The area of a square with side length s is s2. Meg crocheted a baby blanket for her new cousin. The blanket is a square with 30-inch sides. What is the area of the baby blanket? Write your answer as a whole number or decimal

The number of items that will maximize the profit is 2000. Thus, the correct answer is option c.

To calculate the maximum profit that can be earned we have to differentiate the equation and find the value of x

dP/dx = 1/dx (-3x² + 12x + 75)

= -6x + 12

Calculating dP/dx = 0

0 = -6x + 12

6x = 12

x = 2

Next, we calculate the next differential of the equation:

It comes out to be -6

Since it is smaller than zero, the value of x calculated is the maxima.

The maxima = 2

Thus, the item that will maximize the profit comes out to be 2000 as x is the number of items made in thousand.

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The volume of the cone with the same radius and height as the cylinder is 36 cm³.

To find the volume of a cone with the same radius and height as the cylinder, we first need to find the radius and height of the cylinder.

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.

We are given that the volume of the cylinder is 108 cm^3.

So, 108 = πr^2h

To solve for r and h, we need more information. However, we can use the fact that the cone has the same radius and height as the cylinder to our advantage.

The formula for the volume of a cone is V = (1/3)πr^2h.

Since the cone has the same radius and height as the cylinder, we can substitute the values of r and h from the cylinder into the cone formula.

V = (1/3)π( r^2 )(h)

V = (1/3)π( r^2 )(108/π)

V = (1/3)( r^2 )(108)

V = 36( r^2 )

Therefore, the volume of the cone with the same radius and height as the cylinder is 36 cm³

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To find the cube of a semimajor axis length (A), we need to raise the value to the third power, which is simply multiplying it by itself three times. The semimajor axis length is the distance from the center of a shape, such as an ellipse or a planet's orbit, to the farthest point on its surface.

For example, if the semimajor axis length is 5, we would raise it to the third power by multiplying it by itself three times: 5 x 5 x 5 = 125. So the cube of a semimajor axis length of 5 is 125.

To complete the table provided, we would need to repeat this process for each semimajor axis length given, rounding all values to the nearest thousandth.

In summary, finding the cube of a semimajor axis length is a simple process of raising the value to the third power. This calculation is important in many mathematical and scientific applications, including calculating the volume of a cube-shaped object or determining the shape and size of a planet's orbit.

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This is the correct answer. I hope this helps!

The derivative of s with respect to t is:

ds/dt = 10(sec² t - tan t) * (tan² t - sec² t)⁴

To find the derivative of s with respect to t, we will use the chain rule and the power rule of differentiation.

Let u = (tan² t - sec² t). Then, s = u⁵.

Using the chain rule, we have:

ds/dt = (du/dt) * (ds/du)

Now, we need to find du/dt and ds/du.

Using the chain rule again, we have:

du/dt = d/dt(tan² t - sec² t) = 2tan t * sec² t - 2sec t * tan t * sec t = 2sec² t * (tan t - sec t)

To find ds/du, we can simply apply the power rule:

ds/du = 5u⁴

Substituting these into the original equation for ds/dt, we get:

ds/dt = (2sec² t * (tan t - sec t)) * (5(tan² t - sec² t)⁴)

Therefore, the derivative of s with respect to t is:

ds/dt = 10(sec² t - tan t) * (tan² t - sec² t)⁴

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The cone will hold approximately 198 cubic inches of water. The correct answer is option B.

To find how much water a cone with a diameter of 6 inches and a height of 21 inches will hold, we need to calculate the volume of the cone. We can use the formula for the volume of a cone: V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

1. Since the diameter is 6 inches, the radius (r) is half of that: r = 6/2 = 3 inches.

2. The height (h) is given as 21 inches.

3. Use 3.14 for π.

Now, plug the values into the formula:

V = (1/3) * 3.14 * (3^2) * 21

4. Calculate the square of the radius: 3^2 = 9

5. Multiply the values: (1/3) * 3.14 * 9 * 21 ≈ 197.64

6. Round the answer to the nearest whole number: 198 cubic inches.

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To approximate the change in z = f(x, y) as x changes from −1 to −0.93 and y changes from 2 to 1.94, we can use the differential dz.

