A coin is flipped, and a standard number cube is rolled. What is the probability for flipping tails and rolling an odd number.

Answer:

no

Step-by-step explanation:

A function is when x does NOT repeat

The quadrupled functions can be evaluated by transforming them into quadratic functions to solve for the roots as follows;

a. x = ±3, and x = ±3·i

b. x = ±√(5)·i

c. x = ±√3, and ±i·√2

Quadratic functions are functions that have an highest power of 2, and which can be expressed in the form; a·x² + b·x + c = 0, where; a ≠ 0, and a, b, and c are numbers.

The specified roots of the quadrupled functions which can be expressed as quadratic function can be found as follows;

a. x⁴ - 81 = 0

x⁴ - 81 = ((x²)² - 9²) = 0

The difference of two squares equation indicates;

((x²)² - 9²) = (x² - 9) × (x² + 9) = 0

x² = 9, and x² = -9

x = ±3 and x = ±3·i

b. The roots of x⁴ + 10·x² + 25 = 0 can be found by taking x² = a, therefore;

x⁴ + 10·x² + 25 = a² + 10·a + 25 = 0

a² + 10·a + 25 = (a + 5) × (a + 5) = 0

a = -5

Therefore; x² = a = -5

x = √(5)·i

c. x⁴ - 2·x² - 6 = 0

Let x² = a, we get;

a² - 2·a - 6 = 0

(a - 3) × (a + 2) = 0

Therefore; a = 3, and a = -2

x = √a = ±√(3) = ±i·√(2)

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Answer:

Simplify the expression.

x

+

4

Step-by-step explanation:

Answer:

12.5 cubic units

Step-by-step explanation:

The volume formula is l*w*h=v

The length is 2.5, the width is 2.5, and the height is 2.

Multiply these together to get our answer!

A ratio describes a relationship between two or more quantities. When mixing colors, ratios are often used to determine the ratio of different colors required to achieve a desired hue. Ratios can be expressed in 1:, 2:3,.. etc.

Ratios affect the appearance of paint colors. In this scenario, Can A has a higher percentage of red than can B. This means that the shade of pink you get with Can A is likely to be darker and more red due to the higher concentration of red.

Can B, on the other hand, has a lower percentage of red, suggesting that the resulting pink hue is lighter and less red than can A.  

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Answer:

concave up and real roots

Answer:

See attachment.

Step-by-step explanation:

(i) The average values for the variables andre, pri gpa, and act is sum of all the values divided by the total number of values.

(ii) The model atenderte 5 b0 1 b1 prigpa 1 b2act 1 u in equation form  is atenderte = b₀ + b₁ x prigpa + b₂ x act + u

(iii) The slope coefficients is  b₁ and b₂

(iv) The predicted atenderte if prigpa 5 3.65 and act 5 20 is atenderte = b₀ + b₁ x 3.65 + b₂ x 20 + u

(v) if student a has prigpa 5 3.1 and act 5 21 and student b has prigpa 5 2.1 and act 5 26, then the predicted difference in their attendance rates is  0.5

In this exercise, we will be exploring a regression model that predicts the attendance rate of students based on their academic performance variables. We will be using three variables to predict the attendance rate: "andre", "pri gpa", and "act". Here are the answers to the questions:

(i) To obtain the minimum, maximum, and average values for the variables "andre", "pri gpa", and "act", we need to first look at the data. The minimum value is the smallest value for each variable, the maximum value is the largest value for each variable, and the average value is the sum of all the values divided by the total number of values.

(ii) The regression model that predicts the attendance rate is written in equation form as

=> "atenderte = b₀ + b₁ x prigpa + b₂ x act + u".

This equation means that the predicted attendance rate (atenderte) is equal to the intercept (b₀) plus the product of the coefficient for "pri gpa" (b₁) and the value of "pri gpa" plus the product of the coefficient for "act" (b₂) and the value of "act".

(iii) The estimated slope coefficients (b₁ and b₂) tell us the expected change in the attendance rate for each one-unit increase in "pri gpa" or "act". If b₁ is positive, it means that as "pri gpa" increases, the attendance rate is expected to increase. Similarly, if b₂ is positive, it means that as "act" increases, the attendance rate is expected to increase.

