A chocolate company has a new candy bar in the shape of a prism whose base is a 1-inch equilateral triangle and whose sides are rectangles that measure 1 inch by 2 inches. These prisms will be packed in a box that has a regular hexagonal base with 2-inch edges, and rectangular sides that are 6 inches tall. How many candy bars fit in such a box

Answers

Answer 1
BASE AREA OF THE BOX:

Regular hexagon with 2 inch edges contains 180*(6-2) = 180*4 = 720 degrees
That's 120 degrees in each of the corner pockets.
Drawing line segments from the center to each vertex creates 6 congruent isosceles triangles.
Selecting any one of these six triangles and dropping the height from the center to the edge
creates a 30-60-90 right triangle with height equal to the square root of 3 (rad3) and base measure 1.
So the area of each of these triangles is the square root of 3 , or in slang terms "rad 3", which means
the base area is 6*rad3.

The volume of the box is therefore 36*rad3

BASE AREA OF THE CANDY:

Dropping the height from one vertex to the opposite side of this equilateral triangle
creates 2 right triangles with base measure 1/2 and hypotneuse 1. So the height
must be rad3/2. The area of the entire equilateral triangle is rad3/4, which is the base area.

The volume of the candy is rad3/2


36*rad3 divided by rad3/2 =

36 rad3 times 2/rad3 <--- KFC : keep , change, flip

36 * 2 <-- rad3 cancels out

72 candies will fill the box.

Related Questions

Bob and Carol want to hire Able Refinishing to sand and refinish the dining room floor to match the floor in the living room. Able charges $2.41 per square foot to sand and refinish a hardwood floor. The dining room is rectangular and measures 17 feet 10 inches by 11 feet 9 inches. Find the area of the dining room floor and the cost of the work.

Answers

Answer:

Area = 209.5 ft² (nearest tenth)

Cost = $505 (approximated)

Step-by-step explanation:

Step 1: convert the inches to be in feet by dividing length in inches by 12.

17 feet 10 inches => [tex] 17 + \frac{10}{12} = 17.83 ft [/tex]

11 feet 9 inches => [tex]11 + \frac{9}{12} = 11.75 ft[/tex]

Step 2: Find the area of the floor of the dinning room

Area = 17.83*11.75 = 209.5 ft² (nearest tenth)

Step 3: Find the cost of the work.

Cost = 209.5 ft² × $2.41 = $505 (approximated)

construct a right-angled triangle ABC where angle A =90 degree , BC= 4.5cm and AC= 7cm. please ans fast........ Very urgent. Pls don't give wrong answers

Answers

Answer and Step-by-step explanation: The described right triangle is in the attachment.

As it is shown, AC is the hypotenuse and BC and AB are the sides, so use Pytagorean Theorem to find the unknown measure:

AC² = AB² + BC²

[tex]AB^{2} = AC^{2}-BC^{2}[/tex]

[tex]AB =\sqrt{AC^{2}-BC^{2}}[/tex]

[tex]AB =\sqrt{7^{2}-4.5^{2}}[/tex]

[tex]AB =\sqrt{28.75}[/tex]

AB = 5.4

Then, right triangle ABC measures:

AB = 5.4cm

BC = 4.5cm

AC = 7cm

Jami bought 4 cookies that cost $1.45, each. She paid with 6 one-dollar bills. how much change does Jami recive?

Answers

Answer:

$0.20

Step-by-step explanation:

4 x 1.45 = $5.80

6.00 - 5.80 = 0.20

Answer: $0.20

Step-by-step explanation:

Do 4 *$1.45 = $5.80

This is how much her total was.

She gave $6 in cash.

Subtract.

6-5.80=$.20

What is 32 divided by 192

Answers

Do you mean 32/192 or 192/32 because 32/192= 0.1666 where 192/32= 6

Answer:

1/6.

Step-by-step explanation:

32/192       Divide top and bottom by 8:

= 4 / 24       Now by 4:

= 1/6.

PLEASE I REALLY CAN'T THINK OF ANYTHING ELSE
list 2 differences between y = sin x and y = cos x

Answers

Answer:

- sin(x) is the ratio of the opposite leg to the hypotenuse in a right triangle, while cos(x) is the ratio of the adjacent leg to the hypotenuse in a right triangle.

