6 Evaluate without using calculators. -4(-2)+(-12)÷(+3)+-20+(+4)+(-6 ​

The value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex] is 3

Given, [tex]\lim_{x \to 3} f(x)=0[/tex]

[tex]\lim_{x \to 3} g(x)=4[/tex]

[tex]\lim_{x \to 3} h(x)=2[/tex]

We have to find the value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex]

[tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)=\lim_{x \to 3} \frac{6h(x)}{4f(x)+g(x)}[/tex]

[tex]= \frac{\lim_{x \to 3}6h(x)}{\lim_{x \to 3}4f(x)+\lim_{x \to 3}g(x)}[/tex]

[tex]=\frac{6\times 2}{4\times0+4}[/tex]

= 12/4

= 3

Hence, the value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex] is 3

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The constant hourly rate using the given data points is  $100 per hour.

To calculate the constant hourly rate, we can use the given data points. For example, let's use the 5-hour rental for $500:

Hourly rate = Total cost / Number of hours
Hourly rate = $500 / 5 hours
Hourly rate = $100 per hour

Now, we can use this hourly rate to find the cost for the missing hour value in the table:

Cost = Hourly rate × Number of hours
Cost = $100 per hour × 9 hours
Cost = $900

So, the table will look like this:

Hours: _______ 5   |   9   |   _______
Cost (in dollars): 500 | 1,250 | 3,500

Now we can calculate the missing hours for the $3,500 cost:

Number of hours = Total cost / Hourly rate
Number of hours = $3,500 / $100 per hour
Number of hours = 35 hours

Now, the completed table is:

Hours: _______ 5   |   9   |   35
Cost (in dollars): 500 | 1,250 | 3,500

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The best estimate for the elk population is b) 1,250.

To estimate the elk population, you can use the mark and recapture method. The proportion of marked elk to the total marked population should be equal to the proportion of marked elk observed in the sample to the total observed population.

So, (marked elk / total marked population) = (marked elk observed / total observed population)

In this case: (75 / total population) = (15 / 250)

Now, solve for the total population:

75 / total population = 15 / 250

Cross-multiply:

15 * total population = 75 * 250

total population = (75 * 250) / 15

total population = 18,750 / 15

total population = 1,250

The best estimate for the elk population is 1,250 (option b).

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The critical points of the given function f(x) = ** + 5x/ (10x-60) are x = 6 and x = -6/5. The function is decreasing on (-∞, -6/5) and increasing on (-6/5, 6) and (6, ∞). The First Derivative Test shows that x = -6/5 is a local maximum and x = 6 is a local minimum.

To find the critical points, we need to first find the derivative of the function. Using the quotient rule, we get:

f'(x) = (10x - 60)(**)' - **(10x - 60)' / (10x - 60)²

Simplifying, we get:

f'(x) = 50 / (10x - 60)²

The critical points occur where the derivative is zero or undefined. Here, the derivative is never undefined, so we only need to find where it is zero:

50 / (10x - 60)² = 0

This occurs when x = 6 and x = -6/5.

Next, we need to determine the intervals on which the function is increasing or decreasing. To do this, we can use the first derivative test. We test a value in each interval of interest to see if the derivative is positive or negative:

For x < -6/5, we choose x = -2:

f'(-2) = 50 / (10(-2) - 60)² = -5/81 < 0

Therefore, the function is decreasing on (-∞, -6/5).

For -6/5 < x < 6, we choose x = 0:

f'(0) = 50 / (10(0) - 60)² = 5/9 > 0

Therefore, the function is increasing on (-6/5, 6).

For x > 6, we choose x = 10:

f'(10) = 50 / (10(10) - 60)² = 5/81 > 0

Therefore, the function is increasing on (6, ∞).

Finally, we can use the First Derivative Test to determine the nature of the critical points.

For x = -6/5:

f'(-6/5 - ε) < 0 and f'(-6/5 + ε) > 0, for small values of ε.

Therefore, x = -6/5 is a local maximum.

For x = 6:

f'(6 - ε) < 0 and f'(6 + ε) > 0, for small values of ε.

Therefore, x = 6 is a local minimum.

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The cost of one hamburger is $2.50 and the cost of one order of fries is $1.50.

Let's use h to represent the cost of one hamburger and f to represent the cost of one order of fries.

