0.4x+2.9=1.5 solve for x

Answer:18

Step-by-step explanation:

Plan B offers a higher effective annual interest rate than Plan A by 2.9975%. Therefore, Plan B is the better plan by about 2.9975% in the compound interest.

When interest is earned on a loan or investment, it is earned on both the principal and any accumulated interest, which is known as compound interest. In other words, interest is added to the principal, and the resulting sum is then used to determine future interest. Compounding causes an investment or loan to increase more quickly than it would with simple interest, where just the principal is charged interest. Compounding may occur daily, monthly, quarterly, annually, or at any other interval.

To compare the plans of the two accounts we have:

Rate = ( 1 + rate / n)ⁿ - 1

where, n is the compounded period.

For plan A:

Effective annual interest rate = (1 + (0.5%/4))⁴ - 1 ≈ 0.5025%

For Plan B, we have:

Effective annual interest rate = (1 + 3.5%)¹- 1 = 3.5%

Comparing the two we see that Plan B offers higher rates by:

3.5% - 0.5025% ≈ 2.9975%.

Hence, Plan B offers a higher effective annual interest rate than Plan A by 2.9975%. Therefore, Plan B is the better plan by about 2.9975%.

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By factoring and finishing the square , C is the right response. x = -5 or x =5

There are two ways to resolve quadratic equations: factoring and solving the square. A quadratic equation is factored when it is divided into two linear equations with the same solution. A method for rewriting quadratic equations in the form (x+a)²+b (x +a)² +b is known as "completing the square." This method enables us to change a quadratic expression or equation in the form an x² + b x + c to a (x - h) ² + k²from a provided quadratic expression or equation. This method can be applied to ease the process of solving complex quadratic equations .

The following techniques can be used to graphically solve the quadratic equation using at least two separate approaches:

Technique 1: Factoring

- Step 2: Finish the square

- Technique 3: Quadratic equation

- Step Four: Graphing

16x² - 400 = 0 is the quadratic equation that is provided.

First approach: factoring

The quadratic equation presented can be factored as follows:

16x²- 400 = 0

16(x² - 25) = 0

16(x + 5)(x - 5) = 0

Because of this, x = -5 or x = 5.

completing the square using method two

The square of the given quadratic equation can be completed as follows:

16x² - 400 = 0

16x² = 400

x² = (400/16)

x² = 25

x = ±√25

Because of this, x = -5 or x = 5.

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The probability that the spinner lands on an even number or a number greater than 10 is 11/18.

There are two cases where the spinner can land on an even number or a number greater than 10:

Case 1: The spinner lands on an even number.

There are 9 even numbers on the spinner: 2, 4, 6, 8, 10, 12, 14, 16, and 18. The probability of the spinner landing on an even number is 9/18 = 1/2.

Case 2: The spinner lands on a number greater than 10.

There are 7 numbers greater than 10 on the spinner: 11, 12, 13, 14, 15, 16, and 18. The probability of the spinner landing on a number greater than 10 is 7/18.

To find the probability of either event occurring, we add the probabilities of the two cases and subtract the probability of both occurring simultaneously (since the numbers 12, 14, and 16 are even and greater than 10). Therefore, the probability of the spinner landing on an even number or a number greater than 10 is:

(1/2) + (7/18) - (3/18) = 11/18

Thus, the probability that the spinner lands on an even number or a number greater than 10 is 11/18.

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The range of the given function is {-2, 6, 22}.(option c)

What is function?

In mathematics function is an expression, rule, or law that defines a relationship between one variable which is the independent variable and another variable which is the dependent variable.

The given function is f(x)= x² -3

The range is the output of the function for the given inputs.

Here the given domain that is the input of the function is {1,3,5}

For x=1,

f(1)= 1² -3

    = 1-3

     = -2

For x= 3

f(3)= 3² - 3

    = 9-3

     = 6

For x= 5

f(5)= 5²- 3

    = 25-3

     = 22

Hence, the range of the given function is {-2, 6, 22}.

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The correct answer for the given dataset will be: Burger Quick, because it has a larger median.

A box plot,also known as a box-and-whisker plot, is used for graphical representation of summary statistics from a data set. It helps by providing a visual representation of a data set's central tendency, dispersion, and skewness, making it straightforward to identify important data aspects.

