Standard printer paper has a thickness of 0.1mm. write an equation for a function that should approximately the thickness of a sheet of paper after nn folds. f(n)=f(n)=

Answers

Answer 1

Folding a paper will make it thickness become double from it before.
Unfolded paper has 1 thickness
1 times folded paper has 2 thickness
2 times folded paper has 4 thickness
3 times folded paper has 8 thickness

From here it is clear that the pattern is [tex] 2^{n} [/tex]. SInce the paper is 0.1mm, then the function would be:
f(n)= [tex] 2^{n} [/tex] x 0.1mm

Related Questions

Graph the image of the given triangle after the transformation with the rule (x, y)→(y, x) .

Answers

See the attached figure. The original triangle is shown in red (triangle ABC). The line of reflection is the blue dashed line. This is the equation y = x. Reflecting triangle ABC over the line y = x results in the purple triangle A'B'C'.

Note how the x and y values swap places.
We have...
point A = (5,1) turn into point A' = (1,5)
point B = (8,1) turn into point B' = (1,8)
point C = (8,6) turn into point B' = (6,8)
The swap occurs because the rule (x,y) --> (y,x) tells this to happen.

The purple triangle is the final answer.

Explain why the following statement are equivalent 4(x+y)=4x+4y

Answers

They are equivalent because they are showing the Distributive Property....The Distributive Property shows that you can Distribute one number into another one, and still get the same answer.....So, you would have to do 4x+4y!!! I hope this helps!!!

The equation 4(x+y)=4x+4y represents the same value after solving.

What is Distributive Property?

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

Given:

We have 4(x+y)=4x+4y.

We have the Distributive Property

a x ( b+ c )= a x b + a x c

let x= 2 and y = 5

So, 4 (x+ y) = 4 (2+ 5)= 4(7) = 28

and, 4x+ 4y= 4(2)+ 4(5) = 8+ 20 = 28

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If you only have a 1/3 measuring cup and a recipe calls for 8 2/3 cups of flour, how many 1/3 cups would you need to use?

Answers

(8+2/3) cups divided by 1/3 = 26 cups

8*3=24=24/3
24/3+2/3= 26/3
you are going to need 26 1/3 cups

What value of c makes the trinomial below a perfect square x2 + 10x + c?

Answers

hello :
x² + 10x + c
calculate the discriminant Δ = b²-4ac a = 1 b = 10 c = c
Δ = 10²-4c
the trinomial below a perfect square when : Δ = 0
10² -4c = 0
4c = 10²
c= 25
x²+10x+25 = x² +2(5)x+5² = (x+5)²

Find f(x) and g(x) so the function can be expressed as y=f (g (x)).
y=2/x^2 +3

Answers

Since f(g(x)) essentially means that we plug f(x) into what g(x) already is (e.g. if g(x) is x^2 and f(x) is x+1, then f(g(x)) is x^2+1). If g(x) is 2/x^2 (the first part of y) and f(x) is x+3, in f(g(x)) g(x) essentially replaces x to be (2/x^2)+3

NEED HELP BADLY PLEASEEEE WILL GIVE BRAINLY

List the next three terms in the following sequence:
1, 2, 4, 8, 16, 32,...

a. 48, 80, 128
b. 64, 96, 160
c. 64, 128, 256
d. 46, 92, 184

Answers

Its C because it multiplies by 2

The first number multiplied by two is 2. Two multiplied by two is four. Four multiplied by two is eight. Eight multiplied by two is 16....and so on. So in this case, the answer would be C because 32*2=64, 64*2=128, 128*2=256.

Two thirds of a number is no more than -10

Answers

Let x be the number in the problem. When it states that x is "no more than -10", it means than it is less than or equal to -10. So, we have

[tex] \frac{2}{3} [/tex]x≤-10

In order to cancel out the [tex] \frac{2}{3} [/tex] on the left and isolate x, we multiply both sides by [tex] \frac{3}{2} [/tex] (since [tex] \frac{3}{2}[/tex]·[tex] \frac{2}{3} [/tex]=1). Thus, we have

x≤-10·[tex] \frac{3}{2} [/tex]=-15

Therefore, x≤-15

Do you know the answer to this question

Answers

Answer: [C]: " f(x) = log₃ (x − 3) " .
_______________________________________________________

40 students are going on a field trip to the aquarium. Every student needs to be in a group, and all groups must have the same number of students. If there is 1 group, there will be students in the group. If there are groups, there will be 20 students in each group. If there are 4 groups, there will be students in each group.

