Answer:
We can fill 150 paper cup cones.
Step-by-step explanation:
Volume of a cone is
V = 1/3 pi * r^2 *h
The volume of one cone is
pi = 3.14
r = d/2 = 6/2 =3
h=9
Substitute what we know
V = 1/3 * (3.14) * (3^2) * (9)
= 27* 3.14
= 84.78 cm^3
The water cooler has 12717 cm^3 water
Divide the water by the volume of the paper cup cone and we will know how many paper cup cones we can fill, assuming we fill them completely.
12717/ 84.78 = 150
We can fill 150 paper cup cones.
The volume of one cone-shaped paper cup is 84.78 cm³. With 12,717 cm³ of water in the cooler, approximately 150 cups can be filled.
To find out how many paper cups can be filled from the water cooler, we first need to calculate the volume of one paper cup. Given that the cup is shaped like a cone with a height of 9 cm and a base diameter of 6 cm, we can find the volume using the formula for the volume of a cone, which is V = (1/3)\u03c0r^2h, where V is the volume, r is the radius of the base, and h is the height of the cone.
The radius of the base is half the diameter, so r = 3 cm. Plugging in the values into the formula, we get: V = (1/3)*3.14*(3²)*9.
Calculating this, we get V \<= 84.78 cm³ per cup. Now, to determine how many cups can be filled from the cooler containing 12,717 cm³ of water, we divide the total amount of water in the cooler by the volume of one cup:
Number of cups = 12,717 cm³ / 84.78 cm³.
This gives us approximately 150 cups that can be filled from the water cooler.
Write the slope-intercept form of the equation of each line given the slope and y-intercept
1. slope = --1/2 y-intercrept = -2
2. slope = - 4/3, Y intercept = 1
3. Slope = 1/3, Y intercept = -1
4 slope = -1/2, Y intercept 4
If you can, please explain. Thanks!
To write the slope-intercept form of a linear equation, we use the formula y = mx + b, where m represents the slope and b represents the y-intercept.
Explanation:To write the slope-intercept form of a linear equation, we use the formula y = mx + b, where m represents the slope and b represents the y-intercept.
For the first equation, the slope is -1/2 and the y-intercept is -2. So the equation is y = -1/2x - 2.For the second equation, the slope is -4/3 and the y-intercept is 1. Therefore, the equation is y = -4/3x + 1.For the third equation, the slope is 1/3 and the y-intercept is -1. The equation is y = 1/3x - 1.For the fourth equation, the slope is -1/2 and the y-intercept is 4. The equation is y = -1/2x + 4.Learn more about Linear equations here:
https://brainly.com/question/32634451
#SPJ11
A box contains10 pens, 5 of the pens are red, 4 are balck and 1 are bluem What is the probability of pulling out a black pen first, putting it back into the box, and then pulling a red pen ?
Final answer:
The probability of drawing a black pen first and then a red pen with replacement from a box of 10 pens is 20%.
Explanation:
To calculate the probability of drawing a black pen and then a red pen with replacement in a box that contains 10 pens, we should calculate the probability of each event separately and then multiply them since the events are independent.
There are 5 red pens, 4 black pens, and 1 blue pen, making a total of 10 pens. The probability of drawing a black pen is the number of black pens divided by the total number of pens: P(black) = 4/10 or 0.4.
Since the pen is replaced, the total stays the same. Therefore, the probability of then drawing a red pen is the number of red pens divided by the total number of pens: P(red) = 5/10 or 0.5.
To find the combined probability of both events happening in sequence (drawing a black pen and then a red pen), we multiply the two probabilities together: P(black and red) = P(black) × P(red) = 0.4 × 0.5 = 0.2 or 20%.
Which algebraic rule describes the transformation?
A) (x, y) → (x + 1, y − 3)
B) (x, y) → (x + 3, y − 1)
C) (x, y) → (x − 1, y + 3)
D) (x, y) → (x − 3, y + 1)
Answer:
B
Step-by-step explanation:
To get to to triangle Y'X'Z', you need to move triangle YXZ 3 units to the right (+3), and 1 unit down (-1). So (x+3,y-1)
Answer:
b
Step-by-step explanation:
During a recent shopping trip, Erin bought six shirts that cost $15.95 each. How much change did Erin receive if she paid with a $100 bill?
