Find the length of the midsegment of the trapezoid

2n-2
N+12
4n+6

The maximum profit occurs at the endpoint t = 100, where the profit is $5551.20.

To maximize the profit function P(t) = 60t^2 + 420t - 440, we need to find the value of t that will give us the maximum profit.

One way to do this is to use calculus. We can take the derivative of P(t) with respect to t and set it equal to zero to find the critical points:

P'(t) = 120t + 420

Set P'(t) = 0 and solve for t:

120t + 420 = 0

t = -3.5

This gives us one critical point at t = -3.5. However, this value of t doesn't make sense in the context of the problem - we can't sell tickets at a negative price!

So we need to check the endpoints of the domain of the function, which is given by the constraint that t is greater than or equal to zero (we can't charge a negative price for tickets either).

When t = 0, P(0) = -440.

When t is very large, say t = 100, P(100) = 600000 - 44000 - 440 = 555120.

Therefore, the maximum profit occurs at the endpoint t = 100, where the profit is $5551.20.

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The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

We have,

To prove the equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 using mathematical induction,

We will follow the three steps of mathematical induction:

The base case, the induction hypothesis, and the inductive step.

Step 1: Base case

Let's start by checking if the equation holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) is 1² = 1, and the right-hand side (RHS) is 1(1 + 1)(2(1) + 1) / 6 = 1.

Since LHS = RHS for the base case, the equation holds true.

Step 2: Induction hypothesis

Assume the equation holds true for some positive integer k, where k ≥ 1. This is our induction hypothesis:

1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1) / 6

Step 3: Inductive step

We need to prove that if the equation holds true for k, it also holds true for k + 1.

Starting with the left-hand side of the equation, we add (k + 1)² to both sides:

1 + 4 + 9 + ... + k² + (k + 1)² = k(k + 1)(2k + 1) / 6 + (k + 1)²

Simplifying the right-hand side:

= [k(k + 1)(2k + 1) + 6(k + 1)²] / 6

= [(2k³ + 3k² + k) + (6k² + 12k + 6)] / 6

= (2k³ + 9k² + 13k + 6) / 6

= [(k + 1)(k + 2)(2k + 3)] / 6

We can see that the right-hand side is now in the form

(k + 1)((k + 1) + 1)(2(k + 1) + 1) / 6, which matches the equation for k + 1.

Since the equation holds true for k implies it holds true for k + 1, and the base case is true, we have proven the equation using mathematical induction.

Therefore,

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

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a=12,d=17-12=5

nth term =a+(n-1)d

36th term=12+(36-1)5

=12+(35×5)

12+175

36th term=187

Answer: 187

Step-by-step explanation: 17 - 12 = 5 and 22 - 17 = 5

aₙ = a₁ + (n - 1) d

where a₁ = 12, n = 36, d = 5

a₃₆ = 12 + (36 - 1) 5

a₃₆ = 12 + 35 × 5

a₃₆ = 12 + 175

a₃₆ = 187

187 is the 36th term

Answer:

A

Step-by-step explanation:

40/10 will give you your answer

40/10=4m/s

In some circumstances, it might also be essential to demonstrate congruence using various transformations.

In mathematics, transformations are modifications done to a geometric figure in a coordinate plane, such as a shape, point, or line. Applying various operations or functions on the coordinates of the points that make up the figure will result in these changes. Four fundamental types of transformations exist: Translation: A figure is moved horizontally, vertically, or both while maintaining its size, form, and orientation.

Translation, rotation, and reflection are the three fundamental transformations that can be employed to demonstrate the congruence of two figures.

To demonstrate that Figures 1 and 2 are congruent with one another, the following two transformational sequences could be used:

Figure 1 should be translated to overlap with Figure 2, then rotated.

b. Rotate Figure 1 about a point until it aligns with Figure 2's orientation.

c. Evaluate the two figures side by side to ensure that all related sides and angles match.

Rotation after reflection:

a. Create a mirror image of Figure 1 by reflecting it across a line.

b. Rotate the reflected Figure 1 about a certain point until it aligns with Figure 2's orientation.

c. Evaluate the two figures side by side to ensure that all related sides and angles match.

