Evaluate the definite integral:
∫(e^z) + 8/ (e^z+8z)^2

The difference in the shortest collection times before and after the well installation is 20 minutes, calculated by subtracting the shortest time after installation (25 minutes) from before (45 minutes), as shown in the box and whiskers plot.

This is calculated by subtracting the shortest collection time after well installation (25 minutes) from the shortest collection time before well installation (45 minutes):

45 - 25 = 20 minutes.

This can be seen in the box and whiskers plot provided, where the lowest value for each distribution is denoted by the beginning of the whiskers.

So, the difference is before and after the well installation is 20 minutes.

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

" What is the difference in minutes between the shortest collection times before and after the well was installed"--

Step-by-step explanation:

-3x - 2x - 5 = -7

-5x - 5 = -7

-5x = -7 + 5

-5x = -2

x = 2/5

Answer:

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

A linear equation is an equation of a straight line.

It describes the straight-line graph of a set of ordered pairs (x, y) that are solutions to the equation.

There are different forms of linear equations.

The slope-intercept form of a linear equation is y = mx + b.

The equation y = -2x + 10 is in slope-intercept form. Its graph is a line with slope -2 and y-intercept 10. It shows the set of all solutions to the equation.

As per description above, the correct answer choice is B, all the other options are false.

If Chris bought 5 tacos and 2 burritos for $13. 25 and  Brett bought 3 tacos and 2 burritos for $10. 75, the price of one taco is $1.25, and the price of one burrito is $3.50.

Let the price of one taco be T and the price of one burrito be B. We have the following equations:

5T + 2B = $13.25
3T + 2B = $10.75

To find the prices of the taco and the burrito, we can use the system of equations. First, subtract the second equation from the first equation:

(5T + 2B) - (3T + 2B) = $13.25 - $10.75
2T = $2.50

Now, divide by 2 to find the price of one taco:

T = $1.25

Next, plug the value of T back into one of the equations (let's use the second equation):

3($1.25) + 2B = $10.75
$3.75 + 2B = $10.75

Now, subtract $3.75 from both sides:

2B = $7.00

Finally, divide by 2 to find the price of one burrito:

B = $3.50

So, the price of one taco is $1.25, and the price of one burrito is $3.50.

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The missing value in the frequency table from the electronics manufacturers would be 150.

The class interval of the battery life is in fives which means that between 25 and 30, the shaded region on the histogram would represent 28 ≤ x < 30.

Looking at the y axis, we can tell that the class interval is 50 thanks to the 120 achieved by 15 ≤ x < 20. This then means that as 28 ≤ x < 30 is sitting on the third y interval, we know that it has a value of 150.

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The decay of isotope at compound rate is approximately 0.0140.

To find the continuous compound rate of decay of this isotope, we can use the following formula:

Nₜ = N₀e^(-λᵗ)

Where:
Nₜ is the amount of the isotope present after time t (years),
N₀ is the initial amount of the isotope,
λ is the continuous compound rate of decay, and
t is the time in years.

In this case, 91.9% of the isotope is still present 6 years after the disaster,

so Nₜ = 0.919 * N₀, and t = 6 years.

We want to find λ, the continuous compound rate of decay.

We can rewrite the formula as follows:

0.919 * N₀ = N₀ * e^(-λ * 6)

Divide both sides by N₀:

0.919 = e^(-λ * 6)

Now, take the natural logarithm (ln) of both sides:

ln(0.919) = -λ * 6

Divide by -6 to solve for λ:

λ = ln(0.919) / (-6)

Calculate the value:

λ ≈ 0.0140

So, the continuous compound rate of decay of this particular radioactive isotope is approximately 0.0140.

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By applying the Consecutive Angles Theorem, Jim can confirm that the angled section for the steps is indeed a parallelogram, even without accurately proving that any two sides are parallel.

Jim building a deck with an angled section in the shape of a parallelogram. To be assured that he has an actual parallelogram, Jim can use the Consecutive Angles Theorem.

This theorem states that if the consecutive angles of a quadrilateral are supplementary (add up to 180 degrees), then the quadrilateral is a parallelogram.