As per given data, Burger Quick typically has more wait time compared to Super Fast Food.

The box plot for Burger Quick displays a higher interquartile range (from 9.5 to 24) than Super Fast Food (from 8.5 to 15.5), indicating that Burger Quick has a broader dispersion in the middle 50% of the data. Also, the median (shown by the line in the box) for Burger Quick is 15.5, but the median for Super Fast Food is 12. This implies that the average wait time at Burger Quick is longer than at Super Fast Food.

The lines outside the box (whiskers) also demonstrate that the range of values for Burger Quick (from 2 to 30) is greater than for Super Fast Food (from 3 to 27), implying that Burger Quick has a longer wait time.

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Step-by-step explanation:

Refer the attachment!!~

Answer:

Step-by-step explanation:

According to the nearest hundredth, the length of the wire in the photograph is 200 cm.

What in mathematics is a semicircle?

By dividing a circle into two halves along a diameter line, a semicircle is created, which is a half-circle.

The wire will be cut into four semicircles, each of which will have a circumference equal to its length.

Therefore, if one semicircle has a diameter of 32 cm, its radius is 32/2 cm, or 16 cm.

Right now, a circle's circumference equals 2*(pi)*(radius).

Since this is a semicircle, its circumference is equal to (pi)*(radius), or one-half of a circle.

The circumference of four semicircles is then equal to four * pi * radius.

Pi has a value of 22/7.

Thus, the length of the wire is 4*(22/7)*16 cm, which, when rounded to the nearest hundredth, is 200 cm.

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Hence, 201 [tex]cm^{2}[/tex] long is the wire to the nearest hundredth.

In mathematics, a semicircle is a  one-dimensional locus of points that forms  half of a circle. It is a circular arc that  measures 180°.  It has only one line of symmetry.

In geometry, the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure .

In other words ,The meaning of circumference is the distance around a circle or any curved geometrical shape. It is the one-dimensional linear measurement of the boundary across any two-dimensional circular surface.

According to figure

diameter of  all semi circle (d) = 32 cm.

so radius of  all semi circle r = [tex]\frac{32}{2}[/tex] = 16 cm.

length of wire = circumference of semicircle =

⇒ total length length of wire = 4 * circumference of semicircle

                                                                                 {∵ no. of semicircle=4

∴ total length length of wire = 4 * [tex]\pi*r[/tex]      

∴ total length length of wire = 4 *3.14*16              {we know that , [tex]\pi=3.14[/tex]

∴ total length length of wire =200.96[tex]cm^{2}[/tex] ≅ 201[tex]cm^{2}[/tex]

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the ratio of Nonfiction novels to all novels is: Nonfiction novels : Total novels  [tex]= 2 : 11[/tex]  So the correct answer is  [tex]2:11.[/tex]

The ratio of Nonfiction novels to all novels can be calculated by dividing the number of Nonfiction novels by the total number of novels.

The total number of novels is the sum of Nonfiction, mystery, and fiction novels:

Total number of novels = Nonfiction + Mystery + Fiction [tex]= 2 + 4 + 5 = 11[/tex]

The ratio of nonfiction novels to all novels is not a fixed value, as it depends on the specific set of novels being considered. However, it can be calculated if we have the appropriate data.

Therefore, the ratio of Nonfiction novels to all novels is: Nonfiction novels : Total novels  [tex]= 2 : 11[/tex] So the correct answer is 2:11.

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The yearly average inflation rate during that time is 3.75% (option d).

First, we need to adjust the value of $1 in 1860 to its equivalent value in 2018 using the given purchasing power ratio of 1:28.95. This means that $1 in 1860 is equivalent to $28.95 in 2018.

Next, we need to find the CPI for 1860 and 2018. According to the Bureau of Labor Statistics, the CPI for 1860 is not available. However, we can use the CPI for 1913 as a proxy, as it was the year when the CPI was first introduced. The CPI for 1913 was 9.9.

Using the CPI for 1913 as the beginning CPI and the CPI for 2018 as the ending CPI, we can calculate the inflation rate as follows:

Inflation rate = (252.146 - 9.9) / 9.9 x 100% = 3.72%

Hence the correct option D (3.75%).

