1. The road between towns A and B is blocked due to roadworks. A diversion via town P has
been put into place.
Roads AB and AP form a 20° angle with each other, as shown in the diagram. The angle
between roads AP and PB is 110°.
The road from A to P is 4km long.
How much longer is the diversion via town P than the direct route AB?
A -20⁰
AP - 4km
B - 110⁰
P - 50 ⁰

The length of the hypotenuse is approximately 10.63 inches.

What is hypotenuse?

The hypotenuse is the longest side of a right triangle, and it is opposite the right angle. In other words, the hypotenuse is the side that connects the two acute angles of the triangle. The hypotenuse is always opposite the right angle in a right triangle and is also the side that has the largest length compared to the other two sides of the right triangle.

The length of the hypotenuse can be calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides of the right triangle.

According to the question:
We can use the Pythagorean theorem to find the hypotenuse of a right triangle given the lengths of its other two sides. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the length of the opposite side is 7 inches and the length of the adjacent side is 8 inches. Let's label the hypotenuse as c. Then, we can set up the equation:

[tex]c^2 = 7^2 + 8^2[/tex]

[tex]c^2 = 49 + 64[/tex]

[tex]c^2 = 113[/tex]

To solve for c, we take the square root of both sides of the equation:

[tex]c = \sqrt(113)[/tex]

[tex]c \approx 10.63[/tex]

Therefore, the length of the hypotenuse is approximately 10.63 inches.

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Step-by-step explanation:

pi * d  = total 360° circumference....you want 210/360 ths of this total

                pi * 10   *   210 / 360 =   calculate this.....

A) To find the annual rate of change, we can use the formula:

r = (V2/V1)^(1/n) - 1

where:

V1 = initial value ($42,000)

V2 = final value ($11,000)

n = number of years (2006 - 1994 = 12)

Plugging in the values, we get:

r = (11000/42000)^(1/12) - 1 ≈ -0.1135

Therefore, the annual rate of change between 1994 and 2006 is approximately -0.1135.

B) To convert the rate of change to a percentage, we can multiply by 100 and add a percent sign:

r = -0.1135 × 100% ≈ -11.35%

Therefore, the correct answer to part A written in percentage form is approximately -11.35%.

C) Assuming the car value continues to drop by the same percentage, we can use the formula for exponential decay:

V = V0 * (1 - r)^t

where:

V0 = initial value ($11,000 in 2006)

r = annual rate of change (-0.1135)

t = number of years (2010 - 2006 = 4)

Plugging in the values, we get:

V = 11000 * (1 - (-0.1135))^4 ≈ $6,250

Therefore, the value of the car in the year 2010 would be approximately $6,250, rounded to the nearest 50 dollars.

The determinant of the matrix A is 70.

The determinant of a 3x3 matrix can be found using the following formula:

|A| = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)

where aij represents the element in the ith row and jth column of the matrix.

Using this formula, we can find the determinant of the given matrix:

|A| = 2(82 - 4(-2)) - 3(-12 - 4(-6)) + 0(-1*(-2) - 8*(-6))

= 16 + 54 + 0

= 70

Therefore, the determinant of the matrix A is 70.

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The name of shape A is right trapezoid

The congruent shapes are B and D

A right trapezoid is a trapezoid (a four-sided polygon with two parallel sides) in which one of the angles formed by the non-parallel sides is a right angle (90 degrees).

The parallel sides of a right trapezoid are called the bases of the trapezoid, and the other two sides are called the legs. The perpendicular distance between the bases of a right trapezoid is called the height of the trapezoid.

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The correct answer is that if someone simply gets a high school certificate, their salary is most likely to make less than $40,000.

In general, the phrase "income" refers to the sum of money, assets, and other transfers that are worth something obtained over a predetermined period period of time as an exchange for goods or services.

Only having completed high school:

51>24>3

Therefore, it is highly likely that they make less than $40,000.