(iv) To find the predicted attendance rate if "pri gpa" is 3.65 and "act" is 20, we can substitute these values into the regression equation:

atenderte = b₀ + b₁ x prigpa + b₂ x act + u

atenderte = b₀ + b₁ x 3.65 + b₂ x 20 + u

This will give us the predicted attendance rate for a student with "pri gpa" of 3.65 and "act" of 20. If there are any students in the sample with these values of the explanatory variables, then their actual attendance rate should be close to the predicted value.

(v) To find the predicted difference in attendance rates between student A (with "pri gpa" of 3.1 and "act" of 21) and student B (with "pri gpa" of 2.1 and "act" of 26), we can first use the regression equation to predict the attendance rates for each student:

Student A:

atenderteA = b0 + b1 x 3.1 + b2 x 21 + u

Student B:

atenderteB = b0 + b1 x 2.1 + b2 x 26 + u

Then, we can take the difference between the predicted attendance rates for each student:

=> atenderteA - atenderteB

=> 52.6 - 52.1 = 0.5

This will give us the predicted difference in attendance rates between the two students.

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Answer:

1/14 ; 1/35

Step-by-step explanation:

A

6/10 x 5/9 x 4/8 x 3/7

3/5 x 5/9 x 1/2 x 3/7

1 x 1/3 x 3/14

1/14

B

4/10 x 3/9 x 2/8 x 6/7

2/5 x 1/3 x 1/4 x 6/7

2/15 x 3/14

1/5 x 1/7

1/35

The probability that  4 creature cards is pulled is 1/14 and the probability that 3 land cards and 1 creature card is pulled is 4/35

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here there are 4 land cards and 6 creature cards

thus selecting four cards at random from 10 cards is  ¹⁰C₄=210

and the event of selecting 4 creature cards from a total of 6 cards is ⁶C₄ =15

Therefore probability of pulling 4 creature cards is = 15/210

                                                                                     = 1/14

The probability of pulling 3 land cards and 1 creature cards is    

= ⁴C₃ × ⁶C₁   /  ¹⁰C₄

= 4/35

Hence 1/14 and 4/35 are the respective probabilities.

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Alison makes a map of a park by first gathering information about the park's layout, features, and landmarks. She then draws a scale model of the park, using symbols and colors to indicate various attractions and facilities. This map can be used by visitors to navigate through the park, locate different areas, and plan their activities.

To get the answer to this question, we need to understand the process Alison used to make the map and what information she included on it. We also need to know the purpose of the map and how it can be used by park visitors. By knowing these things, we can appreciate the importance of maps as a tool for navigation, exploration, and planning. Overall, Alison's map of the park is a valuable resource that helps people get the most out of their visit.
Alison can make a map of a park by following these steps:

1. Observe: Visit the park and note important features like paths, benches, playgrounds, and bodies of water.
2. Sketch: Create a rough sketch of the park, marking the locations of the features.
3. Measure: Use a measuring tape or GPS app to get approximate distances between features and the park's boundaries.
4. Scale: Decide on a scale for the map (e.g., 1 inch = 50 feet) and adjust the measurements accordingly.
5. Draw: Using the scaled measurements, draw a final version of the map, clearly labeling all features.
6. Review: Double-check the map for accuracy and make any necessary revisions.

By following these steps, Alison will have an accurate map of the park.

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The 95.44% confidence interval for the population mean is approximately (19.87 minutes, 24.73 minutes).

To calculate the 95.44% confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (critical value) * (standard deviation / sqrt(sample size))

First, let's determine the critical value. Since the confidence level is 95.44%, we need to find the z-score that corresponds to a tail probability of (1 - 0.9544)/2 = 0.0228. Looking up this value in the standard normal distribution table or using a statistical calculator, we find that the z-score is approximately 2.17.

Next, we need to determine the standard deviation of the population. Since we don't have that information, we'll use the sample standard deviation as an estimate. Let's assume the sample standard deviation is 5 minutes.