The Smith family's order can be represented by the equation:

6h + 3f = 19.50

The Jansen family's order can be represented by the equation:

8h + 6f = 29.00

We now have a system of two linear equations with two variables:

6h + 3f = 19.50

8h + 6f = 29.00

To solve for h and f, we can use the elimination method. We can start by multiplying the first equation by 2 to eliminate the variable f:

12h + 6f = 39.00

8h + 6f = 29.00

Subtracting the second equation from the first, we get:

4h = 10.00

Solving for h, we get:

h = 2.50

Now that we know the cost of one hamburger, we can substitute this value back into one of the original equations to solve for f. Using the first equation:

6h + 3f = 19.50

6(2.50) + 3f = 19.50

15 + 3f = 19.50

3f = 4.50

f = 1.50

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After depreciating for 3 years at a rate of 16% per year, the computer is worth approximately $788.26.

To find the worth of the computer after depreciating for 3 years at a rate of 16% per year, we can use the formula for compound interest with depreciation.

Given:

Initial value (cost of the computer) = $1,495

Depreciation rate = 16% per year

Number of years = 3

1. Convert the depreciation rate to a decimal: 16% = 0.16.

2. Calculate the depreciation factor, which is (1 - depreciation rate):

Depreciation factor = 1 - 0.16 = 0.84.

3. Apply the formula for compound interest with depreciation:

Worth = Initial value * (Depreciation factor)^(Number of years).

Substituting the given values into the formula:

Worth = $1,495 * (0.84)^3.

Calculating the exponent:

Worth = $1,495 * 0.84 * 0.84 * 0.84.

Simplifying the expression:

Worth ≈ $788.26.

Therefore, after depreciating for 3 years at a rate of 16% per year, the computer is worth approximately $788.26.

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The length of CB is 3 unit.

In the given figure ;

By SAS property of similar of triangles,

ΔCED and ΔCAB are similar.

Therefore,

CE/CB = DE/AB = DC/AC

⇒ CE/CB = DC/AC

⇒ 2/CB = 2.4/3.6

⇒ CB = (3.6/2.4)X2 = 3

Hence CB = 3

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Acute angle ⇒ 0⁰ < m < 90⁰

Straight angle ⇒  m = 180⁰

Obtuse angle ⇒ 90⁰ < m < 180⁰

Right angle ⇒ m = 90⁰

An obtuse angle is an angle that measures greater than 90 degrees but less than 180 degrees. In other words, an obtuse angle is an angle that is wider than a right angle (90 degrees), but not as wide as a straight angle (180 degrees).

When two rays or line segments intersect at a point, they form an angle. If the angle formed is less than 90 degrees, it is called an acute angle. If the angle is exactly 90 degrees, it is called a right angle.

If the angle is greater than 90 degrees but less than 180 degrees, it is called an obtuse angle. Finally, if the angle measures exactly 180 degrees, it is called a straight angle.

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"Based on the data Stephanie collected, the best conclusion she can make is that her commute time varies between walking from home to work and walking from work to home."

Stephanie recorded the time it took for her to walk from home to work and from work to home. The recorded times for walking from home to work are 15, 16, 18, 20, and 21 minutes. The recorded times for walking from work to home are 14, 21, 21, 25, and 27 minutes.

From the given data, we can see that Stephanie's commute time is not consistent. The time it takes for her to walk from home to work varies between 15 and 21 minutes, and the time it takes for her to walk from work to home varies between 14 and 27 minutes. There is no clear pattern or trend in the data.

Therefore, the best conclusion Stephanie can make is that her commute time fluctuates, and it is not fixed or predictable. The specific duration of her commute can vary from day to day.

In conclusion, Stephanie's commute time varies between walking from home to work and walking from work to home, as indicated by the range of recorded times for each direction.

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The distance from point A to point B is approximately 13706.2 feet. Rounded to the nearest tenth of a foot, this is 164474.4 inches or 13706.2 / 12 ≈ 1142.2 feet.

Let's first draw a diagram to visualize the situation:

           Lighthouse

                |

                |  x

                |

                |

          A ------------ B

                y

In the diagram, A is the starting point of the boat, B is the point where the crew measures the angle of elevation to be 6 degrees, and Lighthouse is the location of the lighthouse. We are looking for the distance AB.

From point A, we can use the tangent of the angle of elevation to find the height of the lighthouse beacon above sea level:

tan(15°) = height / 1433 feet

height = 1433 feet * tan(15°) ≈ 383.6 feet

Similarly, from point B, we can find the height of the lighthouse beacon above sea level:

tan(6°) = height / (1433 feet + AB)

height = (1433 feet + AB) * tan(6°)

Now we can set these two expressions for height equal to each other, since they represent the same height:

1433 feet * tan(15°) = (1433 feet + AB) * tan(6°)

Multiplying both sides by the denominator of the right-hand side, we get:

1433 feet * tan(15°) = 1433 feet * tan(6°) + AB * tan(6°)

Subtracting 1433 feet * tan(6°) from both sides, we get:

AB * tan(6°) = 1433 feet * (tan(15°) - tan(6°))

Dividing both sides by tan(6°), we get:

AB = 1433 feet * (tan(15°) - tan(6°)) / tan(6°) ≈ 13706.2 feet

Therefore, the distance from point A to point B when rounded to the nearest tenth of a foot, this is 164474.4 inches or 13706.2 / 12 ≈ 1142.2 feet.