To use the Consecutive Angles Theorem, Jim should follow these steps:

1. Measure the four angles of the quadrilateral he has created for the angled section of the deck.
2. Check if the consecutive angles are supplementary (i.e., the sum of each pair of consecutive angles is equal to 180 degrees).
3. If all consecutive angles are supplementary, he can be assured that the quadrilateral is a parallelogram.

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The coordinates of p so that p partitions the segment of AB in the ratio 7 to 2 if A( -5,4) and B( -8,-2) is P(x, y) = [-22/3, -2/3].

In this scenario, line ratio would be used to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 1 to 4.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical equation:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

P(x, y) = [(7(-8) + 2(-5))/(7 + 2)],  [(7(-2) + 2(4))/(7 + 2)]

P(x, y) = [(-56 - 10)/(9)],  [(-14 + 8)/9]

P(x, y) = [-66/9],  [(-6)/(9)]

P(x, y) = [-22/3, -2/3]

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To find the coordinates of point P on the line, we can solve for x and y in the equation X-7 - Y + 2 = 2 + 6 = 5. Adding 7 to both sides, we get X - Y + 2 = 12. Subtracting 2 from both sides, we get X - Y = 10. We can choose any value for x, and then solve for y using this equation. For example, if we choose x = 0, then y = -10.

So the coordinates of point P on the line could be (0, -10, z), where z is any real number.

To find a vector v parallel to the line, we can take two points on the line and find the vector between them. For example, we could use the points (0, -10, 0) and (1, -9, 0). The vector between these points is (1-0, -9-(-10), 0-0) = (1, 1, 0).

So a vector v parallel to the line is v = (1, 1, 0).
To find the coordinates of a point P on the line and a vector v parallel to the line, we first need to rewrite the given equation in a more standard form. The equation provided seems to be incorrect, but let's assume it's meant to be in the format of Ax + By = C, then we can proceed as follows:

1. Identify the normal vector of the line (A, B): Since the given equation is X - Y = 3 (combining the constants), the normal vector is (1, -1).

2. Determine the direction vector of the line, which is perpendicular to the normal vector. One possible direction vector is the one obtained by swapping the components and negating one of them, so v = (1, 1).

3. To find a point P on the line, we can choose a value for either x or y and solve for the other coordinate. Let's choose x = 0, then we have 0 - Y = 3, which gives Y = -3. Therefore, P(x, y) = (0, -3).

In summary, the point P on the line is (0, -3), and a vector v parallel to the line is (1, 1).

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The total amount of the principal, interest, down payment, and fees described for Brooke's condominium is $1,154,091.59

The first step is to calculate the mortgage amount, which is the purchase price minus the down payment:

Mortgage amount = $413,600 - 9% of $413,600 = $376,576

Next, we need to calculate the total cost of the fees and charges:

Discount points = 1% of $376,576 = $3,766

Origination fee = 0.75% of $376,576 = $2,823.42

Documentary stamp tax on deed = $0.70 per $100 or portion thereof, so for $413,600 it would be:

$0.70 * ($413,600 / $100) = $2,895.20

Documentary stamp tax on mortgage = $0.35 per $100 or portion thereof, so for $376,576 it would be:

$0.35 * ($376,576 / $100) = $1,318.02

Brokerage fee = $175 + 5% of $376,576 = $19411.8

Intangible tax = 0.2% of $376,576 = $753.15

Now we can calculate the total cost of the principal and interest payments over the life of the mortgage. We'll use a mortgage calculator to do this, based on the mortgage amount, interest rate, and term:

Total mortgage payments = $2,244 * 12 months * 25 years = $673,200

Finally, we can add up all of these amounts to get the total cost of the principal, interest, down payment, and fees:

Total cost = Purchase price + Down payment + Mortgage payments + Discount points + Origination fee + Documentary stamp tax on deed + Documentary stamp tax on mortgage + Brokerage fee + Intangible tax

Total cost = $413,600 + $37,224 + $673,200 + $3,766 + $2,823.42 + $2,895.20 + $1,318.02 + $19,411.80 + $753.15

Total cost = $1,154,091.59

Therefore, we got a total cost of $1,154,091.59

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Angela made $350 per week 25 years ago and Walker made $200 per week 25 years ago.

