Graph y=3x−3/4
AND
Graph y=−x/3−3/2

Answer:

3000 x 1.02^10 = 3656.98.. = 3656 people

The fractional equivalent of the repeating decimal is 15/99

What does division of fractions mean?

A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.

n = 0.1515...-------(1)

multiply n by 100 =10²

The reason we multiply x by 100 is because 0.1515... has 2 repeating digits and 100 has two zeros.

100n=15.15......--------(2)

Subtract (1) from (2)

100n=15.15...

n = 0.1515....

___________

99n=15

=> n=15/99

The fractional equivalent of the repeating decimal is 15/99

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Therefore, the regression equation best fits the data set is yˆ=0.728x2−20.213x+179.246.

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides, the left-hand side and the right-hand side, connected by an equal sign (=). The expressions on either side of the equal sign can be made up of numbers, variables, mathematical operations, and other mathematical symbols. Equations are used to represent various mathematical relationships and can be solved to find the value of one or more variables. Solving an equation involves manipulating the expressions on either side of the equal sign to isolate the variable being solved for. This is often done by applying a series of mathematical operations to both sides of the equation, with the goal of eventually isolating the variable on one side of the equal sign and obtaining a numerical value for it.

Here,

Using a graphing calculator, we can plot the data set of x and y values and use the regression feature to find the quadratic regression equation that best fits the data. Here's how we can do it:

Enter the x and y values into the calculator.

Plot the points on a scatter plot.

Choose the regression feature on the calculator.

Select the quadratic regression option.

The calculator will display the quadratic regression equation that best fits the data.

After performing these steps, we get the following quadratic regression equation:

yˆ=0.728x2−20.213x+179.246

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Let w = x^3

Square both sides to find that w^2 = (x^3)^2 = x^(3*2) = x^6

In short: w^2 = x^6

The given expression 2+x^3-3x^6 turns into 2+w-3w^2 and rearranges into -3w^2+w+2

Set this equal to zero and use the quadratic formula. We'll plug in

So,

[tex]w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-1\pm\sqrt{(1)^2-4(-3)(2)}}{2(-3)}\\\\w = \frac{-1\pm\sqrt{25}}{-6}\\\\w = \frac{-1\pm5}{-6}\\\\w = \frac{-1+5}{-6} \ \text{ or } \ w = \frac{-1-5}{-6}\\\\w = \frac{4}{-6} \ \text{ or } \ w = \frac{-6}{-6}\\\\w = -\frac{2}{3} \ \text{ or } \ w = 1\\\\[/tex]

If w = -2/3, then that rearranges to the following

w = -2/3

3w = -2

3w+2 = 0

This makes (3w+2) a factor of -3w^2+w+2

If w = 1, then it rearranges to w-1 = 0.

This makes (w-1) a factor of -3w^2+w+2

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

To summarize the previous section, we found the factors of -3w^2+w+2 were:

It leads to (3w+2)(w-1)

We must stick a negative out front because the leading coefficient is negative.

Therefore, -3w^2+w+2 = -(3w+2)(w-1)

You can use the FOIL rule to confirm.

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

Recall we made w = x^3

Let's replace each w with x^3

-(3w+2)(w-1)

-(3x^3+2)(x^3-1)

This tells us that 2+x^3-3x^6 factors to -(3x^3+2)(x^3-1)

The next task is to factor x^3-1 using the difference of cubes factoring rule.

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

x^3 - 1^3 = (x-1)(x^2 + x*1 + 1^2)

x^3 - 1 = (x-1)(x^2 + x + 1)

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

So,

2+x^3-3x^6

-3x^6 + x^3 + 2

-(3x^3+2)(x^3-1)

-(3x^3+2)(x-1)(x^2 + x + 1)

-(2 + 3x^3)(-(1-x))(1 + x + x^2)

(2 + 3x^3)(1 - x)(1 + x + x^2)

Take careful notice that x-1 turned into -(1-x) in the 3rd step. The negative out front for -(1-x) cancels out with the original negative out front.

