what is the surface area of this figure ?

The graph of circle x² + y² + 16x - 16y + 124 = 0 has centre (-8, 8) and radius 2.

What is radius?

A circle's or sphere's radius is any line segment that connects the object's centre to its edge according to classical geometry; in more contemporary usage, the term also refers to the length of such line segments. The Latin origin of the word "radius" gives it the meanings of "ray" and "the spoke of a chariot wheel."

To graph the circle x² + y² + 16x - 16y + 124 = 0

We rewrite equation in standard form:

x² + 16x + y² - 16y + 124 = 0

(x² + 16x + 64) + (y² - 16y + 64) = -124 + 64 + 64

(x + 8)² + (y - 8)² = 4

The circle's centre (-8, 8) and radius (2) are now visible.

We may graph it by first plotting the centre point and then circling it with a radius of 2.

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Answer: The most appropriate design for this experiment is the third option:

- Number each item from 0000 to 1199.

- Reading from left to right on a random number table, identify 800 unique four-digit numbers from 0000 to 1199. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.

This design ensures that the groups are equally sized and selected randomly without any biases. The use of a random number table to assign the groups helps to avoid any systematic patterns or preferences that might arise from numbering or labeling the items directly.

Step-by-step explanation:

The percentage of tornadoes that were EF1s is 40%.

What is the percentage?

A figure or ratio stated as a fraction of 100 is called a percentage. The acronyms pct., pct., and occasionally pc are also used to indicate it, however, the percent sign is most frequently used. A % is a number without dimensions and without a standard measurement.

Here, we have

Given: the strengths of tornadoes that occurred in Alabama in 2011.

We have to find the percentage of tornadoes that were EF1s.

EF1s = 58

Total = 145

percentage of tornadoes = 58/145 = x/100

5800/145 = x

x = 40%

Hence, the percentage of tornadoes that were EF1s is 40%.

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If Riders have to climb a m staircase to board the ride at its lowest point.

a. sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).

b. a cosine function for Eva, who is just boarding the ride is: h(t) = m + 60 cos(π/6 t).

c.  a sine function for Matthew is: h(t) = 30 sin(π/6 t).

(a) Let's assume that the Ferris wheel completes one full revolution in 12 minutes. The height of the Ferris wheel can be modeled by a sine function as it moves up and down periodically. When the Ferris wheel completes one revolution, it returns to its original position, so the period of the sine function is 12 minutes.

The maximum height of the Ferris wheel is 60 m, so the amplitude of the sine function is 60 m. When t = 0, Emma is at the very top of the ride, which means she is at the maximum height of the Ferris wheel. Therefore, the sine function for Emma's height, h(t), can be written as:

h(t) = 60 sin(2π/12 t)

Simplifying this equation, we get:

h(t) = 60 sin(π/6 t)

(b) Eva is just boarding the ride, which means she is at the lowest point of the ride when t = 0. The cosine function is ideal for modeling this situation, as it starts at its maximum value and reaches its minimum value after one-fourth of the period. Therefore, the cosine function for Eva's height, h(t), can be written as:

h(t) = m + 60 cos(2π/12 t)

Simplifying this equation, we get:

h(t) = m + 60 cos(π/6 t)

where m is the height of the staircase that Eva has to climb to board the ride.

(c) Matthew is at the same height as the central axle of the Ferris wheel, which means he is halfway between the maximum and minimum height of the ride. Therefore, the sine function for Matthew's height, h(t), can be written as:

h(t) = 30 sin(2π/12 t)

Simplifying this equation, we get:

h(t) = 30 sin(π/6 t)

Therefore  sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).

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Step-by-step explanation:

1. w=4 v=-3

2. y=6 x=-2

4. m=6 p=3

5. b=-2 a=4

7. c=8 d=-7

8. g=-3 f=5

10. j=2.5 k=4

11. x=4 y=1.5

13. x=2 y=1

14. y=6 x=5

Answer:

do how to do this is 16 x 16=256 and 8 x 8 =64 so 256+64=320

The exponential function of the population is P(x) = 15000 * 1.046^x

From the question, we have the following parameters that can be used in our computation:

Initial, a = 15000

Rate, r = 4.6%

The equation of the function is represented as

P(x) = a * (1 + r)^x

Substitute the known values in the above equation, so, we have the following representation

P(x) = 15000 * (1 + 4.6%)^x

Evaluate

P(x) = 15000 * 1.046^x

Hence, the function is P(x) = 15000 * 1.046^x

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1. We can see that brainstorming, we discover that sports the graph represents is 100-yard dash. This is because athletes start from a stationary position and accelerate to their maximum speed, which is usually reached halfway through the race, and then slow down to a stop at the finish line.

2. The vocabulary and properties of graphs and functions do you see represented in the graph are:

A graph is a mathematical representation of a set of data or a relationship between two or more variables. It typically consists of a set of points, or vertices, connected by lines or curves, known as edges or arcs. Graphs are used to visualize and analyze data, and to model and solve real-world problems in a variety of fields, including mathematics, science, engineering, economics, and social sciences.

We see here that the vocabulary and properties of the graph shows the choice of sports as it tells us how the speed decreases as time increases.