-The graph of y = sin(x) at x = 0 starts at the origin, and then increases, while the graph of y = cos(x) starts at a max, and then decreases.

Here's a 3rd: sin(x) is the cofunction of cos(x), which means that sin(x) = cos(90-x). This also shows that they are different.

How many films does he have ?

Answers

Answer:

85 films

Step-by-step explanation:

10 + 20 + 25 + 20 + 10

= 85 films

answered by g a u t h m a t h

67.77759 rounded to nearest meter

Answers

Answer:

68

Step-by-step explanation:

0.7 rounds to 1 so add 1 to 67 to get 68

sbajsbisws hsbwks hawk sisswiajaa s

Evaluate ab+bc+ca . If a²+b²+c²=50 and a+b+c=12​

Answers

Answer:

ab+bc+ac=47

Step-by-step explanation:

(a+b+c)=12

Square both sides

a^2+b^2+c^2+2(ab+bc+ac)=144

2(ab+bc+ac)=94

ab+bc+ac=47

Answer:

ab + bc + ca = 47

Step-by-step explanation:

Using the algebraic identity

(a + b + c) = a² + b² + c² + 2(ab + bc + ca) , then

12² = 50 + 2(ab + bc + ca)

144 = 50 + 2(ab + bc + ca) ← subtract 50 from both sides

94 = 2(ab + bc + ca) ← divide both sides by 2

47 = ab + bc + ca

Which expression, in exponential form, is equivalent to 26x3y 47z5r3 A) ( 26x3y 47z5r3 )2 B) (26xy) 1 2 (47zr) 1 2 C) 26 1 2 x 3 2 y 1 2 47 1 2 z 5 2 r 3 2 D) 26x 3 2 y 1 2 47z 5 2 r 3 2

Answers

Answer:

The answer is "all the choices were wrong"

Step-by-step explanation:

Given value:

[tex]\bold{26x^3y 47z^5r^3}[/tex]

In the given question all the choices were wrong because it is not equivalent to given equation:

In choice A) [tex]( 26x^3y 47z^5r^3 )^2[/tex] in the value is whole squared, that's why it is wrong.

In choice B) [tex](26xy)^{12} (47zr)^{12}[/tex] when we open its value it will give different values, that's why it is wrong.

In option C and D( [tex]26^{12} x^{32} y^{12} 47^{12} z^{52} r^{32}[/tex] and [tex]26x^{32} y^{12}47z^{52} r^{32}[/tex]) both values will give different values.  

Answer:

it's C

Step-by-step explanation:

I just did it

Evaluate -3.28 - (-4.4) + (-p) where p = 9.7

Answers

Answer:

-8.58

Step-by-step explanation:

p = 9.7

=> -3.28 - (-4.4) + (-p)

=> -3.28 - (-4.4) + (- (9.7))

=> -3.28 - (-4.4) + (-9.7)

=> -3.28 - (-4.4) -9.7

=> -3.28 +4.4 -9.7

=> -12.98 +4.4

=> -8.58

Answer:

The evaluated answer for this equation is -8.58

Step-by-step explanation:

We are given a value of p so we will use this value for the equation.

-3.28 - (-4.4) + (-p)

Replace p with 9.7

-3.28 - (-4.4) + (-9.7)

Since there is a double negative in front of 4.4, then that means that we are going to be adding -3.28 to 4.4

1.12 + (-9.7)

Subtract 1.42 from 9.7 because there is negative sign in front of 9.7

-8.58

PLEASE HELP ME The graph below shows the distance, y, that a car traveled in x hours:
Rate of Travel
125
100
Distance Traveled
(miles)
75
501
251
0 1 2 3 4 5
Time (hours)
What is the rate of change for the relationship represented in the graph?
о
1
50
O
25
O 25
050

Answers

Answer:

25

Step-by-step explanation:

The graph is going up by 25 each block or point of the way, if im wrong, im sory

The opposite angles of a cyclic quadrilateral are (3x + 10)
and (2x + 20)°. Find the angles.