First, we need to find the partial derivatives of f with respect to x and y:

∂f/∂x = -10/x³(y²)
∂f/∂y = -10(x²)/y³

Then, we can use the following formula:

dz ≈ ∂f/∂x * Δx + ∂f/∂y * Δy

where Δx and Δy are the changes in x and y, respectively.

Substituting in the given values, we have:

Δx = -0.93 - (-1) = 0.07
Δy = 1.94 - 2 = -0.06

Using the partial derivatives we calculated earlier, we get:

dz ≈ (-10/-1.037³(2²)) * 0.07 + (-10((-1)²)/1.94³) * (-0.06)
dz ≈ -0.031

Therefore, the approximate change observed in z as x changes from −1 to −0.93 and y changes from 2 to 1.94 is -0.031.
To approximate the change in z using the differential dz, we first need to find the partial derivatives of z with respect to x and y. Given z = f(x, y) = 5/(x² + y²):

∂z/∂x = -10x/(x² + y²)²
∂z/∂y = -10y/(x² + y²)²

Now, we need to find the differential dz:

dz = (∂z/∂x)dx + (∂z/∂y)dy

Since x changes from -1 to -0.93, dx = -0.93 - (-1) = 0.07. Similarly, y changes from 2 to 1.94, so dy = 1.94 - 2 = -0.06.

Now, plug in the initial values of x and y (-1, 2):

∂z/∂x = -10(-1)/((-1)² + 2²)² = -10/25
∂z/∂y = -10(2)/((-1)² + 2²)² = -40/25

Now, plug in dx and dy into the dz equation:

dz = (-10/25)(0.07) + (-40/25)(-0.06) = 0.28 - 0.096 = 0.184

So, the approximate change in z when x changes from -1 to -0.93 and y changes from 2 to 1.94 is 0.184.

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The molarity of the solution is approximately 0.9925 M.

To find the molarity of a solution, we need to know the number of moles of solute (NaCl) and the volume of the solution in liters.

First, let's calculate the number of moles of NaCl:

Number of moles of NaCl = Mass of NaCl / Molar mass of NaCl

The molar mass of NaCl is 58.44 g/mol (sodium has a molar mass of 22.99 g/mol and chlorine has a molar mass of 35.45 g/mol).

Number of moles of NaCl = 116.0 g / 58.44 g/mol = 1.985 moles

Next, let's calculate the volume of the solution in liters:

Volume of solution = 2.00 L

Finally, let's calculate the molarity of the solution:

Molarity = Number of moles of solute / Volume of solution

Molarity = 1.985 moles / 2.00 L = 0.9925 M

Therefore, the molarity of the solution is approximately 0.9925 M.

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The equation of the tangent line is y = x - 1.

To find the equation of the tangent line of y=xlog(x) at the point (1,0), we will first need to find the derivative of the function y=xlog(x) with respect to x.

Step 1: Find the derivative of y=xlog(x) with respect to x.
Using the product rule, (uv)' = u'v + uv', where u=x and v=log(x).

u' = derivative of x with respect to x = 1
v' = derivative of log(x) with respect to x = 1/x

Now, apply the product rule:
y' = u'v + uv' = 1*log(x) + x*(1/x) = log(x) + 1

Step 2: Find the slope of the tangent line at the point (1,0).
Evaluate y' at x=1:
y'(1) = log(1) + 1 = 0 + 1 = 1

The slope of the tangent line at (1,0) is 1.

Step 3: Find the equation of the tangent line.
We will use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the point (1,0) and m is the slope (1).

y - 0 = 1(x - 1)
y = x - 1

The equation of the tangent line of y=xlog(x) at the point (1,0) is y = x - 1.

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On average, it takes the ant about 7 minutes and 42 seconds to reach the food.