Let's assign variables to represent Angela and Walker's salaries 25 years ago. Let A be Angela's salary 25 years ago and W be Walker's salary 25 years ago.

Using the information given in the problem, we can set up two equations:

A + W = 550 (their total salary 25 years ago)
4A + 3W = 2000 (their total current salary)

To solve for A and W, we can use substitution or elimination. Let's use substitution.

From the first equation, we can rearrange to solve for A:

A = 550 - W

Substitute this into the second equation:

4(550 - W) + 3W = 2000

Distribute the 4:

2200 - 4W + 3W = 2000

Simplify:

W = 800

Now that we know Walker's salary 25 years ago was $800, we can plug that into the first equation to solve for Angela's salary:

A + 800 = 550

A = -250

Uh oh, a negative salary doesn't make sense in this context. We made a mistake somewhere.

Let's go back to our original equations and try elimination instead:

A + W = 550
4A + 3W = 2000

Multiplying the first equation by 4, we get:

4A + 4W = 2200

Subtracting the second equation from this, we get:

W = 200

Now we can plug this into either equation to solve for A:

A + 200 = 550

A = 350

So Angela made $350 per week 25 years ago and Walker made $200 per week 25 years ago.

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Rounding to the nearest whole number, the linear speed of a point on Uranus' equator is approximately 139,424 miles/day.

(a) To find the angular speed of a point on Uranus' equator, we need to convert the rotation period from hours to days and then calculate the angle rotated in one day.

In one day (24 hours), Uranus rotates:

24 hours ÷ 17.2 hours/rotation ≈ 1.3953 rotations

The angle rotated in one day is:

1.3953 rotations × 2π radians/rotation ≈ 8.7674 radians/day

So the angular speed of a point on Uranus' equator is approximately 8.7674 radians/day.

(b) To find the linear speed of a point on Uranus' equator, we can use the formula:

linear speed = radius × angular speed

where the radius is given as 15,881 miles and the angular speed is 8.7674 radians/day (from part (a)).

Substituting these values, we get:

linear speed = 15,881 miles × 8.7674 radians/day ≈ 139,424 miles/day

Rounding to the nearest whole number, the linear speed of a point on Uranus' equator is approximately 139,424 miles/day.

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The area of the commune's summer-autumn rice crop is approximately 570,041.902 square meters. ( rounded to the third decimal place)

To calculate the area of the commune's summer-autumn rice crop, we need to multiply the total area of the commune by the percentage of the area used to grow rice.

First, we need to convert the area from hectares to square meters since the percentage is based on the total land area in square meters.

1 hectare = 10,000 square meters

So, 81.5 hectares = 81.5 x 10,000 = 815,000 square meters

Next, we can calculate the area of the rice crop:

57/81.5 = 0.699386503

0.699386503 x 815,000 = 570,041.902 square meters

Rounding to the third decimal place, the area of the commune's summer-autumn rice crop is approximately 570,041.902 square meters.

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The height of the cone is 3.4cm

A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex.

The volume of a cone is expressed as;

V = 1/3 πr²h

where πr² = base area. therefore the volume can be written as;

V = 1/3 base area × height

base area = 49cm²

height = 45.3 cm³

45 = 1/3 ×40h

135 = 40h

h = 135/40

h = 3.4cm

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Note that in order to map A onto B, Kyle would have to dilate the given figure by a scale factor or 3.

The scale factor is a metric for figures with similar appearances but differing scales or measurements. Assume two circles appear similar but have different radii. The scale factor specifies how much larger or smaller a figure is than the original figure.

The original point of figure A which has 4 points are

(0,02)

(-1, 2)

(0, 1)

(1, 2)

Multiply all th e points by 3, and you get,

(0,02) x 3 = (0, -6) =

(-1, 2) x 3 = (-3, 6)

(0, 1) x 3 = (0, 3)

(1, 2) x3 = (3, 6)

Plotting the new values will give us the transformation (dilation) required. See the attached image.

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To determine the cost of buying different numbers of songs for his mp3 player, Raymond needs to know the cost of a single song and the total number of songs he wants to buy, as well as consider bulk purchasing options like buying an album.