Answers

Just check your work so

mrs tay baked some tarts. 25% of the tarts are pineapple tarts and the rest are strawberry tarts. She baked 90 more strawberry tarts than pineapple tarts. How many strawberry tarts did she bake? ​

Answers

Step-by-step explanation:

100 - 25 = 75

75 + 90 = 165

= 165 strawberry .

Is 512 is not a perfect square​

Answers

Answer:

A perfect square is a number that can be expressed as the product of two equal integers.

The only way to accurately calculate if a number is a perfect square is to find the factors. Before we go through the trouble of finding the factors, there is a quick trick you can use to help determine if you need even need to do the extra work.

Try these steps first:

A number that is a perfect square never ends in 2, 3, 7 or 8. If your number ends in any of those numbers, you can stop here because your number is not a perfect square.

Obtain the digital root of the number. The digital root essentially is the sum of all of the digits. If you're lost, don't worry, we'll go over each step in more detail below.

All possible numbers that are a perfect square have a digital root of 1, 4, 7, 9.

Let's try it...

Step 1:

What is the last number of 512? It is this number: 512. The answer is 2. Is 2 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?

Answer: YES, 2 is in the list of numbers that are never perfect squares. The number 512 is NOT a perfect square and we can stop here as there is not need to complete the rest of the steps.

How much is $100 USD in cross water dollars

Answers

Answer:

62034.74

Step-by-step explanation:

Answer:

62034.74  use a converter

Step-by-step explanation:

The line plot below displays the fraction of incoming calls answered before the second ring by a group of employees. What fraction of employees answered less than of their incoming calls before the second ring?

Answers

Answer:

1/6

Step-by-step explanation:

People who answered less than 1/2 were:  2 +  1 + 3 = 6 people.

There are a total of 36 people.

People who answered their calls before the second ring were only 6/36.

When we simplify the fraction, we get 1/6.

So, the answer is 1/6.

sin(90°-x)=-root 3/2
what value of x satisfies the equation

Answers

Answer:

x = 30 degrees

Step-by-step explanation:

sin( 90 -x) = cos(x)

cos (30) = [tex]\frac{\sqrt{3} }{2}[/tex]

The value of x from the trigonometric relation is x = 210°

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin (-θ) = -sin (θ)

csc (-θ) = -csc (θ)

cos (-θ) = cos (θ)

sec (-θ) = sec (θ)

tan (-θ) = -tan (θ)

cot (-θ) = -cot (θ)

In the first quadrant, sin, cos and tan are all positive.

In the second quadrant going anti-clockwise, only sin is positive.

In the third quadrant going anti-clockwise, only tan is positive.

In the fourth quadrant going anti-clockwise, only cos is positive

Given data ,

Let the trigonometric relation be represented as A

Now , the value of A is

sin ( 90° - x ) = -( √3/2 )   be equation (1)

On simplifying the equation , we get

sin 60° = √3/2

Substituting the values in the equation , we get

sin ( 90° - x ) = - sin ( 60° )

And , sin (-θ) = -sin (θ)

Substituting the values in the equation , we get

sin ( 90° - x ) = sin ( - 60° )

On further simplification , we get

( 90° - x ) = ( - 60° )

Adding x on both sides of the equation , we get

x - 60° = 90°

Adding 60° on both sides of the equation , we get

x = 150°

x = π/3 + 90 + 2πn

x = 2π/3 + 90 + 2πn

Therefore , the value of x is 150° or 210°

Hence , the value of x is 210°

To learn more about trigonometric relations click :

https://brainly.com/question/14450671

#SPJ2

Find the value of x. Round to the nearest tenth.Find the value of x. Round to the nearest tenth.