Answer:

See below

Step-by-step explanation:

The linear function is to be expressed in slope-intercept form:

y = mx + c

where:              

                           m = slope

                               = [tex]\frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]

           Select a pair of x and y coordinates of two points along this graph

e.g (0,1) and (5,0):

                          m = [tex]\frac{(0 - 1)Percent InDecimal}{(5 - 0) hour}[/tex]

                              = [tex]\frac{-1}{5}[/tex]

       ∴ slope = [tex]-\frac{1}{5}[/tex] = [tex]-0.2\frac{PercentInDecimal}{hour}[/tex]

  which means 0.2 × 100%= 20%

∴The slope indicates that the power decreases by 20% per hour

                          c = y-intercept:

   It is the y-value AT which the graph cuts or meets the y-axis. Its corresponding x-coordinate is 0. The y-intercept can be either read directly from the graph or calculated mathematically

       ∴y-intercept = 1

In this scenario, the y-intercept indicates the initial value or the value present in the beginning.
which means 1.0 × 100% = 100%
∴The y-intercept indicates that the battery is at 100% when you turn on the laptop.

∴Linear function relating y to x:

Substituting the values of m and c into the above stated equation:

     [tex]y = -\frac{1}{5}x + 1[/tex]

The x-intercept is the x-value at which the graph crosses or intersects the x-axis. It’s corresponding y-coordinate is zero.

     x-intercept = 5

In this scenario, the x-intercept indicates the point at which the final value is reached or achieved.

∴ The x-intercept indicates that the battery lasts 5 hours.

The battery power is at 75% = [tex]\frac{75}{100}[/tex] = 0.75 (expressed in decimal form. This means y = 0.75, which is to be substituted into the above derived linear function to solve for the corresponding value of x:

[tex]0.75 = -\frac{1}{5}(x) + 1[/tex]

Rearrange the equation to isolate x and make it the subject of the equation:

[tex]\frac{1}{5}x = 1 - 0.75[/tex]

[tex]\frac{1}{5}x = 0.25[/tex]

Cross-multiplication is applied:

[tex](1)(x) = (5)(0.25)[/tex]

x = 1.25 hours

∴The battery power is at 75% after 1.25 hours

To find the percent decrease, we first need to find the amount of the decrease, which is the difference between the regular price and the sale price:

$550 - $456.50 = $93.50

So the amount of the decrease is $93.50.

To find the percent decrease, we divide the amount of the decrease by the original price and then multiply by 100:

($93.50 / $550) x 100 ≈ 17.0%

Therefore, the percent decrease of the sale price from the regular price is approximately 17.0%.

The domain of the function is (-∝, -3) ∪ (-3, +∝)

The range is (-∝, 3) ∪ (3, +∝) and the asymptotes are x = -3 and y = 3

From the question, we have the following parameters that can be used in our computation:

f(x) = 2/(x + 3) + 3

Set the denominator to not equal to 0

So, we have

x + 3 ≠ 0

So, we have

x ≠ -3

As an interval notation, we have

(-∝, -3) ∪ (-3, +∝)

Here, we have

f(x) = 2/(x + 3) + 3

When x = -3, we have

f(-3) = undefined + 3

This means that

f(x) ≠ -3

As an interval notation, we have

(-∝, 3) ∪ (3, +∝)

In (a), we have

x ≠ -3

This means that

Vertical asymptote: x = -3

In (b), we have

f(x) ≠ -3

This means that

Horizontal asymptote: y = 3

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The area of the triangular sail in the sail model is 42 square inches.

The area of a triangular sail is given by the formula:

Area = (1/2)bh

where b is the length of the base and h is the height.

Substituting b = 12 inches and h = 7 inches, we get:

Area = (1/2)(12 inches)(7 inches) = 42 square inches

Therefore, the area of the triangular sail in the sail model is 42 square inches.

The area of a triangle is given by the formula:

Area = (1/2) * base * height

where "base" is the length of the base of the triangle and "height" is the height of the triangle perpendicular to the base.