Answer:
4 Dollars and 30 cents
Step-by-step explanation:
15.95 x 6 = 95.7
100-95.7= 4.30
Final answer:
Erin bought six shirts at $15.95 each, totaling $95.70. After paying with a $100 bill, she would receive $4.30 in change.
Explanation:
The question asks us to calculate the total cost of six shirts and then determine the change from a $100 bill. Erin bought six shirts that cost $15.95 each. To find the total cost, we multiply the price of one shirt by the number of shirts:
$15.95 × 6 = $95.70.
Next, we calculate the change Erin would receive if she paid with a $100 bill:
$100 - $95.70 = $4.30.
Therefore, Erin would receive $4.30 in change.
Which of the following equations is equivalent to 2/3x - 1/2y = 6?
2x - y = 6
2x - y = 36
4x - 3y = 36
Answer:
4x - 3y = 36
Step-by-step explanation:
2/3x - 1/2y = 6
Multiply each side by 6 to get rid of the fractions
6* (2/3x - 1/2y) = 6*6
Distribute the 6
12/3 x - 6/2y = 36
4x -3y = 36
Write an equation in point-slope form for the line with the given slope, passing through the given point. Slope=4/3 , (-2,11)
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We have:
[tex]slope:m=\dfrac{4}{3}[/tex]
[tex]the\ point\ (-2,\ 11)\to x_1=-2,\ y_1=11[/tex]
SubstituteL
[tex]y-11=\dfrac{4}{3}(x-(-2))\\\\\boxed{y-11=\dfrac{4}{3}(x+2)}[/tex]
describe why hawaii was seen as an important territory to the United states
The United States was at war with Spain in Cuba and the Philippines. Hawaii was of importance to the military effort because of its location. ... It was at this time that Congress annexed Hawaii because of the economic and military benefit the islands offered.
mark brainliest :)
hope this helped
Answer:
Because of the oceans and all of the undiscovered stuff there. The fact it was an island and could be used as a navy base. Very dessolite. Not a lot of people the time it was a territory
Step-by-step explanation:
Find three ratios equivalent to 5/7
Answer:
10/14, 15/21
Step-by-step explanation:
WE are given a ratio 5/7
To find equivalent ratios it is sufficient to multiply both numerator and denominator by the same number
Let us take 2,3 for example.
When we multiply both numerator and denominator by 2, value does not change.
Hence we get equivalent fraction.
So 10/14 is one such fraction.
Next is multiply by 3
15/21 is another fraction.
find value of x
pls helpp meeeeeee
[tex]3\times9^{x+1}=27^{x-1}\\\\3\times(3^2)^{x+1}=(3^3)^{x-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\3\times3^{2(x+1)}=3^{3(x-1)}\\\\3\times3^{2x+2}=3^{3x-3}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\3^{1+2x+2}=3^{3x-3}\\\\3^{2x+3}=3^{3x-3}\iff2x+3=3x-3\qquad\text{subtract 3 from both sides}\\\\2x=3x-6\qquad\text{subtract 3x from both sides}\\\\-x=-6\to\boxed{x=6}[/tex]
And this one too!! Thanks in advance
Answer:
20/9 sq.feet
Step-by-step explanation:
The width is 4/3 ft because 1/3 times 4 is 4/3 and the length is 5/3 because 1/3 times 5 is 5/3.
Then to find the area you do length times width.
5/3 ×4/3= 20/9 sq. feet
I hope this helps! :)
Match the following. 1. an angle that measures more than 0° but less than 90° vertical angles 2. two angles that have a common vertex and side but are not overlapping straight angle 3. two angles whose sum is 90° acute angle 4. an angle that measures more than 90° but less than 180° right angle 5. an angle that measures exactly 90° adjacent angles 6. an angle that measures exactly 180° complementary angles 7. two angles whose sum is 180° obtuse angle 8. the point where two line segments, lines, or rays meet to form an angle supplementary angles 9. angles that are opposite from one another at the intersection of two lines; vertical angles are congruent vertex
Answer:
Match the following:
1. An angle that measures more than 0° but less than 90°:
Acute angle.