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The value of the expression is 17/8.

Given is an expression, 7/8 - (-2+3/4) = ( ____+____) + 7/8, we need to solve it,

7/8-(-2+3/4)

= 7/8-(-8+3)/4

= 7/8 + 5/4

= 7+10 /8

= 17/8

Hence, the value of the expression is 17/8.

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Answer:

There are different methods to find the horizontal asymptote of a function, but one common approach is to take the limit of the function as x approaches positive or negative infinity. If the limit exists and is a finite number, then that is the horizontal asymptote.

To apply this method to the given function:

y = (-4x^6+6x +3)/(8x^2+9x+3)

As x becomes very large (either positive or negative), the highest power of x in the numerator and denominator dominates the other terms. This is because exponential functions grow or shrink much faster than polynomials as x goes to infinity or negative infinity.

Therefore, we can simplify the function by dividing both numerator and denominator by x^6:

y = (-4 + 6/x^5 + 3/x^6)/(8/x^4 + 9/x^5 + 3/x^6)

As x approaches infinity, all the terms with negative powers of x go to zero, leaving:

y ≈ (-4 + 0 + 0)/(0 + 0 + 0)

This is an indeterminate form of 0/0, which suggests that we need to do more algebraic simplification. One way to do this is to factor out the highest power of x in both numerator and denominator:

y ≈ (-4/x^6 + 6/x^11)/(8/x^4 + 9/x^5 + 3/x^6)

y ≈ (-4/x^6)(1 - 6x^5)/(8/x^4)(1 + 9x/x^4 + 3/x^2)

Now, as x approaches infinity, the fraction becomes dominated by the leading terms:

y ≈ (-4/x^6)(-6x^5)/(8/x^4)(9x/x^4)

y ≈ (24/72)(1/x)

As x goes to infinity, 1/x goes to zero, so:

y ≈ 1/3x

Therefore, the horizontal asymptote of the graph of y = (-4x^6+6x +3)/(8x^2+9x+3) is y = 1/3x.

C21 represents 4 senior boys.

A matrix, which is used to represent a mathematical object or an attribute of one, is a rectangular array or table containing numbers, symbols, or expressions that are organized in rows and columns. is a matrix having two rows and three columns, for instance

Given:

[tex]\left[\begin{array}{ccc}5&6\\4&3\\\end{array}\right][/tex], [tex]\left[\begin{array}{ccc}c11&c12\\c21&c22\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}\ Junior boy&Junior girl\\Senior boy&Senior girl\\\end{array}\right][/tex]

4 Senior boys is c21 represented.

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Using combinations we know that 24 combinations of the flags can be used.

Combinations are mathematical procedures that count how many different ways a collection of items could be arranged when the order in which they are chosen is immaterial.

Combos' components can be chosen in any hierarchy.

Combinations and permutations can coexist.

The expression "Selection of things" refers to a circumstance in which the chronology of occurrences is unimportant.

So, we know that we have 3 types of flags which are:

4 flags for the top position.

3 flags for the middle position.

2 flags for the bottom position.

Now, different combinations would be:

4 * 3 * 2 = 24

Therefore, using combinations we know that 24 combinations of the flags can be used.

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The probability of a carryout order being ready within 20 minutes is approximately 0.5507

We know that the time required for a carryout order to be ready for customer pickup follows an exponential distribution with a mean of 25 minutes. The probability density function for an exponential distribution is given by

f(x) = λe^(-λx)

where λ is the rate parameter

We can find the rate parameter λ using the mean

mean = 1/λ

λ = 1/mean = 1/25 = 0.04

So the probability of a carryout order being ready within 20 minutes is

P(X ≤ 20) = ∫₀²⁰ λe^(-λx) dx

P(X ≤ 20) = [-e^(-λx)]₀²⁰

P(X ≤ 20) = [-e^(-0.04x)]₀²⁰

P(X ≤ 20) = [-e^(-0.8)] - [-1]

P(X ≤ 20) = 0.5507

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The given question is incomplete, the complete question is:

Collina’s Italian Café in Houston, Texas, advertises that carryout orders take about 25 minutes (Collina’s website, February 27, 2008). Assume that the time required for a carryout order to be ready for customer pickup has an exponential distribution with a mean of 25 minutes. What is the probability than a carryout order will be ready within 20 minutes?

