17. Suppose 17 blackberry plants started growing in a yard. Absent constraint, the blackberry plants will spread by 90% a month. If the yard can only sustain 120 plants, use a logistic growth model to estimate the number of plants after 5 months. plants
Answers
Step 1: Write out the formula for logistic growth model
[tex]P(t)=\frac{KP_0e^{rt}}{K+P_0(e^{rt}-1)}[/tex][tex]\begin{gathered} \text{ Where} \\ K=\text{ the carrying capacity} \\ r=\text{ the growth rate (in decimal form)} \\ P_0=\text{ the initial population} \\ P(t)=\text{ the population at time t} \end{gathered}[/tex]Step 2: Write out the given values and substitute them into the formula
[tex]\begin{gathered} \text{ In this case,} \\ K=120 \\ r=\frac{90}{100}=0.9 \\ P_0=17 \\ t=5 \end{gathered}[/tex]Hence,
[tex]P(5)=\frac{120\times17\times e^{(0.9\times5)}}{120+17(e^{(0.9\times5)}-1)}[/tex][tex]P(5)=112[/tex]Hence, the number of plants after 5 months is approximately 112
Related Questions
In 2008, 1.7m iPhones were sold. In 2012, 35.2m iPhones were sold. Assuming the sales of iPhones increases exponentially, how many iPhones should be expected to be sold in 2017?
Answers
The number of iPhones that should be sold in 2017 (since growth is exponential) is $ 6,476,635 x 10⁶. See the explanation below.
What is exponential Growth?Exponential growth is a data pattern that exhibits greater increases with time. Compounding produces exponential profits in finance. Compounding interest savings accounts may provide exponential growth.
The calculation for the above solution is as follows:
Recall that the formula for exponential growth is:
f(x) = a (1+r)ˣ
Where:
f(x) = exponential growth function
a = initial amount
r = growth rate
{x} = number of time intervals
Hence f(x) = 1.7 (1+ r)⁵
Note that x = 2017-2012 =5
r = (present value - past value)/ past value
Present value = 35.2
Past Value = 1.7
Hence r = (35.2-1.7)/1.7
r = 19.7058823529
Approximately 19.71
Hence,
f(x) = 1.7 (1+ 19.71)⁵
= 1.7 (20.71)⁵
= 1.7 x 3809785.2361
= 6476634.90137
Which is approximately = 6,476,635
Recall that our computation was done in millions hence the answer if left in standard notation is:
Increase in 2017 = $ 6,476,635 x 10⁶
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15 POINT AND BRANLIEST
A 15-gallon gas tank. If you can drive 330 miles on a full tank of gas, what is the unit rate of miles per gallon he gets?
Answers
The unit rate he can drive in mile per gallon is 22 miles per gallon.
How to find unit rate?Unit rate can be defined as the ratio between two measurements with the second term as 1.
In other words, a unit rate describes the ratio of two different units for the quantity of one.
Therefore, the unit rate in miles per gallon can be calculated as follows:
Hence,
unit rate = number of miles / number of gallons
number of miles = 330 miles
number of gallons = 15 gallons
unit rate = 330 / 15
Therefore,
unit rate = 22 miles per gallon
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2) Jennifer makes a hexagon by arranging 6 equilateral triangles, each of which has a vertex at
the center of the hexagon. If the length of one side of a triangle is 4, what is the area in
square units of the hexagon? Leave in simplest radical form if necessary. Show work and
circle final answer
Answers
The area in square units of the hexagon will be 12√3.
What is Hexagon?
A polygon with six sides are called a hexagon.
Given that;
Jennifer makes a hexagon by arranging 6 equilateral triangles.
The length of one side of a triangle is 4.
Now, To find the area of hexagon, we find the height of the equilateral triangle and then multiply by the 6.
So, In ΔABC;
AB = BC = CA = 4
Then, Measure of DC = BD = 2
Now, using Pythagoras theorem to find height of triangle (AD) as;
AD² = AC² - DC²
AD² = 4² - 2²
AD² = 16 - 4
AD² = 12
Take square root both side;
AD = √12
AD = 2√3
So, The area of hexagon = 6 × Height of triangle
= 6 × 2√3
= 12√3
Thus, The area in square units of the hexagon will be 12√3.