2. Two angles that have a common vertex and side but are not overlapping:
Adjacent angles.
3. Two angles whose sum is 90°
Complementary angles.
4. An angle that measures more than 90° but less than 180°:
Obtuse angle.
5. An angle that measures exactly 90°:
Right angle.
6. An angle that measures exactly 180°:
Straight angle.
7. Two angles whose sum is 180°:
Supplementary angles.
8. The point where two line segments, lines, or rays meet to form an angle:
Vertex.
9. Angles that are opposite from one another at the intersection of two lines:
Vertical angles.
Step-by-step explanation:
Match the following:
1. An angle that measures more than 0° but less than 90°:
Acute angle.
2. Two angles that have a common vertex and side but are not overlapping:
Adjacent angles.
3. Two angles whose sum is 90°
Complementary angles.
4. An angle that measures more than 90° but less than 180°:
Obtuse angle.
5. An angle that measures exactly 90°:
Right angle.
6. An angle that measures exactly 180°:
Straight angle.
7. Two angles whose sum is 180°:
Supplementary angles.
8. The point where two line segments, lines, or rays meet to form an angle:
Vertex.
9. Angles that are opposite from one another at the intersection of two lines:
Vertical angles.
The terms such as acute angle, adjacent angles, complementary angles, obtuse angle, right angle, straight angle, supplementary angles, vertex, and vertical angles are correctly matched with their respective definitions.
Explanation:The correct matching for the provided terms are as follows:
An angle that measures more than 0° but less than 90° is an acute angle.Two angles that have a common vertex and side but are not overlapping are adjacent angles.Two angles whose sum is 90° are referred to as complementary angles.An angle that measures more than 90° but less than 180° is an obtuse angle.An angle that measures exactly 90° is a right angle.An angle that measures exactly 180° is a straight angle.Two angles whose sum is 180° are supplementary angles.The point where two line segments, lines, or rays meet to form an angle is a vertex.Angles that are opposite from one another at the intersection of two lines; vertical angles are congruent are vertical angles.Learn more about Angles here:https://brainly.com/question/33354646
#SPJ6
Which of the following is an irrational number?
Answer:
7.25252525
Step-by-step explanation:
Irrational numbers are numbers that never end, therefore 7.25 is an irrational number. also, none of the other ones are never ending
25 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!PLEASE HELP ME QUICK !!!!!!!!!!!!!!!!!!!!! Will Give Brainliest!!!!!!!Cara and Cody have there first job. They need to make 9 quarts of violet paint. Cody has figured out that violet paint is made by mixing 1/3 red with 2/3 blue paint.
How much red paint will they need?
How much blue paint?
Explain how you figured it out.
Is this a proportional relationship?
If so, model this using two of the three ways that proportional relationships are represented ( table, graph or equation)
Indicate what the constant of proportionality is in this problem.
Answer:
a 3 quarts
b 6 quarts
c thats in the step by step
d yes
Step-by-step explanation:
c since they have to make 9 quarts of violet paint if you add the number of red and blue paint mixed together you get 1 quart meaning you have to multiply both by nine and if you simply you get what i have above
This is a proportional relationship because you decide whether two quantities are in a proportional relationship, by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
-hope this helps :D
The ratio of students who walk home from school to the students who ride the bus is 2:7
The number of bus riders is how many times the number of students who walk home?
Answer:
2.5 is the answer
Step-by-step explanation:
7/2 = 2.5
You need to divide the no of bus rider with no of students
Please answer in detail
Answer:
[tex]\dfrac{1}{24}[/tex]
Step-by-step explanation:
1. The student is allowed to choose white, blue, green or black Polo shirts. So the student has 4 possibilities to select shirt and the probability of wearing the blue shirt is [tex]\dfrac{1}{4}.[/tex]
2. The student is allowed to choose khaki, black or plaid skirts/pants. So the student has 3 possibilities to select skirt and the probability of wearing the plaid skirt is [tex]\dfrac{1}{3}.[/tex]
3. The student is allowed to choose black or brown shoes. So the student has 2 possibilities to select shoes and the probability of wearing black shoes is [tex]\dfrac{1}{2}.[/tex]
Now use the product rule for probabilities:
[tex]Pr=\dfrac{1}{4}\cdot \dfrac{1}{3}\cdot \dfrac{1}{2}=\dfrac{1}{24}.[/tex]
Factor -.36 out of -1.8w+3.96
[tex]-1.8w+3.96=(-0.36)(5w)+(-0.36)(11)\\\\=\boxed{-0.36(5w+11)}[/tex]
what is the answer to 4r + 9r - 11r + 7r
Answer:
9r
Step-by-step explanation:
Simplify:
4r + 9r - 11r + 7r
13r - 11r + 7r
2r + 7r
9r
The answer to the given expression i.e. 4r + 9r - 11r + 7r is 9r.
