What is an explicit formula for the sequence 0,3,8,15,24,...? What is the 20th term?​

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Hello!

A linear equation has the form y = ax +b.

We also can call it the slope-intercept form.

We have two points, that I will name 1 and 2:

• (x1, y1) = (3, 4)

• (x2, y2) = (8, 3)

The first step is to find the slope (variable a). We must use the formula below:

So, let's replace it with the values that we know:

Now we know variable a, we must find the variable b too. So, we can replace x and y in the equation with the coordinates of the point (x1, y1). Look:

So, the equation will be:

Look at the graph of this equation below:

Answer:

40

Step-by-step explanation:

To solve this question you will need to use BEDMAS which is the order of which numbers you have to solve first. In this case you need to solve the brackets first, then the exponent, and then lastly the addition.

 3^3 + 3(4 + 1/3)

= 3^3 + 3(13/3)

= 27 + 3 x 13/3

= 27 + 13

= 40

Answer:

19 and 21

Step-by-step explanation:

... 17, 18, 19 , 20, 21, 22, 23 ,24, 25

Step-by-step explanation:

The x-intercept of the line will be at (-4, 0).

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

We know that at x-intercept the value of the ordinate will be zero.

From the table, the intersection of the x-axis and line will be at (-4, 0).

Then the x-intercept of the line will be at (-4, 0).

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What the first person said

Answer:

Hi! The answer to your question is the range is 23

Step-by-step explanation:

Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is 62-39=23

VOCAB:

Minumum Data = Smallest Number

Maximum Data = Largest Number

Data Range = The set of y-values that a function passes through, Also the right coordinate in a coordinate pair.

In statistics, the difference between the largest number and the smallest numbers in a data set.

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Hope this helps!!

- Brooklynn Deka

First and foremost, it is important to note that human skin color is determined by a variety of factors, including genetics, environmental influences, and geographic location. In fact, skin color is the result of the amount and type of melanin pigment produced by specialized cells in the skin called melanocytes.

There are two main types of melanin pigment: eumelanin and pheomelanin. Eumelanin is responsible for producing darker skin colors, while pheomelanin produces lighter skin colors. However, the amount and distribution of these pigments can vary greatly between individuals, resulting in a wide range of skin tones.

Additionally, skin color can also be influenced by factors such as sun exposure, age, and hormonal changes. For example, prolonged sun exposure can lead to darker skin, while aging and hormonal changes can cause changes in skin pigmentation. Furthermore, it is important to note that skin color is not always clearly defined or easily categorized into specific shades. There can be a great deal of variation within a single skin tone, as well as overlap between different skin tones. This is due to the complex interplay of genetic and environmental factors that contribute to skin color.

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By applying the Mean Value Theorem, it can be concluded that Mike's claim of never exceeding 55 miles/hour cannot be supported.

x = -1 and x = 1 are the critical values.

According to the Mean Value Theorem, if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in the interval (a, b) where the instantaneous rate of change (the derivative) is equal to the average rate of change (the slope of the secant line between the endpoints).

In this case, if we consider the function f(x) = x^4 + 2x^2 - 3x^2 - 4x + 4, we can calculate the derivative as f'(x) = 4x^3 + 4x - 4. To find the critical values, we set f'(x) equal to zero and solve for x: 4x^3 + 4x - 4 = 0.

Solving this equation, we find that x = -1 and x = 1 are the critical values.

To determine the intervals where the function is increasing or decreasing, we can analyze the sign of the derivative.

By choosing test points within each interval, we find that f'(x) is negative for x < -1, positive for -1 < x < 1, and negative for x > 1. This means that the function is decreasing on the intervals (-∞, -1) and (1, +∞) and increasing on the interval (-1, 1).

Therefore, based on the analysis of critical values and the intervals of increase and decrease, we can conclude that the function f(x) does not support Mike's claim of never exceeding 55 miles/hour. The Mean Value Theorem states that if the function is continuous and differentiable, there must exist a point where the derivative is equal to the average rate of change. Since the function f(x) is not a linear function, its derivative can vary at different points, and thus, it is likely that the instantaneous rate of change exceeds 55 miles/hour at some point between the two hours of travel.