Now we can calculate the confidence interval:

Confidence Interval = 22.3 ± (2.17) * (5 / sqrt(20))

Calculating the expression inside the parentheses:

= 22.3 ± (2.17) * (5 / sqrt(20))

= 22.3 ± 2.17 * (5 / 4.472)

= 22.3 ± 2.17 * 1.118

Calculating the confidence interval:

Lower Limit = 22.3 - (2.17 * 1.118)

Upper Limit = 22.3 + (2.17 * 1.118)

Lower Limit = 22.3 - 2.42706 ≈ 19.87294

Upper Limit = 22.3 + 2.42706 ≈ 24.72706

Therefore, the 95.44% confidence interval for the population mean is approximately (19.87 minutes, 24.73 minutes).

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A. To determine if an integral is convergent, we analyze the function's behavior, integrability, apply integration techniques, and examine its limits, ensuring they are finite, leading to a finite result.

B. To determine if an integral is divergent, we look for infinite limits, vertical asymptotes, and erratic behavior within the integration interval, indicating the lack of a finite value for the integral.

A. To determine if an integral is convergent, we need to consider several approaches. First, we check for basic convergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, ensuring the function is continuous or has a finite number of discontinuities. Next, we simplify the integral using integration techniques.

Finally, we analyze the behavior of the function at infinity and apply comparison tests if necessary to establish convergence.

B. To determine if an integral is divergent, we follow a series of steps. First, we check for basic divergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, looking for discontinuities that prevent integration. Next, we simplify the integral using integration techniques. Finally, if the integral does not converge, it is deemed divergent.

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Answer:

Step-by-step explanation:

18.95+.16 = 19.11

answer is 2 miles is the maximum

The value of CDF Pr[28 < X ≤ 41] = F(41) - F(28) = 0.6 - 0.55 = 0.05.

Given that X is a discrete random variable that takes only positive integer values, we know the cumulative distribution function (CDF) values for certain values of X. We can use this information to find the value of k, which is missing.

First, we note that the CDF is a non-decreasing function, meaning that as X increases, F(X) cannot decrease. Therefore, we know that 0.55 ≤ k ≤ 0.6.

Next, we use the fact that the CDF is a step function, meaning that it increases by a finite amount at each integer value of X. Using this, we can find the difference in CDF values between adjacent values of X. For example, F(21) - F(13) = 0.49 - 0.45 = 0.04.

Using this method, we can find that F(47) - F(28) = 0.67 - 0.55 = 0.12 and F(54) - F(41) = 0.7 - k. We can then set these two expressions equal to each other and solve for k:

0.7 - k = 0.12
k = 0.58

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Answer:

1 litro de leche cuesta 2.5

1 kg de jamón serrano cuesta 35

1 litro de aceite de oliva cuesta 7,5

Step-by-step explanation:

Pregunta correcta completa

Un cliente de un supermercado ha pagado un total de 240 por 16 litros de leche,4kg de hamon serrano y 8 litros de aceite de oliva. Sabiendo que 1 litro de aceite cuesta el tripe de 1 litro de leche; que 1kg de jamon cuesta igual que el cliente tendria que pagar si hubiera comprado 5 litros de leche y 3 litros de aceite de oliva. Calcule el precio de cada artículo.

Solución

Deje que el precio de un litro de leche, un kilogramo de jamón serrano y un litro de aceite de oliva sea x, y y z respectivamente.

16 litros de leche, 4 kg de hamon serrano y 8 litros de aceite de oliva cuestan 240

16x + 4y + 8z = 240 (ecuación 1)

1 litro de aceite cuesta el triple de 1 litro de leche

z = 3x (ecuación 2)

Y ese 1 kg de jamón cuesta lo mismo que el cliente tendría que pagar si hubiera comprado 5 litros de leche y 3 litros de aceite de oliva.

y = 5x + 3z (ecuación 3)

Sustituyendo las ecuaciones 2 y 3 en la ecuación 1

16x + 4(5x + 3z) + 8(3x) = 240

16x + 20x + 12z + 24x = 240

Recordemos que z = 3x

36x + 12(3x) + 24x = 240

36x + 36x + 24x = 240

96x = 240

x = (240/96) = 2.5

z = 3x = 3 × 2.5 = 7.5

y = 5x + 3z = (5×2.5) + (3×7.5) = 35

English Translation

A supermarket customer has paid a total of 240 for 16 liters of milk, 4kg of hamon serrano and 8 liters of olive oil. Knowing that 1 liter of oil costs the tripe of 1 liter of milk; t that 1kg of ham costs the same as the customer would have to pay if he had bought 5 liters of milk and 3 liters of olive oil. Calculate the price of each item.