Answers

Answer:

x = 55.6

Step-by-step explanation:

In order to find the value of x we use sine

sin ∅ = opposite / hypotenuse

From the question

x is the hypotenuse

the opposite is 19

So we have

sin 20 = 19/x

x = 19/sin 20

x = 55.55

We have the final answer as

x = 55.6 to the nearest tenth

Hope this helps you

Answer:

x = 55.6

Step-by-step explanation:

Solve for a.
-4a – 2a – 7 = 11
a =
[?]
Not a fraction answer

Answers

Answer:

sorry for point

plz

plz

plz

plz

Answer:

Hello,

Answer: a=-3

Step-by-step explanation:

[tex]-4a-2a-7=11\\\\\Longleftrightarrow\ -6a-7=11\\\\\Longleftrightarrow\ 6a=-7-11\\\\\Longleftrightarrow\ 6a=-18\\\\\Longleftrightarrow\ a=-3\\[/tex]

24 is 75% percent of what number?

Answers

Answer:

32

Step-by-step explanation:

We can call the number x. 75% can be expressed as 0.75 so we can write the following equation: 0.75x = 24. Dividing both sides by 0.75 to get rid of the coefficient of x, we get that x = 32.

Answer:

32.

Step-by-step explanation:

Let's say the number we are trying to find is x.

24 = 0.75x

0.75x = 24

x = 24 / 0.75

x = 32

Hope this helps!

please help me.
find the real solution of the equation.​

Answers

Answer:

[tex]x = -5 \text{ or } x =3[/tex]

Step-by-step explanation:

We want to find the real solutions to the equation:

[tex]\displaystyle 8^{x^2 + 2x - 15} = 1[/tex]

Recall that any value raised to zero (except for zero itself) is one.

In other words, the exponent must equal zero:

[tex]x^2 + 2x - 15 = 0[/tex]

Solve for x. Factor:

[tex](x+5)(x-3) = 0[/tex]

Zero Product Property:

[tex]x + 5 = 0\text{ or } x - 3 = 0[/tex]

Solve for each case. Hence:

[tex]x = -5 \text{ or } x =3[/tex]

In conclusion, our two real solutions are:

[tex]x = -5 \text{ or } x =3[/tex]

If Paul and Steve are the same height and they are both correct, write an equation to represent this relationship. Put Paul's expression on the left side of the equal sign and Steve's expression on the right.

Answers

Answer:

Theresa's height=60 inches

Paul's height= Steve's height=74 inches

Step-by-step explanation:

Theresa has two brothers,Paul and Steve, who are both the same height. Paul says he is 16 inches shorter than 1 1/2 times Theresa's height. Steve says he's 6 inches shorter than 1 1/3 times Theresa's height. If they're both right, how tall is Theresa ?

Let

p=paul's height

s=steve's height

t=theresa's height

Paul's height = Steve's height

p=s

Paul says he is 16 inches shorter than 1 1/2 times Theresa's height

1 1/2 * t -16

=3/2t -16

Steve says he is 6 inches shorter than 1 1/3 times Theresa's height

1 1/3 * t - 6

=4/3t - 6

P=S

3/2t -16 = 4/3t - 6

Collect like terms

3/2t-4/3t= -6+16

9t-8t/6 =10

t/6=10

Cross product

t=60

Theresa's height=60 inches

P=3/2t -16

=3/2(60) -16

=180/2 -16

=90-16

=74 inches

p=s

Paul's height=74 inches

Which equation represents a parabola that has a focus of (0,0) and a directix of y = 2?​

Answers

Answer: D

Step-by-step explanation:

[tex]a=0,\ b=0,\ k=2\\equation\ of\ the\ parabola:\\\\y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} \\\\\\y=-\dfrac{x^2}{4}+1 \\\\x^2=-4(y-1)\\\\Answer\ D[/tex]

Consider the functions F and G in the tables below
PLEASE HELP PLEASE

Answers

Answer:

Option A, As x increases, the rate of change exceeds the rate of f

( 2x - 9) x ( x + 5 )

Answers

[tex]2x \times x + 2x \times 5 - 9 \times x - 9 \times 5[/tex]

[tex] {2x }^{2} + 10x - 9x - 45 [/tex]

[tex] {2x}^{2} + x - 45 [/tex]

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Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]\boxed{x=14}[/tex]

Reorder the terms:

[tex]-9 + 2x = 5 + x[/tex]

Solving

[tex]-9 + 2x = 5 + x[/tex]

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.