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How many units are (-2,-3) & (5,7) from each other on the coordinate plane
Answers
Let's begin by listing out the information given to us:
(x, y) = (-2, -3), (5, 7)
The distance between the two points is given by:
[tex]\begin{gathered} d=\sqrt[]{\mleft(\mleft(x_2-x_1\mright)^2+\mleft(y_2-y_1\mright)^2\mright)} \\ d=\sqrt[]{(5--2)^2+(7--3)^2} \\ d=\sqrt[]{7^2+10^2} \\ d=\sqrt[]{49+100} \\ d=12.207\approx12.21 \\ d=12.21 \end{gathered}[/tex]Help.
A. RS
B. ST
C. Ut
Answers
Answer: THE ANSWER TO THAT IS B
Step-by-step explanation:
Determine the solution of the given system of equations.
-x+y=-5
-4x - 5y=7
Answers
Answer:
x =2 y = -3
Step-by-step explanation:
hope it helps!!!!!
Based on this data what is the probability that the next car will not be white why
Answers
The probability of the next car not being a white car is 0.92
What is probability?The probability of an event is the chance or the likelihood that the event would occur.
Note that the chance or the likelihood is represented as a numerical value
How to determine the probability?The complete question is added as an attachment
From the attached question, we have the following parameters
P(White Vehicle) = 0.25
P(Car) = 0.36
P(White Car) = 0.08
Using the complement rule of probability, we have the following equation
P(White Car) + P(Not White Car) = 1
Substitute the known values in the above equation
So, we have the following equation
0.08 + P(Not White Car) = 1
Subtract 0.08 from both sides of the equation
So, we have
P(Not White Car) = 1 - 0.08
Evaluate the difference
P(Not White Car) = 0.92
Hence, the probability that the next car will not be a white car is 0.92
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When using the standard algorithm to find the product 5,917x29, the first step is multiplying 9 ones by 7 ones. Explain why you regroup before the next step
Answers
When using the standard algorithm to find the product 5,917x29, the first step is multiplying 9 ones by 7 ones, it's important to regroup in order to correctly multiply the values.
How to illustrate the information?Using partial products or multiplying in parts is how the conventional method does multiplication. A word that also signifies multiplication is "product," so keep that in mind. Any two numbers, regardless of how tiny or how large, can be multiplied using this standard technique.
The top number is multiplied by the bottom number, one digit at a time, working your way from right to left, using this procedure.
In this case, it should be noted that the value of 5,917 × 29 is 171593.
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The function f(x) = 2x − 1 is transformed to function g through a horizontal shift of 7 units left. What is the equation of function g?
Replace the values of h and k in the equation.
g(x) = 2x+h + k
Answers
When the function f is transformed to g, the equation is g(x) = 2x + 14 - 1
How to determine the equation of function g?The equation of function f is given as
f(x) = 2x - 1
The transformation is given as
Horizontal shift of 7 units left.
The above transformation rule can be represented as
Horizontal shift of 7 units left.: (x, y) = (x + 7, y)
When the above rule is applied, we have the following equation
g(x) = f(x + 7)
So, we have
g(x) = 2(x + 7) - 1
Open the brackets
g(x) = 2x + 14 - 1
Hence, the equation of function g is g(x) = 2x + 14 - 1
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Find the surface area and volume of the hemisphere FormulaSA = 3 * 3.14 * r^2V = 2/3 * 3.14 * r^3
Answers
ANSWER
[tex]\begin{gathered} SA=98\pi ft^2 \\ V=228.7\pi ft^3 \end{gathered}[/tex]EXPLANATION
To find the surface area of the hemisphere, we apply the formula for the surface area of a hemisphere (without a base):
[tex]SA=2\cdot\pi\cdot r^2[/tex]where r = radius = 7 ft
Therefore, the surface area of the hemisphere is:
[tex]\begin{gathered} SA=2\cdot\pi\cdot7^2 \\ SA=98\pi ft^2 \end{gathered}[/tex]To find the volume of the hemisphere, we apply the formula for the volume of a hemisphere:
[tex]V=\frac{2}{3}\cdot\pi\cdot r^3[/tex]Therefore, the volume of the hemisphere is:
[tex]\begin{gathered} V=\frac{2}{3}\cdot\pi\cdot7^3 \\ V=228.7\pi ft^3 \end{gathered}[/tex]A company borrows $68,000 for 8 years at a simple interest rate of 15.5%. Find the interest paid on the loan and the total amount paid.