Answers

10 is the answer because 40/1 = 40, 40/2= 20 and 40/= 10

If there is 1 group there will be 40 students in the group. There will be 20 students in each group if there are 2 groups. If there are 4 groups, there will be 10 students in each group.

What is Division?

Division is one of the four basic operations of mathematics.

On performing the operation division, a number is divided into some number of equal parts.

The number which is being divided is called the dividend, the number which divides the dividend is called divisor and the number got when division is performed is called the quotient and the remaining number which has not divided is called the remainder.

Total number of students = 40

If there is 1 group, number of students in the group = 40/1 = 40

If there are 20 students in each group, then the number of groups = 40/20 = 2.

If there are 4 groups, then number of students in each group = 40/4 = 10.

Hence there will be 40 students in the group if there is 1 group. There are 2 groups if there will be 20 students in each group. There will be 10 students in each group if there are 4 groups.

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What is the 100th term in the following arithmetic number pattern: 2,7,12

Answers

So the change in between terms is 5 so you would put 5x, then for the first term, which is 2, 5*1(x)(because it's first term) then the difference between 5-2(because it's the 2nd term) So you would plug 100 in for x so 5(100)-3=497. Hope this helped!

Is 0 prime odd or even prime or composite?

Answers

0 is a unique case. It is neither prime nor composite, and is neither odd nor even. Zero is an absence of value case which is not made from other numbers...and didn't appear in numbering systems until the past couple of thousand years...it's a weird concept!

Answer:

0 is nor prime or composite

Step-by-step explanation:

The definition of a prime number is a positive integer that has exactly two positive divisors. Therefore, the simplest reason why 0 is not prime is that 0 is not a positive integer, and the axiom says that all whole numbers greater than 1 are either prime or composite.

what property is illustrated by this problem 2(3 + 4) = 2x 3 +2 x 4

Answers

Distributive Property

Four times the difference of a number and seven is 32

Answers

as a formula, you're saying 4*(n-7)=32

This solves to n-7 = 8, so n=15

Y = -27x + 577, where x represents the number of weeks and y represents the amount of money left in her account. After how many weeks will Alma have $145 left in her account?

Answers

To solve this problem, plugin 145 where the y is located and then solve for x
y = -27x +577
145 = -27x +577
145 -577 = -27x
-432 = -27x
-432/-27 = -27x/-27
16 = x
x = 16
After 16 weeks she will have $145 dollars in her account.

16 pound turkey cost $14.24 what is the price per pound

Answers

$.89 per pound is the answer

The answer would be $0.89,
$14.24 divided by 16

Steven investigates the amount of damage to the head gaskets on the trucks in his fleet and finds that the damage index depends on the ambient temperature. He develops the equation y = - 2 3 x + 14 to model the relationship. If the temperature increases 1 degree, what happens to the damage index for the head gasket?

Answers

It's D because it decreases by 2/3 of a point

Answer:

Step-by-step explanation:

Express the volume v of the box as a function of the length x of the sidfe of the square cut from each corner

Answers

i dont know what the word sidfe

A given cube has a volume of 1728 cubic inches. Find the length of an edge, area of one side, surface area, and surface area in square feet.

Answers

for a cube
v=s³
SA=6s²
area of 1 side=s²
s=length of 1 edge

so

1728=s³
cube root both sides
12=s

length of an edge is 12in

the area of one side is 12² or 144 in²

surface area is 6s² or 6(144) or 864 in²

A given cube with a volume of 1728 cubic inches:

Find the length of an edge:
The edge length (s) can be found using the formula for the volume of a cube: s³ = 1728. Therefore, s = 12 inches.Find the area of one side:
Each face of the cube is a square, so area of one face = s² = 12² = 144 square inches.Find the surface area:
Total surface area = 6 * (area of one face) = 6 * 144 = 864 square inches.Find the surface area in square feet:
To convert square inches to square feet, divide by 144 (since 1 square foot = 144 square inches). Therefore, surface area in square feet = 864 / 144 = 6 square feet.