[tex]-9 + 2x + -1x = 5 + x + -1x[/tex]

Combine like terms: [tex]2x + -1x = 1x[/tex]

[tex]-9 + 1x = 5 + x + -1x[/tex]

Combine like terms: [tex]x + -1x = 0[/tex]

[tex]-9 + 1x = 5 + 0\\-9 + 1x = 5[/tex]

Add '9' to each side of the equation.

[tex]-9 + 9 + 1x = 5 + 9[/tex]

Combine like terms: [tex]-9 + 9 = 0[/tex]

[tex]0 + 1x = 5 + 9\\1x = 5 + 9[/tex]

Combine like terms: [tex]5 + 9 = 14[/tex]

[tex]1x = 14[/tex]

Divide each side by '[tex]1[/tex]'.

[tex]x = 14[/tex]

Simplifying

[tex]x = 14[/tex]

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Have a great day/night!

❀*May*❀

Solve for x.
5x + 3 – 2x = 24
X = [?]

Answers

[tex]\\ \sf \longmapsto 5x+3-2x=24[/tex]

[tex]\\ \sf \longmapsto 5x-2x+3=24[/tex]

[tex]\\ \sf \longmapsto 3x+3=24[/tex]

[tex]\\ \sf \longmapsto 3x=24-3[/tex]

[tex]\\ \sf \longmapsto 3x=21[/tex]

[tex]\\ \sf \longmapsto x=\dfrac{21}{3}[/tex]

[tex]\\ \sf \longmapsto x=7[/tex]

Answer:

x = [7]

Step-by-step explanation:

5x + 3 - 2x = 24

Combine like terms

5x - 2x + 3 = 24

Subtract 5x - 2x

3x + 3 = 24

Subtract 3 from both sides

3x = 21

Isolate the variable

x = 21/3

x = 7

Find the squares of the following:
1)2a+1 2) 3b+2c 3) 2p²+3q²

Answers

Answer:

1. 4a^2 + 4a + 1

2 9b^2 + 12bc + 4c^2

3 4p^4 + 12p^2q^2 + 9q^4

Step-by-step explanation:

SOMEBODY PLEASE HELP ME ON THIS ; DUE TODAY, i’ll mark u the brainliest

Answers

Answer: Angle Addition Postulate

Step-by-step explanation:

According to the angle addition postulate, the measure of an angle formed by two angles side by side is the sum of the measures of the two angles. It is used to evaluate the measure of an angle formed by two or more angles .

In the given picture, we have ∠MRO and ∠MRS on line SRO.

So, ∠SRO = ∠MRO +∠MRS  [By angle addition postulate]

So the postulate that justify the statement " ∠SRO = ∠MRO +∠MRS" is Angle Addition Postulate.

ASAP
Which of the following points is in the solution set of y > -x^2 + 5?
A.) (2, 4)
b.)(1, 3)
c.)(0, 5)
wrong = reported
ty

Answers

The answer is C.) (0, 5)

Explaintion is in the pictures

I believe this is the answer if it isn't I'm sorry for wasting your time by answering.

Hope this helps!

(3-1) (4+2) + 9 - 3 I need help

Answers

Answer:

18

Step-by-step explanation:

(3-1) (4+2) + 9-3 =

2 • 6 + 6 = 12 + 6

= 18

Answer:

[tex]\displaystyle 18[/tex]

Step-by-step explanation:

[tex]\displaystyle (3 - 1)(4 + 2) + 9 - 3 = [(2)(6)] + 9 - 3 = 12 + 9 - 3 = 12 + 6 = 18\:[OR\:21 - 3 = 18][/tex]

G - Grouping Symbols

E - Exponents

M\D - Division & Multiplication [left to right]

A - Subtraction & Addition [right to left OR vice versa]

I am joyous to assist you at any time.