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The length of the hypotenuse is approximately 7.21 ft.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). In mathematical terms, it looks like this:

a² + b² = c²

Where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.

In your case, we can substitute the given values into the equation:

6² + 4² = c²

Simplifying:

36 + 16 = c²

52 = c²

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

√(52) = c

We can simplify the square root of 52 to be 2 times the square root of 13. Therefore:

c ≈ 7.21 ft

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Complete Question:

Find the value of hypotenuse of the given triangle by using the Pythagoras theorem.

The area under the standard normal distribution curve between z = 0 and z = 0.98 is:

                         0.8365 - 0.5000 = 0.3365

To find the area under the standard normal distribution curve between z = 0 and z = 0.98, we can use a standard normal distribution table or a calculator that can compute normal probabilities.

Using a standard normal distribution table, we can look up the area corresponding to a z-score of 0 and a z-score of 0.98 separately and then subtract the two areas to find the area between them.

The area under the standard normal distribution curve to the left of z = 0 is 0.5000 (by definition). The area under the curve to the left of z = 0.98 is 0.8365 (from the standard normal distribution table).

So the area under the standard normal distribution curve between z=0 and z=0.98 is approximately 0.3365.

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The probability of 3 rainy days in a row when the probability of rain on each single day is 56% ≈ 17.6%

The probability of 3 sunny days in a row when the probability of rain on each single day is 56% ≈ 8.5%

To determine the probability of 3 rainy days in a row, you need to multiply the probability of rain on each single day (56%). In percent form, this would be:

56% × 56% × 56% = 0.56 × 0.56 × 0.56 ≈ 0.175616

To express this as a percentage rounded to the nearest tenth, we have:

0.175616 × 100% ≈ 17.6%

Now, to determine the probability of 3 sunny days in a row, you first need to find the probability of a sunny day, which is the complement of the probability of rain:

100% - 56% = 44%

Next, multiply the probability of a sunny day (44%) for three days:

44% × 44% × 44% = 0.44 × 0.44 × 0.44 ≈ 0.085184

To express this as a percentage rounded to the nearest tenth, we have:

0.085184 × 100% ≈ 8.5%

So, the probability of 3 rainy days in a row is approximately 17.6%, and the probability of 3 sunny days in a row is approximately 8.5%.

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Answer:

y = 8 - 4x

" is" is express the equal sighn

"less than" express - sighn so you will write the equestion as

y = 8 - 4x

Frank needs to pay $233.10 for each installment.

To determine how much Frank still owes on the refrigerator after paying the down payment. We can subtract the down payment from the total cost of the refrigerator:

Total cost of refrigerator = $1036

Down payment = $103.60

Amount owed = Total cost of refrigerator - Down payment

Amount owed = $1036 - $103.60

Amount owed = $932.40

Next, we need to determine how much Frank will pay for each installment. Since he will pay the remaining balance in 4 equal installments, we can divide the amount owed by 4:

Amount owed = $932.40

Number of installments = 4

Amount per installment = Amount owed / Number of installments

Amount per installment = $932.40 / 4

Amount per installment = $233.10

Therefore, Frank needs to pay $233.10 for each installment to fully pay off the refrigerator. By breaking down the cost into smaller payments, Frank can manage his budget more effectively and avoid the burden of making a large payment all at once.

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The minimum and maximum measurements taken by Joshua is 44.5 inches and 45.5 inches, under the condition that Joshua is building a model airplane that measures 45 inches.

Now in order to find the scale factor necessary to find the minimum and maximum measurements of Joshua's model airplane, we have to apply the given information.
The given information include that the difference in measurements of the model vary by 0. 5 inches.
Therefore,
Minimum measurement = 45 - 0.5 = 44.5 inches
Maximum measurement = 45 + 0.5 = 45.5 inches

Hence, the minimum measurement is 44.5 inches and the maximum measurement is 45.5 inches.