To find the area of a triangle, you simply need to plug in the values of the base and height into the formula and perform the calculation. The resulting value will be the area of the triangle.

Note that the base and height of the triangle must be measured in the same units (e.g., inches, centimeters) in order for the formula to work correctly.

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Answer:

24

Step-by-step explanation:

N/A

Answer: The formula D = R * T relates the distance traveled (D) to the rate of speed (R) and the time elapsed (T). Using the given values, we can substitute R = 20 km/h and T = 1.6 h to find:

D = R * T = 20 km/h * 1.6 h = 32 km

Therefore, the bicyclist traveled a total distance of 32 kilometers.

Step-by-step explanation:

Answer:

Step-by-step explanation: To expand the algebraic expression using the distributive property, we distribute the 3 to each term inside the parentheses:

3(3d + 2) = 33d + 32

Simplifying, we get:

3(3d + 2) = 9d + 6

Therefore, the expanded form of the expression 3(3d+2) is 9d + 6.

Answer: el enunciado cinco veces la diferencia de un numero y 3 es 17

Step-by-step explanation:

Answer:

ATQ, 5( x -3 ) = 17

5 x - 15 = 17

5x = 17 + 15

x = 32 /5

x = 6.4 ,

We expect that, on average, 1 out of 25 patients calling in claiming to have the flu will actually have the flu.

According to the nurse's observation, there is a 4% chance that a patient who calls the medical advice line and claims to have the flu truly has.

As a result, we anticipate that 4 out of every 25 people who phone in will truly have the flu.

To figure this out, we can use the formula below:

Probability of having the flu multiplied by the total number of patients equals the anticipated number of flu patients.

Estimated number of influenza patients = 0.04 times 25

Expected number of influenza patients is one.

Hence, on average, we anticipate that 1 out of every 25 individuals who call in and claim to have the flu will truly have it.

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Answer:

To calculate the periodic interest rate for an account billed monthly with an APR of 21.99%, we need to divide the APR by the number of billing periods in a year.

Since there are 12 months in a year for a monthly billing cycle, we can divide 21.99% by 12 to get the monthly periodic interest rate.

Periodic Interest Rate = APR / Number of Billing Periods in a Year

Periodic Interest Rate = 21.99% / 12

Periodic Interest Rate = 1.8325%

Rounding this answer to the nearest hundredth, we get a periodic interest rate of 1.83%.

The values for this problem are given as follows:

a) lim x -> 2^- f(x) = 3.

b) lim x -> 2^+ f(x) = 1.

c) lim x -> 2 f(x) is not defined.

d) f(2) = 3.

e) lim x -> 4 f(x) = 4.

f) f(4) is not defined.

To the left of x = 2, the graph of f(x) approaches x = 2 at y = 3, hence:

lim x -> 2^- f(x) = 3.

To the right of x = 2, the graph of f(x) approaches x = 2 at y = 1, hence:

lim x -> 2^+ f(x) = 1.

As the lateral limits are different, the limit of f(x) as x -> 2 is not defined.

Due to the closed circle, at x = 2, the function has a numeric value of f(2) = 3.

At x = 4, the graph of the function approaches x = 4 both left and right at y = 4, hence:

lim x -> 4 f(x) = 4.

Due to the open circle at x = 4, we have that f(4) is not defined.

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Answer:

a) {0,1,3,5,8}

b) -

Step-by-step explanation:

the composition cannot be performed cos 3 is mapped to 2 by g, but 2 is not in the domain of f

Sara need 9/4 ounces of chopped nuts

Sara wants to make dinner for herself
The recipe she will use calls for 13 1/2 ounces

The recipe feeds 6 people

The number of ounces of chopped nuts that Sara needs can be calculated as follows

13 1/2

= 27/2 ÷ 6

= 27/2 × 1/6

= 27/12

= 9/4

Hence Sara needs 9/4 ounces of chopped nuts for one serving

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Answer:

5 = $ 5.25.    10= $ 6.50.   20= $9.00

Step-by-step explanation:

if this is wrong you can completely write me a really rude email or message or something

6 cups of dal may be used to make eight bowls of sambar.