An exhibit at Tabu World Square in Japan includes a scale model of the Empire State Building. The model was built using a scale of 1 m : 25 m. The height of the actual Empire State Building is 443.2 meters. What is the height of the model? Round your answer to the nearest thousanths place.

Answers

The scale is 1 m : 25 m.
The actual height = 443.2 m

Therefore the scaled height is 443.2/25 = 17.7280 m

Answer: 17.728 m (nearest thousandth)

Add the following military times: 0645 + 0745

Answers

14:30 is the answer.
(Aka 2:30 PM)

Long Division for a quadratic polynomial and binomial, please show your work!
Quadratic polynomial: x^2-x-6=f(x)
Binomial: (x-3)

Answers

answer is given above

[tex]$x^2 - x - 6$[/tex] can be expressed as the product of [tex]$(x - 3)$ and $(x - 2)$[/tex]. The long division image is given below.

Long division for polynomials is similar to long division for numbers. We'll divide the quadratic polynomial [tex]$f(x) = x^2 - x - 6$[/tex] by the binomial [tex]$(x - 3)$[/tex].

Here's a step-by-step breakdown of the process:

1. Start by dividing the highest-degree term of the dividend (in this case, [tex]$x^2$[/tex]) by the highest-degree term of the divisor (in this case, [tex]$x$)[/tex]. This gives us [tex]$x$[/tex].

2. Multiply the divisor [tex]$(x - 3)$[/tex] by the result from step 1, which is [tex]$x$,[/tex] and write the result below the dividend, aligning like terms. So, [tex]$x \cdot (x - 3) = x^2 - 3x$[/tex].

3. Subtract the result from step [tex]2 ($x^2 - 3x$)[/tex] from the dividend ([tex]$x^2 - x - 6$[/tex]). This gives us [tex]$x^2 - x - 6 - (x^2 - 3x)$[/tex], which simplifies to [tex]$-x + 3x - 6$,[/tex] resulting in [tex]$2x - 6$[/tex].

4. Now, we repeat the process with the new expression [tex]$2x - 6$[/tex]. We divide the highest-degree term ([tex]$2x$[/tex]) by the highest-degree term of the divisor [tex]($x$),[/tex] which gives us [tex]$2$.[/tex]

5. Multiply the divisor [tex]$(x - 3)$[/tex] by the result from step 4, which is [tex]$2$[/tex], and write the result below the previous result: [tex]$2 \cdot (x - 3) = 2x - 6$[/tex].

6. Subtract the result from step [tex]5 ($2x - 6$)[/tex] from the previous expression [tex]($2x - 6$)[/tex], which results in [tex]$0$[/tex].

Since we have a remainder of [tex]$0$,[/tex] this means that [tex]$x^2 - x - 6$[/tex] is evenly divisible by [tex]$(x - 3)$[/tex], and the quotient is [tex]$x - 2$.[/tex] The final result is:

[tex]\[ \frac{x^2 - x - 6}{x - 3} = x - 2 \][/tex]

This tells us that [tex]$x^2 - x - 6$[/tex] can be expressed as the product of [tex]$(x - 3)$ and $(x - 2)$[/tex].

The sum of the first and third of three consecutive even integers is 128. find the three even integers.

Answers

62, 64, and 66. 62+66=128

Final answer:

The three even integers are 62, 64, and 66.

Explanation:

The sum of the first and third of three consecutive even integers is 128. To find the three even integers, we start by letting the first integer be x. Because the integers are consecutive even numbers, the second integer will be x + 2 and the third will be x + 4. The sum of the first and third integers gives us the equation:

x + (x + 4) = 128

Solving this equation:

Combine like terms: 2x + 4 = 128.

Subtract 4 from both sides: 2x = 124.

Divide both sides by 2: x = 62.

So, the first even integer is 62. Consequently, the second is 62 + 2 = 64, and the third is 62 + 4 = 66. Therefore, the three consecutive even integers are 62, 64, and 66.

The circumference of a circular field is 295.16 yards what is the radius of the field use 3.14 for pi and do not round your answer

Answers

Circumference = 2 x 3.14 x radius

295.16 = 6.28 x radius

295.16 / 6.28 = radius

47 = radius

The radius of circle is 47 yards.