Has a salary of at least 60,000.

6<17<48

Therefore, a Master's degree is most likely their greatest level of education.

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The hypotenuse of the right angled triangle is [tex]$14\sqrt{2}$[/tex].

What is hypotenuse?

The hypotenuse is the longest side of a right-angled triangle and is opposite to the right angle. It is the side that is opposite to the 90-degree angle and is located opposite the right angle.

To solve this problem, we can use the concept of special right triangles, specifically the 45-45-90 right triangle. In a 45-45-90 right triangle, the sides are in the ratio of 1:1:sqrt(2).

Let's label the length of the triangle as [tex]$L$[/tex], the hypotenuse as [tex]$H$[/tex], and the angle between the hypotenuse and base length as [tex]45[/tex]°.

We are given that the angle formed between the hypotenuse and the base length is 45 degrees. In a 45-45-90 right triangle, the two legs are congruent, so the ratio of the sides is 1:1:sqrt(2).

Since we know that the ratio of the sides is 1:1:sqrt(2), we can set up the following equation:

[tex]$L:L:H = 1:1:\sqrt{2}$[/tex]

We are given that [tex]$L = 14$[/tex], so we can substitute this value into the equation:

[tex]$14:14:H = 1:1:\sqrt{2}$[/tex]

Solve for H.

Since the ratio of the sides is 1:1:sqrt(2), we know that [tex]$H$[/tex] is equal to [tex]$L$[/tex] multiplied by [tex]$\sqrt{2}$[/tex]. Therefore, we can solve for [tex]$H$[/tex] by multiplying [tex]$14$[/tex] by [tex]$\sqrt{2}$[/tex]:

[tex]$H = 14\sqrt{2}$[/tex]

Therefore, the hypotenuse of the right angled triangle is [tex]$14\sqrt{2}$[/tex].

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The randοm variable in this case is the range οf the 12 data values, which is equal tο 27.

The range οf a data set is the difference between the highest and lοwest value in a given set.

The range οf a data set is the difference between the largest and smallest values in the set.

In this case, the smallest value is 38 and the largest value is 65. Therefοre, the range οf the data set is:

Range = Largest value - Smallest value

Range = 65 - 38

Range = 27

Sο, the randοm variable in this case is the range οf the 12 data values, which is equal tο 27.

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Answer:

[tex] \frac{ {6}^{5} }{ {6}^{ - 2} } = {6}^{5 - ( - 2))} = {6}^{5 + 2} = {6}^{7} [/tex]

Because we can use the standard normal to find probabilities for a normal random variable with any mean and any standard deviation, it is significant.

Probability is the concept that describes the likelihood of an event occurring.

In real life, we frequently have to make predictions about how things will turn out.

We may be aware of the result of an occurrence or not.

When this occurs, we state that there is a possibility that the event will occur.

In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

According to our question-

If x is your data point, is the mean, and is the standard deviation,

z = (x - ) /

Hence, Because we can use the standard normal to find probabilities for a normal random variable with any mean and any standard deviation, it is significant.

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The length of major arc PQ is 35π units.

What is major arc?

In geometry, an arc is a portion of the circumference of a circle. A major arc is an arc that spans more than 180 degrees of the circle. In other words, a major arc is an arc that is greater than a semicircle (which spans exactly 180 degrees).

we know that,

length of arc = s = 2 π r (θ/360°)

where, r is the radius and θ is the angle of arc.

we have, r = 30

               θ = 210

so, length of major arc PQ :

   =  2 π r (θ/360°)

   = 2 π × 30 × (210/360)

   = 60  π  × 7/12

   = 35π units.