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$750 was withheld from my pay after deductions form the gross pay

Gross pay is the money that an employee gets before tax and other deduction are made

Net pay is the amount of money given to am employee after deduction of tax and other mandatory expenses

The gross pay is $2,500

The net pay is $1,750

The money withheld can be calculated as follows

= 2500 - 1750

= 750

The money withheld from the gross pay is $750

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To find the derivative of sin(y²)+x=eʸ using implicit differentiation, we need to differentiate both sides of the equation with respect to x.

Starting with the left side, we use the chain rule and the derivative of sin(u), which is cos(u) times the derivative of u with respect to x:

d/dx(sin(y²)) = cos(y²) * d/dx(y²)

Using the power rule, we get:

d/dx(y²) = 2y * d/dx(y)

Putting it all together:

d/dx(sin(y²)) = 2y * cos(y²) * d/dx(y)

Now let's move on to the right side of the equation. The derivative of implicit function eʸ with respect to x is simply eʸ times the derivative of y with respect to x:

d/dx(eʸ) = eʸ * d/dx(y)

Putting it all together, we have:

2y * cos(y²) * d/dx(y) + 1 = eʸ * d/dx(y)

We can now solve for d/dx(y):

d/dx(y) = (1 - 2y * cos(y²)) / eʸ

Therefore, the derivative of sin(y²)+x=eʸ is:

d/dx(y) = (1 - 2y * cos(y²)) / eʸ.

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Answer:

The speed of the ship =21 km/h

Speed of the current = 3 km/h

Step-by-step explanation:

Let's denote the speed of the ship in still water as s and the speed of the current as c.

When the ship is traveling with the current, the effective speed is (s + c). (we have to sum up both the speeds) Therefore, in 3 hours, the ship can travel a distance of:

distance = speed × time = (s + c) × 3

We know that this distance is 72 km, so we can write:

(s + c) × 3 = 72

Simplifying this equation, we get:

s + c = 24

Similarly, when the ship is traveling against the current, the effective speed is (s - c). (The difference between the speeds). Therefore, in 4 hours, the ship can travel a distance of:

distance = speed × time = (s - c) × 4

We know that this distance is also 72 km, so we can write:

(s - c) × 4 = 72

Simplifying this equation, we get:

s - c = 18

We now have two equations:

s + c = 24 ; s - c = 18

We can solve for s and c by adding these two equations:

2s = 42

Therefore, s = 21 km/h.

Substituting this value of s into one of the equations above, we can solve for c:

s + c = 24

21 + c = 24

c = 3 km/h.

Therefore, the speed of the ship in still water is 21 km/h, and the speed of the current is 3 km/hs

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Using the Adjusted Balance Method:

Interest: $4.15

New Balance: $569.15

To calculate the interest and new balance using the Adjusted Balance Method, we need to first find the adjusted balance.

This method takes the previous balance, adds the purchases made before the payment, and then subtracts the payment.

Here's the calculation:

Calculate the adjusted balance:

Previous balance: $500

Purchases before May 20: $25 (May 12)

Subtotal: $525

Payment: $110

Adjusted balance: $525 - $110 = $415

Calculate the interest:

Interest rate: 1% per month

Interest: $415 * 1% = $4.15

Calculate the new balance:

Adjusted balance: $415

Purchases after May 20: $100 (May 22) + $50 (May 30) = $150

Interest: $4.15

New balance: $415 + $150 + $4.15 = $569.15

So, using the Adjusted Balance Method:

Interest: $4.15

New Balance: $569.15

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Answer:Blue one.71.82

Step-by-step explanation:

6.3*11.4=71.82

Answer:

71.82 I think

Step-by-step explanation:

The parameters of the function S(t)=31,500(1.034)t are the initial number of digital subscriptions, which is 31,500, and the monthly growth rate, which is 3.4%.

The given function S(t)=31,500(1.034)t is a exponential growth function that models the number of digital subscriptions S as a function of t months after the launch of the advertising campaign. The parameters of the function are the initial number of digital subscriptions, which is 31,500, and the monthly growth rate, which is 3.4%.

The initial value of 31,500 represents the number of digital subscriptions at the start of the advertising campaign. This means that the campaign began with 31,500 digital subscribers.

The monthly growth rate of 3.4% represents the rate at which the number of digital subscriptions is increasing each month due to the advertising campaign. This means that for each month after the launch of the campaign, the number of digital subscribers is increasing by 3.4% of the previous month's total.

For example, after one month, the number of digital subscribers would be:

S(1) = 31,500(1.034)1 = 32,687

After two months, the number of digital subscribers would be:

S(2) = 31,500(1.034)2 = 33,912

And so on...

Therefore, the initial value and monthly growth rate are important parameters that help us understand how the number of digital subscriptions is changing over time due to the advertising campaign.

