Below is the graph of a trigonometric
function. It intersects its midline at
(1.25, -2.75), and it has a minimum point
at (4.75, -6.25).
什 +
-6 -4 -2
I
4
3
2
1
-2
-3 +
GA
-4
Y
-5+
-6
-7-
-8-
co
-9
2
4 6
(1.25, -2.75)
8
(4.75, -6.25)
10 12 14
I
→x
I
What is the amplitude of the function?
I

The correct choice is a straight line with a positive slope that intersects the y-axis at (0, 4). This is because f(x) = 3x + 4 is a linear function with a slope of 3 and a y-intercept of 4. The graph of this function will be a straight line with a positive slope that crosses the y-axis at (0, 4).

A graph is a visual representation of data or a function, usually in the form of a plot with one or more variables on the x and y axes. It is a way to show relationships between variables or patterns in data.

An intercept is a point at which a curve or line intersects an axis, usually the x-axis or y-axis. The x-intercept is where the line crosses the x-axis, and the y-intercept is where the line crosses the y-axis.

According to the given information:

Without a visual component, it is impossible to identify which of the following choices represents the graph of the linear function f(x) = 3x + 4:

a) a straight line with a negative slope that intersects the y-axis at (0, -4)

b) a straight line with a positive slope that intersects the y-axis at (0, 4)

c) a curved line that increases as x increases and passes through the point (0, 4)

However, we know that the graph of f(x) = 3x + 4 is a straight line with a slope of 3 and a y-intercept of 4. So, the correct choice would be b) a straight line with a positive slope that intersects the y-axis at (0, 4). This graph would show the function increasing at a steady rate of 3 units for every 1 unit of horizontal change, with the y-intercept at the point (0, 4).

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Answer:

y = 1/2x + 2

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0,2) (2,3)

We see the y increase by 1 and the x increase by 2, so the slope is

m = 1/2

Y-intercept is located at (0,2)

So, the equation of the line is y = 1/2x + 2

The photo taken from point B is twice the size of the photo taken from point A.

In this scenario, Fran is likely adjusting her distance from her family to fit everyone in the photo, which means she is changing the scale of the image. To find the center of dilation and the scale factor, we can consider the initial distance between Fran and her family and the new distance she moves back to.

The center of dilation is the point where Fran stands to take the photo, and the scale factor is the ratio of the new distance to the initial distance. If we assume Fran initially stood at point A and moved back to point B, the scale factor would be:

scale factor = AB/AD

where AD is the initial distance between Fran and her family and AB is the new distance after she moves back.

For example, if Fran initially stood 5 feet away from her family and moved back to 10 feet away to fit everyone in the photo, the scale factor would be:

scale factor = AB/AD = 10/5 = 2

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Complete question is:

For each real-world context or circumstance, determine the center of the dilation and an approximate scale factor or way to determine the scale factor.

Fran walks backward to a distance that will allow her family to all show up in the photo she is about to take.

Answer:

AOC=

130 degrees

Step-by-step explanation:

(circle)3x + (square)94 + (circle)x + square)18 + (circle)2x (square)-4 = 180

circles = 3x + x + 2x = 6x

squares = 94 + 18 + (-4) = 108

6x + 108 = 180

- 108 -108

6x = 72

6x/6 = 72/6

x= 12

angle AOC =

3x + 94

3 times 12 + 94

36+94 = 130 degrees

Answer:To find the dimensions of the new deck, we need to scale the base and height of the original deck by a factor of 3:5.

The scaled base will be:

16 feet x (3/5) = 9.6 feet

The scaled height will be:

9 feet x (3/5) = 5.4 feet

Therefore, the dimensions of the new deck will be 9.6 feet for the base and 5.4 feet for the height.

Step-by-step explanation:

Answer:

Part A:

The ratio of the sides of the new deck to the original deck is 2:5. Therefore, the base and height of the new deck can be found by multiplying the base and height of the original deck by the scale factor, which is 2/5.

Base of new deck = 15 * (2/5) = 6 feet

Height of new deck = 9 * (2/5) = 3.6 feet

Therefore, the dimensions of the new deck are 6 feet for the base and 3.6 feet for the height.