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To solve the equation √6x+3 = x-2, we can start by squaring both sides of the equation:

(√6x+3)² = (x-2)²

Simplifying the left side of the equation, we get:

6x+3 = (x-2)²

Expanding the right side of the equation, we get:

6x+3 = x² - 4x + 4

Moving all the terms to one side, we get a quadratic equation:

x² - 10x + 1 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Where a = 1, b = -10, and c = 1. Plugging these values into the formula, we get:

x = (10 ± √(100 - 4))/2

x = (10 ± √96)/2

x = 5 ± 2√6

Therefore, the solutions to the equation √6x+3 = x-2 are x = 5 + 2√6 and x = 5 - 2√6.

Answer:

Let's start by assigning variables to represent the number of nickels, dimes, and quarters in the jar.

Let x be the number of nickels.

Then the number of dimes is 3 times as many as nickels, so the number of dimes is 3x.

And the number of quarters is twice as many as dimes, so the number of quarters is 2(3x) = 6x.

We know that the total amount of money in the jar is $5.55, which is equal to:

0.05x (for the value of the nickels) + 0.10(3x) (for the value of the dimes) + 0.25(6x) (for the value of the quarters)

Simplifying this expression, we get:

0.05x + 0.30x + 1.50x = 5.55

Combining like terms, we have:

1.85x = 5.55

Dividing both sides by 1.85, we get:

x = 3

So there are 3 nickels in the jar.

Using this value, we can find the number of dimes and quarters:

Number of dimes = 3x = 3(3) = 9

Number of quarters = 6x = 6(3) = 18

Therefore, there are 3 nickels, 9 dimes, and 18 quarters in the jar.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find out how much shorter the pencil was after the student completed the project, we need to subtract the final length from the initial length:

7 1/2 - 5 7/8

To subtract these two mixed numbers, we need to convert them to a common denominator. The smallest common multiple of 2 and 8 (the denominators of the fractions) is 8, so we can rewrite the numbers as:

15/2 - 47/8

Now we can find a common denominator of 8:

(15/2) * (4/4) - (47/8) = 30/8 - 47/8

Subtracting the numerators, we get:

-17/8

Therefore, the pencil was 17/8 inches shorter after the student completed the project than when the student started the project. We can simplify this fraction to a mixed number:

-2 1/8

So the answer is C) 2 3/8 inches.

Ed's total monthly expenses for each loan option includes:

The lists of banks and their annual interest rates are as follows:

Because the interest rate at the first bank is 7.5%, the total interest:

= 7.5% of $20000

= 0.075 * $20000

= $1500.

Since the interest rate at City Bank is 8.2%, the total interest:

= 8.2% of $20000

= 0.082 * $20000

= $1640.

Because the interest rate at Star Bank is 9%, the total interest:

= 9% of $20000

= 0.09 * $20000

= $1800.

The annual loan plus interest for banks is:

First bank:

= $20,000 + $1500

= $21,500

City bank:

= $20000 + $1640

= $21640

Star Bank:

= $20000 + $1900

= $21900

The banks' monthly payments are as follows:

First bank = $21500 / 12 months = $1,792.

City bank = $21640 / 12 months = $1,803

Star bank = $21800 / 12 months = $1,817

Now, since monthly cost of running the gym is $5,000. Ed's total monthly expenses for each loan option are equal to the monthly payments plus the cost for each month. It is calculated as follows:

First bank = $5000 + $1792 = $6792.

City bank = $5000 + $1803 = $6803

Star bank = $5000 + $1817 = $6817

Full question "Ed wants to borrow $20,000 from a bank to open a small gym. Three banks charge different interest rates. To help decide the best loan option, Ed wants to know the percent profit he will make each month. Part A The cost to run the gym each month is $5,000. Find Ed's total monthly expenses for each loan option.

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Using the formula σr = 3Fx/yz², we can easily compute the Modulus of Rupture.

The term "bending strength" is occasionally used to refer to the measure of a specimen's strength prior to rupture, also known as the "modulus of rupture," or MOR.

Contrary to the modulus of elasticity, which measures the wood's deflection but not its total strength, it can be used to evaluate a species' strength.

The formula σr = 3Fx/yz² for the load force F and the material's size dimensions in the three directions of x, y, and z can be used to compute the modulus of rupture, or "sigma."