Assuming the cost of a single song is $1, if Raymond wants to buy 10 songs, the cost would be 10 x $1 = $10. Similarly, if Raymond wants to buy 20 songs, the cost would be 20 x $1 = $20. In general, the cost of buying n songs would be n x $1.

If the cost of a single song is not $1, then Raymond would need to adjust his calculations accordingly. For example, if the cost of a single song is $0.99, then the cost of buying 10 songs would be 10 x $0.99 = $9.90, and the cost of buying 20 songs would be 20 x $0.99 = $19.80.

Raymond could also consider purchasing songs in bulk, such as by buying an album, which typically offers a discounted price compared to purchasing individual songs. In this case, the cost of buying different numbers of songs would depend on the number of songs in the album and the cost of the album.

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Complete Question:

Raymond wants to know the costs of buying different numbers of songs for his MP3 player. The cost of each song is the same.

• Let s represent the possible number of songs Raymond could buy.

• Let d represent the amount of money, in dollars, Raymond would need to buy the songs.

Fill in the table for all missing values of s and d.

Number of songs, s

Amount of money ($), d

2

2.58

5.16

7

11

21.93

To estimate the weekly profit of producing and selling 81 cars, we first need to find the current weekly profit for producing and selling 80 cars using P(80):

P(80) = -0.005(80)^(2) - 0.2(80) + 1000(80) - 1300
P(80) = $75,800

Now we need to find the marginal profit at x = 80, which is the derivative of the profit function P(x):

P'(x) = -0.01x - 0.4x + 1000

P'(80) = -0.01(80) - 0.4(80) + 1000
P'(80) = $920

The marginal profit at x = 80 is $920. This means that for each additional car produced and sold beyond 80, the profit will increase by $920.

To estimate the weekly profit of producing and selling 81 cars, we can use the approximation formula:

ΔP ≈ P'(80)Δx

where ΔP is the change in profit, Δx is the change in the number of cars produced and sold, and P'(80) is the marginal profit at x = 80.

We want to find the change in profit when the number of cars produced and sold increases from 80 to 81, so Δx = 1. Plugging in the values we have:

ΔP ≈ $920(1)
ΔP ≈ $920

This means that the estimated weekly profit for producing and selling 81 cars is:

P(81) ≈ P(80) + ΔP
P(81) ≈ $75,800 + $920
P(81) ≈ $75,720

Rounding to the nearest dollar, the answer is $75,720. So the correct option is: $75,720.

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By using the compass a ruler and a protractor a circle having a Radius MO of 3 cm, Diameter OP of 6cm, Chord QR of 4cm, and Central angle <OMS of 60° has been Drawn.

Given data:

Radius MO = 3 cm

Diameter OP = 6cm

Chord QR = 4cm

Central angle <OMS = 60°

Steps to follow to draw the circle,

Step 1: Mark the M point as the center.

Step 2: Now take the compass and take a 3 cm reading on it by using the ruler.

Step 3: Draw the circle by using M as the center

Step 4: Mark a point O on the circle

Step 5: Draw a straight line segment OP passing through M

Step 6: Mark a point Q on the circle

Step 7: Using compass width and take a 3 cm reading on it and by taking Q as center cut the circle at R.

Step 8: Now join Q and R points.

Step 9: Using compass width and take a 3 cm reading on it and by taking O as the center cut the circle at S.

Step 10: Now join S and M points

Therefore, The circle, central angle on the circle, and chord on the circle are drawn.

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The complete question is,

1. Directions: Using a compass, ruler, and protractor, draw a circle having:

1.) M as the center

2.) radius MO of 3 cm

3.) diameter OP of 6cm

4.) chord QR of 4cm

5.) central angle:<OMS of 60°

The expression 6 * 6^(-2) is equivalent to 1/6.