Part B:

The area of a triangle can be found by multiplying the base and height and dividing by 2.

Area of original deck = (15 * 9) / 2 = 67.5 square feet

Area of new deck = (6 * 3.6) / 2 = 10.8 square feet

Therefore, the area of the original deck is 67.5 square feet and the area of the new deck is 10.8 square feet.

Part C:

The ratio of the areas of the new deck to the original deck is:

Area of new deck / Area of original deck = 10.8 / 67.5 = 0.16

The scale factor is 2:5, or 0.4 as a decimal. The ratio of the areas is smaller than the scale factor. This means that the new deck is smaller than what it would be if it were built to scale.

Answer:

$120

EXPLANATION

since the total cost is $8880

and his parents are giving $6000

so left money he need to save is $2880

now he has time of 2 years which means 24 months

so using unitary method

24 months = $2880

1 month= $2880/24

1 month = $116.66

which is nearly $120

The factored form of the equation f(x) = 2x² – 9x – 18 is  (2x-3)(x+6)

The given equation is 2x² – 9x – 18

We have to factor out the expression

Let us take a=2, b=-9 and c =-18

To factor the equation, we need to find two numbers that add to -9 (which is the b variable in the equation) and multiply to -36

2x²+12x-3x – 18

2x(x+6)-3(x+6)

(2x-3)(x+6)

Hence, the factored form of the equation f(x) = 2x² – 9x – 18 is  (2x-3)(x+6)

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A digit that makes the number 6,197,34_ divisible by 6 is given as follows:

0.

(6 is another possible answer).

A number is said to be divisible by six when it is:

A number is divisible by 2 when it is an even number, meaning that it finishes in either 0, 2, 4, 6 or 8.

A number is divisible by 3 when the sum of the digits is a multiple of 3.

The sum of the digits is given as follows:

6 + 1 + 9 + 7 + 3 + 4 + x = 30 + x.

Hence with a final digit of zero or six, the number is divisible by six.

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Answer:

x = 7

Step-by-step explanation:

           When two secants intersect outside the circle, the product of their segments are equal.

               (3x + 15) * 15 = (x+20) * 20

            3x * 15 + 15*15 = x*20 + 20*20   {Distributive property}

                45x + 225  = 20x + 400

Subtract 225 from both sides,

                            45x = 20x + 400 - 225

                            45x = 20x + 175

Subtract 20x from both sides,

                 45x - 20x = 175

                           25x = 175

Divide both sides by 25,

                               x = 175 ÷ 25

                               [tex]\boxed{x=7}[/tex]

The ordered pairs for the equation is ( 0 , 0.5 ) and ( 1 , 0 )

Given data ,

Let the equation be represented as A

Now , the value of A is

-3x - 6y = -3

To generate two ordered pairs by substituting zero for x and y, we can substitute x = 0 and y = 0 into the given equation -3x - 6y = -3 and solve for y.

For x = 0:

-3(0) - 6y = -3

0 - 6y = -3

-6y = -3

y = -3 / -6

y = 0.5

So the first ordered pair is (0, 0.5)

For y = 0:

-3x - 6(0) = -3

-3x - 0 = -3

-3x = -3

x = -3 / -3

x = 1

So the second ordered pair is (1, 0)

The rate of change is the change in y-coordinate divided by the change in x-coordinate.

In this case, as we move from the first ordered pair (0, 0.5) to the second ordered pair (1, 0), the change in y-coordinate is -0.5 and the change in x-coordinate is 1.

Therefore, the rate of change is -0.5 / 1 = -0.5.

Hence , the ordered pairs are ( 0 , 0.5 ) and ( 1 , 0 )

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Answer:

70 people out of 108 prefer pizza

Answer:

L = 15 and W = 15. Hence, the dimensions of the rectangle with the smallest perimeter and area of 225 sq.ft. are 15 ft x 15 ft (i.e. a square).

