In ABC, the bisector of A divides BC into segment BD with a length of


28 units and segment DC with a length of 24 units. If AB -31. 5 units, what


could be the length of AC ?

The function in vertex form is f(x) = 4(x - 6)² - 26.

The function in vertex form is f(x) = 4(x - 6)² - 26.

To get to this form, the first step is to factor out the coefficient of x², which is 4:

f(x) = 4(x² - 12x) + 10

Next, complete the square by adding and subtracting (12/2)² = 36 inside the parenthesis:

f(x) = 4(x² - 12x + 36 - 36) + 10

Simplify the expression inside the parenthesis and combine like terms:

f(x) = 4((x - 6)² - 36) + 10

f(x) = 4(x - 6)² - 134

Therefore, the function in vertex form is f(x) = 4(x - 6)² - 26.

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The term f(4) < f(11) means that the temperature is lower at 4 A.M. than it is at 11 A.M., and this inequality can be used to make predictions about temperature changes over time.

The function f(t) represents the temperature at a specific time t. In this case, f(t) is the outside temperature (in degrees Fahrenheit) 7 hours after 2 A.M. So, we can think of f(4) as the temperature 4 hours after 2 A.M. and f(11) as the temperature 11 hours after 2 A.M.

Now, the inequality f(4) < f(11) means that the temperature 4 hours after 2 A.M. is less than the temperature 11 hours after 2 A.M. In other words, the temperature is lower at 4 A.M. than it is at 11 A.M. This might seem obvious, as we generally expect temperatures to rise as the day progresses and the sun comes up. However, this inequality is useful for making more specific predictions about temperature changes.

For example, if we know that f(4) < f(11), we can predict that the temperature will increase between 4 A.M. and 11 A.M. This might be important information if you're planning outdoor activities or need to dress appropriately for the day's weather.

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The equations represent four different parabolas with different shapes and orientations, but all of them have the same axis of symmetry, which is the y-axis (because there is no x term).

The collection of all points in a plane that are equally spaced from a fixed line and another fixed point in the plane that is not on the line is known as a parabola. The focus of the parabola is the fixed point (F) and the fixed point (D) is known as the directrix.

The equation of a parabola in standard form is:

y = a x² + b x + c

where "a" is the coefficient of the quadratic term (x^2), "b" is the coefficient of the linear term (x), and "c" is the constant term.

Looking at the given equations:

So, the equations represent four different parabolas with different shapes and orientations, but all of them have the same axis of symmetry, which is the y-axis (because there is no x term).

To graph each parabola, you can use the vertex form of the equation:

y = a (x - h)² + k

where (h, k) is the vertex of the parabola.

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The measure of angle U in triangle UVW is approximately 28 degrees. This is found by using the inverse tangent function to solve for angle U given the lengths of two sides and the fact that angle W is a right angle.

To find the measure of ∠U in ΔUVW, we can use trigonometry. We know that sin(∠U) = opposite/hypotenuse, which is equal to UW/VW. Therefore, we can plug in the given values and solve for sin(∠U)

sin(∠U) = UW/VW = 2.2/4.7 = 0.4681

Next, we can use the inverse sine function (sin⁻¹) to find the measure of ∠U

∠U = sin⁻¹(0.4681) = 28.34 degrees (rounded to the nearest degree)

Therefore, the measure of ∠U in ΔUVW is approximately 28 degrees.

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Answer:

Step-by-step explanation:

There are 26 letters in the alphabet and 10 digits that you can use (0,1,2,3,4,5,6,7,8,9)

As a result, we can find the number of combinations by doing the following:

26 x 26 x 10 x 10 x 10

since the first two symbols are alphabets and the last three are digits. After doing the math you get

26 x 26 x 10 x 10 x 10 = 676000 => You can make a total of 676,000 PIN codes

The actual measure of major arc JML is approximately 289.33°, which is closest to 287°.

