how many memebrs of each party were there in the senate?
Answers
As per the unitary method, the number of democrats are 53 and the number of republicans are 47.
Unitary method:
Unitary method is the process of finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given,
The U.S senate has 100 members. after a certain election, there were 6 more democrats than republicans, with no other parties represented.
Here we need to find the number of democrats and the number of republicans.
Let us consider the number of Republican's be "x"
And then the number of Democrats is "x+6".
We know that the total number of members in the senate is 100.
So, it can be written as
x + (x + 6) = 100
2x + 6 = 100
2x = 100 - 6
2x = 94
x = 94/2
Then the value of x is,
x = 47
Therefore, there are 47 republicans in the senate then the number of democrats is
x + 6 => 47 + 6 => 53
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15% of 80 is 60% of what number?
Answers
Let x be the required number.
[tex]15\text{ \% of 80 =}60\text{ \% of x}[/tex]
[tex]15\text{ \% }\times\text{ 80 =}60\text{ \% }\times\text{ x}[/tex]
[tex]\frac{15}{100}\text{ }\times\text{ 80 =}\frac{60}{100}\text{ }\times\text{ x}[/tex]
Using the cross-product method, we get
[tex]\frac{15\times80}{100}\times\frac{100}{60}=x[/tex][tex]x=20[/tex]
Hence 15% of 80 is 60% of 20.
The answer is 20.
caluculate the length of AC to 1 decimal place in the trapezium below.
Answers
Check the picture below.
usign the pythagorean theorem let's find the side CD, then let's get the side AC using the same pythagorean threorem.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{16}\\ a=\stackrel{adjacent}{CD}\\ b=\stackrel{opposite}{7}\\ \end{cases} \\\\\\ \sqrt{16^2 - 7^2}=CD\implies \sqrt{207}=CD \\\\[-0.35em] ~\dotfill[/tex]
[tex]c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{AC}\\ a=\stackrel{adjacent}{CD}\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ AC=\sqrt{(\sqrt{207})^2~~ + ~~11^2}\implies AC=\sqrt{207 + 121}\implies \boxed{AC\approx 18.1}[/tex]
Write the slope-intercept form of the equation of each line.3) 10 = -2y-x
Answers
Recall that the slope-intercept form of the line equation is of the form y=mx+b, where m is the slope and b is the y-intercept.
To transform the equation 10=-2y-x into the slope-intercept form we should apply algebraic operations so we isolate the y on one side of the equation.
Let's add x on both sides, we get
[tex]-2y=10+x[/tex]
Now, lets divide by -2 on both sides, we get
[tex]y=\frac{10}{-2}+\frac{x}{-2}=-\frac{1}{2}\cdot x-5[/tex]
we see that this now has the slope-intercept form, where the slope is m=(-1/2) and b=-5
Perform the indicated operation -27÷-9
Answers
-27/9 = -3
answer is -3
The rectangular floor of a classroom is 28 feet in length and 30 feet in width. A scale drawing of the floor has a length of 14 inches. What is the perimeter, in inches, of the floor in the scale drawing?
Answers
The Solution:
Given:
Required:
To find the perimeter (in inches) of the floor in the scale drawing.
Step 1:
Find the value of x.
By the similarity theorem:
[tex]\frac{14}{x}=\frac{28}{30}[/tex]
Cross multiplying, we get:
[tex]\begin{gathered} 28x=14\times30 \\ \\ Dividing\text{ both sides by 28, we get} \\ \\ x=\frac{14\times30}{28}=\frac{30}{2}=15\text{ in.} \end{gathered}[/tex]
Step 2:
Find the perimeter, in inches, of the floor in the scale drawing.
By formula, the perimeter is:
[tex]\begin{gathered} P=2(L+W) \\ \text{ Where:} \\ L=14\text{ inches} \\ W=x=15\text{ inches} \\ P=perimeter=? \end{gathered}[/tex]
Substituting these values in the formula, we get:
[tex]P=2(14+15)=2\times29=58\text{ inches}[/tex]
Therefore, the correct answer is 58 inches.