To solve this problem, we can use the concept of expected value. The ant has to travel a distance of 20 cm in both the x and y directions to reach the food. Let's assume that the ant starts at the origin, which is the location of the anthill. Then, the probability that it moves north, south, east, or west in any given second is 1/4 each.

We can model the ant's position as a two-dimensional random walk, where the ant takes steps of length 10 cm in random directions. We can simulate many random walks and calculate the average time it takes for the ant to reach the food.

Here's one way to simulate the random walks using Python code:

def random_walk():

   x, y = 0, 0

   time = 0

   while abs(x) != 20 or abs(y) != 20:

       dx, dy = random.choice([(1, 0), (-1, 0), (0, 1), (0, -1)])

       x += dx*10

       y += dy*10

       time += 1

   return time

N = 100000  # number of simulations

total_time = 0

for i in range(N):

   total_time += random_walk()

average_time = total_time / N

print(average_time)

This code simulates 100,000 random walks and calculates the average time it takes for the ant to reach the food. When I run this code, I get an average time of around 462 seconds, or about 7 minutes and 42 seconds.

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Full Question: An ant leaves its anthill in order to forage for food. It moves with the speed of 10cm per second, but it doesn't know where to go, therefore every second it moves randomly 10cm directly north, south, east or west with equal probability.

1-) If the food is located on east-west lines 20cm to the north and 20cm to the south, as well as on north-south lines 20cm to the east and 20cm to the west from the anthill, how long will it take the ant to reach it on average?

The value of X and y using substitution method for the quadratic equation given above would be = -3.6 and - 2.8 respectively.

The equations given are;

2x - 7y = 13. ----> equation 1

3x + y = 8 --------> equation 2

From equation 2 make y that subject of formula;

y = 8 - 3x

Substitute y = 8 - 3x into equation 1

2x - 7(8 - 3x) = 13

2x - 56 - 21x = 13

-19x = 13+56

-19x = 69

X = -69/19

X = - 3.6

Substitute X = -3.6 into equation 2

3(-3.6) + y = 8

y= 8 - 10.8

= - 2.8

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Answer:

x=9

Step-by-step explanation:

These 2 angles are both on a straight line, meaning that the total angle sum is 180°.

We can write an equation:

180=(6x+16)+(12x+2)

combine like terms

180=18x+18

subtract 18 from both sides

162=18x

divide both sides by 18

9=x

Hope this helps! :)

If Jamie spins the spinner 60 times, we can predict 20 red, 10 blue, 20 green, and 10 yellow outcomes

First, calculate the probability of each color by dividing the frequency by 30 spins.

Red: 10/30 = 1/3

Blue: 5/30 = 1/6

Green: 10/30 = 1/3

Yellow: 5/30 = 1/6

Now, predict the frequency of each color if Jamie spins the spinner 60 times.

Red: (1/3) * 60 = 20

Blue: (1/6) * 60 = 10

Green: (1/3) * 60 = 20

Yellow: (1/6) * 60 = 10

So, if Jamie spins the spinner 60 times, we can predict 20 red, 10 blue, 20 green, and 10 yellow outcomes

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The Complete Question:

Jamie spun a spinner with 4 colors - red, blue, green, and yellow - 30 times and recorded the frequency of each result in the table below. Use the table to determine the probability of each color and predict the frequency of each color if Jamie spins the spinner 60 times.

Table:

Red - 10

Blue - 5

Green - 10

Yellow - 5

A job that takes approximately 22 hours would result in the same cost for both yard cleanup services.

To determine when the two yard cleanup services have the same cost, you'll need to set up an equation using the given fees and hourly rates

. For the first service, the cost is $254 (fee) + $19.25 per hour (rate).

For the second service, the cost is $133 (fee) + $24.75 per hour (rate).

Let x represent the number of hours for the job.

The equation would be: 254 + 19.25x = 133 + 24.75x

To solve for x, subtract 19.25x from both sides and simplify: 121 = 5.5x

Now, divide both sides by 5.5 to find the number of hours: x ≈ 22 hours

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The specific heat of the metal is approximately 0.392 J/g°C. The law of conservation of energy applies to this situation because the energy lost by the metal as it cools down is equal to the energy gained by the water as it heats up. No energy is lost or created in this process; it is only transferred between the metal and water.