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The expression is simplified to give 2(9x + 2√3x - 5)

First, we need to know that surds are mathematical forms that can no longer be simplified to smaller forms

From the information given, we have that;

(2√3x - 2)(3√3x + 5)

expand the bracket, we get;

6√9x² + 5(2√3x) - 6√3x - 10

Find the square root factor

6(3x)  + 10√3x - 6√3x - 10

collect the like terms, we have;

18x + 4√3x - 10

Factorize the expression, we have;

2(9x + 2√3x - 5)

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98/100, 98%, 0.98                      

That's it.

The number of cases per batch that should be produced to minimize cost is: 300 units

The number of cases per batch that should be produced to minimize cost can be found by using the Economic Order Quantity.

The Economic Order Quantity (EOQ) is a calculation performed by a business that represents the ideal order size that allows the business to meet demand without overspending. The inventory manager calculates her EOQ to minimize storage costs and excess inventory.  

Thus:

Number of cases per batch = √((2 * Setup costs * annual demand)/ holding costs for the year)

Solving gives:

√((2 * 30 * 15000)/10)

= √90000

= 300 units

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The total length of the fence is 48 m if the rectangular swimming pool measures 7.5 m by 4.5 m.

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that:

A rectangular swimming pool measures 7.5 m by 4.5 m.

It is completely surrounded by a fence parallel to each edge of the pool and at a distance of 3 m from each edge of the pool.

The total length of the fence = 2(7.5+3×2 + 4.5+3×2)

The total length of the fence = 2(7.5+6 + 4.5+6)

The total length of the fence = 2(24)

The total length of the fence = 48 m

Thus, the total length of the fence is 48 m if the rectangular swimming pool measures 7.5 m by 4.5 m.

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Answer:

(2 + 6i)²

(2 + 6i)(2 + 6i)

2 + 12i + 12i -36

24i - 34

Answer:

No

Step-by-step explanation:

Jerry - 15 x 7 = 105

400 - 105 = 295

Jerry will have 295 in his account

Jack- 5 x 7 = 35

230 + 35 = 265

Jack will have 265 in his account

So no they will not have the same amount in both of their banks

Answer: The linear function is represented by f(x) = (4x/3) + 12

Step-by-step explanation: Taking a linear function's equation pattern to be the graph of y = ax + b, plot the sollutions for such:

(8) = (-3)a + b, and similarly: (-4) = 6a + b, solving for that will lead to a = (4/3) and b = (12), thus: f(x) = (4x/3) + 12.

The Missing number for each fraction is ---

a) 3/7 = 12/28

b)5/8 = 25/40

c)3/4 =12/16

d)7/3 = 14/6

Fraction:

A fraction (from Latin: fracturs, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples {1}/{2}} and ) consists of a numerator, displayed above a line (or before a slash like 1⁄2), and a non-zero denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.

Given that

a) \(\frac{3}{7}\) = 12/_

  let x

3/7 = 12/x

3x = 84

x = 28

3/7 = 12/28

b) x/8 = 25/40

40x = 200

x = 5

5/8 = 25/40

c)3/4 = x/16

4x =48

x =12

3/4 =12/16

d)7/x = 14/6

42 = 14x

x = 3

7/3 = 14/6

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Answer:

Suppose that the batch has N liters of paint.

we know that the recipe is:

1/2 of red paint

1/3 of yellow paint

1/6 of white paint.

Then, out of the N liters, 1/2 is red.

This means that we must use:

N/2 liters of red paint.

And the same for the other two colors:

N/3 liters of yellow paint

N/6 liters of white paint.

When we add those 3, we have:

(N/2 + N/3 + N/6)  = (3*N/6 + 2*N/6 + N/6) = N.