Step-by-step explanation:

Let's assume the length of the rectangle is L and the width is W. The area of the rectangle is given as 225 sq.ft. Therefore, we have:

L x W = 225

The perimeter of the rectangle is given by:

2L + 2W

We need to find the dimensions of the rectangle that will give the smallest possible perimeter. To do this, we need to minimize the expression for the perimeter subject to the constraint that the area is 225 sq.ft. We can use the method of Lagrange multipliers to solve this problem.

Let f(L, W) = 2L + 2W be the expression for the perimeter and g(L, W) = L x W - 225 be the expression for the area. We want to minimize f(L, W) subject to the constraint g(L, W) = 0.

The Lagrange function is given by:

L(L, W, λ) = f(L, W) - λg(L, W)

= 2L + 2W - λ(LW - 225)

Taking partial derivatives and setting them equal to zero, we get:

∂L/∂λ = W = 0

∂W/∂λ = L = 0

∂L/∂λ = -λW = 0

∂W/∂λ = -λL = 0

∂L/∂λ = 2 - Wλ = 0

∂W/∂λ = 2 - Lλ = 0

Solving these equations, we get:

λ = 2/L = 2/W

Substituting λ in the expression for the area, we get:

L^2 = 225

Therefore, L = 15 and W = 15. Hence, the dimensions of the rectangle with the smallest perimeter and area of 225 sq.ft. are 15 ft x 15 ft (i.e. a square).

Answer:

width = 15 ft

length = 15 ft

Step-by-step explanation:

Let x = length and y = width.

area = length × width

A = xy

perimeter = 2(length + width)

P = 2(x + y)

P = 2x + 2y

A = 225

xy = 225

y = 225/x

P = 2x + 2(225/y)

P = 2x + 450/x

P = 2x + 450x^-1

dP/dx = 2 + 450(-1)(x^-2)

dP/dx = 2 - 450/x²

2 - 450/x² = 0

2x² - 450 = 0

x² - 225 = 0

x = ±√225

x = ±15

Discard x = -15.

width = 15 ft

length = 15 ft

If the length of a rectangle is 4 units less than its width w+10, the area of the rectangle is expressed in terms of w as w² + 6w.

Let's assume that the width of the rectangle is w. As given, the length of the rectangle is 4 units less than its width plus 10, which means the length is (w + 10) - 4 = w + 6.

So, the width of the rectangle is w units and the length is (w + 6) units.

The area of a rectangle is calculated by multiplying its length and width. Therefore, the area of the rectangle is:

Area = length x width

Area = (w + 6) x w

Area = w² + 6w

If we are given the value of w, we can find the area by substituting the value of w in the equation. If the value of w is not given, then the area of the rectangle cannot be calculated.

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Complete question is:

The length of a rectangle is 4 units less than its width w+10. Find expression for area of rectangle.

The coordinates of the vertices for the image, triangle U′V′W′, if the preimage is rotated 90° counterclockwise include the following:

U' = (1, 1).

V' = (-4, 0).

W' = (-1, 4).

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of triangle UVW, the coordinates of the vertices of the image are as follows:

(x, y)                               →            (-y, x)

Ordered pair U = (-1, 1)   →  Ordered pair U' = (1, -(-1)) = (1, 1).

Ordered pair V = (0, -4)   →  Ordered pair V' = (-4, -(0)) = (-4, 0).

Ordered pair W = (-4, -1)   →  Ordered pair W' = (-1, -(-4)) = (-1, 4).

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The shares that has the highest price today is shares B. The Option D is correct.

Share price means the value of a company's stock. The total value of a public company is market capitalization which is arrived at by adding up the value of all of the stock outstanding.

Let the initial unit price of each share be $1.

After the first year, the prices become:

$1 * (1 - 10%), $1 * (1-20%), $1 * (1-30%)

A=$0.9, B=$0.8, C=$0.7.

After the second year, the prices become:

$0.9 (1 - 30%), $0.8*(1-20%), $1 * (1-10%)

A = $0.63, B = $0.64, C = $0.49.

Therefore, the Share B has the highest price today which is $0.64.

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The graph B is the best choice as a result.

Graph is a data structure used to represent a mathematical relationship between two or more objects. It is composed of nodes and edges, where nodes represent objects and edges represent the relationships between them. Graphs are used to solve various types of problems in computer science, such as finding the shortest path between two points, or determining whether a graph contains a cycle. Graphs can also be used to represent social networks, transportation networks, and many other types of networks.