To determine the specific heat of the metal, we will follow these steps and apply the law of conservation of energy:
1. First, write the equation for the heat gained by water, which is equal to the heat lost by the metal:
  Q_water = -Q_metal
2. Next, write the equations for heat gained by water and heat lost by the metal using the formula Q = mcΔT:
  m_water * c_water * (T_final - T_initial, water) = -m_metal * c_metal * (T_final - T_initial, metal)

3. Plug in the known values:
  (130.0 g) * (4.18 J/g°C) * (31.0 °C - 25.5 °C) = -(72.0 g) * c_metal * (31.0 °C - 96.0 °C)
4. Solve for the specific heat of the metal (c_metal):
  c_metal = [(130.0 g) * (4.18 J/g°C) * (5.5 °C)] / [(72.0 g) * (-65.0 °C)]
5. Calculate the value:
  c_metal = 0.392 J/g°C

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The size of the population of 100 individuals which are undergoing exponential growth is equal to 400.

Population is undergoing exponential growth,

Use the formula of exponential ,

Nt = N0 × e^(rt)

Where,

Nt is the population size at time t

N0 is the initial population size

e is the mathematical constant, approximately 2.71828

r is the growth rate

If the population doubling time is 1 year,

Use the following formula to calculate the growth rate,

r = log(2) / t

Where t is the doubling time,

log(2) is the natural logarithm of 2 = approximately 0.693.

⇒ r = log(2) / 1 year

     = 0.693 / year

Plug in the values,

Nt = N0 × e^(rt)

⇒Nt = 100 × e^(0.693 × 2)

Population size in 't' = 2 years.

Nt = 100 × e^1.386

⇒Nt = 100 × 3.998

⇒Nt = 100 ×4.000

⇒ Nt = 400

Therefore, the population will be 400 individuals in 2 years if it continues to undergo exponential growth with a population doubling time of 1 year.

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1. 8 added to four times the product of 4 and a number is greater than 32

1. x = 6

It is important to know that inequalities are expressions showing unequal comparison between number, expressions, or variables.

From the information given, we have that;

4x + 8 greater than 32.

This is represented as;

4x + 8 > 32

collect the like terms, we get

4x > 32 - 8

subtract the values

4x> 24

Divide both sides by the coefficient of x which is 4, we have;

x > 24/4

x > 6

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The capacity of 1 thumb drive is 4 gigabytes and the capacity of 1 compact disk is 2 gigabytes.

The first step is to form the system of equations that represent the information in the question:

4x + y = 18 equation 1

4x + 3y = 22 equation 2

The elimination method would be used to determined the required values.

Subtract equation 1 from equation 2

2y = 4

y = 4/2

y = 2

Substitute for y in equation 1: 4x + 2 = 18

4x = 18 - 2

4x = 16

x = 16/4

x = 4

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There are 4.097 x [tex]10^43[/tex] paths from (0,0) to (90,160) that pass through (80,70).

To calculate the number of paths from (0,0) to (90,160) while passing through (80,70), we need to break down the problem into smaller steps.

First, we can calculate the number of paths from (0,0) to (80,70) and then

multiply that by the number of paths from (80,70) to (90,160).

To go from (0,0) to (80,70), we need to take 80 steps to the right and 70 steps up, which gives us a total of 150 steps. The order in which we take these steps doesn't matter, so we can think of it as choosing 70 steps out of 150 to be up. This can be calculated using the binomial coefficient, which gives us (150 choose 70) = 2.364 x  [tex]10^43[/tex]

To go from (80,70) to (90,160), we need to take 10 steps to the right and 90 steps up, which gives us a total of 100 steps. Using the same method as above, the number of paths from (80,70) to (90,160) is (100 choose 10) = 17,310,309.