Solution

Let the price of a liter of milk, a kilogram of Serrano ham and a liter of olive oil be x, y and z respectively.

16 liters of milk, 4kg of hamon serrano and 8 liters of olive oil cost 240

16x + 4y + 8z = 240 (eqn 1)

1 liter of oil costs the triple of 1 liter of milk

z = 3x (eqn 2)

And that 1kg of ham costs the same as the customer would have to pay if he had bought 5 liters of milk and 3 liters of olive oil

y = 5x + 3z (eqn 3)

Substituting eqn 2 and 3 into eqn 1

16x + 4(5x + 3z) + 8(3x) = 240

16x + 20x + 12z + 24x = 240

Recall that z = 3x

36x + 12(3x) + 24x = 240

36x + 36x + 24x = 240

96x = 240

x = (240/96) = 2.5

z = 3x = 3 × 2.5 = 7.5

y = 5x + 3z = (5×2.5) + (3×7.5) = 35

1 liter of milk costs 2.5

1 kg of Serrano ham costs 35

1 liter of olive oil costs 7.5

Hope this Helps!!!

In a circle with diameter AB, point C lies on AB such that 2AC = CB.

The relationship between AC and CB in this scenario indicates that AC is half the length of CB. This can be inferred from the given condition that 2 times AC is equal to CB. It suggests that point C divides the diameter AB into two unequal segments.

The ratio of the length of segment $\overline{AC}$ to the length of segment $\overline{CB}$ is 2:1.

In a circle, when a diameter is divided by a point on it, the ratio of the segments formed is equal to 2:1. This property is known as the Intercept Theorem. In this case, segment $\overline{AB}$ is the diameter of the circle, and point $C$ divides it into two segments: $\overline{AC}$ and $\overline{CB}$. The theorem states that the length of $\overline{AC}$ is twice the length of $\overline{CB}$. This relationship holds true for any point $C$ on the diameter of the circle.

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The city that has the biggest difference between the maximum and minimum temperatures is Glasgow.

In order to determine which city has the biggest difference, subtract the difference between the minimum temperature from the maximum temperature.

Range = maximum temperature - minimum temperature

Range of Glasgow = 2 - (-8)

2 + 8 = 10

Range of Cardiff = 6 - (-1)

6 + 1 = 7

Range of Exeter = 8 - 0 = 8

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Answer:

If the missing data value was 55, the range of the data would change significantly

If the missing data value was 22, the interquartile range of the data would change significantly

Step-by-step explanation:

Given the data

8, 9, 12, 12, 13, 15, 16, 16, 16, 18, 21, 22, 23, 27, 28, 32, 34,40

The range of the data is the difference between the highest value and the lowest value of the data.

Highest value = 40

Lowest value = 8

Range = 40-8

Range = 32

If 55 was missing, we need yo find the range of the data if 55 was included.

Highest value will be 55

Lowest value = 8

Range in this case = 55-8

Range = 47

Difference in range = 47-32= 15

This means that if 55 was missing, it will significantly affect the value of the range.

- Interquartile range = Q3-Q1

Q3 is the median value of the other half of the data.

Q1 is the median value of the first half of the data.

If 55 wasn't included, the first part of the data:

8, 9, 12, 12), 13, (15, 16, 16, 16

Q1 = 13 (median value of the extracted data)

The second part of the data if 55 wasn't included:

18, 21, 22, 23), 27, (28, 32, 34, 40

Q3 = 27 (median value of the second part of the data)

IQR = Q3-Q1

IQR = 27-13

IQR = 14

If 55 was included, the data will be;

8, 9, 12, 12, 13, 15, 16, 16, 16, 18, 21, 22, 23, 27, 28, 32, 34, 40,55

Q1 = N+1/4 the value

N is the sample size = 19

Q1 = 19+1/4

Q1 = 20/4

Q1 = 5th value

The 5th value in the data is 13, hence Q1 is 13

Q3 = 3(N+1)/4th value

Q3 = 3(19+1)/4

Q3 = 60/4

Q3 is the 15th value in the dataset. Since the 15th value is 28, Q3 is 28

IQR = 28-13

IQR = 15 (if 55 was included)

Difference in IQR = 15-14 = 1

This means that if 55 was the missing data, the IQR will not change significantly.