The equation 12x + 3(x - 5) = 6x + 9x - 15 has infinite many solutions

Part A:

Starting with the given equation:

12x + 3(x - 5) = 6x + 9x - 15

Simplify by distributing the 3:

12x + 3x - 15 = 6x + 9x - 15

Combine like terms on both sides:

15x - 15 = 15x - 15

Add 15 to both sides:

0 = 0

Therefore, the equation has infinite many solutions

Part B:

The property used to solve this equation is the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. In this case, we used the distributive property to simplify 3(x - 5) to 3x - 15.

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The cost to charge an electric car's home battery charger is $3.355 (to the nearest penny).

The cost to charge an electric car's home battery charger can be calculated using the following equation:

Cost = (kW x hours x rate)

Where kW stands for kilowatts, hrs stands for hours and rate stands for the rate per kilowatt-hour.

In this case, we have: kW = 6.1, hrs = 11 and rate = $0.05

Therefore, Cost = (6.1 x 11 x 0.05) = $3.355

Therefore, it will cost $3.35(to the nearest penny) to charge the car's battery.

To calculate this cost, we first multiply the kW (6.1) by the hours (11) to get the total kWh used (67.1). We then multiply this number by the rate ($0.05) to get the total cost of charging the battery ($3.355). This cost is to the nearest penny as we rounded up to the nearest cent when multiplying the kWh by the rate.

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Complete Question:

An  electric car's home battery charger uses 6.1 kilowatts for 11 hours. If electricity costs $0.05 per kilowatt-hour, how much (in dollars, to the nearest penny) does it cost to charge the car's battery? Use  exact numbers; do not estimate.

The value of r/s is equal to 9.

There exists a theorem that states that the square of a hypotenuse in a right-angled triangle is equal to the sum of squares of the perpendicular side and the base side.  This theorem is known as Pythagoras theorem. By applying Pythagoras' theorem in this right-angled triangle formed in our image, we obtain the given formula

[tex]H^2 = P^2 + B^2[/tex]

[tex](r + s)^2 = (r - s)^2 + (r - 3s)^2[/tex]

[tex]r^2 + 2r.s + s^2 = 2r^2 - 8r.s + 10.s^2[/tex]

[tex]r^2 - 10.r.s + 9s^2 = 0[/tex]

(r - 9s) (r - s) = 0

Now we will equate these two factors to 0.

By equating, we get r/s = 9 and r/s = 1.

r/s = 1 does not apply to the geometry in this question.

So, r/s = 9 is the solution for the given equation.

Therefore, our answer is 9.

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The complete question is -

"Three circles of radius s are drawn in the first quadrant of the xy-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the x-axis, and the third is tangent to the first circle and the y-axis. A circle of radius r>s is tangent to both axes and to the second and third circles. What is r/s? "

The function f has a relative maximum at x = -√[(2 + sqrt(2))/5], so the answer is (b) - root 5/5.

To find the relative maximum of a function, we need to find the critical points of the function, where the derivative of the function is zero or undefined.

Let's start by finding the derivative of f(x)

f'(x) = 15x⁴ - 12x² - 3

Now, we can find the critical points by solving the equation f'(x) = 0

15x⁴ - 12x² - 3 = 0

We can factor this equation by substituting y = x²

15y² - 12y - 3 = 0

Solving for y, we get

y = (2 ± √(2))/5

Substituting back x² for y, we get

x² = (2 ± √(2))/5

Taking the square root of both sides, we get

x = ± √[(2 ± √(2))/5]

Therefore, the critical points are

x = -√[(2 + √(2))/5], √[(2 - √(2))/5]

Now, we need to determine whether these critical points are relative maximum or minimum.

We can use the second derivative test to determine the nature of the critical points. The second derivative of f(x) is

f''(x) = 60x³ - 24x

Plugging in the critical points, we get

f''(-√[(2 + √(2))/5]) = -48√(2) < 0 (relative maximum)

f''(√[(2 - √(2))/5]) = 48√(2) > 0 (relative minimum)

Therefore, the relative maximum of the function f(x) is at

x = -√[(2 + √(2))/5]

So, the correct answer is (b) - root 5/5.