Use graph to find the slope and y-intercept of the line. Compare the values to the equation y= -x+5
Answers
As given by the question
There are given that the graph of the line.
Now,
To find the slope and y-intercept of the line, first select two intersect point from the graph.
Then,
The points are:
[tex](0,\text{ 5) and (5, 0)}[/tex]
Then,
First find the slope,
So,
From the formula of slope,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where,
[tex]x_1=0,y_1=5,x_2=5,y_2=0[/tex]
Then,
Put all the value into the given formula.
So,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0_{}-5_{}}{5_{}-0_{}} \\ m=-\frac{5}{5} \\ m=-1 \end{gathered}[/tex]
Now,
From the standard form of the line,
[tex]y=mx+b[/tex]
Then,
Put y is 5, x is 0 and m is -5 into the above equation to find the y-intercept
So,
[tex]\begin{gathered} y=mx+b \\ 5=-1(0)+b \\ b=5 \end{gathered}[/tex]
Hence, the value of the y-intercept is 5.
Now,
The line equation is shown below:
[tex]\begin{gathered} y=mx+b \\ y=-1x+b \\ y=-x+5 \end{gathered}[/tex]
Hence, the slope of the line is -1, y-intercept of the line is 5 and the equation of line is y = -x + 5.
Find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept. When typing the point (x,y) be sure to include parentheses and a comma between your x and y components. Do not put any spaces between your characters. If a value is not an integer type your answer rounded to the nearest hundredth.3x+8y=24the x-intercept is Answerthe y-intercept is Answer
Answers
We want to find the x and y-intercepts of
[tex]3x+8y=24[/tex]
The x-intercept is where the graph cuts the x-axis, when y = 0. To find this in our equation, we just need to evaluate it at y = 0.
[tex]\begin{gathered} 3x+8\times0=24 \\ 3x=24 \\ x=\frac{24}{3}=8 \end{gathered}[/tex]
Then, the x-intercept is (8, 0).
The y-intercept is where the graph cuts the y-axis, when x = 0. To find this in our equation, we just need to evaluate it at x = 0.
[tex]\begin{gathered} 3\times0+8y=24 \\ 8y=24 \\ y=\frac{24}{8}=3 \end{gathered}[/tex]
The y-intercept is (0, 3).
Use the table of values for f and g below to find the indicated compositions. (f \circ g)(8) =Answerg(f(3))=Answerf(f(1))=Answer (g \circ g)(6) =Answer
Answers
In order to find the value of a composition of functions at x = a, (f º g)(a), we first find the value of g(a), then find the value of f(x) at x = g(a).
(f º g)(a) = f(g(a))
In this problem, the values of f(x) and g(x) are shown in the table, for integer values of x from 0 to 9.
So, we have:
1. (f º g)(8) = f(g(8))
From the table, we see that
g(8) = 4 (value of g(x) in the line corresponding to x = 8)
Then:
f(g(8)) = f(4) = 4 (value of f(x) in the line corresponding to x = 4)
Thus:
[tex]\mleft(f\circ g\mright)\mleft(8\mright)=4[/tex]
2. g(f(3))
f(3) = 8
g(8) = 4
Thus:
[tex]g(f(3))=4[/tex]
3. f(f(1))
f(1) = 6
f(6) = 2
Thus:
[tex]f(f(1))=2[/tex]
4. (g º g)(6) = g(g(6))
g(6) = 7
g(7) = 3
Thus:
[tex]\mleft(g\circ g\mright)\mleft(6\mright)=3[/tex]
Convert 77.6% to an
equivalent decimal.
Answers
Answer:
Step-by-step explanation:
0.776 in decimal form.
1. Which of the following is not a radical expression that is equivalent to √1087A.B.C.D.√2-√54√3-√36√5-√21√6-√18
Answers
The radical expression √108 is not equivalent to the expression √5√21 .
Given the radical expression as √108 .
Now the number 108 can be broken down into factors as
108 = 54 × 2 , 36 × 3 , 18×6
therefore we can see that the radical expression is equivalent to
√108 = √54 × √2
√108 = √36 × √3
√108 = √18 × √6
But 21 × 5 = 105 ≠ 108.