Note that the range of the data will not change if the missing value is 22 because, the 22 is a value lower than the highest value of the dataset, hence the range will remain the same (40-8 = 32) irrespective of 22 missing or not.

For the Interquartile range

If 22 was in

Q3 = 3(N+1)/4th value

Q3 = 3(19+1)/4

Q3 = 60/4

Q3 is the 15th value in the dataset. Since the 15th value is 28, Q3 is 28

IQR = 28-13

IQR = 15 (if 55 was included)

Difference in IQR = 15-14 = 1

This means that if 55 was the missing data, the IQR will not change significantly.

Based on the calculation, the correct options are:

- If the missing data value was 55, the range of the data would change significantly

- If the missing data value was 22, the interquartile range of the data would change significantly

Answer:

a

Step-by-step explanation:

edge 2021

Answer:

Slope=0.10

Interpretation: For every minute Olivia is in the cafe she is getting charged 10 cents

Step-by-step explanation:

The slope is a constant followed by a variable (a,x,b,z,etc...) So the only constant with a variable after it was the 10.

Answer:

The slope of the function is 0.10 which represents the additional charge per minute.

Step-by-step explanation:

The slope shows how much the amount Olivia must pay increases each minute, representing the cost per minute of using the computer after the initial charge.

Answer: 3

Step-by-step explanation: try to solve for a by itself by multiplying it on both sides that give you 3 = 1*a. that simply just means that a is equal to 3, so you substitute three to the a variable that will give 3/3 that's equal to 1.

The dimensions of the rectangle are 10 feet (length) and 8 feet (width).

To find the dimensions of the rectangle with an area of 80 square feet and a width that is 2 feet less than the length,

follow these steps:

1. Let the length of the rectangle be L feet and the width be W feet.

2. According to the given information, W = L - 2.

3. The area of a rectangle is calculated by multiplying its length and width: Area = L × W.

4. Substitute the given area and the relationship between L and W into the equation: 80 = L × (L - 2).

5. Solve the quadratic equation: 80 = L² - 2L.

6. Rearrange the equation: L² - 2L - 80 = 0.

7. Factor the equation: (L - 10)(L + 8) = 0.

8. Solve for L: L = 10 or L = -8 (since the length cannot be negative, L = 10).

9. Substitute L back into the equation for W: W = 10 - 2 = 8.

So, the dimensions of the rectangle are 10 feet (length) and 8 feet (width).

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The solution of the given expression is 3.

It is required to evaluate the given expression.

An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined.

Given that:

The given expression is

4+2×6÷3−5

By the use of BODMAS we have,

4+2×2-5

=4+4-5

=8-5

=3

Hence, the solution of the given expression is 3.

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Mia can create a scale drawing of a football field using a scale of 1:1,000. The scale drawing will provide a Visual representation of the field, allowing for easier analysis and planning.

To create a scale drawing of a football field using a scale of 1:1,000, Mia can follow these steps:

1. Determine the dimensions: The football field's dimensions are given as 120 yards by 53 1/3 yards. Convert the fractional measurement to a decimal for simplicity. In this case, 1/3 yard is approximately 0.333 yards.

2. Decide on the units: Since the scale is 1:1,000, Mia needs to determine the unit of measurement she will use in her scale drawing. For consistency, she can choose to use feet as the unit.

3. Calculate the scaled dimensions: To create the scale drawing, Mia needs to scale down the dimensions of the football field. Since the scale is 1:1,000, she can divide the actual dimensions by 1,000 to obtain the scaled dimensions. The scaled dimensions would be 120 yards / 1,000 = 0.12 yards (or 0.36 feet) for the length and 53.333 yards / 1,000 = 0.053333 yards (or 0.16 feet) for the width.

4. Draw the scaled football field: Using a ruler and a grid paper, Mia can draw a rectangle with dimensions of 0.12 feet by 0.053333 feet (or inches, depending on the size of the grid paper). She can label the sides of the rectangle with the corresponding measurements in feet.