The external force applied to the substance of interest in this instance is the load.

Therefore, using the formula σr = 3Fx/yz², we can easily compute the Modulus of Rupture.

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Correct question:

How do you compute MOR?

Answer: 54.43 miligrams

Step-by-step explanation:

To calculate the dose of ibuprofen for an 18-month-old child weighing 24 pounds, we need to convert the weight from pounds to kilograms.

1 pound is equal to 0.453592 kilograms.

So, the weight of the child in kilograms is:

24 pounds × 0.453592 kg/pound = 10.886kg (rounded to three decimal places)

Now we can use the given dosage information to calculate the usual dose of ibuprofen for the child.

The usual dose of ibuprofen is 5 mg/kg of body weight when the fever is under 102.5 degrees Fahrenheit.

So, for the 18-month-old child weighing 10.886 kg, the usual dose of ibuprofen would be:

5 mg/kg × 10.886 kg = 54.43 mg

Therefore, the usual dose of ibuprofen for an 18-month-old child weighing 24 pounds is 54.43 mg.

Answer:

First, we need to convert the weight of the child from pounds to kilograms since the dosage is given in milligrams per kilogram.

We can use the conversion factor: 1 pound = 0.453592 kilograms.

So, 24 pounds = 24 x 0.453592 = 10.8862 kg (rounded to 4 decimal places).

Next, we can calculate the usual dose of Ibuprofen by multiplying the weight of the child (in kg) by the dose per kg:

Usual dose = 5 mg/kg x 10.8862 kg = 54.431 mg

Therefore, the usual dose of Ibuprofen for an 18 month old weighing 24 pounds would be 54.431 mg when the fever is under 102.5 degrees Fahrenheit. However, it is important to note that dosages may vary depending on the specific circumstances, and it is always best to consult a healthcare provider for proper dosing instructions.

Step-by-step explanation:

Answer:

[tex]a=3\sqrt{5}[/tex] or 6.7 approximately (Yes you did it correctly)

Step-by-step explanation:

Find leg [tex]a[/tex] of a right triangle if leg [tex]b[/tex] =6 and hypotenuse = 9.

To find side [tex]a[/tex] use Pythagorean Theorem:

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

After substituting b = 6 and c = 9 we have:

[tex]a^2+6^2=9^2[/tex]

[tex]a^2=9^2-6^2[/tex]

[tex]a^2=81-36[/tex]

[tex]a^2=45[/tex]

[tex]a=\sqrt{45}[/tex]

[tex]a=3\sqrt{5}[/tex]

[tex]a=6.7[/tex]

Answer:

8:15

Step-by-step explanation:

To find the probability that a given tree has between 270 and 330 apples, we need to calculate the area under the normal curve between the z-scores corresponding to 270 and 330.

First, we need to convert the values of 270 and 330 to z-scores using the formula:

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean of the distribution, and σ is the standard deviation.

For x = 270, we get:

z = (270 - 300) / 30 = -1

For x = 330, we get:

z = (330 - 300) / 30 = 1

Using the 68-95-99.7 rule, we know that approximately 68% of the area under the normal curve is within one standard deviation of the mean, 95% is within two standard deviations, and 99.7% is within three standard deviations.

Since the z-scores for 270 and 330 are within one standard deviation of the mean (i.e., they are both less than 1 standard deviation away from the mean of 300), we can use the 68% rule to estimate the probability that a given tree has between 270 and 330 apples.

According to the 68% rule, approximately 68% of the trees will have between 270 and 330 apples.

Therefore, P = 68%.

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Answer:

Multiply the given numbers by a factor of 2.5, then find the perimeter by adding up all 4 of the sides.

Step-by-step explanation:

While there isn't a picture given, it can be assumed that the shape given is a rectangle.

Then, simply multiply all 4 sides by a factor of 2.5, since that's the number it is being enlarged by.