The graph depicted in option B is the one that corresponds to the equation y = - 2x - 4.

The equation is expressed in slope-intercept form in the following way:

The angle is - 2
The intercept equals -4.
This indicates that the graph's slope is negative and that the trend line crosses the y axis at minus four.

Only the option B graph has a graph with a negative slope and an intercept of -4.

The graph B is the best choice as a result.

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Answer:

Step-by-step explanation:

Since there are 4 equally sized teams and Kara is only assigned to one of them, the probability of Kara being assigned to the red team is:

Probability of Kara being on red team = Number of ways Kara can be on red team / Total number of possible outcomes

Number of ways Kara can be on red team = 20/4 = 5 (since each team has 5 students)

Total number of possible outcomes = Total number of ways of dividing 20 students into 4 teams

To find the total number of ways of dividing 20 students into 4 teams, we can use the formula for combinations:

Total number of possible outcomes = C(20,5) x C(15,5) x C(10,5) x C(5,5)

where C(n,r) represents the number of ways to choose r items from a set of n items.

Simplifying the expression:

Total number of possible outcomes = (20! / (5!15!)) x (15! / (5!10!)) x (10! / (5!5!)) x (5! / (5!0!))

Total number of possible outcomes = 15,504,000

Therefore, the probability of Kara being on the red team is:

Probability of Kara being on red team = Number of ways Kara can be on red team / Total number of possible outcomes

Probability of Kara being on red team = 5 / 15,504,000

Probability of Kara being on red team = 0.0000323 (rounded to 7 decimal places)

So the probability of Kara being assigned to the red team is approximately 0.0000323 or 0.00323%.

Answer:

ddd

Step-by-step explanation:

The value of x for the given attached triangle satisfies the proportion of similar triangles is equal to 10.

From the attached figure,

In triangle ΔNMO and ΔTUV we have,

NM = 7,

MO = 9

TU = 3x - 9,

UV = 27

The corresponding sides of similar triangles are proportional,

Set up the proportion we get,

ΔNMO ~ ΔTUV

⇒ NM/TU = MO/UV

Substituting the given values, we get,

⇒ 7/(3x - 9) = 9/27

Simplifying, we get,

⇒ 7/(3x - 9) = 1/3

Cross-multiplying, we get,

⇒ 21 = 3x -9

Adding 9 to both sides, we get,

⇒ 3x = 30

Dividing both sides by 3, we get,

⇒ x = 30/3

⇒ x = 10

Therefore, the value of x that satisfies the proportion is x = 10.

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The above question is incomplete, the complete question is:

Solve for x. Set up the proportion.

In triangle ΔNMO ~ ΔTUV.

NM = 7, MO = 9

TU = 3x - 9, UV = 27

Attached figure.

Step-by-step explanation:

To determine which team had the best overall record for the season, we need to compare the total points earned by each team across all the games they played. We can calculate the total points for each team by adding up the points earned in each game.

For the Eagles:

Total points = 3 + 24 + 14 + 27 + 10 + 13 + 10 + 21 + 24 + 17 + 27 + 7 + 40 + 37 + 55

= 310

For the Falcons:

Total points = 24 + 24 + 10 + 7 + 30 + 28 + 21 + 6 + 17 + 16 + 35 + 30 + 28 + 24 + 14

= 300

Based on these calculations, the Eagles earned a total of 310 points while the Falcons earned a total of 300 points, making the Eagles the team with the best overall record for the season.

To determine the best measure of center to compare, we need to consider whether the data is skewed or not. A skewed dataset has a long tail on one side, which can affect the mean value. In this case, we can calculate both the mean and the median to compare the central tendency of the data.

For the Eagles, the mean is:

Mean = (3 + 24 + 14 + 27 + 10 + 13 + 10 + 21 + 24 + 17 + 27 + 7 + 40 + 37 + 55) / 15

= 20.67

For the Falcons, the mean is:

Mean = (24 + 24 + 10 + 7 + 30 + 28 + 21 + 6 + 17 + 16 + 35 + 30 + 28 + 24 + 14) / 15

= 20.00

The median for the Eagles is 21, which is higher than the median for the Falcons, which is 24. Therefore, the best measure of center to compare is the median. This suggests that the Eagles were more consistent in their point-scoring throughout the season, with fewer extreme values that might have skewed the mean.