Given that,
The given expression is 4r + 9r - 11r + 7r.We need to solve the above expression.Based on the above information, the calculation is as follows:
= 4r + 9r - 11r + 7r
= 20r - 11r
= 9r
Therefore we can conclude that the answer to the given expression i.e. 4r + 9r - 11r + 7r is 9r.
Learn more: brainly.com/question/18293528
There were 48 ants on a hill. Then 13 of the ants marched away.how many ants are still on the hill?
Answer: 35
Step-by-step explanation: 48 - 13 = 35
Answer:
35 ants left
Step-by-step explanation:
you start with 48-13then you turn the problem to 40-10=30then subtract 3 from 8 and get 5then you add 30+5 and get 357x(x+1.8)=0 please help !
The solutions to the equation 7x(x+1.8)=0 are x = 0 and x = -1.8.
The highest power of the polynomial function is defined as the degree.
The Fundamental Theorem of Algebra asserts that a polynomial has n roots if its degree is n.
The equation is 7x(x+1.8)=0.
To solve this equation, we can use the property that if the product of two factors is equal to zero, then at least one of the factors must be zero.
Therefore, we set each factor equal to zero and solve for x:
7x = 0
x = 0
x + 1.8 = 0
x = -1.8
So, the solutions to the equation 7x(x+1.8)=0 are x = 0 and x = -1.8.
To solve the equation 7x(x+1.8)=0, set each factor equal to zero to find the two possible solutions for x, which are 0 and -1.8.
Explanation:To solve the equation 7x(x+1.8)=0, we need to set each factor equal to zero and solve for x.
Setting 7x=0, we find x=0. Setting x+1.8=0, we subtract 1.8 from both sides to get x=-1.8. Therefore, the solutions to the equation are x=0 and x=-1.8.
SEO Keywords: quadratic equation, solve, factor, solutionsThe given equation is 7x(x+1.8)=0. This is a quadratic equation that can be easily solved by setting each factor equal to zero. Here's how you can find the value(s) of x:
Set 7x equal to zero: 7x = 0 ---> x = 0.Set (x + 1.8) equal to zero: x + 1.8 = 0 ---> x = -1.8.Therefore, the two possible values for x are 0 and -1.8.
Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. The oil change for one car required 5 quarts of oil and cost $25.50. The oil change for the other car required 7 quarts of oil and cost $30.00. How much is the labor fee and how much is each quart of oil?
Answer:
The labor fee is $14.25, each quart of oil costs $2.25.
Step-by-step explanation:
Let $x be thee price of each quart of oil and $y be a flat fee for labor.
1. If the oil change for one car required 5 quarts of oil, then these 5 quarts cost $5x and together with a flat fee for labor it cost $25.50. Thus,
5x+y=25.50.
2. If the oil change for another car required 7 quarts of oil, then these 7 quarts cost $7x and together with a flat fee for labor it cost $30.00. Thus,
7x+y=30.00.
3. Subtract from the second equation the first one, then
[tex]7x+y-(5x+y)=30.00-25.50,\\ \\7x+y-5x-y=4.50,\\ \\2x=4.50,\\ \\x=\$2.25.[/tex]
Substitute it into the first equation:
[tex]5\cdot 2.25+y=25.50,\\ \\y=25.50-11.25,\\ \\y=\$14.25.[/tex]
The labor fee is $14.25, each quart of oil costs $2.25.
The labor fee is $14.25 and the cost per quart of oil is $2.25.