Then to find the "framing" of said rectangle, add up all 4 of the sides that you just calculated to find the perimeter.

Answer:

Sure, I can help you with that!

To start, let's look at the ingredient list and see what information we have:

- 8 cups water

- ½ cup garlic

- ½ cup onion

- 1 ½ cups chopped carrots

- ½ cup tomato paste

- 2 cups sliced potatoes

- 1 cup olive oil

To make the calculations, we can set up ratios that relate the amount of each ingredient to the number of servings of soup. For example, if we want to know how much garlic we need for 40 servings of soup, we can set up the following ratio:

½ cup garlic / 10 servings = x cups garlic / 40 servings

To solve for x, we can cross-multiply and simplify:

(½ cup garlic) * 40 servings = (10 servings) * x cups garlic

20 cups = 10x

x = 2 cups

So we would need 2 cups of garlic to make 40 servings of soup.

Similarly, we can set up ratios for the other questions:

Question 2:

½ cup tomato paste / 10 servings = x cups tomato paste / 60 servings

(½ cup tomato paste) * 60 servings = (10 servings) * x cups tomato paste

30 cups = 10x

x = 3 cups

So we would need 3 cups of tomato paste to make 60 servings of soup.

Question 3:

1 ½ cups chopped carrots / 10 servings = x cups chopped carrots / 30 servings

(1 ½ cups chopped carrots) * 30 servings = (10 servings) * x cups chopped carrots

45 cups = 10x

x = 4.5 cups

So we would need 4.5 cups of chopped carrots to make 30 servings of soup.

here I simplified and checked the cross products of the ratios.

Question 1:

½ cup garlic / 10 servings = x cups garlic / 40 servings

Cross-multiplying, we get:

(½ cup garlic) * 40 servings = (10 servings) * x cups garlic

20 cups = 10x

Dividing both sides by 10, we get:

x = 2 cups garlic

Therefore, we need 2 cups of garlic to make 40 servings of soup.

Checking the cross products:

(½ cup garlic) * 40 servings = (10 servings) * 2 cups garlic

20 cups = 20 cups

The cross products are equal, so my answer is correct.

Question 2:

½ cup tomato paste / 10 servings = x cups tomato paste / 60 servings

Cross-multiplying, we get:

(½ cup tomato paste) * 60 servings = (10 servings) * x cups tomato paste

30 cups = 10x

Dividing both sides by 10, we get:

x = 3 cups tomato paste

Therefore, we need 3 cups of tomato paste to make 60 servings of soup.

Checking the cross products:

(½ cup tomato paste) * 60 servings = (10 servings) * 3 cups tomato paste

30 cups = 30 cups

The cross products are equal, so my answer is correct.

Question 3:

1 ½ cups chopped carrots / 10 servings = x cups chopped carrots / 30 servings

Cross-multiplying, we get:

(1 ½ cups chopped carrots) * 30 servings = (10 servings) * x cups chopped carrots

45 cups = 10x

Dividing both sides by 10, we get:

x = 4.5 cups chopped carrots

Therefore, we need 4.5 cups of chopped carrots to make 30 servings of soup.

Checking the cross products:

(1 ½ cups chopped carrots) * 30 servings = (10 servings) * 4.5 cups chopped carrots

45 cups = 45 cups

The cross products are equal, so my answer is correct.

By responding to the prompt, we may deduce that in order to circle and finish the copied triangle, a polygon should be drawn through the points D, E, and F.

A circle, which appears to be a 2D component, is made up of all the points in a jet that are uniformly spaced out from the hub. The capital "O" for the centre and the bottom component "r" for the radius stand for the distance from the origin to any point on a circle, respectively.

The formula πr², where (pi) is a proportionality constant roughly equal to 3.14159, determines the girth (the distance from the centre of the circle). The formula 2πr is used to determine a circle's circumference.