Therefore the radical expression √108 is not equivalent to √5√21 .
Expressions in mathematics are statements with variables, numbers, or both, and at least two terms joined by an operator. Mathematical operations include addition, subtraction, multiplication, and division.
In mathematics, there are two types of expressions: numerical expressions, which only contain numbers, and algebraic expressions, which also contain variables.
A symbol with an unknown value is called a variable. A term can be made up of a single constant, a single variable, or a group of variables and constants multiplied or divided. A number that has been further multiplied by a variable serves as the coefficient in an equation.
Disclaimer: The complete question is :
Which of the following is not a radical expression that is equivalent to √108?
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The population P of a city is given by P = 115600e^0.024t, where t is the time in years. According to this model, after how many years will the population be 130,000?4.29 years4.89 years5.19 years4.49 years
Answers
Given:
The population P of a city is given by,
[tex]P=115600e^{0.024t,}[/tex]
To find:
The time taken for the population to reach 130,000.
Explanation:
Substituting P = 130,000 in the given function, we get
[tex]\begin{gathered} 130000=115600 \\ e^{0.024t}=\frac{130000}{115600} \\ e^{0.024t}=1.1245 \\ 0.024t=\ln1.1245 \\ 0.024t=0.1174 \\ t=4.891 \\ t\approx4.89years \end{gathered}[/tex]
Therefore, the number of years required for the population to reach 130,000 is 4.89years.
Final answer:
The number of years required is 4.89years.
The number of students showing up for a high school football team is 10% smaller than the previous year. A few minutes before tryouts begin, another 5 students show up. There are 75 students on the field to try out for football. Which equation represents this situation?
Answers
Given data:
The expression for the given statement is,
[tex]0.9x+5=75[/tex]
Thus, the option (C) is correct.
solve the problem and show your work below. I have a rectangular garden. i usually grow cucumbers in2/3 of my garden but i want to take 3/4 of the cucumber section to grow radishes. After i make the change, how much of my whole garden will be radishes?
Answers
Given data;
The area in which cucumbers usually grown are 2/3 x.
Here, x is the total area of the garden.
The area of the cucumber taken to grow raddish are,
[tex]\begin{gathered} R=\frac{3}{4}\times\frac{2}{3}x \\ =\frac{1}{2}x \end{gathered}[/tex]
Thus, the area of the raddish is 50% of the total area of the garden sfter the changes.
1 ptsQuestion 5Jane started jogging 5 miles from home, at a rate of 2 mph. Write the slope-intercept form of an equation for Jane's position relative to home.
Answers
Answer
[tex]y=2x+5[/tex]
SOLUTION
Problem Statement
The question wants us to model the distance Jane is from her home given her initial starting point (5 miles from home) and her speed (2 mph)
Explanation
To solve the question, we simply need to model her jogging using the equation of a line.
The general equation of a line is given as:
[tex]\begin{gathered} y=mx+c \\ \text{where,} \\ m=\text{slope}=\text{this represents Jane's speed} \\ c=y-\text{intercept}=\text{this represents her initial position from her home} \\ x=\text{time taken for Jane to move} \\ y=\text{Jane's final position after moving for time, x} \end{gathered}[/tex]
We have been told that her speed is 2 mph. Thus, m = 2. We have also been given her initial position from her house to be 5 miles.
Jane starts jogging 5 miles from her home, thus, her position relative to her home will continue to increase as she jogs on at 2 mph. Thus, c = 5 and NOT -5.
This means we can write the equation for her position is:
[tex]\begin{gathered} m=2,c=5 \\ \therefore y=2x+5 \end{gathered}[/tex]
Final Answer
[tex]y=2x+5[/tex]
An empty shipping box weighs 250 grams. The box is then filled with t-shirts. Each tshirts weighs 132.5 grams. The equation W = 250 + 132.5T represents the relationship between the quantities in this solution where W is the weight in grams of the filled box and T the number of shirts in the box. Consider this equation 2900 = 250 + 132.5T. What does the solution to this equation tell us?