We know that minor arc KL is supplementary to major arc JML. So,

m∠KL = 180° - m∠JML

Substituting the given values, we get:

8x - 6 = 180 - (25x - 13)

Solving for x, we get:

33x = 193

x = 193/33

Substituting this value of x in the expression for m∠JML, we get:

m∠JML = 25(193/33) - 13

m∠JML = 1468/3

m∠JML ≈ 489.33°

However, since lines KL and JM appear tangent, we know that minor arc KL and major arc JML share the same endpoint and thus are part of the same circle. So, the actual measure of major arc JML is:

m(arc JML) = 360° - m(arc KL)

We can find m(arc KL) by subtracting m∠KLM from 180°:

m(arc KL) = 180° - m∠KLM

m(arc KL) = 180° - (8(193/33) - 6)

m(arc KL) ≈ 70.67°

Substituting in the formula for m(arc JML), we get:

m(arc JML) = 360° - 70.67°

m(arc JML) ≈ 289.33°

Therefore, the actual measure of major arc JML is approximately 289.33°, which is closest to option (b) 287°.

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Answer:

[tex]20,000 \text{ kWh}[/tex]

Step-by-step explanation:

We can convert 68 million British Thermal Units (BTUs) to kilowatt-hours (kWh) using the given conversion ratio:

[tex]\dfrac{1 \text{ kWh}}{3400 \text{ BTUs}}[/tex]

Multiplying by the ratio:

[tex]68,000,000 \text{ BTUs} \cdot \dfrac{1 \text{ kWh}}{3,400 \text{ BTUs}}[/tex]

↓ canceling the BTU units

[tex]68,000,000\cdot \dfrac{1 \text{ kWh}}{3,400}[/tex]

↓ executing multiplication

[tex]\dfrac{68,000,000}{3,400} \text{ kWh}[/tex]

↓ rewriting as a decimal

[tex]\boxed{20,000 \text{ kWh}}[/tex]

The soccer ball will land approximately 1 seconds after it was kicked upward. This is found by setting the height equation to 0 and solving for t using the quadratic formula.

To solve for the time the soccer ball lands, we need to find the time when h = 0. We can use the given equation

h = -4.9t² + vt + s

where v = 4.9 m/s (since it's kicked upward) and s = 0 (since it starts at ground level).

Substituting those values, we get

0 = -4.9t² + 4.9t

Factoring out 4.9t, we get

0 = 4.9t(-t + 1)

So, either t = 0 or -t + 1 = 0

Since time cannot be negative, we discard the second solution and solve for t

-t + 1 = 0

t = 1

Therefore, the soccer ball lands after approximately 1 second.

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La probabilidad de sacar un producto defectuoso al azar de las tres cajas es aproximadamente 0.0917, o un 9.17%.

La probabilidad de sacar un producto defectuoso al azar de las tres cajas se puede calcular utilizando la fórmula de la probabilidad.

Primero, calculemos la probabilidad de sacar un producto defectuoso de cada caja:

1. En la primera caja, hay 3 productos defectuosos entre 20 productos en total. La probabilidad es 3/20.

2. En la segunda caja, hay 2 productos defectuosos entre 16 productos en total. La probabilidad es 2/16.

3. En la tercera caja, no hay productos defectuosos entre 10 productos en total. La probabilidad es 0/10.

Para encontrar la probabilidad total, sumamos las probabilidades de cada caja y luego dividimos por el número total de cajas:

(3/20 + 2/16 + 0/10) / 3 ≈ (0.15 + 0.125 + 0) / 3 ≈ 0.0917

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The total mass of the rod is 81622.5 kg. To find the total mass of the rod, you need to integrate the linear density function with respect to the length of the rod.

To find the total mass of the rod, we need to integrate the linear density function over the entire length of the rod.
Let's start by finding the linear density function at the end of the rod, which is a = 9:
p(9) = 3 + 2017 = 2020 kg/m
Now we can integrate the linear density function from a = 0 to a = 9 to find the total mass:
m = ∫₀⁹ p(a) da
m = ∫₀⁹ (3 + 2017a) da
m = [3a + 1008.5a²] from 0 to 9
m = (3(9) + 1008.5(9)²) - (3(0) + 1008.5(0)²)
m = 81622.5 kg
Therefore, the total mass of the rod is 81622.5 kg.