The ratio can be defined as the number that can represent one quantity as a percentage of another. They can be compared only when the two numbers in a ratio have the same unit. Ratios are used to compare two objects.

Given, One bowl of sambar is made the use of 3/four cup dal.

If 1 bowl of sambar is made using 3/4 cup of dal, then the number of bowls of sambar that can be made from 6 cups of dal can be found by dividing 6 cups by 3/4 cup per bowl:

6 cups / (3/4 cup per bowl)

We can simplify by multiplying the numerator and denominator by the reciprocal of 3/4:

6 cups / (3/4 cup per bowl) * (4/3)

Simplifying, we get:

8 bowls

Therefore, 6 cups of dal can be used to make 8 bowls of sambar.

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The values are Q1 ≈ 11.7375 months, Q3 ≈ 12.2625 months, and range  IQR ≈ 0.5250 months.

The IQR for the average first-time walking age for groups of 33 people can be found as follows:

The standard deviation of the sample mean is given by:

σM = σ/√n = 2.2/√33 ≈ 0.3839

Using the standard normal distribution, the z-scores for the first and third quartiles are:

zQ1 = invNorm(0.25) ≈ -0.6745

zQ3 = invNorm(0.75) ≈ 0.6745

The corresponding sample means can be found using:

M = μ ± z(σM)

Where μ = 12, the population mean.

M1 = 12 - 0.6745(0.3839) ≈ 11.7375

M3 = 12 + 0.6745(0.3839) ≈ 12.2625

Therefore, the first quartile Q1 is approximately equal to 11.7375 months and the third quartile Q3 is approximately equal to 12.2625 months.

The IQR is given by:

IQR = Q3 - Q1 = 12.2625 - 11.7375 ≈ 0.5250 months.

Rounding to 4 decimal places gives Q1 ≈ 11.7375 months, Q3 ≈ 12.2625 months, and IQR ≈ 0.5250 months.

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The required measure of the unknown side in similar triangles is 4.

Similar triangles are two triangles that have the same shape but are not necessarily the same size. More specifically, two triangles are similar if their corresponding angles are congruent (i.e., have the same measure), and the corresponding sides are proportional (i.e., have the same ratio).

Here,
Two similar triangles are given in the figure,

Let the unknown side be x
For a similar triangle, the ratio of the corresponding sides are equal So,
a / 8 = 6 / 12
a = 8/2
a = 4

Thus, the required measure of the unknown side in similar triangles is 4.

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Simplifying this expression, we get: E[X] = n * (1 + (1-pm)/(n-1)) * H_{n-1} where H_{n-1} is the (n-1)th harmonic number.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

In the first scenario where we have imperfect throwers, the probability that a ball lands in a particular bin is (1-pm)/n, where pm is the probability that the ball misses all the bins. The probability that a ball does not land in a particular bin after k throws is (1- (1-pm)/n)^k.

Let X_i be a random variable representing the number of throws required to fill the ith bin for the first time. We know that X_i follows a geometric distribution with probability of success p_i = (1-pm)/n.

The expected value of X_i is given by:

E[X_i] = 1/p_i = n/(n - (1-pm))

Now, let X be the random variable representing the number of throws required to fill all n bins for the first time. We want to find the expected value of X, denoted as E[X].

Since each bin is being filled independently, the number of throws required to fill all n bins is given by the maximum of the X_i. Therefore, we have:

X = max(X_1, X_2, ..., X_n)

Using the formula for the expected value of the maximum of n independent and identically distributed random variables, we can write:

E[X] = n * E[X_i] - (n-1) * E[X_i, X_j]

where E[X_i, X_j] is the expected value of the minimum of X_i and X_j.

Since the X_i are identically distributed, we have E[X_i, X_j] = E[X_i]^2.