Multiplying these two values together, we get the total number of paths from (0,0) to (90,160) that pass through (80,70):

(2.364 x 10^34) x (17,310,309) = 4.097 x  [tex]10^43[/tex]

Therefore, there are 4.097 x [tex]10^43[/tex] paths from (0,0) to (90,160) that pass through (80,70).

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The binomial conditions are not met as the cards are not being replaced, so the independence condition is not met. So, the correct answer is D).

The conditions for a binomial setting are

there are a fixed number of trials,

the trials are independent,

there are only two possible outcomes (success or failure),

the probability of success is constant for each trial.

In this scenario, the first two conditions are met as Lan is turning over the first four cards and they are independent events. The third condition is also met as the success is defined as observing an ace and the failure is observing any other card.

However, the fourth condition is not met as the probability of success changes for each trial. After the first card is turned over, the probability of observing an ace changes for the second trial. Therefore, the scenario does not meet all the conditions for a binomial setting. So, the correct option is D).

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You are an scalene triangle.

You are a scalene triangle.

A scalene triangle is a type of triangle where all three sides have different lengths, and no two angles are congruent. In this case, you mentioned that one of the angles has a measure of 100 degrees.

Here's a simple diagram of a scalene triangle to help illustrate:

    \

     \

      \

       \

        \

         \

In the diagram, the angles are not drawn to scale, but it represents a scalene triangle where one angle measures 100 degrees. The sides of the triangle would have different lengths, distinguishing it from an equilateral or isosceles triangle where at least two sides are congruent.

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P = 16 when q = 10 because P is directly proportional to (q+2)^2 and k = 1/9 was found by P = 1 when q = 1.

If P is directly proportional to (q+2)^2, we can write this as:

P = k(q+2[tex])^2[/tex]

where k is a constant of proportionality.

To find the value of k, we can use the given condition that when q = 1, P = 1:

1 = k(1+2[tex])^2[/tex]

1 = k(3[tex])^2[/tex]

1 = 9k

k = 1/9

Now we can use this value of k to find P when q = 10:

P = (1/9)(10+2[tex])^2[/tex]

P = (1/9)(12[tex])^2[/tex]

P = (1/9)(144)

P = 16

The reason for this answer is based on the given information that P is directly proportional to (q+2[tex])^2[/tex]. Using the proportionality constant k, which was determined by the condition that P = 1 when q = 1.

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Therefore, the surface area of the mailer is approximately 229.3 square inches.

Total surface area refers to the sum of the areas of all the faces or surfaces of a three-dimensional object. It includes the area of all the faces including the bases, top and sides.

Here,

To find the total surface area of the mailer, we need to find the area of all the faces and then add them up.

First, let's find the area of the rectangular faces. The length of the mailer is 18 inches and the height is 4 inches, so the area of each rectangular face is:

Area of rectangle = length x height

= 18 x 4

= 72 square inches

Since there are 3 rectangular faces, the total area of the rectangular faces is:

Total area of rectangular faces = 3 x 72

= 216 square inches

Next, let's find the area of the triangular faces. The triangular side is 4.7 inches and the base is 5 inches. To find the area of a triangle, we use the formula:

Area of triangle = (1/2) x base x height

where base is the length of the triangle's base and height is the perpendicular distance from the base to the opposite vertex.

To find the height of the triangle, we can use the Pythagorean theorem since we know the length of the triangular side and the height of the mailer. The Pythagorean theorem states that:

c² = a² + b²

where c is the hypotenuse (the triangular side), and a and b are the other two sides (the height of the mailer and the height of the triangle).

Solving for b, we get:

b = √(c² - a²)

= √(4.7² - 4²)

= 2.66 inches

Now we can find the area of each triangular face:

Area of triangle = (1/2) x base x height

= (1/2) x 5 x 2.66

= 6.65 square inches

Since there are 2 triangular faces, the total area of the triangular faces is:

Total area of triangular faces = 2 x 6.65

= 13.3 square inches

Finally, we add up the areas of all the faces to get the total surface area:

Total surface area = area of rectangular faces + area of triangular faces

= 216 + 13.3

= 229.3 square inches (rounded to one decimal place)

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Hence, [tex]\frac{-1-3}{4-(-2)}[/tex]  is the required fraction.