We can simplify this expression using the rule of exponents that states a^m / a^n = a^(m-n), which gives:

6 * 6^(-2) = 6 / 6^2 = 6 / 36 = 1/6

Let's break down the expression and simplify it step by step:

6 * 6^(-2)

We start by evaluating the exponent, which means we take the reciprocal of 6^2:

6 * (1/6^2)

Now we simplify the denominator of the fraction:

6 * (1/36)

Finally, we can simplify the expression by dividing 6 by 36:

1/6

So, the expression 6 * 6^(-2) is equivalent to 1/6. This means that if we multiply 6 by 6 raised to the power of -2 (or 1/6^2), we get the same result as dividing 6 by 6^2 (or 36), which is  1/6.

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a) The graph of the given lines is as attached

b) The area of the enclosed triangle is: 8 square units

The general form of expression of linear equations in slope intercept form is expressed as:

y = mx + c

where:

m is slope

c is y-intercept

We are given the equations as:

y = x + 5

y = 5

x = 4

The graph of these three linear equations is as shown in the attached file

2) The area of the given triangle enclosed by the three lines is gotten from the formula:

A = ¹/₂ * b * h

where:

A is area

b is base

h is height

Thus:

A = ¹/₂ * 4 * 4

A = 8 square units

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I see that this is a rate of change time of problem

If andy can run 20 miles in 6 hours, than our goal is to find out how much he runs in a hour

So, we just have to divide 20 by 6.

It's sorta hard to explain

Questions?

Anyhow, the answer is around 3.3 miles per hour

Answer:

3.33 miles

Step-by-step explanation:

We Know

Andy can run 20 miles in 6 hours.

How many miles can he run in 1 hour?

We Take

20 / 6 ≈ 3.33 miles

So, Andy can run about 3.33 miles in 1 hour.

Martin expects to wait longer than Selena. This can be Mathematically represented as: t > s

To determine who expects to wait longer, we need to compare the values on the number lines for Selena and Martin. Let's say Selena expects to wait for t minutes, and Martin expects to wait for s minutes. Looking at the number lines, we can see that Selena's expected wait time is closer to 10 minutes, while Martin's expected wait time is closer to 5 minutes. Therefore, we can say that Martin expects to wait longer than Selena.

Mathematically, we can represent this as:

t > s

This means that Selena's expected wait time is greater than Martin's expected wait time. Therefore, Martin expects to wait longer than Selena.

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A. The missing value for P(X = 1) is 0.20.

B.  The value of P(X ≤ 2) is 0.85.

C.  The value of P(X > 2) is 0.15.

D. The probability of "At least 2" is equivalent to P(X >= 2), which is 0.75.

In probability theory, a probability distribution is a function that assigns probabilities to each possible value of a random variable.

In this Problem, we have a probability distribution for the score on a quiz, with X being the random variable and the table providing the probability of each possible score. In this answer, we will use the given probability distribution to answer the questions posed.

A) Find the missing value for P(X = 1) in the probability distribution.

To find the missing value for P(X = 1), we need to use the fact that the sum of the probabilities for all possible values of X must be equal to 1. Therefore, we can set up an equation:

P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 1

Substituting in the given probabilities, we get:

0.05 + P(X = 1) + 0.60 + 0.15 = 1

Simplifying, we get:

P(X = 1) = 0.20

Therefore, the missing value for P(X = 1) is 0.20.

B) P(X ≤ 2) =

To find P(X ≤ 2), we need to add up the probabilities of X being less than or equal to 2. This is equivalent to:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

Substituting in the given probabilities, we get:

P(X ≤ 2) = 0.05 + 0.20 + 0.60 = 0.85

Therefore, P(X ≤ 2) is 0.85.

C) P(X > 2) =

To find P(X > 2), we need to add up the probabilities of X being greater than 2. This is equivalent to:

P(X > 2) = P(X = 3)

Substituting in the given probabilities, we get:

P(X > 2) = 0.15

Therefore, P(X > 2) is 0.15.

D) The probability of "At least 2" is equivalent to P(X >= 2)

To find the probability of "At least 2," we need to add up the probabilities of X being greater than or equal to 2. This is equivalent to:

P(X ≥ 2) = P(X = 2) + P(X = 3)

Substituting in the given probabilities, we get:

P(X ≥ 2) = 0.60 + 0.15 = 0.75

Therefore, the probability of "At least 2" is equivalent to P(X ≥ 2), which is 0.75.