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Answer: 44 ft²

Step-by-step explanation:

     We will find the area of the large rectangle and subtract the area of the square. The area of a rectangle (and square) can be used with this formula:

       A = LW

Large Rectangle:

       A = LW

       A = (12 ft)(4 ft)

       A = 48 ft²

Square:

       A = LW

       A = (2 ft)(2 ft)

       A = 4 ft²

Subtract:

48 ft² - 4 ft² = 44 ft²

The candy company's package can be modeled as a right circular cone with a height of 13 inches and a base diameter of 9 inches.

The circular base of the cone holds the chocolates, while the curved surface extends up to a point at the top. To calculate the surface area, we need to find the area of the circular base and the area of the curved surface. The formula for the area of a circle is pi times the radius squared, so the radius of the base is 4.5 inches.

The area of the base is pi times the radius squared, or approximately 63.62 square inches. The formula for the curved surface area of a cone is pi times the radius times the slant height, which is the square root of the height squared plus the base radius squared. Substituting the given values into the formula, the curved surface area is approximately 207.35 square inches. Thus, the approximate surface area of the package is the sum of the area of the base and the curved surface area, or approximately 271.97 square inches.

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Answer:

the diameter of the softball is approximately 4.72 inches.

Step-by-step explanation:

The formula to calculate the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.

We can rearrange the formula to find the radius of the softball:

r = cube root of [(3V)/(4π)]

r = cube root of [(3 x 33.5)/(4π)]

r ≈ 2.36 inches

The diameter is twice the radius:

d = 2r

d ≈ 4.72 inches

Therefore, the diameter of the softball is approximately 4.72 inches.

Answer: the diameter of the softball is approximately 4.22 inches.

Step-by-step explanation: The volume of a sphere can be calculated using the formula:

V = (4/3)πr^3

where V is the volume of the sphere, r is the radius of the sphere, and π is the mathematical constant pi.

To find the diameter of the softball, we can use the formula:

d = 2r

where d is the diameter of the sphere.

We know that the volume of the softball is 33.5 in^3. So, we can solve for the radius as follows:

33.5 = (4/3)πr^3

r^3 = (3/4)(33.5/π)

r^3 = 8.9375

r = ∛(8.9375)

r ≈ 2.11 inches

Now, we can find the diameter of the softball:

d = 2r

d = 2(2.11)

d ≈ 4.22 inches

Using multiplication we know that after 141 min there will be 400,000 bacteria present.

One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication.

A product is the output of a multiplication operation.

When you take a single number and multiply it by several, you are multiplying.

A 5 multiplied by 4 results in 20 (5 + 5 + 5 + 5).

We multiplied the number five by four times.

Multiplication is commonly referred to as "times" because of this.

So, in the given situation:

At the initial stage, the number of bacteria is: 50,000

Then, after 47 min: 50,000 * 2 = 100,000

Then, after 47 min which is after 94 min: 100,000 * 2 = 200,000

Then, after 47 min which is after 141 min: 200,000 * 2 = 400,000

Therefore, using multiplication we know that after 141 min there will be 400,000 bacteria present.

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The value of the variables as identified from the reciprocal function are;

a = 5

h = -6

k = 7

2. The correct option is Option A

A reciprocal function is a mathematical function that can be represented as f(x) = 1/x, where x ≠ 0.

The graph of a reciprocal function is a hyperbola with two branches that approach the x and y axes, but never touch them.

From the information given, we have the function as;

y = a/x - h + k

Given that the function with numbers is written as;

y = 5/x + 6 + 7

To determine the values of a, h and k, we get;

The variable, a = 5

The variable, k = 7

The variable, h = -(6) = -6

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Answer:

13

Step-by-step explanation:

The given angles are on a straight line and they are supplementary angles which means their sum is 180°

According to the above mentioned information, we can write the following equation to find the value of t:

9t + 3 + 4t - 5 = 180

13t - 2 = 180

13t = 182

t = 14

Answer:

C. DEFG and VWXY

Step-by-step explanation:

It is the better answer choice here

Answer:

1Step-by-step explanation:

As Almay walks through a local park and passes an old man in pain, the presence of many other walkers in the park will most likely increase the probability that Almay will experience the "bystander effect."