Substituting the value of E[X_i] in the above equation, we get:

E[X] = n * (n / (n - (1-pm))) - (n-1) * (n / (n - (1-pm)))^2

This is the expected number of throws required to fill each bin at least once, accounting for the probability that the balls may miss all bins with probability pm.

Therefore, Simplifying this expression, we get: E[X] = n * (1 + (1-pm)/(n-1)) * H_{n-1} where H_{n-1} is the (n-1)th harmonic number.

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The correct answers are

1)  2x^2 + 12

2) Option C.

3) Option B.

1. You must apply the Distributive property as following:

(-5x^2 - 2x +4) + (8x^2 -x -1) - (x^2 -5x + 2x -10)

2. Now, you must distribute the negative sign, then you have:

3. Finally, you must add the like terms. Then you obtain the polynomial:

2x^2 + 13

4. By definition, a polynomial that has two terms is classified as a binomial. Therefore, the answer is the option C.

5. The degree of a polynomial is determined by highest exponent of the variable. So, it is a polynomial of degree 2 (option B).

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Answer:

12 teams means 6 games each match day. Each team can play all the 11 other teams so 11 match days. So 66 games.

The value of z is 27 when the value of w is 5, when w varies inversely with z.

The ratio of two proportional values at a constant value is the proportionality constant. When either the ratio or the product of two variables results in a constant, the connection between the two is proportional. The ratio between the two stated quantities affects the proportionality constant's value. Direct variation and inverse variation are two different sorts of this relationship.

Given that, w is 15 when z is 9, and w varies inversely with z.

This can be represented as:

w = k (1 /z)

where, k is the proportionality constant.

Substituting the value of w = 15 and z = 9 we have:

15 = k(1/9)

k = 15(9)

k = 135

Substituting the value of k and w = 5:

5 = 135(1/z)

z = 135/5

z = 27

Hence, the value of z is 27 when the value of w is 5.

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The probability that it is necessary to examine at least 6 bulbs before obtaining a 23-watt bulb is 9/10 or 0.9 (approximately).

To calculate the probability that it is necessary to examine at least 6 bulbs before obtaining a 23-watt bulb, we can use the complementary probability. That is, we can calculate the probability that a 23-watt bulb is obtained within the first 5 selections and then subtract this from 1 to get the probability that at least 6 bulbs must be examined.

The probability of obtaining a 23-watt bulb on the first selection is 1/50. If a 23-watt bulb is not obtained on the first selection, the probability of obtaining one on the second selection is 49/50 x 1/49 = 1/50.

Similarly, the probability of obtaining a 23-watt bulb on the third, fourth, or fifth selection is also 1/50.

Therefore, the probability of obtaining a 23-watt bulb within the first 5 selections is:

P(23-watt bulb in first 5 selections) = P(23-watt bulb on first selection) + P(23-watt bulb on second selection) + P(23-watt bulb on third selection) + P(23-watt bulb on fourth selection) + P(23-watt bulb on fifth selection)

= 1/50 + 1/50 + 1/50 + 1/50 + 1/50

= 1/10

The probability of needing to examine at least 6 bulbs before obtaining a 23-watt bulb is therefore:

P(need to examine at least 6 bulbs) = 1 - P(23-watt bulb in first 5 selections)

= 1 - 1/10

= 9/10

Therefore, the probability that it is necessary to examine at least 6 bulbs before obtaining a 23-watt bulb is 9/10 or 0.9 (approximately).

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We do not have information about whether the two events are mutually exclusive or not, we cannot determine whether P(full-time college student and 65 or older) is nonzero.

Probability is a method for assessing how likely something is to happen. Many occurrences cannot be foreseen with 100% accuracy. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

We cannot determine whether the probability of an adult being a full-time college student and 65 or older is nonzero based on the given information alone.

To see why, consider the following two scenarios:

Scenario 1: The proportion of adults who are both full-time college students and 65 or older is 0%.