5. Add additional markings: Mia can add other markings to the scale drawing, such as the goal posts, yard markers, and any other important features of the football field. She can refer to the actual measurements and proportions of these elements to ensure accuracy.

By following these steps, Mia can create a scale drawing of a football field using a scale of 1:1,000. The scale drawing will provide a visual representation of the field, allowing for easier analysis and planning.

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The ratio of trick-or-treaters who were not dressed as snow white last Halloween is 5/9

Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.

It can be expressed in different ways:

1) Use the ":" to separate the values : a : b

2) Use the word "to" : a to b

3) Write it in fraction: a / b

On the other hand, proportion is the equality of two or more ratios.

example: a : b = c : d

If four out of every nine trick-or-treaters that came to your house last Halloween were dressed as snow white, then the rest were not dressed as snow white.

9 - 4 = 5

If five out every nine trick-or-treaters that came to your house last Halloween were not dressed as snow white, we can express the ratio as

5 out of 9 or 5 : 9 or 5/9

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Answer:

12

Step-by-step explanation:

3 shirts x 2 pants x 2 pair shoes= 12 outfits

To show that `(n + 3)7 ∈ Θ(n7)`, we need to prove that `(n + 3)7 = Θ(n7)`.This can be done by showing that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)` .Now, let's prove the two parts separately:

Proof for `(n + 3)7 = O(n7)`.

We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≤ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≤ n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + n7
≤ 2n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6
≤ 2n7 + 84n6 + 441n5 + 2205n4 + 10395n3 + 45045n2 + 153609n + 729
```Thus, we can take `c = 153610` and `k = 1` to satisfy the definition of big-Oh notation. Hence, `(n + 3)7 = O(n7)`.Proof for `(n + 3)7 = Ω(n7)`We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≥ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≥ n7
```Thus, we can take `c = 1` and `k = 1` to satisfy the definition of big-Omega notation. Hence, `(n + 3)7 = Ω(n7)`.

As we have proved that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)`, therefore `(n + 3)7 = Θ(n7)`.Thus, we have shown that `(n + 3)7 ∈ Θ(n7)`.From the proof, we can see that we used the Binomial theorem to expand `(n + 3)7` and used algebraic manipulation to bound it from above and below with suitable constants. This technique can be used to prove the time complexity of various algorithms, where we have to find the tightest possible upper and lower bounds on the number of operations performed by the algorithm.

Hence, we have shown that `(n + 3)7 ∈ Θ(n7)` for non-negative integer n.

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Solution:

The exact form of the given expression would be \(\frac{7}{5436}\).

Hope this helps! If not, feel free to comment below on what else I can do to better assist you. Other than that, I wish you the best of luck on your studies!

Answer:

D

Step-by-step explanation:

Rounded to the nearest cent, the monthly charge for 4000 kWh is $450.82.

We have the following piecewise function for the monthly charge based on the usage (x) in kilowatt hours (kWh):

For 0 ≤ x ≤ 500: C(x) = 7.52 + 0.1079x
For x > 500: C(x) = 19.22 + 0.1079x

Now, let's find the monthly charges for the given usages:

(a) 5 kWh
Since 0 ≤ 5 ≤ 500, we'll use the first equation:
C(5) = 7.52 + 0.1079(5)
C(5) = 7.52 + 0.5395
C(5) = 8.0595
Rounded to the nearest cent, the monthly charge for 5 kWh is $8.06.

(b) 13 kWh
Since 0 ≤ 13 ≤ 500, we'll use the first equation:
C(13) = 7.52 + 0.1079(13)
C(13) = 7.52 + 1.4027
C(13) = 8.9227
Rounded to the nearest cent, the monthly charge for 13 kWh is $8.92.

(c) 4000 kWh
Since 4000 > 500, we'll use the second equation:
C(4000) = 19.22 + 0.1079(4000)
C(4000) = 19.22 + 431.6
C(4000) = 450.82

Rounded to the nearest cent, the monthly charge for 4000 kWh is $450.82.

To know more about kilowatt hours (kWh), refer here:

https://brainly.com/question/30498337

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