To ensure that the two figures are congruent, the transformations must be used in a precise order.

In some circumstances, it might also be essential to demonstrate congruence using various transformations.

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Answer:

1. 5x

2. 1x or x

3.-1x

4. -5x

5. 0

6. 3x

7. 11x

8. 2x

9. 6x+2y

10. 2x+4y

11. 3x+6y+z

12. 3x+3y

13.-9x+2y

14. 7x+5y

15. 3x-y

16. -7x-5y

17. 0

18. 9xy

19. 7x-2y+3z

20. -8+10

21. 2y

22.5x

23. -6x+11

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

mean= (10+19+20+13+13+2+10+8+25+10)/10=130/10=13

The mean number of first cousins for the given sample is 13. Thus, Option C is correct.

Mean is the arithmetic average of the given set of observations.

Mean for ungrouped or raw data is obtained by adding all the observations and dividing it by the number of observations.

Mean = Sum of all the observations/ Total number of observations.

Mean = ∑( x1 + x2 + x3 .... xn /n)

Where X bar represents mean, n is no. of observations and ∑ denotes sigma i.e. sum of all the values.

No. of observations (n) =10

Mean = ∑ (10 + 19 + 20 + 13 + 13 + 2 + 10 + 8 + 25 + 10) / 10

Mean = 130 / 10

= 13

Therefore, Option C is the correct answer.

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Therefore the solution of the given problem is  product of the equation is 3\(x^{3}\) + 12x.

The equals sign (=) must appear in an equation. You can think of an equation as having a left and a right side since there will be a mathematical expression on either side of it. Consider an equation to be a set of scales. Although you can use different amounts on either side, for it to be solved, each side must be equally balanced .An unknown will always be present in an algebraic equation. This is symbolized by a symbol, such x, y, or z.

Here,

We must calculate the product of 3x(\(x^{2}\) + 4).

In light of the query

Follow all of the instructions listed below to obtain the equation's product.

Equation; 3x(\(x^{2}\) + 4).

Then,

The product of the equation is,

=>3x(\(x^{2}\) + 4).

=>3\(x^{3}\) + 12x

Therefore the solution of the given problem is  product of the equation is 3\(x^{3}\) + 12x.

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Answer:

12

Step-by-step explanation:

4 types of flowers, 3 messages, therefore 3x4=12

Sunflower:           Daisy:                   Tulip:                   Roses:

Birthday               Birthday               Birthday              Birthday

Holiday                Holiday                Holiday                Holiday

Anniversary         Anniversary         Anniversary        Anniversary

COUNT ALL OF THE HOLIDAYS AND THAT NUMBER IS GONNA BE YOUR ANSWER.

The given information is,

→ Length (l) = 7 ft

→ Breadth (b) = 4 ft

→ Height (h) = 4 ft

Formula we use,

→ l × b × h

The volume of cuboid will be,

→ l × b × h

→ 7 × 4 × 4

→ [ 112 ft³ ]

Hence, the volume is 112 ft³.

3.1.1. Solvent

3.1.2. Debt burden

3.1.3. Financially stable

3.1.4. Return on investment

3.1.5. Liquidity

3.1.1. A company with total assets exceeding total liabilities is financially solvent or has a positive net worth.

3.1.2. A company that relies heavily on loans will have high leverage or a high debt burden.

3.1.3. A company that controls its income and expenses properly will be financially stable or financially healthy.

3.1.4. The percentage net income on equity indicates the profitability or return on investment earned by shareholders.

3.1.5. A company that is able to settle its immediate debts is financially liquid or has good liquidity.

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Answer:

$5 is the answer.......

Answer:

one box cost is $5

Step-by-step explanation:

$25 - $5 = $20 - this is the cos of four cereal boxes

$20 / 4 = $5 each box cost

EXPLANATION

Let's see the facts:

charge----> 7% sales tax -----> 0.07 in decimal form

-----> plus rental fees

Let's call y to the rental fees, x to the sale price and and z to the final price.