Answers
Given the next equation
2900 = 250 + 132.5T
its solution is:
2900 - 250 = 132.5T
2650 = 132.5T
2650/132.5 = T
T = 20
Given that W is weigth and T is t-shirts, the solution tell us that a box with 20 t-shirts weights 2900 grams
Felipe states that he can use the
inequality 1 ≤ x ≤ 4 to describe the domain
{1, 2, 3, 4} for a given function. Explain Felipe's
error.
Answers
For the inequality 1 ≤ x ≤ 4 given by Felipe the domain of the function is stated as {1,2,3,4} which shows the error of x belongs to which set of numbers is not specified.
As given in the question,
Given inequality is equal to :
1 ≤ x ≤ 4
Domain of the given inequality function is given by :
x belongs to all real numbers as it is not specified which set of numbers x belongs.
Consider x as set of real numbers
Given domain is {1,2,3,4}
Error is Felipe needs to specify x must belongs to integers or natural numbers then only domain is {1,2,3,4} for the given inequality else there are infinite many numbers between 1 to 4.
Therefore, for the inequality 1 ≤ x ≤ 4 given by Felipe the domain of the function is stated as {1,2,3,4} which shows the error of x belongs to which set of numbers is not specified.
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Find the measure of each angle in the proplem RE contains point P
Answers
In the given figure, line LP is lie on the line RE, thus from the linear property
Angle LPR + Angle LPE = 180°
It is given that Angle LPR = 3z, angle LPE = 2z
Angle LPR + Angle LPE = 180°
3z° + 2z° = 180°
5z° = 180°
z = 180/5
z=36
Substitute the value of z = 36 in the angle LPR;
Angle LPR = 3z
= 3(36)
=108°
Angle LPE = 2z
= 2(36)
= 72°
Answer : B) 108 and 72
Which relationship can be represented by the equation y = 1/5x A) One wager jug hold 5 quarts. Let x represent the number of water jugs and y represent the number of quartsB) Bananas are on sale for $0.20 per banana. Let x represent the number of bananas and y represent the total cost, in dollars.C) David runs ar a constant rate. He runs 15 mines in 3 hours. Let x represent the number of hours and y present the number of miles.D) For every 10 gallons of water, Jasmine adds 2 cups of soap. Let x represent the number of hours and y represent the number of miles.E) The library charges a few at a rate of $5 for every 10 days a book is late. Let x represent the number of days late and y represent the fee, in dollars.
Answers
Answer:
Explanation:
Option A
[tex]\begin{gathered} \text{One wager jug hold 5 quarts} \\ y=kx \\ 5=1k \\ y=5x \end{gathered}[/tex]
Option B
[tex]\begin{gathered} 1\text{ banana costs \$}$0.20$ \\ y=0.20x \\ y=\frac{1}{5}x \end{gathered}[/tex]
The correct choice is B.
Write the coordinates of the vertices after a rotation of 90 degrees counter clock wise around the origin. Give me the coordinates and that’s it no explanation
Answers
[tex]\begin{gathered} C(1,9) \\ D(4,9) \\ E\left(0,3\right) \\ Rotation\text{ of 90\degree counterclockwise} \\ The\text{ new coordinates will be \lparen-y,x\rparen} \\ Hence \\ C^{\prime}(-9,1) \\ D^{\prime}(-9,4) \\ E^{\prime}(-3,0) \end{gathered}[/tex]
Look at the system of equations shown.y = 3x + 7y = 2x + 8What is the x-coordinate of the solution to the system?Select one:10- 10O- 1o
Answers
We have a system of 2 equation (Eq):
y = 3x + 7 (Eq 1)
y = 2x + 8 (Eq 2)
To solve the system, we can match both equations.
3x + 7 = 2x + 8
3x - 2x = 8 - 7
x = 1
if the point (-1,4)and (2,13)are on the graph of the quadratic function [tex]y = 7x {}^{2} + bx + c[/tex]what are the values of b and c
Answers
The Solution:
Given:
[tex]y=7x^2+bx+c[/tex]
Given that the points: (-1,4) and (2,13) are on the graph of the given equation,
We are required to find the values of a and b.
