the general term for the sequence m, -m, m, -m, . . . is
The correct option is (A).
The given sequence is: m, -m, m, -m, ...
Let's analyze the pattern:
1. For n = 1, the term is m.
2. For n = 2, the term is -m.
3. For n = 3, the term is m.
4. For n = 4, the term is -m.
5. And so on...
From the pattern, we can see that the sign alternates between positive and negative, and the term alternates between m and -m. This suggests that we can use [tex](-1)^(n-1)[/tex] to control the sign alternation and m to control the alternation between m and -m.
Now, let's check the options one by one:
A. [tex]m(-1)^(n-1)[/tex]
Substituting n = 1, we get[tex]m * (-1)^(1-1) = m * (-1)^0 = m * 1 = m[/tex]
Substituting n = 2, we get [tex]m * (-1)^(2-1) = m * (-1)^1 = m * -1 = -m[/tex]
This matches our sequence. So, Option A seems correct.
B.[tex](-m)^n[/tex]
This doesn't match our sequence because it would give us [tex](-m)^1 = -m,[/tex][tex](-m)^2 = m^2, (-m)^3 = -m^3[/tex], and so on, which doesn't alternate between m and -m.
C.[tex](-1)m^(n + 1)[/tex]
Substituting n = 1, we get [tex](-1)m^(1 + 1) = (-1)m^2 = -m^2[/tex]
Substituting n = 2, we get [tex](-1)m^(2 + 1) = (-1)m^3 = -m^3[/tex]
This doesn't match our sequence because it doesn't alternate between m and -m.
D.[tex](-1)m^(n - 1)[/tex]
Substituting n = 1, we get [tex](-1)m^(1 - 1) = (-1)m^0 = -1[/tex]
Substituting n = 2, we get[tex](-1)m^(2 - 1) = (-1)m^1 = -m[/tex]
This also doesn't match our sequence because it doesn't alternate between m and -m.
So, the correct answer is Option A:[tex]m(-1)^(n-1).[/tex]
which set of directions correctly describes how to plot the point (6,2) on the coordinate plane?
Start at the origin. Move 6 units to the right, then move 2 units up.
Start at the origin. Move 6 units up, then move 2 units to the right
Start at the origin. Move 6 units to the left, then move 2 units up.
Start at the origin. Move 6 units up then move 2 units to the left
The first one. Start at origin. Move 6 units to the right and up 2 units
Answer:
Option 1 - Start at the origin. Move 6 units to the right, then move 2 units up.
Step-by-step explanation:
To find : Which set of directions correctly describes how to plot the point (6,2) on the coordinate plane?
Solution :
The point (6,2) means the x-coordinate is 6 and y-coordinate is 2.
According to graphing,
As the x-coordinate is positive it moves to right side.
So, From origin there is a shift of 6 units right.
As the y-coordinate is positive it moves to upward side.
So, From origin there is a shift of 2 units up.
Therefore, 'Start at the origin. Move 6 units to the right, then move 2 units up'.
Hence, Option 1 is correct.
The table shows the reduction in costs (in hundreds) after a manager found ways each month to cut back in his store. Identify the best fit mathematical model with its corresponding R^2 value and tell whether it is a good model.
Month: 1. 2. 3. 4. 5
Profit Loss: 86. 82. 72. 45. 15
A: Quadratic model, 0.997
No 0.997 is too high an R^2 value.
B: quadratic model, 0.997
Yes, 0.997 is very close to 1.
C. linear model, 0.902
No, 0.902 is too high an R^2 value.
D. linear model, 0.902
Yes, 0.902 is very close to 1.
Answer:
B: quadratic model, 0.997
Yes, 0.997 is very close to 1.
Step-by-step explanation:
In general, the better the model, the closer the R²-value is to 1. A graph shows the quadratic model to be a good fit.
_____
Comment on "better models"
A 4th-degree polynomial can be written that will fit each of the 5 points exactly and give an R²-value of 1. However, the model does not appear to interpolate or extrapolate well. The quadratic offers a reasonable fit that is better than that of the linear model and seems to have reasonable behavior between and beyond the given data points.
find the missing measure for the cone. round your answer to the nearest tenth.
diameter = 6 cm
height = _____ cm
volume = 84.78 cm3
Final answer:
To find the missing height of a cone with a given diameter of 6 cm and volume of 84.78 cm³, the volume formula for a cone is used, and after plugging in the known values, solving for the height gives an approximate value of 3.0 cm when rounded to the nearest tenth.