The appropiate algebraic expression is:

0.07x + yx = z

Answer:

20%

Step-by-step explanation:

35/175=x/100

35 divided by 1.75/ 175 divided by 1.75 =x/100

20/100=x/100

20=x

or

35/175=.2

.2= 20 %

Answer: 20%

Step-by-step explanation: hope this helps

Answer:

4x^2 - 10x + 1 units

Step-by-step explanation:

(3x - 1) + (x + 2) + (3x^2 - 11x) + (x^2 - 3x)

Adding like terms:

3x^2 + x^2         = 4x^2

-11x - 3x + 3x + x    = -10x

-1 + 2            = 1

Summing it up; the perimeter is
4x^2 - 10x + 1 units

b) To find the joint density of the minimum and maximum of the U_i's, we can use the following approach:

Let M = min(U_1, U_2, U_3, U_4, U_5) and let X = max(U_1, U_2, U_3, U_4, U_5). Then we have:

P(M > m, X < x) = P(U_1 > m, U_2 > m, U_3 > m, U_4 > m, U_5 > m, U_1 < x, U_2 < x, U_3 < x, U_4 < x, U_5 < x)

Since the U_i's are independent and uniformly distributed on (0,1), we have:

P(U_i > m) = 1 - m, for 0 < m < 1

P(U_i < x) = x, for 0 < x < 1

Substituting these expressions, we get:

P(M > m, X < x) = (1 - m)^5 * x^5

Therefore, the joint density of M and X is:

f(M,X) = d^2/dm dx (1-m)^5 * x^5 = 30(1-m)^4 * x^4, for 0 < m < x < 1.

c) To find P(R > 0.5), we need to find the probability that the distance between the minimum and maximum of the U_i's is greater than 0.5. We can use the following approach:

P(R > 0.5) = 1 - P(R <= 0.5)

Now, R <= 0.5 if and only if the difference between the maximum and minimum of the U_i's is less than or equal to 0.5. Therefore, we have:

P(R <= 0.5) = P(X - M <= 0.5)

To find this probability, we can integrate the joint density of M and X over the region where X - M <= 0.5:

P(R <= 0.5) = ∫∫_{x-m<=0.5} f(M,X) dm dx

The region of integration is the triangle with vertices (0,0), (0.5,0.5), and (1,1). We can split this triangle into two regions: the rectangle with vertices (0,0), (0.5,0), (0.5,0.5), and (0,0.5), and the triangle with vertices (0.5,0.5), (1,0.5), and (1,1). Therefore, we have:

P(R <= 0.5) = ∫_{0}^{0.5} ∫_{0}^{m+0.5} 30(1-m)^4 * x^4 dx dm + ∫_{0.5}^{1} ∫_{x-0.5}^{x} 30(1-m)^4 * x^4 dm dx

Evaluating these integrals, we get:

P(R <= 0.5) ≈ 0.5798

Therefore,

P(R > 0.5) = 1 - P(R <= 0.5) ≈ 0.4202.

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Answer:

(-4, 5) Quadrant ll

Step-by-step explanation:

Hope this helps

The solution for system of equation provided as per the given question will be x = -19 and y = 55 or (-19,55).

It is given that the equations are:

y = –3x – 2

Simplifying it further, we get:

y + 3x = -2 (equation 1)

5x + 2y = 15 (equation 2)

Multiplying y + 3x = -2 by 2 and subtracting from 5x + 2y = 15, we get:

2y - 2y + 5x -6x = 15 + 4

-x = 19

x = -19

Plugging the value of x in the equation y + 3x = -2, we get:

y + 3 × - 19 = -2

y - 57 = -2

y = -2 + 57

y = 55

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The mean and standard deviation of the population is 19.8 and 0.004 respectively.

Mean:

The mean is the simple mathematical average of a set of two or more numbers. The mean of a given set of numbers can be calculated in several ways, including the arithmetic mean, which uses the sum of the numbers in the range, and the geometric mean, which takes the mean product of a set. However, all major methods of calculating simple averages produce the same approximate result most of the time.