Answers
The interest paid on the loan and the total amount paid are $84,320 and $152,320 respectively.
It is given in the question that:-
Money borrowed by the company (Principal) = $68,000
Time period for which the money is borrowed = 8 years
Simple Interest rate = 15.5 %
We have to find the interest paid on the loan and the total amount paid.
We know that,
Simple interest = (Principal * Interest * Rate)/100
Hence, we can write,
Simple interest = (68000 * 15.5 * 8)/100 = $84,320
Also, we know that,
Amount = Principal + Interest
Hence, we can write
Amount = 68,000 + 84,320 = $152,320
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Two accounts each begin with a deposit of $9000. Both accounts have rates of 3.1%, but one account compounds interest once a year while
the other account compounds interest continuously. Make a table that shows the amount in each account and the interest earned after one
year, five years, ten years, and 20 years.
Answers
Given : Initial deposit or the principal amount = $ 9000
Rate of interest = 3.1 %
Compound interest annually
= principal (1 + r/ 100)^t
here put value principal rate and time period 1, 5 10 and 20 years
and we get the amount for each time period
than for interest = amount - principal we get interest
as that we calculate all value:
given in the attachment
When do we use compound interest ?When interest on a balance in a savings or investment account is reinvested, you receive compound interest, which results in higher interest payments. Money makes money, a wise man once said. And money makes money by making more money. Compound interest speeds up the long-term growth of your savings and investments.
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Given P(A) = 0.2, P(B) = 0.31 and P(AB) = 0.152, find the value of
P(AUB), rounding to the nearest thousandth, if necessary.
Answers
Probability - The value of P(AUB) = 0.557
What is Probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given,
P(A) = 0.2,
P(B) = 0.31 and
P(A/B) = 0.152,
Since, we know that
P(A⋃B) = P(A)+P(B)-P(A⋂B)
So, we have to find P(A⋂B)
We know that,
P(A/B) = P(A⋂B)/P(B)
Putting the values we get,
0.152 = P(A⋂B) / 0.31
P(A⋂B) = 0.152 x 0.31
P(A⋂B) = 0.047
Now, lets find the value of P(A⋃B)
P(A⋃B) = P(A)+P(B)-P(A⋂B)
Putting the values we get,
P(A⋃B) = 0.2 + 0.31 + 0.047
P(A⋃B) = 0.557
Hence the value of P(A⋃B) = 0.557
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3. a) Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. The actual
was 4.1 ft. What is John's percent decrease on his measurement?
measurement
Answers
Jack's percentage decrease on his measurement of painting by 18%.
What is meant by percentage change?
Measures of percent change include percent increase and percent decease, which indicate how much an element of a variable changes in terms of intensity, size, extent, or value.
Given that,
Jack's measurement for his room = 5 ft (taking this as old value)
Actual measurement for Jack's room = 4.1 ft (taking this as new value)
Using formula for Percent change = [tex]\frac{new - old}{old}[/tex] × 100% = [tex]\frac{4.1 - 5}{5}[/tex] × 100%
= [tex]\frac{-0.9}{5}[/tex] × 100% = -0.18 × 100%
= -18%
Here, minus sign represents the decrease in percentage.
Hence, Jack's percentage decrease on his measurement of painting by 18%.