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A compound inequality to show the distance from the boys home to the chief's camp is 5 < d < 8

The distance from the boy's home to the school is 5km.

The distance from the boy's home to the market is 8km.

The chief's camp is closer to the boy's home than the market, but further than the school

The chief's camp is closer to the boy's home than the market, so the distance from the boy's home to the chief's camp is less than 8km.

Putting these together, we can write a compound inequality to show the possible distances d from the boy's home to the chief's camp:

distance from home to school < distance < home to maket

5 < d < 8

The inequality is 5 < d < 8.

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The statements are classified as follows:

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.

8 is a low outlier, hence it is a value lower than the mean, meaning that the mean increases if we remove the observation of 8.

The range of a data-set is calculated as the difference between the highest value and the lowest value in the data-set, thus if we remove the low value of 8, the next low value is of 47, meaning that the range decreases.

The ordered data-set is given as follows:

8, 47, 48, 50, 51, 51.

The data-set has an even cardinality of 6, hence the median is calculated as the mean of the two middle elements as follows:

Median = (48 + 50)/2

Median = 49.

Removing 8, the data-set is given as follows:

47, 48, 50, 51, 51.

Hence the median increases, as it will be the middle value of 50.

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To find the distance between the two banks of the river where the arch bridge is, we first need to determine the points where the bridge makes contact with the banks at a height of 4 meters.

We are given the parabola shape of the arch with the equation y = -0.1(x - 5)^2 + 12.

1. Set the height y equal to 4 meters:

4 = -0.1(x - 5)^2 + 12

2. Subtract 12 from both sides:

-8 = -0.1(x - 5)^2

3. Divide both sides by -0.1:

80 = (x - 5)^2

4. Take the square root of both sides:

sqrt(80) = x - 5

5. Now, we find the two x-values where the bridge contacts the banks:

x1 = sqrt(80) + 5

x2 = -sqrt(80) + 5

6. Calculate the distance between the two banks by subtracting x2 from x1:

Distance = x1 - x2 = (sqrt(80) + 5) - (-sqrt(80) + 5)

7. Simplify the expression:

Distance = 2 * sqrt(80)

8. Round your answer to the nearest whole number:

Distance ≈ 18 meters

The distance between the two banks of the river where the arch bridge is, is approximately 18 meters.

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The number of whole numbers whose square roots of a natural number from 1 to 200 will be 14

The natural number of square roots from 1 to 200 are mentioned below

1² = 1,

2² = 4,

3² = 9,

4² = 16,

5² = 25,

6² = 36,

7² = 49,

8² = 64,

9² = 81,

10² = 100,

11² = 121,

12² = 144,

13² = 169,

14² = 196

The number of whole numbers = 14

Above 14 the square will be greater than 200

All the whole numbers are natural number except zero. zero is a whole number not a natural number.

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Answer:

7.6 cm

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]a^{2}[/tex] + [tex]6.5^{2}[/tex] = [tex]10^{2}[/tex]

[tex]a^{2}[/tex] + 42.25 = 100 Subtract 42.25 from both sides

[tex]a^{2}[/tex] = 57.57

[tex]\sqrt{\a^{a} }[/tex] = [tex]\sqrt{57.57}[/tex]

a ≈ 7.6

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Answer:

7.6 cm

Step-by-step explanation:

a^2+ b^2=c^2

a^2+6.5^2=10^2

a^2+42.25=100 subtract 42.25 from both sides

a^2=57.57

a=√57.57

a=7.6 cm

The function that can be used to find the amount in dollars a passenger has to pay to fly with `p` pieces of luggage, where `p > 2` is: `C(p) = 439 + 25(p-2)`

- The base cost of the flight is $439.

- Customers may check 2 pieces of luggage without any additional fee.

- For each additional piece of luggage beyond 2, there is a fee of $25.

- If `p` is the number of pieces of luggage checked, then the number of additional pieces of luggage beyond 2 is `p - 2`.

- Therefore, the additional fee for `p` pieces of luggage beyond the first 2 is `25(p - 2)`.

- Adding this fee to the base cost gives the total cost `C(p)`:

C(p) = base cost + additional fee for (p-2) pieces of luggage

    = 439 + 25(p-2)

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