Explanation:To find the labor fee and cost per quart of oil, we can set up a system of equations using the given information. Let x represent the cost of each quart of oil and y represent the labor fee.
We have the equations:
5x + y = 25.50
7x + y = 30.00
We can solve this system of equations using substitution or elimination. Substituting y from the first equation into the second equation, we get:
7x + (25.50 - 5x) = 30.00
2x = 4.50
x = 2.25
Substituting x back into the first equation, we get:
5(2.25) + y = 25.50
11.25 + y = 25.50
y = 14.25
Therefore, the labor fee is $14.25 and the cost per quart of oil is $2.25.
Please Help!
Write an inequality and solve each problem.
Two less than a number is less than 9.
Answer:
Step-by-step explanation:
Unknown number be 'x'
X-2<9
An explanation of solving an inequality where the number is two less than a number less than 9.
An inequality can be written as: x - 2 < 9, where x is the number.
To solve the inequality:
Add 2 to both sides: x < 11
So, the solution to the inequality is: x < 11
athaniel is using the quadratic formula to solve 0 = x2 + 5x - 6. His steps are shown below. What are the solutions to the equation? x = –1, 6 x = –6, 1 x = –22, 27 x = –27, 22
Answer:
x = - 6 or x = 1
Step-by-step explanation:
given a quadratic equation in standard form : ax² + bx + c = 0 : a ≠ 0
then the equation can be solved using the quadratic formula
• x = ( - b ± [tex]\sqrt{b^2-4ac}[/tex]) / 2a
x² + 5x - 6 = 0 is in standard form
with a = 1, b = 5 and c = - 6
x = (- 5 ± [tex]\sqrt{5^2-(4(1)(-6)}[/tex]) / 2
= (- 5 ± [tex]\sqrt{25+24}[/tex]) / 2
= (- 5 ± [tex]\sqrt{49}[/tex]) / 2
x = [tex]\frac{-5-7}{2}[/tex] = [tex]\frac{-12}{2}[/tex] = - 6
or x = [tex]\frac{-5+7}{2}[/tex] = [tex]\frac{2}{2}[/tex] = 1
The solutions to the quadratic equation x² + 5x - 6 = 0 are x = 1 and x = -6.
Explanation:To solve the quadratic equation x² + 5x - 6 = 0, Nathaniel used the quadratic formula.
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c correspond to the coefficients of the quadratic equation.
In this case, a = 1, b = 5, and c = -6.
Substituting these values into the quadratic formula, we get x = (-5 ± √(5² - 4(1)(-6))) / (2(1)).
Simplifying further, we have x = (-5 ± √(25 + 24)) / 2.
This yields two solutions: x = (-5 + √49) / 2 and x = (-5 - √49) / 2.
Simplifying the square root, we get x = (-5 + 7) / 2 and x = (-5 - 7) / 2.
Therefore, the solutions to the quadratic equation are x = 1 and x = -6.
What is the x-intercept of the graph below?
-3
-2
2
3
Answer:
-3
Step-by-step explanation:
What does t equal ?
Answer:
t = 56.67
Step-by-step explanation:
Remark
If you are given a rhombus, what you are being told is that all 4 sides are equal. So WX = XY
Equation
6t - 82 = 3t + 88 Add 82 to both sides
Solution
6t - 82 + 82 = 3t + 88 + 82 Combine6t = 3t + 170 Subtract 3t from both sides6t - 3t = 3t - 3t + 170 Combine3t= 170 Divide by 3t = 170/3t = 56.67It takes Sam 5/8 days to drive to his aunt's house. He has now been driving for 3/8 days.
Answer:
He needs to drive for 2 more days to get to his aunt's house.
Step-by-step explanation:
Answer:
hello
Step-by-step explanation:
Mrs.Barkley has 75 feet ribbon. If each of the 18 students in her class gets an equal length of ribbon, how many inches of ribbon will each student get?
Answer:
Each student would get 4 inches of ribbon
Step-by-step explanation:
Mrs. Barkley has 75 inches of ribbon and is splitting it between 18 students so you would divide 75 by 18. When you divide you get 4.166666... etc. So the answer would be 4
Each of the 18 students in Mrs. Barkley's class will receive 50 inches of ribbon when 75 feet of ribbon are divided equally among them.