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Correct question will be :
Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. But the actual measured painting is 4.1 ft. What is Jack's percent decrease on his measurement of the painting?
n
Find the value of x that makes m ||
(180 − x)°
m
An
to
W
Answers
Answer:
The value of x will be 90°
Which statements about the line that passes through (-2, 0) and (2, -4) are true? Select all that apply.
OA. The slope of the line is 1.
B. The line intersects the y-axis at (0, -2).
Answers
Considering the expression of a line, the statements:
"The line intersects the y-axis at (0, −2).""The equation of the line is y = −x − 2.""The line intersects the x-axis at (−2, 0)."about the line that passes through (-2, 0) and (2, -4) are true.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷(x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
This caseBeing (x₁, y₁)= (-2, 0) and (x₂, y₂)= (2, -4), the slope m can be calculated as:
m= (-4 - 0)÷(2 - (-2))
m= (-4)÷ 4
m= -1
Considering point 1 and the slope m, you obtain:
0= -1×(-2) + b
0= 2 +b
-2= b
Finally, the equation of the line that passes through the pair of points (-2,0) and (2,-4) is y= -x -2, wich has a slope of -1. The line intersects the x-axis at (−2, 0).
If x=0, you get:
0= -x -2
2= -x
2÷ (-1)=x
-2= x
Finally, the line line intersects the y-axis at (0, −2).
Your question was incomplete. Please check below the full content.
Which statements about the line that passes through (−2, 0) and (2, −4) are true? Select all that apply.
A. The slope of the line is 1.
B. The line intersects the y-axis at (0, −2).
C. The equation of the line is y = −x − 2.
D. The line intersects the x-axis at (−2, 0).
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There are 6 triangles and 15 squares. What is the simplest ratio of triangles to squares?
Answers
Answer:
2:5
Step-by-step explanation:
6:15= 2:5
15 divided by 3 = 5
2:5
The line y=kx+4 goes through the point (2,-2)
K=-3
Sketch the graph of the line (need ASAP!)
Answers
The graph of the linear equation:
y = -3x + 4
Can be seen in the image at the end.
How to sketch a graph of the line?
Here we know that the equation for the line is:
y = k*x + 4
We know that this line goes through the point (2, -2), then we can replace these values in the above line so we get the value of k.
-2 = k*2 + 4
With this, we can find the value of k.
-2 - 4 = k*2
-6 = k*2
-6/2 = k = -3
Then the line is:
y = -3*x + 4
If we evaluate in x = 0, we get:
y = -3*0 + 4 = 4
So, at this point we know that the line passes through points (0, 4) and (2, -2), so to graph the line, we just need to graph these two points and draw a line that connects them, like in the example below.
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solve for x if the equation is[tex]3 \sqrt{x + a - z = b} [/tex]
Answers
EXPLANATION
Given the expression:
[tex]b=\sqrt[3]{x+a-z}[/tex]Applying the cubic power to both sides:
[tex]b^3=(\sqrt[3]{x+a-z})^3[/tex]Simplifying the cubic root with the cubic power:
[tex]b^3=x+a-z[/tex]Subtracting -a to both sides:
[tex]b^3-a=x+a-a-z_{}[/tex]Adding z to both sides:
[tex]b^3-a\text{ +z = x + a - a -z + z}[/tex]Simplifying terms:
[tex]b^3-a+z=x[/tex]Switching sides:
[tex]x=b^3-a+z[/tex]Joanne deposits $4,300 into a l-year CD at a rate of 2.3%, compounded daily.a. What is her ending balance after the year, to the nearest cent?b. How much interest does she earn, to the nearest cent?c. What is her annual percentage yield to the nearest hundredth of a
Answers
Joanne deposits $4,300 into a l-year CD at a rate of 2.3%, compounded daily.
a. What is her ending balance after the year, to the nearest cent?
b. How much interest does she earn, to the nearest cent?
c. What is her annual percentage yield to the nearest hundredth
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$4,300
t=1 year
r=2.3%=2.3/100=0.023
n=365
Part a
Find out the value of A
substitute the given values in the formula
[tex]A=4,300(1+\frac{0.023}{365})^{365\cdot1}[/tex]A=$4,400.04
Part b
I=A-P
I=4,400.04-4,300
I=$100.04
Part c
we have
4,300 -----> represent 100%
so
Applying proportion
Find out how much percentage is 4,400.04
100/4,300=x/4,400.04
x=(100/4,300)*4,400.04
x=102.33%
therefore
102.33-100=2.33%
What happens to the x and y-values when you translate an object up?