Answer:

Step-by-step explanation:

Global warming is the change in the climate of the earth causing it to heat up whereas the greenhouse effect is a naturally occurring phenomenon, constantly occurring due to the atmosphere and sunlight.

The Greenhouse effect is when the heat goes up into space, Greenhouse Gases, block the heat going into space, and it goes back to Earth. Global Warming is when the earth is overheated by Fossil fuels and Greenhouse gases causing the Greenhouse effect.

Global warming is the observation, and the atmospheric greenhouse effect is the explanation. The atmospheric greenhouse effect is a theory based on well-established physics that explains why the Earth has not been covered in ice for most of its history.

global warming and the greenhouse effect are not the same things. Global warming refers to a change in the Earth's climate that is causing it to heat up. The greenhouse effect, on the other hand, is a natural process that happens constantly, due to sunlight and the atmosphere.

Answer:

Step-by-step explanation:

The greenhouse effect occurs because the Earth's gasses trap the heat from the sun in our atmosphere. global warming is more than the greenhouse effect, many other things cause global warming INCLUDING the greenhouse effect. The greenhouse effect is trapping heat and global warming is when the global climate rises, partly due to the greenhouse effect.

The factored form of x² - 3x - 10 is (x-5)(x+2).

The given quadratic expression: x² - 3x - 10.

Step 1: Identify the terms in the expression
- Quadratic term: x²
- Linear term: -3x
- Constant term: -10

Step 2: Find two numbers that multiply to the constant term (-10) and add up to the linear term's coefficient (-3)
- Factors of -10: (-1, 10), (1, -10), (-2, 5), (2, -5)
- The pair (2, -5) adds up to -3

Step 3: Rewrite the expression using the factors found in Step 2
- x² - 3x - 10 = x² + 2x - 5x - 10

Step 4: Factor by grouping
- Group the terms: (x² + 2x) + (-5x - 10)
- Factor out the greatest common factor (GCF) from each group:
 - x(x + 2) - 5(x + 2)

Step 5: Factor out the common binomial
- (x + 2)(x - 5)

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A fence of 15 m with the start of the fence at coordinates (8,5), the coordinates of the other end of the fence is equals to the (5.75, 2).

Grady's father wants to build a 15-meter fence with the start point of the fence at coordinates (8,5). Midpoint of fence at coordinates (3.5,-1). We have to determine the coordinates of the other end of the fence. The midpoint is defined as the centre point of a line segment. It is at equal distance from both endpoints,

Let the cordinate of other side point be (x,y). Using the mid point formula, [tex](x,y) = (\frac{x_1 + x_2 }{2}, \frac{y_1 + y_2 {2}[/tex]), where

For x-coordinate, 2x = 3.5 + 8

=> 2x = 11.5

=> x = 5.75

for y-coordinate, 2y = 5 - 1 = 4

=> y= 2

Hence, required value is (5.75, 2).

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Answer:

12

Step-by-step explanation:

12-5

There are 66 possible combinations of two committee members that can be chosen from the 12 applicants.

To determine the number of combinations possible for choosing two committee members out of twelve applicants, we can use the formula for combinations, which is:

[tex]nCk = n! / (k!(n-k)!)[/tex]

Where n is the total number of applicants (12), and k is the number of committee members to be chosen (2).

Plugging in the values, we get:

[tex]12C2 = 12! / (2!(12-2)!)[/tex]

12C2 = 66

The formula for combinations takes into account the number of ways to choose k items from a total of n items, without regard to order. This is why we use the combination formula instead of the permutation formula, which would take into account the order of the items chosen.

In this case, we want to choose two committee members out of 12 applicants, so we use the combination formula with n=12 and k=2 to get the answer of 66 possible combinations.