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The area of the playground include the following: 900 square yards.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = base area × height

Area of playground, A = 45 × 20

Area of a playground, A = 900 square yards.

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The location of the point Kristin will add to represent the 13 bottles of water sold at 39 degrees Fahrenheit is the bottom left of the scatter plot.

A scatter plot represents the relationship between two variables. In this case, the temperature (independent variable) is plotted along the x-axis, while the number of bottles of water sold (dependent variable) is plotted along the y-axis. As the temperature increases, it is expected that more bottles of water would be sold.

The bottom left area of the scatter plot is where lower values of both temperature and the number of bottles sold would be found. Since 39 degrees Fahrenheit is relatively low and 13 bottles of water is a lower quantity, the point representing this data will be in the bottom left quadrant of the scatter plot.

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Complete question:

Kristin made a scatter plot to represent the relationship between the temperature and the number of bottles of water sold at her concession stand at a soccer tournament. Which is a description of the location of the point Kristin will add to represent the 13 bottles of water that were sold when the temperature was 39 degrees Fahrenheit? Select one:

O  Top left of the scatter plot

O  Bottom right of the scatter plot

O  Top right of the scatter plot

O  Bottom left of the scatter plotâ

The height of the new player is given as follows:

210 cm.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Considering the frequencies and the height of the new player of x, the sum of the observations is given as follows:

198 x 1 + 199 x 3 + 200 x 2 + 201 x 5 + 202 x 2 + x = 2604 + x.

The total number of players, considering the new player, is given as follows:

1 + 3 + 2 + 5 + 2 + 1 = 14.

The mean is of 201 cm, hence the height of the new player is obtained as follows:

(2604 + x)/14 = 201

2604 + x = 14 x 201

x = 14 x 201 - 2604

x = 210 cm.

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The sample space for a child choosing one entrée and one side is A) BA, BF, CA, CF, PA, PF, SA, SF.So, the correct answer is A). Probability of a child choosing pizza or spaghetti with mixed vegetables is 2/15 or 0.1333 (rounded to four decimal places) or approximately 13.33%.

The sample space represents choose of one entrée and one side for his or her meal is BA, BF, CA, CF, PA, PF, SA, SF. So, the correct option is A).

After the addition of grilled cheese as an entrée choice and mixed vegetables as a side choice, there are now five entrée choices (B, C, P, S, G) and three side choices (A, F, MV). The total number of possible meal combinations is 5*3 = 15.

The number of meal combinations where the child chooses pizza or spaghetti with mixed vegetables is 2 (pizza with mixed vegetables and spaghetti with mixed vegetables). Therefore, the probability of choosing spaghetti or pizza with mixed vegetables for her or his meal is

P(pizza or spaghetti with mixed vegetables) = 2/15 = 0.1333 (rounded to four decimal places) or approximately 13.33%.

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--The given question is incomplete, the complete question is given

"At a restaurant, a children's meal gives a choice of four entrées: burger (B), chicken (C), pizza (P), or spaghetti (S), and two sides: apple (A) or fries (F).

Part A

Which sample space represents all the ways a child could choose one entrée and one side for his or her meal?

A) BA, BF, CA, CF, PA, PF, SA, SF

B) BA, CA, PA, SA

C) BF, CF, PF, SF

D) B, C, P, S, A, F

Part B

The restaurant decides to add another choice for the entrée and another choice for the side on the children's menu. The additional entrée choice is grilled cheese and the additional side choice is mixed vegetables. What is the probability that a child will choose pizza or spaghetti with mixed vegetables for his or her meal?"--

(a) Boris performed better on the aptitude test, since its z-score was higher.

(b) Callie performed better on the knowledge test.

(c) The z-score for the aptitude test was still higher than the z-score for the knowledge test, so Boris performed better on the aptitude test.

(a) To determine which test Boris performed better on, we need to compare his z-scores for the knowledge test and the aptitude test.

For the knowledge test, his z-score is calculated as:

z = (55 - 60) / 3 = -1.67

For the aptitude test, his z-score is:

z = (106 - 110) / 6.8 = -0.59

Since the z-score for the aptitude test is higher than the z-score for the knowledge test, Boris performed better on the aptitude test.