Explanation:
The student is asking for the missing height of a cone given the diameter and the volume. The formula to calculate the volume of a cone is V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height of the cone. Since the diameter is given as 6 cm, the radius is half of that, which is 3 cm. The known volume of the cone is 84.78 cm³. Plugging these values into the formula gives:
84.78 cm³ = (1/3)π(3 cm)²h
After solving for h, we get:
h = ³ × 84.78 cm³ / (π × (3 cm)²)
h = 84.78 cm³ / (9π cm²)
h = 84.78 / (9 × 3.14159)
Now calculating h and rounding to the nearest tenth:
h = 84.78 / 28.27431
h ≈ 3.0 cm
Therefore, the height of the cone is approximately 3.0 cm.
Remove the parentheses from the following expression: (+6) – (+2)
A. –6 – 2
B. 6 – 2
C. –6 + 3
D. 6 + 2
The correct answer:
B. 6 - 2
Answer:
B. 6-2
Step-by-step explanation:
We have been given expression : [tex]\left(+6\right)-\left(+2\right)[/tex]
Now we need to rewrite that expression [tex]\left(+6\right)-\left(+2\right)[/tex], without parenthesis then select which of the given choices are correct.
[tex]\left(+6\right)-\left(+2\right)[/tex]
We know that product of opposite sign is always negative sign.
Then product of - and +2 gives -2
So we can rewrite the problem as:
[tex]=6-2[/tex]
Hence choice B. 6-2 is the final answer.
Is this right idk but i need work fir it
Answer:
The answer is C 5/4
Step-by-step explanation:
When lines are parallel and you know there is a scalar factor, make the ratio by putting the original over the dilation 15:12 or 15/12 this is the ratio and after you need to reduce by dividing by the greatest common factor. 15 and 12's GCF is 3 so (15/3)/(12/3) = 5/4.
Finnegan shot 2 rolls of film film with 36 exposures on each roll. It costs $39.60 to develope all the pictures. How much did it cost for each person.
Answer:
$0.55
Step-by-step explanation:
2x36= 72
39.60/ 72
A small island in the middle of a river is eroding away. Each year, the island has 85% of the area from the previous year. After one year the island has an area of 10.2 thousand square yards. Graph the sequence and describe the pattern. How much of the island is left after 6 years?
Answer:
see the attachment for a graph
4.53 thousand square yards remain after 6 years
Step-by-step explanation:
The area can be described by an exponential equation that multiplies the area by 0.85 when the time variable increases by 1 year. Such an equation might be ...
a(t) = 10.2·0.85^(t-1)
The graph of this is attached.
After 6 years, the equation predicts
a(6) = 10.2·0.85^(6-1) ≈ 4.53 thousand square yards
of island will remain.
A farm supply store sells a variety of treat balls for small and large animals. Martha wants to purchase a ball that can hold 1437 cubic centimeters of treats. What is the diameter of the ball she should purchase? Round to the nearest whole number.
The volume of a sphere is v=4/3 x 3.14 r to the the third power
Answer: 14 centimeters.
Step-by-step explanation:
You need to use the formula for calculate the volume of a sphere:
[tex]V=\frac{4}{3}(3.14r^3)[/tex]
Where the radius of the sphere is "r".
As you know the volume of the ball, you can susbtitute it into the formula [tex]V=\frac{4}{3}(3.14r^3)[/tex], and solve for the radius "r":
[tex]1437=\frac{4}{3}(3.14r^3)\\\\3( 1437)=4(3.14r^3)\\\\4311=12.56r^3\\\\r=\sqrt[3]{\frac{4311}{12.56}}\\\\r=7.0cm[/tex]
The diameter of the ball can be calculated with:
[tex]D=2r[/tex]
Where r is the radius of the ball.