Substitute (x= -1, y = 4) in the equation, we get:
[tex]\begin{gathered} 4=7(-1)^2+b(-1)+c \\ 4=7-b+c \\ -3=-b+c...eqn(1) \end{gathered}[/tex]
Substitute (x= 2, y = 13) in the equation, we get:
[tex]\begin{gathered} 13=7(2)^2+b(2)+c \\ 13=28+2b+c \\ -15=2b+c...eqn(2) \end{gathered}[/tex]
Solving eqn(1) and eqn(2) simultaneously by the elimination method:
Subtract eqn(1) from eqn(2):
[tex]\begin{gathered} -15--3=2b--b+c-c \\ -12=3b \end{gathered}[/tex]
Divide both sides by 3.
[tex]b=\frac{-12}{3}=-4[/tex]
Substitute -6 for b in eqn(1).
[tex]\begin{gathered} -3=-b+c \\ -3=-(-4)+c \\ \\ -3=4+c \\ -3-4=c \\ -7=c \\ c=-7 \end{gathered}[/tex]
Therefore, the correct answers are:
b = -4
c = -7
Simplity the expression:4b+9b
Answers
Since both variables are equal (b) we can add them:
[tex]4b+9b[/tex][tex]13b[/tex]
Food Express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on their receipt. So far, 219 of the first 264 customers have not received a star on their receipt. What is the experimental probability of winning a free gallon of milk?options: 3/11....15/88....73/88.....1/78
Answers
Solution:
Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood, and each repetition is known as a trial.
[tex]\begin{gathered} P(E)=\frac{n(E)}{n(T)} \\ \\ Where; \\ n(E)=\text{ number of event} \\ \\ n(T)=\text{ total outcome} \end{gathered}[/tex]
If 219 of the first 264 customers have not received a star on the receipt, then a customer that would win a free gallon of milk would be among (264 - 219) customers. Thus;
The experimental probability of winning a free gallon of milk is;
[tex]\begin{gathered} =\frac{264-219}{264} \\ \\ =\frac{45}{264} \\ \\ =\frac{15}{88} \end{gathered}[/tex]
CORRECT OPTION:
[tex]\frac{15}{88}[/tex]
cellusTranslate the triangle.Then enter the new coordinates.A -1,61B(0,4)A'([?], [])B'([],[])C'([],[])C (-6,1)< 10.2 >IEnter
Answers
The coordinates of the images are;
[tex]undefined[/tex]
Here, we want to translate the given triangle
The translation is in the units of (10,2)
What this mean is that we are going to make a translation of 10 in the x-axis direction and 2 units in the y-axis direction
Hence, we are having a unit of 10 rightwards (positive x-axia) and 2 unit of 2 units upwards (vertically on the y-axis)
So what we do now in respective cases is add 10 to the x-axis values of each point and add 2 to the y-axis values of each point
Thus, we have;
[tex]\begin{gathered} A(-1,6)\text{ to A'(-1+10, 6+2)= A'(9,8)} \\ B(0,4)\text{ to B'(0+10, 4+2) = B'(10,6)} \\ C(-6,1)\text{ to C'(-6+10,1+2) = C'(4,3)} \end{gathered}[/tex]
10^4 divided by 10^6 in expanded form, then find out what the answer is with a single power.
Answers
The given expression is:
[tex]\frac{10^4}{10^6}[/tex]
Exapanding the above expression,
[tex]\frac{10\times10\times10\times10}{10\times10\times10\times10\times10\times10}[/tex]
(The number of 10s are the same as the power of 10).
Now, cancel out the common terms in the numerator and the denominator of the above expression.
[tex]\frac{1}{10\times10}[/tex]
The denominator of the above expression can now be expressed as the power of 10 as,
[tex]\frac{1}{10^2}[/tex]
According to the law of exponents,
[tex]\frac{1}{x_{^{^m}}}=x^{-m}[/tex]
Hence, we can write
[tex]\frac{1}{10^2}=10^{-2}[/tex]
Therefore, 10^4 divided by 10^6 can be expressed as a term with a single power as,
[tex]10^{-2}[/tex]