(b) To determine which test Callie performed better on, we need to compare her z-scores for the knowledge test and the aptitude test.

For the knowledge test, her z-score is:

z = (67 - 60) / 3 = 2.33

For the aptitude test, her z-score is:

z = (119 - 110) / 6.8 = 1.32

Since the z-score for the knowledge test is higher than the z-score for the aptitude test, Callie performed better on the knowledge test.

(c) Boris' z-score on the logic test (-0.43) is unrelated to his performance on the knowledge and aptitude tests, so it does not change the answer to which test he performed better on. The z-score for the aptitude test was still higher than the z-score for the knowledge test, so Boris performed better on the aptitude test.

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Therefore, the height of the cone is approximately 4.23 centimeters.

Volume is a measure of the amount of space occupied by a three-dimensional object or region. It is the total amount of space enclosed by the boundaries of the object or region. Volume is usually measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³). Knowing the volume of an object can be useful for many purposes, such as determining how much material is needed to fill a container or how much space is needed to store a certain quantity of objects.

Here,

The formula for the volume of a cone is given by:

V = (1/3)πr²h

where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cone is 3.0144 cubic centimeters, so we can plug this into the formula:

3.0144 = (1/3)πr²h

Next, we need to find the radius of the cone. Since we are not given the radius directly, we may need to use other information that is not given in the problem. If we assume that the cone is a right circular cone, then we can use the fact that the radius and height are proportional to find the radius:

r/h = 1/3

r = (1/3)h

We can substitute this expression for r into the volume formula:

3.0144 = (1/3)π((1/3)h)²h

Simplifying this equation:

3.0144 = (1/27)πh³

Multiplying both sides by 27/π:

h³ = 84.96

Taking the cube root of both sides:

h = 4.23 (rounded to the nearest hundredth)

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The function g(x)=-1/2f(x)+3 containing points (a) (0, 4) and (a) (2, 0).

The function g(x) = -1/2f(x) + 3 is obtained by applying certain transformations to the original function f(x) = 3^x - 3.

To find the points on the graph of g(x), we need to substitute the x-values from the given points into the function g(x) and determine the corresponding y-values.

Given:

Original function f(x) = 3^x - 3

Points on f(x): (0, -2) and (2, 6)

To find the points for g(x), we substitute the x-values into g(x) = -1/2f(x) + 3:

1. For the point (0, -2):

g(0) = -1/2f(0) + 3

      = -1/2(-2) + 3

      = 1 + 3

      = 4

2. For the point (2, 6):

g(2) = -1/2f(2) + 3

      = -1/2(6) + 3

      = -3 + 3

      = 0

Therefore, the points for the function g(x) = -1/2f(x) + 3 are:

(a) (0, 4)

and

(a) (2, 0)

Hence, the correct answer is:

(a) (0, 4) and (a) (2, 0).

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Based on the information provided, Madeline and Ben invested $1500 for their son Peter's education on the day he was born at an interest rate of 6.7% compounded quarterly. Since Peter is now 19 years old and wants to go to college, we can calculate the current value of his education fund.

To do this, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time in years

In this case, we have:

P = $1500
r = 6.7% = 0.067 (as a decimal)
n = 4 (since the interest is compounded quarterly)
t = 19 (since Peter is now 19 years old)

So, the current value of Peter's education fund is:

A = $1500(1 + 0.067/4)^(4*19)
A = $1500(1.01675)^76
A = $1500(2.4826)
A = $3,723.90

Therefore, the current value of Peter's education fund is $3,723.90. This should help Madeline and Ben determine how much more they need to save for Peter's college expenses.

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Answer:

Step-by-step explanation

π corresponds to 180 degrees.

so

180 : 8 = 22.5°

Its translation is 5×3-3=12

Answer:

-----------------------

F(x) is in the format of a quadratic function:

Hence it is a parabola.

The table represents a relation with two x-intercepts and two y-intercepts (points with the coordinate of 0).