Substituting the radius of the ball into [tex]D=2r[/tex], you get that the diameter of the ball that she should purchase, rounded to the nearest whole number, is:
[tex]D=2(7.0cm)\\D=14.0cm\\D=14cm[/tex]
Final answer:
To solve for the diameter of the ball, the volume of a sphere formula is used. The calculated diameter is rounded to the nearest whole number, and Martha should purchase a treat ball with a diameter of approximately 14 centimeters.
Explanation:
To find the diameter of the ball that can hold 1437 cubic centimeters of treats, we need to use the formula for the volume of a sphere: V = (4/3) π r^3, where V is the volume and r is the radius. We will solve for r and then multiply by 2 to find the diameter. Given that the volume, V, is 1437 cubic centimeters, the formula becomes:
1437 = (4/3) × 3.14 × r^3
To isolate r, we first divide both sides of the equation by (4/3) × 3.14:
r^3 = 1437 / ((4/3) × 3.14)
Calculating the right side gives us the approximate value of r^3. Then, we take the cube root of both sides to solve for r:
r = ∛(1437 / ((4/3) × 3.14))
Once we find r, we can calculate the diameter, D, by:
D = 2 × r
Calculating the above with the given volume, we find:
r ≈ ∛(1437 / ((4/3) × 3.14)) ≈ 6.83 cm
D ≈ 2 × 6.83 cm ≈ 13.66 cm
So, rounding the diameter to the nearest whole number, Martha should purchase a treat ball with a diameter of approximately 14 centimeters.
Isosceles △ABC (AC=BC) is inscribed in the circle k(O). Prove that the tangent to the circle at point C is parallel to AB .
Explanation:
Let M be the midpoint of AB. Then CM is the perpendicular bisector of AB. As such, center O is on CM, and OC is a radius (and CM). The tangent is perpendicular to that radius (and CM), so is parallel to AB, which is also perpendicular to CM.
If you need to go any further, you can show that triangles CMA and CMB are congruent, so (linear) angles CMA and CMB are congruent, hence both 90°.
Which expression gives the distance between the points
Apex!!!!
Need help so also comment if you have used apex learning
Answer:
D. √((2 +4)² +(5 -8)²)
Step-by-step explanation:
The distance is found using the formula ...
d = √((x1 -x2)² +(y1 -y2)²)
Selection D has this formula properly filled in with the values ...
(x1, y1) = (2, 5)
(x2, y2) = (-4, 8)
I need someone’s help please
Answer: 90 pounds.
Step-by-step explanation:
Let's call:
A: pounds of type A coffee.
B: pounds of type B coffee.
Based on the information given in the problem you can set up the following system of equations:
[tex]\left \{ {{A+B=153} \atop {4.25A+5.45B=758.25}} \right.[/tex]
You can use the Elimination method:
- Multiply the first equation by -4.25.
- Add both equations.
- Solve for B.
Then, you obtain:
[tex]\left \{ {{-4.25A-4.25B=-650.25} \atop {4.25A+5.45B=758.25}} \right.\\----------\\1.2B=108\\B=90[/tex]
He used 90 pounds of type B coffee.
Answer:
B = 90 pounds
Step-by-step explanation:
We know that Han's Coffee shop uses coffee A at $4225 per pound and coffee B at $5.45 per pound and this month it made 153 pounds of blend for a total cost of $758.25.
We are find the number of pounds for coffee B used.
[tex]A+B=153[/tex]
[tex]A=153-B[/tex] --- (1)
[tex]4.25A+5.45B =758.25[/tex] --- (2)
Substituting equation (1) in (2) to get:
[tex]4.25(153-B)+5.45B=758.25[/tex]
[tex]650.25-4.25B+5.45B=758.25[/tex]
[tex]1.2B=758.25-650.25[/tex]
[tex]1.2B=108[/tex]
B = 90 pounds
Does anyone know #11
Answer:
C. both student 1 and student 2
Step-by-step explanation:
Dilation does not change any angles, so the triangles are similar and the trig functions of corresponding angles will be identical.
The slope of CB is -1/3 and the slope of BA is 3, so they multiply together to give -1. That means the segments are at right angles and the triangle is a right triangle.