Answers
When we translate an object up, the values of x remain the same, but the values of y change by a positive value.
Solve the quadratic equation using the method indicated. See attached photo. Thanks in advance!
Answers
The quadratic formula is given by th following formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a, b and c are the coefficients of the quadratic equation. In this case, you have:
a = 6
b = 9
c = -22
replace the previous values into the quadratic formula and simplify:
[tex]\begin{gathered} x=\frac{-9\pm\sqrt[]{(9)^2-4(6)(-22)}}{2(6)} \\ x=\frac{-9\pm\sqrt[]{609}}{12} \\ x_1\approx1.31 \\ x_2\approx-2.81 \end{gathered}[/tex]Hence, the solutions for the given equation are 1.31 and -2.81
find the slope of the line that goes through the given points (-2,-4) (1/4,5)
Answers
Solution
find the slope of the line that goes through the given points (-2,-4) (1/4,5)
[tex]\begin{gathered} slope\text{ =m} \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex][tex]\begin{gathered} x_1=-2 \\ x_2=\frac{1}{4} \\ y_1=-4 \\ y_2=5 \end{gathered}[/tex][tex]m=\frac{5--4}{\frac{1}{4}--2}=\frac{9}{2.25}=4[/tex]Therefore the slope of the line = 4
1)
Solve the equation for y. Then, complete the
5x + 4y = 20
y=
Preview
20
Answers
Answer:
-5/4
Step-by-step explanation:
debemos de usar la ecuacion dy/dx
Show how you can make a ten to find the sum of 6+5
Answers
By rewritting the 6 as 5 + 1 we will get:
1 + 5 + 5 = 1 + (5 + 5) = 11
How to make a ten to simplify the sum?
One trick we do a lot when we do additions os making tens (or hundreds, thousands, etc... depending on the case).
This means that we play with the numbers in such a way that we can make tens, in this case we have the sum:
6 + 5
We can rewrite this as:
6 + 5 = 1 + 5 + 5
Using the associative property we rewrite:
1 + 5 + 5 = 1 + (5 + 5)
1 + (5 + 5) = 1 + 10 = 11
The sum is equal to 11.
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Perform the indicated operation. Don't forget to simplify if possible.
Subtract 6x + 2 from 4x-6.
Answers
Answer: 2x + 8
Step-by-step explanation:
( 6x + 2 ) - ( 4x - 6 ) =
6x - 4x = 2x
2 - -6 = 8
Simplify
Y exponent -5/ y exponent -4
Answers
Answer:
"Simplify" is an instruction to rewrite the expression with as few symbols as possible. 5y-4 and 5/y4 have the same number of symbols.
A possible alternative direction might have been to rewrite without the negative exponent.
Answer:
[tex]\frac{1}{y}[/tex]
Step-by-step explanation:
using the rule of exponents
• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
given
[tex]\frac{y^{-5} }{y^{-4} }[/tex]
= [tex]y^{(-5-(-4))}[/tex]
= [tex]y^{(-5+4)}[/tex]
= [tex]y^{-1}[/tex]
= [tex]\frac{1}{y}[/tex]
Use the number line to answer the question.
A number line is shown with end points 0 and 2. Hash marks are at every 0.2. Heavy marks are at 0, 1, and 2.
Zach bought 8 pieces of bubble gum that were $0.20 each. He used a number line to find the total cost. Choose the numbers to complete the sentences.
Zach started on the number line at 0.2 for the cost of one piece of gum. He moved
Choose...
hash marks. The total cost is
Choose...
.
Answers
Zach began at 0.2 for the price of one piece of gum on the number line. Has moved eight times. The whole price is $1.60.