We know that parabola can have maximum of one y-intercept, hence G(x) is not a parabola.

The matching answer choice is the first one.

Answer:

p = 38

Step-by-step explanation:

We Know

The 104° angle + (2p) angle must be equal to 180°.

Solve for the value of p.

Let's solve

104° + 2p = 180°

2p = 76°

p = 38

The sound level of the vocalizations of a blue whale is approximately 140.28 decibels.

The question asks us to find the sound level in decibels (db) of the vocalizations of a blue whale, given its sound intensity of 106.8 watts/meter2.

The formula for sound level in decibels is:

L = 10log(i/I0)

Where L is the sound level in decibels, i is the sound intensity in watts/meter2, and I0 is the smallest sound intensity that can be heard by the human ear (approximately 1x10⁻¹² watts/meter2).

Plugging in the given values, we get:

L = 10log(106.8/1x10⁻¹² )

Simplifying this expression, we get:

L = 10log(1.068x10¹⁴)

L = 10(14.028)

L = 140.28

Therefore, the sound level of the vocalizations of a blue whale is approximately 140.28 decibels.

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Using  net worth statement, Andre's net worth is $159,573.

Andre's net worth can be calculated by subtracting his total liabilities from his total assets.

Total assets = $155,000 (condominium) + $8,100 (stock portfolio) + $9,100 (car value) + $2,600 (bank account) = $174,800

Total liabilities = $3,300 (car loan) + $7,600 (student loans) + $4,327 (credit card balance) = $15,227

Net worth = Total assets - Total liabilities = $174,800 - $15,227 = $159,573

Therefore, Andre's net worth is $159,573.

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She requires 55 consecutive successful throws to get a success rate of 60%

The number of successful throws she made is 8 out of 50

Now to calculate the percentage we will use the formula

[tex]\frac{8}{50} X 100 = 16[/tex]

According to the problem, she needs to make her success percentage 60% and for that, we need to estimate the number of consecutive successful throws. Hence the new equation will be

[tex]\frac{8+x}{50+x} X 100 = 60[/tex]

[tex]or, \frac{8+x}{50+x} = 0.6[/tex]

This is the equation concerned.

Now,to solve this, we will take the denominator on the other side will give us

[tex]or, 8+x = 0.6(50+x)[/tex]

[tex]or, 8+x = 30+ 0.6x[/tex]

[tex]or, x - 0.6x = 30 -8[/tex]

[tex]or, 0.4x= 22[/tex]

or, x = 55

Hence we see that she requires 55 consecutive successful throws to get a success rate of 60%

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Complete Question

A basketball player made 8 out of 50 free throws she attempted which is 16%. She wants to know how many consecutive free throws more in a row she would have to make to raise her overall successful baskets divided by attempts or percent of successful free throws to 60%.

(a) Write an equation to represent this situation.

(b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 60%?

Thus, the coordinates of ΔF'I'G' after a rotation of 90° clockwise about the origin. are - F'(4,-2), I'(4,-5) and G'(2,-3).

A rotation is a turn made about a specific axis. Both clockwise and anticlockwise rotations are possible. Whereas the image is really the rotating image, the pre-image is the original item.

From the pre-image point, calculate the image. The listed pre-image point is (x , y). Change the x and y coordinates, then multiply this same previous y coordinate by -1 to get a 90 degree anticlockwise rotation. Use the guidelines mentioned below to calculate each rotation.

Clockwise :

Given :

F(2, 4), I(5, 4) and G(3, 2)

After 90 degree rotation: (x , y) ----> (y , -x)

F'(4,-2), I'(4,-5) and G'(2,-3).

Thus, the coordinates of ΔF'I'G' after a rotation of 90° clockwise about the origin. are - F'(4,-2), I'(4,-5) and G'(2,-3).

Graphs for the both triangles are obtained.