To recreate the original triangle using just two of its sides and the included angle, follow these steps:

Locate the location where the circle and the ray cross. Draw an arc that twice intersects the circle starting at point E on the compass. The point that is adjacent to point B on side AC should be designated as point F.

Create a polygon that passes across points D, E, and F to finish the copied triangle.

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Triangle DEF should be congruent with triangle AED because they share two sides and the included angle.

A circle looks to be a two-dimensional component described as the collection of all equidistant points in a jet from the hub. A circle is usually represented by a capital "O" for the centre and a lower section "r" for the Radius, which refers to the distance between the origin and any point on the circle.

Based on your directions, it appears that you are constructing a triangle using the SAS (side-angle-side) method. The stages are as follows:

Draw a line segment DE of the length determined in component B.

Draw a circle with a radius equivalent to the length of DE using point E as the centre.

Draw an angle equivalent to the measure of angle AED using line segment ED as one of its sides and point E as the vertex. To expand this angle, draw ray EF from vertex E.

Find the spot of intersection of ray EF and the circle and label it F.

Draw a line section connecting points E and F.

Finally, connect the locations D, E, and F with line segments to form the triangle DEF.

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Image is attached below,

Answer:

[tex]384 \: {cm}^{3} [/tex]

Step-by-step explanation:

Given:

h = 8 cm

a (base) = 48 cm^2

Find: V - ?

[tex]v = a(base) \times h[/tex]

[tex]v = 48 \times 8 = 384 \: {cm}^{3} [/tex]

Answer: 4/5

Step-by-step explanation:

Total marbles = 5 + 7 + 3

P(Red) = 5/15

P(Purple) = 7/15

P(Not Blue) = P(Red) + P(Purple)

= 5/15 + 7/15

= 12/15 or 4/5

Answer: 144

Step-by-step explanation:

60/100 times x/240

Cross multiply!!!

I hope this helps, have a nice day!!

The answer of the given question based on the matching  the equation with the graph is , Y=3x -5 , Y= -5x + 3  , Y= x - 1  , Y= (x + 3)² -2  , Y= 1/2x + 2 , Y= x .

An equation is  mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by equal sign (=). The LHS and RHS may contain numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division. The purpose of an equation is to solve for the value of an unknown variable.

Equations are used in many areas of mathematics and science, including algebra, calculus, physics, and engineering. They are essential for modeling and solving real-world problems and are a fundamental tool for understanding the natural world.

Here are the equations that match the graphs in the given image:

Y=3x -5 (Line passing through points (0,-5), (1,-2), and (2,1))

Y= -5x + 3 (Line passing through points (0,3) and (1,-2))

Y= x - 1 (Line passing through points (0,-1) and (1,0))

Y= (x + 3)² -2 (Parabola opening upwards with vertex at (-3,-2))

Y= 1/2x + 2 (Line passing through points (0,2) and (2,3))

Y= x (Line passing through points (-2,-2), (0,0), and (2,2))

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Answer:

- 2x + 6

Step-by-step explanation:

Expand

5(x+1)-7(x-1) = 5x + 5 - 7x + 1 and upon adding, = - 2x +6

- 2x + 6 can also be written as 6 - 2x

Answer:

1. Decay of 51%

2. Growth of 51%

3. Decay of 49%

4. Growth of 49%

Step-by-step explanation:

Look at the number in the parentheses raised to the power t.

In the formula, you have (1 + r)^t.

The number in parentheses is 1 + r.

Set each number in parentheses equal to 1 + r and solve for r.

If r is positive, it is growth.

If r is negative, it is decay.

1.

1 + r = 0.49

r = 0.49 - 1

r = -0.51

Decay of 51%

2.

1 + r = 1.51

r = 1.51 - 1

r = 0.51

Growth of 51%

3.

1 + r = 0.51

r = 0.51 - 1

r = -0.49

Decay of 49%

4.

1 + r = 1.49

r = 1.49 - 1

r = 0.49

Growth of 49%