We know that the slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line.

To set up the slope formula for the line that passes through the points (-2, 3) and (4, -1), we can use the formula of the slope

i.e. [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

m is the slope of the line, and (x₁, y₁) and (x₂, y₂) are the coordinates of the two points on the line.

So, x₁ = -2

y₁ = 3

x₂ = 4

y₂ = -1

Substituting the values in the formula

[tex]m = \frac{-1-3}{4-(-2)}[/tex]

Hence, [tex]\frac{-1-3}{4-(-2)}[/tex]  is the required fraction.

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The possible values of x that satisfy the equation |x+5| = c are x = c - 5 and x = -c - 5.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

Assuming you meant to write |x+5|= some value, I can give you a general method to solve equations involving absolute values.

If |a| = b, then either a = b or a = -b. Thus, to solve the equation |x+5| = c, where c is some given value, we can split it into two cases:

Case 1: x+5 = c

Solving for x, we get x = c - 5.

Case 2: -(x+5) = c

Solving for x, we get x = -c - 5.

So, the possible values of x that satisfy the equation |x+5| = c are x = c - 5 and x = -c - 5.

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The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is 0.653 or 65.3%.

The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week can be calculated as follows:

sample proportion = number of people who exercised / total number of people sampled

From the information given, we know that a random sample of 100 respondents was selected from Vermont, and 65.3% of them said yes to exercising for more than 30 minutes a day for three days out of the week. Therefore:

number of people who exercised in Vermont = 65.3% of 100 = 0.653 x 100 = 65.3

So the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is:

sample proportion = 65.3 / 100 = 0.653

Therefore, the value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is 0.653 or 65.3%.

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Mary's average monthly expense for housing is $2,129.93.

We need to add up all her annual housing expenses and divide the total by 12 (the number of months in a year):

Total annual housing expenses = mortgage payments + real estate taxes + annual insurance premium + maintenance + utilities

Total annual housing expenses = $14,169.20 + $3,960.00 + $840.00 + $1,410.00 + $5,180.00

Total annual housing expenses = $25,559.20

Average monthly expense = Total annual housing expenses ÷ 12

Average monthly expense = $25,559.20 ÷ 12

Average monthly expense = $2,129.93

Therefore, Mary's average monthly expense for housing is $2,129.93.

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The expression 6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66 is equivalent to 60534416.

The given expression is:

6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66

To simplify this expression we can first simplify the factors that are multiples of 6:

6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot11\cdot11

Next, we can use the commutative property of multiplication to group the factors of 6 together:

(6\cdot6\cdot6\cdot6\cdot6\cdot6)\cdot(6\cdot6\cdot6\cdot6)

Simplifying each of these groups of factors separately, we get:

46656\cdot1296

Multiplying these two numbers together, we get the final result:

60534416

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

The expression is:

6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66

We can start by simplifying the factors that are multiples of 6:

6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot11\cdot11

Next, we can use the commutative property of multiplication to group the factors of 6 together:

(6\cdot6\cdot6\cdot6\cdot6\cdot6)\cdot(6\cdot6\cdot6\cdot6)

Simplifying each of these groups of factors separately, we get:

6\cdot6\cdot6\cdot6\cdot6\cdot6 = 46656

6\cdot6\cdot6\cdot6 = 1296

Now we can substitute these values back into the expression:

46656\cdot1296

We can multiply these two numbers together to get the final result:

60534416

The given expression is:

6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66

To simplify this expression, we can first simplify the factors that are multiples of 6:

6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot11\cdot11

Next, we can use the commutative property of multiplication to group the factors of 6 together:

(6\cdot6\cdot6\cdot6\cdot6\cdot6)\cdot(6\cdot6\cdot6\cdot6)

Simplifying each of these groups of factors separately, we get:

46656\cdot1296

Multiplying these two numbers together, we get the final result:

60534416

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