What is Circumference of circle?

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle. It is typically expressed in units like cm or unit m.

The radius of the circle is considered when applying the formula to determine the circumference of the circle. Therefore, in order to calculate the circle's perimeter, we need to know the radius or diameter value.

Given:

Circumference of circle= 295.16 yards

Now,

circumference of circle= 2πr

295.16= 2 x 3.14 x r

295.16 = 6.28 x r

r = 295.16/ 6.28

r = 47 yards.

Hence, the radius of circle is 47 yards.

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A kennel owner needs 4 1/2 feet of wall space for each crate. How many crates can she fit along a 27 foot wall?

Answers

6 /////////////////////////////////////

Question 1 (3 points) study the Proof Given.

List the reasons for Items 2,3, & 4.

Right the number and then the answer.
Question 2 (3 points
)Study the Proof: Give the reasons for the missing reason. List the number and then state the reason.

Answers

Question 1
2. Definition of midpoint
3. Given
4. Transitive Property

Question 2
1. Given
2. Addition Property of Equality
3. Segment Postulate Property.

It snowed 4 times during October. The snowfall amounts were 0.75 inches, 1.93 inches, 4.73 inches, and 2.33 inches. What was the total snowfall for October?

Answers

9.74 inches i did this problem yesterday

The total snowfall for October was 9.74 inches. Adding the snowfall amounts of 0.75, 1.93, 4.73, and 2.33 inches resulted in this sum.

Let's break down the calculation step-by-step:

Identify the given snowfall amounts for October:

The snowfall amounts are 0.75 inches, 1.93 inches, 4.73 inches, and 2.33 inches.

Add up the snowfall amounts to find the total:

Total snowfall = 0.75 inches + 1.93 inches + 4.73 inches + 2.33 inches.

Perform the addition

Total snowfall = 9.74 inches.

The total snowfall for October was 9.74 inches. This result is obtained by adding all four individual snowfall amounts together.

So, the calculation in step-by-step form is as follows:

0.75 + 1.93 + 4.73 + 2.33 = 9.74 inches.

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What is the area of a circle with a radius of 14 feet? use 22/7 for π?

Answers

So the formula is pi*r^2 and if you plug that in it is 22/7* 14^2 and you get 616

Solve the following problem for the roots by completing the square

3x^2 -12x = 9

Answers

3(x^2+3) is the answer you are looking for. :)

3x^2 - 12x = 9
Divide both sides by 3
x^2 - 4x = 3
To make a square with "x^2 - 4x", you need to have a "+ 4" after it so it can be simplified as (x-2)^2. So add 4 to both sides.
x^2 - 4x + 4 = 7
(x-2)^2 = 7
x - 2 = (square root) of 7
x = 2 (+/-) (square root) of 7.
x = {-0.65, 4.65}

The solutions are -0.65 and 4.65.

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The perimeter of a rectangle is 44 inches, and its area is 105 square inches. find the length and width of the rectangle.

Answers

Perimeter = (Length + Width)x2
Area = LengthxWidth

P=(L+W)x2
P/2=L+W
L=P/2 - W

Area=(P/2 - W)(W)
A=WP/2-W^2
105=W(44)/2 - W^2
105=22W - W^2
W^2-22W+105=0
(W-7)(W-15)=0
Width= 7 or 15

A=LxW
105=Lx7
105/7=L
L=15

Length is 15 inches, Width is 7 inches.

Can someone help me with these maths questions? I totally don't get them.

Do the following coordinates lie on the following graphs?

1) y=2x+4 (7,20)
2) y=4x-14 (-1,-18)
3) y=5x-1 (0.5,2.5)
4) y=-2x+6 (0.8,5.4)
[tex] 5) y=\frac{1}{2}x+2 (0.7,1.6) [/tex]

Answers

1. 2(7) +4 = 18, does not = 20, does not lie on graph

2. 4(-1) -14 = -18, equals -18, does lie on the graph

3. 5(.5)-1 = 1.5, does not = 2.5, does not lie on the graph

4. -2(0.8)+6 = 4.4, does not = 5.4 does not lie on graph

5. 1/2(0.7) +2 = 2.35, does not = 1.6, does not lie on graph

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