As Almay walks through the local park and comes across an old man who is in pain, the presence of many other walkers in the park will most likely increase the probability that Almay will seek help for the man.

This is because the bystander effect, which is the tendency for individuals to be less likely to intervene in an emergency situation when others are present, is less likely to occur when there are more people around. With more people present, Almay may feel a greater sense of responsibility to act and seek help for the man.

Additionally, the presence of other walkers may also make it easier for Almay to quickly locate someone who can assist with medical attention or call for emergency services.

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The volume of Ganymede is approximately 3.48 times the volume of the Moon, based on the given diameters of the two moons and the formula for the volume of a sphere.

The volume of a sphere is the amount of space occupied by the sphere in three-dimensional space. It can be calculated using the formula V = (4/3)πr³, where V is the volume of the sphere, r is the radius of the sphere, and π (pi) is a mathematical constant approximately equal to 3.14159. This formula states that the volume of a sphere is four-thirds of the product of pi and the cube of the sphere's radius.

In the given question,

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. Since we are given the diameters of the two moons, we can calculate their radii by dividing the diameters by 2. Therefore, the radius of Ganymede is 3,388/2 = 1,694 km, and the radius of the Moon is 1,245/2 = 622.5 km.

Now, we can calculate the volumes of the two moons:

V_Ganymede = (4/3)π(1694)³ ≈ 7.66 x 10^10 km³

V_Moon = (4/3)π(622.5)³ ≈ 2.2 x 10^10 km³

To find how many times larger Ganymede's volume is compared to the Moon's volume, we can divide the volume of Ganymede by the volume of the Moon:

V_Ganymede / V_Moon ≈ (7.66 x 10¹⁰) / (2.2 x 10¹⁰) ≈ 3.48

Therefore, the volume of Ganymede is approximately 3.48 times the volume of the Moon.

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the average rate of change over the interval (-1, 2] in the given function is 1.17.all three functions have the same average rate of change over the interval [1, 2], which is 2

A function is a mathematical rule that takes an input and produces an output. The average rate of change of a function over an interval is the average amount the output changes per unit change in the input over that interval.

For the function f(x) = 2x + 3:

Let x1 = -1 and x2 = 2

f(x1) = 2(-1) + 3 = 1

f(x2) = 2(2) + 3 = 7

The average rate of change is:

[f(x2) - f(x1)] / [x2 - x1] = [7 - 1] / [2 - (-1)] = 6 / 3 = 2

Therefore, the average rate of change of f(x) over the interval (-1, 2] is 2.

For the function g(x) = x^2 - 1:

Let x1 = -1 and x2 = 2

g(x1) = (-1)^2 - 1 = 0

g(x2) = 2^2 - 1 = 3

The average rate of change is:

[g(x2) - g(x1)] / [x2 - x1] = [3 - 0] / [2 - (-1)] = 3 / 3 = 1

Therefore, the average rate of change of g(x) over the interval (-1, 2] is 1.

For the function h(x) = 2^x + 1:

Let x1 = -1 and x2 = 2

h(x1) = 2^(-1) + 1 = 1.5

h(x2) = 2^2 + 1 = 5

The average rate of change is:

[h(x2) - h(x1)] / [x2 - x1] = [5 - 1.5] / [2 - (-1)] = 3.5 / 3 = 1.17 (rounded to 2 decimal places)

Therefore, the average rate of change of h(x) over the interval (-1, 2] is approximately 1.17.

b)To determine which function has the greatest average rate of change over the interval [1, 2], we need to calculate the average rate of change for each function over that interval and compare the results.

Let's assume the functions are f(x), g(x), and h(x).

The average rate of change for f(x) over the interval [1, 2] is:

[f(2) - f(1)] / [2 - 1] = (2(2) + 3 - 2(1) - 3) / 1 = 2

The average rate of change for g(x) over the interval [1, 2] is:

[g(2) - g(1)] / [2 - 1] = (2^2 - 1 - 1^2 + 1) / 1 = 2

The average rate of change for h(x) over the interval [1, 2] is:

[h(2) - h(1)] / [2 - 1] = (2^2 + 1 - 2^1 - 1) / 1 = 2

Therefore, all three functions have the same average rate of change over the interval [1, 2], which is 2.

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