Since each hash mark is worth.2, moving eight times will result in 1.6, or eight times $0.20.
This is further explained below.
What is a Number line?Generally, A number line is a depiction of a graded straight line that is used to represent real numbers visually.
It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
A horizontal line with evenly spaced numerical increments is referred to as a number line.
How the number on the line may be answered depends on the numbers present. How a number is utilized depends on the issue it is associated with, such as when graphing a point
In conclusion, On the number line, Zach started at 0.2, which was equal to the cost of one piece of gum. Has relocated a total of eight times. The whole cost is a dollar and sixty cents.
Moving eight times will result in 1.6, which is equal to eight times $0.20, given that each hash mark is worth.2.
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Each of the four shapes represents a positive whole number. The sum of the shapes in
each row and column is displayed at the end of each row and column. Using this
information, determine the numerical value of each shape.
Answers
The numerical value of each of the four given shapes filled in the rows and columns are;
pentagon shape = 8star shapes = 6spiral shapes = 3rectangle shape = 5How to find numerical value of each shape.let
pentagon shape = AStar shape = BSpiral shape = Crectangle shape = DRow 1: There are 2 stars, one pentagon and one spiral shape.
A + 2B + C = 23 .....(equation 1)
Row 2: There are 2 spiral shapes and 2 rectangle shape.
2C + 2D = 16 ......( equation 2)
Row 3: There are 1 star, one pentagon and 2 rectangle shape.
A + B + 2D = 24 ....(equation 3)
Row 4: There are 3 spiral shapes and one star shape.
B + 3C = 15 ....(equation 4)
Column 1:
2C + A + D = 19 ....(equation 5)
Column 2:
2B + C + D = 20 .....(equation 6)
From equation 4;
B = 15 - 3C
From equation 2:
D = 8 - C
Substitute B = 15 - 3C into equation 1;A + 2B + C = 23
A + 2(15 - 3C) + C = 23
A + 30 - 6C + C = 23
A = 5C - 7
Substituting D = 8 - C and A = 5C - 7 into equation 5;2C + A + D = 19
2C + (5C - 7) + 8 - C = 19
6C + 1 = 19
6C = 18
C = 3
Substitute 3 for C inA = 5C - 7
A = 5(3) - 7
A = 8
Substitute 3 for C inB = 15 - 3C
B = 15 - 3(3)
B = 6
Substitute 3 for C inD = 8 - C
D = 8 - 3
D = 5
Therefore, there are 8 pentagon shape, 6 star shapes, 3 spiral shapes and 5 rectangle shape.
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Which has a terminal point of (square root 2/2 and square root 2/2). What is the terminal point of 5pi/4?
Answers
To find 5π/4 as terminal point, we will take the angle as 5π/4
The first coordinate is the x coordinate = cos θ
The second coordinate is the y coordinate = sin θ
[tex]\begin{gathered} We\text{ n}eed\text{ to convert the angle to degre}e\colon \\ 1\pi\text{ rad = 180}\degree \\ \frac{5\pi}{4}\text{ rad = 225}\degree \\ \\ sin\text{ is negative in third quadrant} \\ 225\text{ - 180 = 45} \\ \sin \text{ 45 = }\frac{\sqrt[]{2}}{2} \\ \\ \sin \text{ 225}\degree\text{ =- }\frac{\sqrt[]{2}}{2} \end{gathered}[/tex][tex]\begin{gathered} \theta\text{ = 225}\degree\text{ }is\text{ in third quadrant} \\ \\ 180\text{ -225 = 45}\degree \\ \cos \text{ 45}\degree\text{ = }\frac{\sqrt[]{2}}{2} \\ \text{ 225 is negative in third quadrant} \\ \\ \cos \text{ 225}\degree\text{ =- }\frac{\sqrt[]{2}}{2} \end{gathered}[/tex]Hence, the terminal of 5π/4:
[tex]\text{(-}\frac{\sqrt[]{2}}{2},\text{ -}\frac{\sqrt[]{2}}{2})\text{ (option C)}[/tex]