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Correct question:

ΔFIG has vertices at F(2, 4), I(5, 4) and G(3, 2). Graph ΔFIG and ΔF'I'G' after a rotation of 90° clockwise about the origin.​

a) Where the information about triangle ABC is given above, the measure of angle B is 60°

Using the Cos Rules,

(15√3)² = 30² + 15² - 2(15 x 30) cos B

⇒ 657 = 1125 - 900 cosB

⇒ 2 Cos B = 1 Cos B = 1/2

So

B = Cos ⁻¹(1/2)

Hence,

B = 60°

B) Given the above,

Now, we can use the tangent function to find tan B:

tan B = sin B / cos B

  = sin (π/3) / cos (π /3)

  = (√3 / 2) / 0.5

tan B = √3

C ) the area of the rriangle is given as

s = (a + b + c) /2

Substituting

s = (15 + 15√ 3 + 30)/2

s = 30 + 15√3

Area = √ [ (30 + 15√3)(15√3) (15)(30  - 15 - 15√3))

Simplifying  we can say

Area = √(30 + 15√3  )( 15√3)(15)(15 - 5√3 )]

= √[3(10 + 5√3)(15)(3√3 - 1)]

  = √[2250 - 1125√3]

Hence,

Area ≈ 17.36in

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The equations that have the same value of x as 3/5 (30 x - 15) = 72 are C, D, and E.

To solve for x in 3/5 (30 x - 15) = 72, we can first simplify the left side by distributing the 3/5:

3/5 (30 x - 15) = 18 x - 9

Now we can solve for x by setting the right side equal to 72:

18 x - 9 = 72

Adding 9 to both sides:

18 x = 81

Dividing by 18:

x = 4.5

So we know that option E is one of the correct answers.

To check which of the other options have the same value of x, we can substitute x = 4.5 into each equation and see if it simplifies to 72:

A. 18 x - 15 = 72

18(4.5) - 15 = 72

81 - 15 = 72 (not equivalent)

B. 50 x - 25 = 72

50(4.5) - 25 = 200 - 25 = 175 (not equivalent)

C. 18 x - 9 = 72

18(4.5) - 9 = 72 (equivalent)

D. 3 (6 x - 3) = 72

3(6(4.5) - 3) = 3(24) = 72 (equivalent)

Therefore, the equations that have the same value of x as 3/5 (30 x - 15) = 72 are C, D, and E.

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The paper initial area of the paper is 90 square inches and needs to be folded at least 5 times before its area becomes less than 1 square inch.

a. When n=0, the expression for the area of the paper after folding becomes:

a = 90•(1/3)⁰ = 90•1 = 90 square inches

This means that the initial area of the paper before any folding is 90 square inches.

b. To find out how many folds are needed before the area is less than 1 square inch, we can set the expression for the area of the paper after folding to be less than 1 and solve for n:

a = 90•(1/3)ⁿ < 1

(1/3)ⁿ < 1/90

Taking the logarithm of both sides with base 1/3, we get:

n > log(1/90)/log(1/3)

n > 4.8

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The balance when $3000 is invested at 4% rate for 20 years and compounded annually, semi-annually, quarterly, monthly, daily, and continuously are $6,372.76, $6,454.81, $6,506.71, $6,535.94, $6,546.49, and $6,549.18 respectively.

Compounding Frequency Balance after 20 Years

Annually $6,372.76

Semi-annually $6,454.81

Quarterly $6,506.71

Monthly $6,535.94

Daily $6,546.49

Continuous $6,549.18

Using the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the balance after t years, P is the principal (amount invested), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

For p = $3000, r = 4%, t = 20 years, and the different compounding frequencies, we get:

Annually: A = $3000(1 + 0.04/1)^(1*20) = $6,372.76

Semi-annually: A = $3000(1 + 0.04/2)^(2*20) = $6,454.81

Quarterly: A = $3000(1 + 0.04/4)^(4*20) = $6,506.71

Monthly: A = $3000(1 + 0.04/12)^(12*20) = $6,535.94

Daily: A = $3000(1 + 0.04/365)^(365*20) = $6,546.49

Continuous: A = $3000e^(0.0420) = $6,549.18 (where e is the constant 2.71828...)

Therefore, the balance a when $3000 is invested at 4% rate for 20 years and compounded n times per year (where n is the different frequencies given) are as mentioned above.

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