Both the premise and the conclusion of each student is correct.
a sprinkler that sprays water in a circular area can be adjusted to spray up to 30 feet. turning the radius-reduction screw on the top of the nozzle lets people the radius by up to 25 percent. to the nearest tenth, what is the maximum area of lawn that can be watered by the sprinkler if the radius-reduction is used at full capacity.
Answer:
1590.4 square ft
Step-by-step explanation:
r=30 so you need to multiply that by 25% (30*.25=7.5)
30-7.5=22.5
A= pi(r)^2
A=pi*(22.5)^2
A=506.25pi
A=1590.43 or 1590.4 (to the nearest tenth)
Answer: 1590.4 square feet
Step-by-step explanation:
Given: The radius of the circular area = 30 feet
Now, 25% of the radius = [tex]0.25\times30=7.5[/tex] feet
If the we reduce the radius by 25%, then the radius of the circular area =
[tex]30-7.5=22.5\text{ feet}[/tex]
Now, the circular area of the spray is given by :-
[tex]\text{Area}=\pi r^2\\\\\Rightarrow\text{ Area}=(3.143.141592653)(22.5)^2\\\\\Rightarrow\text{ Area}=1590.43128088\approx1590.4\text{ ft}^2[/tex]
Therefore, the maximum area of lawn that can be watered by the sprinkler if the radius-reduction is used at full capacity = 1590.4 square feet.
Anyone know how to 1.8
Hope this helps , use SOHCAHTOA
Some
Old
Hag
Cracked
All
Her
Teeth
On
Apples
To remember, hope this helps !
Which Circle has the greater area I circled with the radius of 16 where is the cup with the circumference of 34 pie support your answer
Answer:
a circle with a circumference of 34π
Step-by-step explanation:
The circumference is given by ...
C = 2πr
so the circle with a radius of 16 has a circumference of ...
C = 2π·16 = 32π
The area is proportional to the square of the circumference, so the circle with a larger circumference will have a larger area.
The circle with the circumference of 34π has the largest area.
What is the length of one side of a die if the volume of the die is 27 cm3? A) 3 cm B) 7 cm C) 9 cm D) 24 cm
Answer:
3 cm
Step-by-step explanation:
The volume of a cube is the cube of the side dimension, hence the side dimension is the cube root of the volume.
∛(27 cm³) = 3 cm
_____
Problems like this are worked readily if you memorize the cubes of small integers. I suggest 1–5 at least, perhaps 1–10.
1827641252163435127291000For what values of p is the value of the binomial 1.5p−1 smaller than the value of the binomial 1+1.1p?
Answer:
p < 5
Step-by-step explanation:
We want to find p for ...
1.5p -1 < 1 +1.1p
0.4p < 2 . . . . add 1-1.1p
p < 5 . . . . . . . multiply by 2.5
The desired relationship will be the case for values of p less than 5.
assuming that the pentagon is regular, what is the area of the shaded region below? PLEASE HELP ASAP
Answer:
46.20 square units
Step-by-step explanation:
The area of a regular polygon can be found from the side length and apothem as ...
A = (1/2)ap . . . . . where a = apothem, p = perimeter (# of sides times side length)
The total area of the pentagon is then ...
A = (1/2)(5.51)(5·8) = 110.20 . . . . . square units
__
The shaded area is the difference between the area of the pentagon and the area of a square with side length 8. The square's area is ...
A = s^2 = 8^2 = 64 . . . . . . square units
__
Then the shaded area is ...
A = (pentagon area) - (square area) = 110.20 -64.00 = 46.20 . . . . . square units
Which fraction is NOT equivalent to
8/12
?
A)
2/3
B)
24/36
C)
4/6
D)
6/10
PLEASE HELP QUICK!
the answer is D because 6 and 10 aren't multiples of 8 and 12
To find the fraction that is not equivalent to 8/12, simplify each given fraction and check for equivalence.
Explanation:To find which fraction is not equivalent to 8/12, we need to simplify or reduce each of the given fractions. If the simplified form of a fraction is not equal to 8/12, then it is not equivalent. Let's simplify each option:
A) 2/3 - already in simplest form, not equivalent to 8/12
B) 24/36 - can be simplified to 2/3, equivalent to 8/12
C) 4/6 - can be simplified to 2/3, equivalent to 8/12
D) 6/10 - can be simplified to 3/5, not equivalent to 8/12
Therefore, option D is NOT equivalent to 8/12.