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The probability of not rolling a 2 or 3 is 2/3

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes

Since Paris is not interested in rolling a 2 or 3, the number of favorable outcomes will be ?

Number of favorable outcomes = 6 - 2 = 4

Total number of outcomes = 6

The probability of not rolling 2 or 3 = 4 / 6 = 2/3

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The probability that it is snowing in Greenland when glaciers are growing is approximately 0.7165.

To solve this problem, we can use Bayes' theorem, which states that the probability of an event A given that event B has occurred is equal to the probability of event B given that event A has occurred, multiplied by the probability of event A, divided by the probability of event B.

Let A be the event that it is snowing in Greenland, and let B be the event that glaciers are growing. We want to find P(A|B), the probability that it is snowing in Greenland given that glaciers are growing.

We are given that the probability of glaciers growing when it snows in Greenland is 0.21, and the probability of glaciers growing when it does not snow is 0.03. We are also given that it snows in Greenland once every 24 days, so the probability of it snowing is 1/24 = 0.0417.

Using Bayes' theorem, we can calculate P(A|B) as follows:

P(A|B) = P(B|A) * P(A) / P(B)

P(B|A) is the probability of glaciers growing given that it is snowing, which is 0.21.

P(A) is the probability of it snowing, which is 0.0417.

P(B) is the overall probability of glaciers growing, which is the weighted average of the probabilities of glaciers growing when it snows and when it does not snow:

P(B) = 0.21 * 0.0417 + 0.03 * (1 - 0.0417) = 0.0342

Substituting these values into Bayes' theorem, we get:

P(A|B) = 0.21 * 0.0417 / 0.0342 = 0.2558

Therefore, the probability that it is snowing in Greenland when glaciers are growing is approximately 0.7165 (rounded to four decimal places).

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The 98% confidence interval of 93 course evaluation the estimation of the population standard deviation is (0.454, 0.681). For 93 professor evaluations, it is (0.318, 0.457). The course evaluations have a wider interval, indicating more variability compared to professor evaluations.

The construction of 98% confidence interval from which the 93 course evaluations were obtained, by using the formula

Confidence interval = (√((n-1)*s²)/√(chi-square upper)-√((n-1)*s²)/√(chi-square lower)),

where n is the sample size, s is the sample standard deviation, and chi-square upper and chi-square lower are the values from the chi-square distribution table with degrees of freedom (df) equal to n-1 and a cumulative probability of 0.99/2 = 0.495.

Using the given data, we have n = 93 and s = 0.56. From the chi-square distribution table with df = 92 and cumulative probability of 0.495, we obtain chi-square upper and chi-square lower as 67.339 and 49.645, respectively.

putting the values in the formula, we get

Confidence interval = (√((93-1)*0.56²)/√(67.339)-√((93-1)*0.56²)/√(49.645))

Confidence interval = (0.454, 0.681)

Therefore, we are 98% confident that the standard deviation of the population from which the 93 course evaluations were obtained falls within the interval (0.454, 0.681).

To construct a 98% confidence interval estimate of the standard deviation of the population from which the 93 professor evaluations were obtained, we can use the same formula as in above part, but with n = 93 and s = 0.41 (the sample standard deviation for professor evaluations).

From the chi-square distribution table with df = 92 and cumulative probability of 0.495, we obtain chi-square upper and chi-square lower as 67.339 and 49.645, respectively.

putting the values in the formula, we get

Confidence interval = (√((93-1)*0.41²)/√(67.339)-√((93-1)*0.41²)/√(49.645))

Confidence interval = (0.318, 0.457)

Therefore, we are 98% confident that the standard deviation of the population from which the 93 professor evaluations were obtained falls within the interval (0.318, 0.457).

Comparing the results from other parts, we can see that the confidence interval for the standard deviation of the population from which the course evaluations were obtained is wider than that for the population from which the professor evaluations were obtained. This suggests that there is more variability in the course evaluations than in the professor evaluations.

To know more about confidence interval:

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 1200}}{\left( \cfrac{30}{100} \right)1200}\implies 360~\hfill \underset{\textit{Jacob's apartment} }{\stackrel{1200~~ - ~~360 }{\text{\LARGE 840}}}[/tex]