The student has asked how many inches of ribbon each student will get if Mrs. Barkley has 75 feet of ribbon and splits it equally among 18 students. To solve this problem, we first need to convert feet to inches because there are 12 inches in a foot. Then we divide the total inches of ribbon by the number of students.
Total length of ribbon for each student= 75/18
The total length of ribbon for each student≈4.1667
So, each student will receive approximately 4.1667 feet of ribbon.
To find out how many inches this is, we'll convert this value to inches. Since 1 foot is equal to 12 inches, we can multiply the total length of the ribbon for each student by 12:
The total length of ribbon for each student (in inches)=4.1667×12
The total length of ribbon for each student (in inches)≈49.9999
Therefore, each student will receive approximately 50 inches of ribbon.
Which transformation changes triangle ABC to triangle A’B’C’?
Answer: rotation 180 degrees counterclockwise about the origin
Step-by-step explanation: the formula for rotating 180 degrees is (x , y) = (-x , -y). thus, an example of point A is (2 , -4), and it results in being (-2, 4), and so forth for the following points.
Answer:
Reflection about the y axis, and then about the x- axis
Step-by-step explanation:
When reflecting an object about the y- axis, the x-coordinates are multiplied with -1.
When reflecting an object about the x-axis, the y-coordinates are multiplied with -.
When reflecting about both axes, both coordinates are multiplied by -1.
Now looking at the coordinates of the two triangles:
A(2, -4) → A'(-2, 4)
B(5, -5) → B'(-5, 1)
C(4, -5) → C'(-4, 5)
All of the coordinates are multiplied by -1.
The location of four game stops are on a coordinate grid are as follows:
Stop 1 at (−2,1)
Stop 2 at (−2, −7)
Stop 3 at (5,−7)
Stop 4 at (5, 1)
Paulo begins at Stop 1 and then walks to Stop 2, then Stop 3, and then Stop 4. Then he walks to Stop 1 again. The path between each stop is a straight line. One unit on the coordinate grid equals 125 feet.
What is the total distance Paulo walked?
Answer:
3750 feet
Step-by-step explanation:
Given that Paulo begins at Stop 1 and then walks to Stop 2, then Stop 3, and then Stop 4. Then he walks to Stop 1 again.
Where stops are given by coordinates:
Stop 1 at (−2,1)
Stop 2 at (−2, −7)
Stop 3 at (5,−7)
Stop 4 at (5, 1)
The path between each stop is a straight line. One unit on the coordinate grid equals 125 feet.
Now we need to find about what is the total distance Paulo walked.
So first we graph those points so that we can easily count the length of each side. then add each side to get the total length
length of rectangular path = 8+7+8+7=30
since one unit on the coordinate grid equals 125 feet. So to find the actual length we need to multiply 30 by 125 feet.
Hence final answer will be 125*30 = 3750 feet.
Norah has 2/3 ton of stone to spread equally in 4 square yards. How many tons of stone will be spread in each square yard?
Answer:
The answer is 1/6.
In each square yard, Norah would spread 1 / 6 ton of stone.
Given that,
Norah has 2/3 tons of stone to spread equally in 4 square yards, how many tons of stone will be spread in each square yard is ot be determined.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Quantity if Stone = 2/3 ton
Area = 4 square yards
Quantity per yard = [2/3] / 4= 1 / 6
Thus, in each square yard, Norah would spread 1 / 6 ton of stone.
Learn more about ratios here:
brainly.com/question/13419413
#SPJ5
what is the factored for of the polynomial x2 - 16x + 48
Answer:
[tex](x-12)(x-4)[/tex]
Step-by-step explanation:
[tex]x^2 - 16x + 48[/tex]
In the given expression , the product is 48 and sum is -16
-4 times -12 gives us 48
-4 plus -12 gives us -16. So two factors are -4 and -12
Beak the middle term using factors
[tex]x^2 -4x-12x+48[/tex]
Group first two terms and last two terms
[tex](x^2 -4x)+(-12x+48)[/tex]
FActor out GCF from each group
[tex]x(x -4)-12(x-4)[/tex]
FActor out x-4 that is in common
[tex](x-12)(x-4)[/tex]