An incoming airplane is x miles due north from the control tower at an airport. A second incoming airplane is y miles due east of the same control tower. The shortest distance between the two airplanes is z miles.
Which of the following functions would best model the situation above?
A.
cube root
B.
square root
C.
piecewise
D.
step
Answer:
B. Square root
Step-by-step explanation:
using distance formula:
x = √z^2 - y^2
y = √z^2 - x^2
=> z = √x^2 + y^2
Answer:
Option B. square root
Step-by-step explanation:
An incoming airplane is x miles due North at A from the control tower and a second airplane is y miles East at B of the same control tower.
The shortest distance between the two airplanes is z miles.
By Pythagoras Theorem
z² = x² + y²
z = √(x² + y²)
So function which models the situation best is "square root".
Therefore, option B. square root is the answer.
Write the absolute value equations in the form |x−b|=c (where b is a number and c can be either number or expression) that have the following solution sets: One solution: x=23.
Answer:
|x -23| = 0
Step-by-step explanation:
In order for there to be one x-intercept, the x-intercept must be the vertex. The vertex of your form will be (b, c), and you want that to be (23, 0). Hence your equation is ...
|x -23| = 0
An absolute value equation with the single solution set x=23 can be expressed as |x-23|=0, where b=23 and c=0 in the formula |x-b|=c.
To write an absolute value equation with the solution set x=23, we need to express this in the form |x-b|=c. The value of c must be positive, as the absolute value is always non-negative, and b will be the number that x is being compared to within the absolute value.
In this case, since we only have a single solution, this means that b=23 and c=0 because we want the equation to be true only when x is exactly 23. Thus, the absolute value equation that has only the solution set x=23 is |x-23|=0.
Find x and y for the following problem.
Answer:
x = 5/4
y = 7/4
Step-by-step explanation:
The smaller triangle and the larger one are similar, so the sides are proportional.
(x+5)/5 = 10/8
x/5 + 1 = 1/4 + 1 . . . . . divide it out
x/5 = 1/4 . . . . . . . . . . .subtract 1
x = 5/4 . . . . . . . . . . . . multiply by 5
___
For y, you can do exactly the same computations, replacing every instance of 5 with a 7. Then you get ...
y = 7/4
What is the measure of angle x? please help
➷ First find the angle on the opposite side of x.
We can find this using the rule that angles on a straight line equal 180 degrees
180 - (90 + 47) = 43
Vertically opposite angles are equal
Therefore, x would also be 43 degrees.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
x=43
Step-by-step explanation:
The angle between x and 47 is a right angle because it is a vertical angle to the right angle and vertical angles are equal.
Starting with x, we add x + the right angle +47 and we have a straight line. We know straight lines are 180 degrees
x + 90 + 47 = straight line
x+ 137 = 180
Subtract 137 from each side
x+137-137 = 180-137
x = 43
1. Write an equation in point slope form for the line through the given point with the given slope.
(8,3);m=6
A. Y+3=6(x-8)
B. Y-3=6(x-8)
C. Y-3=6(x+8)
D. Y+3=6x +8
2. Write an equation in point slope form for the line through the given point with the given slope.
(-3,-5);m= -2/5
A. Y+5= -2/5(x+3)
B. Y+5= (-2/5) x+3)
C. Y-5= -2/5 (x+3)
D. Y-5= -2/5 (x-3)
To write an equation in point slope form, we use the formula: y - y1 = m(x - x1). The correct equations are: Y + 3 = 6(x - 8) and Y + 5 = -2/5(x + 3).
Explanation:To write an equation in point slope form, we use the formula: y - y1 = m(x - x1). Where (x1, y1) is the given point and m is the given slope.
Question 1:
Given point: (8, 3) and slope: 6
Substituting the values into the formula, we have: y - 3 = 6(x - 8)
Therefore, the correct answer is option A: Y + 3 = 6(x - 8).
Question 2:
Given point: (-3, -5) and slope: -2/5
Substituting the values into the formula, we have: y + 5 = -2/5(x + 3)
Therefore, the correct answer is option A: Y + 5 = -2/5(x + 3).