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The equipment for the project would be depreciated by the straight-line method over the project's 3-year life, after which it would be worth nothing and thus it would have a zero salvage value. No new working capital would be required, and revenues and other operating costs would be constant over the project's 3-year life. What is the project's NPV? (Hint: Cash flows are constant in Years 1-3.) Portia Grant is an employee who is paid monthly. For the month of January of the current year, she earned a total of 8,588. The FICA tax for social security is 6.2% of the first $118,500 of employee earnings each calendar year and the FICA tax rate for Medicare is 1.45% of all earnings. The FUTA tax rate of 0.6% and the SUTA tax rate of 5.4% are applied to the first $7,000 of an employee's pay. The amount of federal income tax withheld from her earnings was $1,424.97. Her net pay for the month is: (Round your intermediate calculations to two decimal places.) a) $7,038.50 b) $5,141.03 c) $6,072.04 d) $6,566.00 e) $6,506.04 Joy Manufacturing Company needs to know its anticipated cash inflows for the next quarter by month. Cash sales are 25 percent of total sales each month. Historically, sales on account have been collected as follows: 50 percent in the month of the sale, 30 percent in the month after the sale, and the remaining 20 percent two months after the sale. Gross sales for the quarter are projected as follows: January $20,000 February $10,000 March $40,000 Accounts receivable on December 31 were $30,000. Joy's expected cash collections for March would be:________. A. $37,000 B. $32,000 C. $30,250 D. $47,200 A united states presidential coin is made from an alloy of 4 metals-copper, zinc, manganese, and nickel- with weights in the ratio of 177:12:7:4 respectively. The coin weighs a total of 8 grams. What is the weight of the zinc in this coin? ACTIVIDAD 1 (30 puntos/3 puntos cada palabra): completa el texto con las palabras delrecuadro. Complete the text with the words in the box (you will not use all the words; use each given wordonly once). roja sociable alta rubia los es dentista se tiene altosimptico azules est bonita un el marrn blancas abogada rubio Familia pequeaMi familia no es muy grande. Somos mi padre, mi madre, mi hermano, y yo. Tambin tenemos(1) __________ perro. Yo soy mayor que mi hermano, pero l es ms (2) __________. Vamosjuntos al colegio. Yo tengo trece aos y l doce. Mis padres se llaman Carlos y Marta. Mihermano se llama lvaro, y yo Noelia. Vivimos en una casa muy (3) __________. Mi padre es (4) __________, y mi madre enfermera. Por la maana, desayunamos juntos en lacocina. Me gusta desayunar con mi familia. Adems, por las maanas siempre tengo hambre. Despus del colegio, mi madre prepara una comida deliciosa. Mi madre tiene muchas amigasporque es muy (5) __________. Por la tarde, mi madre queda con sus amigas, y mi padre juegaal tenis. Mi hermano y yo hacemos (6) __________ deberes, y despus vemos la televisin. Losviernes por la tarde vamos los cuatro de compras.Mi padre (7) __________ alto, castao y tiene los ojos (8) __________. Mi madre tiene el pelo(9) __________ y los ojos marrones. Mi hermano y yo somos los dos castaos y con ojosmarrones. A mi hermano le gusta jugar a videojuegos con sus amigos. Yo prefiero salir a la calle y jugar conmis amigas en el parque. En el parque hay muchas flores. Mis favoritas son las flores (10) __________. -----------------------------------------------------------------------------------------------------------------ACTIVIDAD 2 (20 puntos/2 puntos cada verbo): completa la siguiente tabla con las formascorrespondientes de los verbos para t y usted en presente simple. Fill in the table with the right forms of the verbs for t and usted in the present simple. Verbo T Usted1. ser2. beber3. estar4. bailar5. mirar6. saludar7. subir8. llamarse9. tener10. abrir---------------------------------------------------------------------ACTIVIDAD 3 (25 puntos/5 puntos cada pregunta): escucha el audio del link y eligeverdadero o falso. https://aedue- my.sharepoint.com/:u:/g/personal/belen_garcia_aum_edu_kw/EeM3YV6SjBZLgifVlwpU8YsBgN50aGw7v0BW8uORok8Fkg?e=dQoNLT1. Jorge est soltero. Verdadero Falso2. Pablo y yo somos primos. Verdadero Falso3. Hugo es nieto de Teresa. Verdadero Falso4. Ftima es la hermana de Teresa. Verdadero Falso5. Miguel y Manuela son mis abuelos. Verdadero Falso--------------------------------------------------------------------------------