Now, if for example N = 2

Then the batch has 2 liters of paint, this would mean that we must use:

2/2 liters of red paint

2/3 liters of yellow paint

2/6 liters of white paint.

a. P(A) = 1/12, P(B) = 1/3, P(C) = 1/6 based on counting outcomes.

b. P(A|B) = 1/12, calculated using the definition of conditional probability.

c. P(B|C) = 1/3, calculated using the definition of conditional probability.

d. P(A|C) = 1/6, calculated using the definition of conditional probability.

e. A and B are not independent, B and C are not independent, A and C are independent based on the observations and calculations.

a. We have:

P(A): The only ways to get a sum of at least 10 are (4,6), (5,5), (6,4). Each of these outcomes has probability 1/36. So, P(A) = 3/36 = 1/12.

P(B): The only ways to get an odd sum are (1,2), (1,4), (1,6), (3,2), (3,4), (3,6), (5,2), (5,4), (5,6), (6,1), (6,3), (6,5). Each of these outcomes has probability 1/36. So, P(B) = 12/36 = 1/3.

P(C): The blue die has a probability of 1/6 of landing on 5, regardless of what the red die shows. So, P(C) = 1/6.

b. We have:

P(A|B) = P(A and B) / P(B)

To find P(A and B), we need to count the number of outcomes that satisfy both A and B. There are 6 outcomes that satisfy B: (1,2), (1,4), (1,6), (3,2), (3,4), and (5,4). Out of these, only (5,4) satisfies A as well. So, P(A and B) = 1/36.

Therefore, P(A|B) = (1/36) / (1/3) = 1/12.

c. We have:

P(B|C) = P(B and C) / P(C)

To find P(B and C), we need to count the number of outcomes that satisfy both B and C. There are only two such outcomes: (1,4) and (3,2). So, P(B and C) = 2/36 = 1/18.

Therefore, P(B|C) = (1/18) / (1/6) = 1/3.

d. We have:

P(A|C) = P(A and C) / P(C)

To find P(A and C), we need to count the number of outcomes that satisfy both A and C. Since C requires the blue die to show 5, there is only one outcome that satisfies both A and C: (5,5). So, P(A and C) = 1/36.

Therefore, P(A|C) = (1/36) / (1/6) = 1/6.

e. We have:

A and B are not independent, because knowing that the sum is odd affects the probability of the sum being at least 10 (it makes it impossible).

B and C are not independent, because knowing that the blue die shows 5 affects the probability of the sum being odd (it makes it even).

A and C are independent, because knowing that the blue die shows 5 does not affect the probability of the sum being at least 10.

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Answer: -5x=15

Step-by-step explanation:

f

Answer:

2.3

Step-by-step explanation:

Answer:

x = 0.05

x = 1.57

Step-by-step explanation:

The given equation is:

\(e^x-\ln 2x = 3.7\)

Moving all terms to the left side:

\(e^x-\ln 2x - 3.7=0\)

Now we define a function:

\(y=f(x)=e^x-\ln 2x - 3.7\)

The solutions of the equation are the values of x such that y=0.

Since the function cannot be solved by algebraic methods, we use a graphing tool.

Those points where the graph crosses the x-axis are solutions of the equation.

Please refer to the graph in the figure below.

We can clearly identify there are two solutions at

x = 0.05

x = 1.57

The solutions to \((x+5)^(3/2) = (x-1)^3\)are x ≈ -4.65 and x ≈ 0.51, obtained by graphing the functions in Desmos.

To solve \((x+5)^(3/2) = (x-1)^3\) by graphing, we can plot both sides of the equation on the same graph using a tool like Desmos. The solution will be where the two curves intersect.

First, we can simplify the equation by cubing both sides:

\((x+5)^3 = (x-1)^6\)

Next, we can plot \(y1 = (x+5)^3 and y2 = (x-1)^6\) on the same graph in Desmos. The intersection of the two curves will give us the solutions to the equation.

By examining the graph, we can see that there are two real solutions: x ≈ -4.65 and x ≈ 0.51.

Therefore, the solutions to the equation \((x+5)^(3/2) = (x-1)^3\) are x ≈ -4.65 and x ≈ 0.51.

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Answer:

it's the second option

Step-by-step explanation:

Answer:

Translate 2 units up and reflect over the line x = 1

Step-by-step explanation:

The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.

If the they work at the same rate, find the time needed for the 8 painters to finish their job!