Final answer:
The point-slope form equations for the given points and slopes are y - 3 = 6(x - 8) for the first set and y + 5 = (-2/5)(x + 3) for the second set.
Explanation:
The equation of a line in point-slope form is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a given point on the line.
1. With the given point (8,3) and slope m = 6, the equation in point-slope form will be y - 3 = 6(x - 8). This corresponds to option B. Y-3=6(x-8).
2. For the given point (-3,-5) and slope m = -2/5, the point-slope form of the equation is y + 5 = (-2/5)(x + 3), which matches option A. Y+5= -2/5(x+3).
I need help understanding this rather simple math.
5.48x+x=.844 ans =.130
show steps please.
Write the coordinates of the vertices after a reflection over the line y = 1
B (0, 5) —> B’ (__, __)
-
C (0, 7) —> C’ (__, __)
-
D (4, 5 —> D’ (__, __)
-
E (4, 0) —> E’ (__, __)
-
Please fill all of there out :) Will give brainiest!
B'(0,-7)
C'(0,-9)
D'(-4,-7
E'(-4.-2)
Which of the following values do not satisfy the inequality -2x-6<_1
Values that do not satisfy the inequality -2x - 6 ≤ 1 are those which are less than -3.5. This is found by isolating x and solving the inequality.
The question asks which values do not satisfy the inequality -2x - 6 ≤ 1. To solve this, first, let's isolate x on one side of the inequality. We follow these steps:
Add 6 to both sides of the inequality to get -2x ≤ 7.Divide both sides by -2, remembering that dividing by a negative flips the inequality sign, to get x ≥ -3.5.This means that all values of x that are greater than or equal to -3.5 satisfy the inequality. Thus, values that do not satisfy the inequality are those less than -3.5.
Determine the Domain of the relation
{(x, y): y = x/x-8}
Answer:
Domain: (-∞ , 8) ∪ (8, +∞)
Step-by-step explanation:
Since denominator is x - 8 so x ≠ 8
If x = 8 then y = 8/0 : undefined.
Hence, the domain is all real numbers except 8
So
Domain: (-∞ , 8) ∪ (8, +∞)
Answer:
The correct answer is A) x does not equal 8
Step-by-step explanation:
In order to find gaps in the domain, we look for two things. The first we look for is negatives under square roots (which are not an issue here since there are none) and then we look for 0, denominators. So to find the gap, we set the denominator equal to 0 and see what the x value cannot be.
x - 8 = 0
x = 8
Put this into Y=Mx+B form please
the volume of a cylinder cone and sphere are shown below. The three figures have the same radius. The cylinder and the cone have the same height with h = r.
if the volume of the cone is 36 cubic units, what are the volumes of the cylinder and sphere? Explain your answer.
answers: Cylinder:_______cubic units
sphere:________cubic units
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Answer:
Part 1) The volume of the cylinder is [tex]V=108\ units^{3}[/tex]
part 2) The volume of the sphere is [tex]V=144\ units^{3}[/tex]
Step-by-step explanation:
step 1
Find the radius of the cone
we know that
the volume of the cone is equal to
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]V=36\ units^{3}[/tex]
[tex]h=r\ units[/tex]
substitute and solve for r
[tex]36=\frac{1}{3}\pi r^{2} (r)[/tex]
[tex]108=\pi r^{3}[/tex]
[tex]r^{3}=108/ \pi[/tex] ------> equation A
step 2
Find the volume of the cylinder
we know that
the volume of the cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]h=r\ units[/tex]
substitute
[tex]V=\pi r^{2} (r)[/tex]
[tex]V=\pi r^{3}\ units^{3}[/tex]
substitute the equation A in the formula above
[tex]r^{3}=108/ \pi[/tex] ----> equation A
[tex]V=\pi (108/ \pi)\ units^{3}[/tex]
[tex]V=108\ units^{3}[/tex]
step 3
Find the volume of the sphere
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}\ units^{3}[/tex]
substitute the equation A in the formula above
[tex]r^{3}=108/ \pi[/tex] ----> equation A
[tex]V=\frac{4}{3}\pi (108/ \pi)[/tex]
[tex]V=144\ units^{3}[/tex]