Standard Deviation:

In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values.  A low standard deviation indicates that the values ​​tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values ​​are spread over a wider range.

Given that:

E(x) = μ = 19.8

var(x) = σ²/n = 0.2/50 = 0.004

from here can say that mean = 19.8 and

standard Deviation is 0.004.

Now,

295 -298 P(Bottle x < 295) =P(Z< ) =-1.00 =.15873

Thus, there is nearly a 16% probability that just 1 randomly selected

bottle contains < 295 ml.

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When evaluating an exercise, evaluators record their observations in the exercise evaluation guide (eeg). observations that should be recorded include d.) a and b

When analyzing an activity, evaluators record their observations in the Exercise Evaluation Guide (EEG) (EEG). Actual time needed by exercise participants to perform the necessary tasks and resources used are among the observations that should be recorded.

EEGs (Exercise Evaluation Guides) offer a reliable instrument to direct exercise monitoring and data gathering. EEGs list capability aims and crucial tasks that are in line with exercise objectives and core capabilities.

EEGs achieve a number of objectives:

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The height of the pyramid is approximately 90.81 inches.

A pyramid is a type of geometric solid with a triangle base and polygonal faces that meet at the top, or apex. Any polygon, such as a triangle, square, or pentagon, can serve as the pyramid's base, and the number of faces, edges, and vertices depends on the base's form. The pyramids of Giza in Egypt are only one example of the numerous ancient civilizations that employed pyramids as a frequent architectural element.

The Pythagorean theorem may be used to calculate the height of a pyramid, which is the vertical distance between its peak and base. Call this height "h" for short. We may construct the equation shown below:

h² = slant height² - (1/2 × base side)²

Substituting the given values, we get:

h² = (92.4 in)² - (0.5 * 24.8 in)²

h² = 8559.36 in² - 307.52 in²

h² = 8251.84 in²

Taking the square root of both sides, we get:

h = √(8251.84 in²)

h = 90.81 in

Therefore, the height of the pyramid is approximately 90.81 inches.

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Answer:

$22.17

Step-by-step explanation:

105.36 multiplyed by 0.22 ( you need to change the 22% to a decimal so just make it 0.22) then once you multiplyed them then you get your answer.

The statements that is always true or false given that  A is an n × n matrix are; A. True. B. True C. True, D. True

A. A stochastic matrix always has 1 as an eigenvalue, and the corresponding eigenvector forms a line, the 1-eigenspace. in other words, A stochastic matrix is a matrix whose rows sum to 1. This means that the sum of the elements in each row of A is equal to 1.

B. a stochastic matrix always has 1 as an eigenvalue. The eigenvalues of a matrix are the roots of its characteristic polynomial.

C. A positive stochastic matrix is a stochastic matrix whose entries are all non-negative. If A is a positive stochastic matrix, then repeated multiplication by A pushes each vector toward the 1-eigenspace.

D. For a square matrix, the eigenvalues of a matrix and its transpose are the same.

The above answer for D is based on the assumption that question D is

d. If A is a square matrix, then A and A^T must have the same eigenvalues.

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Seema left 6/11 of the book for reading over the weekend.

To calculate the part of the book left for reading during the weekend, we need to subtract the part of the book Seema read during the weekday from the total book.

If Seema reads 5/11 of the book during the weekday, then:

This means 6/11 of the book is left for reading during the weekend. It is important to note that the fraction of the book read during the weekday and the fraction left for reading during the weekend add up to the total book. This means that 11/11 of the book will be read by Seema in total.

This question should be written as:

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Answer:

Both ate 12 sunscreens all together

5 + 7 = 12

Srsly tho, like who in their right mind eats sunscreen

Designing control charts involves two key issues: sample size and sampling frequency is a true statement.

Control Charts depict how the process [ data ] changes over time. It comprises a central line for average, lower line for the lower control limit and an upper line for upper control limit.

There are many types of control chart -X bar control chart.

Sample size can be defined as the number of measurement values  taken for a test feature .

Sampling frequency can be defined as the average number of samples obtained in one second.

Hence, designing control charts involves two key issues: sample size and sampling frequency is a true statement.

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