Let's say

We convert the unit of time in hours.

t₁ = 7 h 36 min

t₁ = (7 + 36/60) h

t₁ = (7 + 0.6) h

t₁ = 7.6 hours

If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,

w₁/w₂ = t₁/t₂

5/8 = 7.6/t₂

t₂ = 8/5 × 7.6

t₂ = 12.16 hours

In hours and minutes,

t₂ = 12 h + (0.16 × 60) min

t₂ = 12 h 9.6 min

Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.

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The system equation that models the amount of calories from fats (f) and proteins (p) that the individual can consume to reach 1,800 calories is: f + p = 1,200. The equation that relates calories from protein (p) to calories from fat (f) based on the prescribed diet is: p = 3f. Solving the system of equations, we find that the individual should consume 300 calories from fats and 900 calories from proteins.

To find the equation that models the amount of calories from fats and proteins that the individual can consume in order to reach 1,800 calories, we consider that 600 calories will come from carbohydrates. Since the total goal is 1,800 calories, the remaining calories from fats and proteins should add up to 1,800 - 600 = 1,200 calories. Therefore, the equation is f + p = 1,200.

Based on the prescribed diet, the individual is required to consume calories from protein that are three times the calories from fat. This relationship can be expressed as p = 3f, where p represents the calories from protein and f represents the calories from fat.

To solve the system of equations, we substitute the value of p from the second equation into the first equation: f + 3f = 1,200. Combining like terms, we get 4f = 1,200, and dividing both sides by 4 yields f = 300. Substituting this value back into the second equation, we find p = 3(300) = 900.

Therefore, the individual should consume 300 calories from fats and 900 calories from proteins to meet the diet requirements and achieve a total of 1,800 calories.

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The marginal cost function is: C'(x) = 3 + 0.02x + 0.0006x^2 , C'(100) = 605, which means that the cost is increasing by $605 for each additional unit of x.

a. To find the marginal cost function, we need to find the derivative of the cost function C(x) with respect to x.

C(x) = 2000 + 3x + 0.01x^2 + 0.0002x^3

To find the derivative, we can apply the power rule and sum rule:

C'(x) = d(2000)/dx + d(3x)/dx + d(0.01x^2)/dx + d(0.0002x^3)/dx

C'(x) = 0 + 3 + 0.02x + 0.0006x^2

Simplifying, the marginal cost function is:

C'(x) = 3 + 0.02x + 0.0006x^2

b. To find C'(100), we substitute x = 100 into the marginal cost function:

C'(100) = 3 + 0.02(100) + 0.0006(100)^2

       = 3 + 2 + 0.06(100)^2

       = 3 + 2 + 0.06(10000)

       = 3 + 2 + 600

       = 605

Interpretation: C'(100) represents the rate of change of the cost function C(x) with respect to x when x = 100. In this case, C'(100) = 605, which means that the cost is increasing by $605 for each additional unit of x.

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The equation of the Circle centered at (9, -5) that passes through (5, 0) is:(x - 9)² + (y + 5)² = 41.

The equation of a circle centered at (9, -5) that passes through the point (5, 0), we can utilize the standard form of the equation for a circle.

The equation of a circle with center (h, k) and radius r is given by:

(x - h)² + (y - k)² = r²

Given that the center of the circle is (9, -5), we can substitute these values into the equation:

(x - 9)² + (y - (-5))² = r²

Simplifying further, we have:

(x - 9)² + (y + 5)² = r²

Now, we need to find the radius of the circle. Since the circle passes through the point (5, 0), we can use the distance formula between two points to calculate the radius.

The distance between the center (9, -5) and the point (5, 0) is:

√[(x₂ - x₁)² + (y₂ - y₁)²]

Substituting the values, we have:

√[(5 - 9)² + (0 - (-5))²] = √[(-4)² + 5²] = √[16 + 25] = √41

Therefore, the radius of the circle is √41.

Plugging this value back into the equation, we have:

(x - 9)² + (y + 5)² = (√41)²

Simplifying, we get:

(x - 9)² + (y + 5)² = 41

Hence, the equation of the circle centered at (9, -5) that passes through (5, 0) is:

(x - 9)² + (y + 5)² = 41.

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