In this case, the events "full-time college student" and "65 or older" are mutually exclusive. That is, no adult can be both a full-time college student and 65 or older. Therefore, P(full-time college student and 65 or older) = 0%.

Scenario 2: The proportion of adults who are both full-time college students and 65 or older is greater than 0%.

In this case, the events "full-time college student" and "65 or older" are not mutually exclusive. That is, there may be some adults who are both full-time college students and 65 or older. Therefore, P(full-time college student and 65 or older) is greater than 0%.

Since we do not have information about whether the two events are mutually exclusive or not, we cannot determine whether P(full-time college student and 65 or older) is nonzero.

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Answer:Mike has $100. He wants to buy a bike that costs $75 and three speakers that cost $30 each. trade of is example of Opportunity cost

Step-by-step explanation:

The height of the lighthouse is 48 feet.

To find the height of the lighthouse, we can use the concept of similar triangles. When two triangles are similar, it means that they have the same shape but different sizes. In this case, the two triangles are similar because they have the same angle to the sun. That is, the angle between the ground and the line from the top of the lighthouse to the sun is the same as the angle between the ground and the line from Zara to the sun.

This proportion is based on the fact that the two triangles are similar, so the corresponding sides are in proportion.

So, we have:

(height of lighthouse) / 36 feet = 4 feet / 3 feet

We can solve for the height of the lighthouse by cross-multiplying:

(height of lighthouse) = 36 feet × (4 feet / 3 feet)

Simplifying the expression, we get:

(height of lighthouse) = 48 feet

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The given question is incomplete, the complete question is

A lighthouse has a shadow that is 36 36 feet long. Zara is 4 4 feet tall, and has a shadow that is 3 3 feet long. The two triangles formed are similar because the angle to the sun is the same. Use this information to complete the statement about the lighthouse.

The height of the lighthouse is ___ feet .

Answer:

Step-by-step explanation:

You want to know how long Hoang and Bill have worked at the hospital if Hoang has worked there 5 years longer, and 5 years ago that was twice as long as her friend Bill.

Hoang's longevity will be twice Bills when Bill's is equal to the difference. That is, 5 years ago, Bill had been there 5 years and Hoang had been there 10 years.

Now, each has been there 5 years longer, so ...

If h represents Hoang's time at the hospital, 5 years ago it was (h-5). Currently, Bill's time at the hospital is (h-5), and 5 years ago it was (h-10). The relation between the times 5 years ago is ...

  (h -5) = 2(h -10)

  15 = h . . . . . . . . . . add 20-h to both sides

  h-5 = 15 -5 = 10 . . . . Bill's time at the hospital

Hoang and Bill have been at the hospital 15 years and 10 years, respectively.

To find the total distance of Alanah's trip to the arena, we need to add up the distances of each segment of her trip. We can use the distance formula to calculate the distances between the different points.

First, let's calculate the distance between Alanah's house (A) and Mia's house (M). Using the distance formula, we get:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance = sqrt((4 - 2)^2 + (14 - 10)^2)

distance = sqrt(4 + 16)

distance = sqrt(20)

distance ≈ 4.5

So the distance between A and M is approximately 4.5 miles.

Next, let's calculate the distance between Mia's house (M) and Teresa's house (N). Using the distance formula, we get:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance = sqrt((14 - 6)^2 + (16 - 12)^2)

distance = sqrt(64 + 16)

distance = sqrt(80)

distance ≈ 8.9

So the distance between M and N is approximately 8.9 miles.

Finally, let's calculate the distance between Teresa's house (N) and the arena. Using the distance formula, we get:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance = sqrt((16 - 10)^2 + (8 - 16)^2)

distance = sqrt(36 + 64)

distance = sqrt(100)

distance = 10

So the distance between N and the arena is exactly 10 miles.

Now we can add up the distances of the three segments to get the total distance of Alanah's trip to the arena:

total distance = 4.5 + 8.9 + 10

total distance ≈ 23.4

Therefore, the total distance of Alanah's trip to the arena is approximately 23.4 miles