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The expression that represents the change in Emilio's savings each week is $7.50.

Emilio saving 25% of the money he earns babysitting, which means that he saves a quarter of his earnings. This can be expressed mathematically as:

savings = 0.25 x earnings

where "savings" is the amount Emilio saves and "earnings" is the amount he earns each week.

Substituting the given value of Emilio's average weekly earnings of $30, we get:

savings = 0.25 x $30

savings = $7.50

Therefore, Emilio saves $7.50 each week.

Since the question asks for the change in Emilio's savings each week, the expression that represents this is simply:

$7.50

This means that Emilio's savings increase by $7.50 each week.

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The monthly payment for a new car priced at $29,950 with financing the 8% TT&L and making a 25% down payment at a current finance rate of 3.16% for 36 months is approximately $698.62.

How to find calculate the monthly payment?

To calculate the monthly payment for a new car priced at $29,950 with the current finance rate of 3.16% for 36 months, we need to consider several factors, including the down payment and taxes.

First, we need to calculate the total cost of the car, including the taxes, title, and license (TT&L) fees. We can do this by adding 8% of the car's price ($29,950) to the price of the car, which comes to $32,346 ($29,950 + 8% of $29,950).

Next, we need to calculate the amount of the down payment. A 25% down payment on $32,346 comes to $8,086.50 ($32,346 x 0.25).

Subtracting the down payment from the total cost of the car gives us the amount we need to finance, which is $24,259.50 ($32,346 - $8,086.50).

Now, we can use a loan calculator to determine the monthly payment. Based on these figures, the monthly payment would be approximately $698.62 per month for 36 months.

In summary, to calculate the monthly payment for a new car priced at $29,950 with the current finance rate of 3.16% for 36 months, we need to consider the total cost of the car, including taxes and fees, the down payment, and the amount to be financed. The monthly payment is then calculated using a loan calculator, which gives us a monthly payment of $698.62 for 36 months.

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Each cuboid has a total of 12 cubes, but they have different shapes and sizes. The table is attached below.

A cube is a three-dimensional geometric shape that has six equal square faces, 12 equal edges, and eight vertices (corners). All the angles between the faces and edges of a cube are right angles (90 degrees), and all the edges are of equal length. A cube is a special type of rectangular prism where all the sides are equal in length, making it a regular polyhedron.

Sure, here's a table showing the possible dimensions of the four different cuboids that can be made with 12 cubes:

Cuboid Length Width Height

A                1       2 6

B                1       3 4

C                2       2 3

D                1        1 12

Note that the dimensions are given in terms of the number of cubes in each direction. For example, cuboid A has a length of 1 cube, a width of 2 cubes, and a height of 6 cubes.

Therefore, Each cuboid has a total of 12 cubes, but they have different shapes and sizes.

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The range of costs that Kenny could spend on his last gift would be any amount less than or equal to $33.03. So the range would be: $0 ≤ x ≤ $33.03

To determine the range of costs Kenny could spend on the last gift, we'll first calculate the total amount he has spent so far and subtract that from the $150 he started with.

Kenny has spent $68.99 (watch) + $38.99 (arrows) + $8.99 (lunch) = $116.97.

Now, let x represent the cost of the last gift. The inequality to represent the situation is:

116.97 + x ≤ 150

To find the range of costs for the last gift, subtract 116.97 from both sides of the inequality:

x ≤ 150 - 116.97
x ≤ 33.03

So, the range of costs Kenny could spend on the last gift is $0 to $33.03.

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The equation of the line that is parallel to the graph of 2x-3y=7 and contains the point (-3, -3) is expressed as: y = (2/3)x - 1.

To find the equation of a line that is parallel to the graph of 2x - 3y = 7, we need to determine the slope of the given line. We can rewrite the equation in slope-intercept form:

2x - 3y = 7

-3y = -2x + 7

y = (2/3)x - 7/3

This implies that the slope of this line is m = 2/3.

Thus, the equation of the line we are to find will take the following form:

y = (2/3)x + b

where b is the y-intercept of the line.

To find the y-intercept (b), substitute (x, y) = (-3, -3) and m = 2/3 into y = mx + b:

-3 = (2/3)(-3) + b

-3 = -2 + b

b = -1

Substitute m = 2/3 and b = -1 into y = mx + b:

y = (2/3)x - 1

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Answer:

Radius = 18 m

Step-by-step explanation:

Given:

Diameter = 36 m

To find:

Radius

Explanation:

We know that,

Radius = Diameter/2 = 36/2 = 18 m

Final Answer:

18 m