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The complete question is:

Portfolio Option 1: Sports Graph

This portfolio problem will have you write. You will turn in a “mathematical paper” of about 1 page of writing. You can use this handout to write rough draft ideas first.

Brainstorm: Which of the above sports do you think the graph could represent? Why?

Brainstorm: What vocabulary and properties of graphs and functions do you see represented in the graph? How did any of those affect your choice for the sport?

Use your brainstorms above to write a 1 page paper that talks about this graph, what sport you believe it could represent, and what properties of functions and graphs support your answer. You can add diagrams as well.

Pi is the ratio of the circumference of a circle to its diameter.

Answer:

14cm

Step-by-step explanation:

112÷8=14

base length=14cm

Answer:

To find the base length of a rectangle, given its area and height, you can use the formula for calculating the area of a rectangle, which is:

Area = Length x Width

In this case, you are given that the area is 112 square inches and the height is 8 inches. Let's denote the base length as "x" inches.

So, the equation for the area of the rectangle becomes:

112 = x * 8

To solve for "x", you can divide both sides of the equation by 8:

112 / 8 = x

x = 14

Therefore, the base length of the rectangle is 14 inches.

The income tax payable can be calculated as follows:

Taxable income = $500,000

Tax rate = 40%

Income tax payable = $500,000 x 40% = $200,000

The DTA (Deferred Tax Asset) year-end balance can be calculated as follows:

Beginning balance DTA = $20,000

Future deductible amounts = $55,000

DTA year-end balance = $20,000 + $55,000 = $75,000

The DTL (Deferred Tax Liability) year-end balance can be calculated as follows:

Beginning balance DTL = $50,000

Future taxable amounts = $45,000

DTL year-end balance = $50,000 - $45,000 = $5,000

The income tax expense can be calculated as follows:

Income tax payable = $200,000

Add: Increase in DTL = $5,000

Less: Increase in DTA = $55,000 - $20,000 = $35,000

Income tax expense = $200,000 + $5,000 - $35,000 = $170,000

The originating/reversing amount for the future taxable amount and for the deductible amount of the current year can be calculated as follows:

Future taxable amount:

Origination amount = $45,000 x 40% = $18,000

Reversing amount = $18,000

Future deductible amount:

Origination amount = $55,000 x 40% = $22,000

Reversing amount = $22,000 - $20,000 = $2,000 (since the beginning balance of DTA was $20,000)

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Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.

A prism having a pentagonal base is referred to as a pentagonal prism. It has two hexagonal bases, five parallelogram faces, and seven faces. Seven faces, fifteen edges, and ten vertices make up a pentagonal prism.

The two bases of each of the seven faces—two pentagons—and the remaining five faces—parallelograms—connect the bases of the pentagons.

Given data:

surface area of pentagonal prism = 2* base area + 5*rectangle area

surface area of pentagonal prism = 2* B + 5*L*w

surface area of pentagonal prism = 2* 84.3 + 5*7*4

surface area of pentagonal prism = 168.6 + 140

surface area of pentagonal prism = 308.6 sq. ft

Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.

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The two equations that can be most appropriately solved by using the zero product property are:

3x² - 6x = 0 and -(x - 1)(x + 9) = 0.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The zero product property can be used to solve equations that can be factored into the product of two or more expressions, where one or more of those expressions is equal to zero.

Therefore, the two equations that can be solved using the zero product property are:

3x² - 6x = 0

This equation can be factored as:

3x(x - 2) = 0

Using the zero product property, we get:

3x = 0 or x - 2 = 0

Solving for x, we get:

x = 0 or x = 2

-(x - 1)(x + 9) = 0

This equation can be factored using the difference of squares:

-(x - 1)(x + 9) = -(x² - 1² - 9x + 1x) = -(x² - 8x - 9) = 0

Using the zero product property, we get:

x - 1 = 0 or x + 9 = 0

Solving for x, we get:

x = 1 or x = -9

Therefore, the two equations that can be most appropriately solved by using the zero product property are:

3x² - 6x = 0 and -(x - 1)(x + 9) = 0.

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We see that f(-1) = g(1) = 5. Therefore, the solution to the system of equations is x = -1.

A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values for the variables that satisfy all of the equations in the system.

One way to solve a system of equations is by substitution. We can solve one of the equations for one of the variables in terms of the other variable, and then substitute that expression into the other equation to get an equation in one variable. We can then solve that equation for the variable, and use that value to find the value of the other variable.

Another way to solve a system of equations is by elimination. We can add or subtract the equations in the system to eliminate one of the variables, and then solve for the other variable. We can then use that value to find the value of the eliminated variable.

To find a solution to the system of equations that includes the quadratic function f(x) and the linear function g(x), we need to find the value of f(x) for each value of x and compare it to the corresponding value of g(x). If f(x) and g(x) are equal for any value of x, then that value is a solution to the system.

Substituting each value of x into the quadratic function f(x), we get:

f(-2) = 2(-2)² + (-2) + 4 = 10

f(-1) = 2(-1)² + (-1) + 4 = 5

f(0) = 2(0)² + 0 + 4 = 4

f(1) = 2(1)² + 1 + 4 = 7

f(2) = 2(2)² + 2 + 4 = 14

Comparing these values to the corresponding values of g(x), we see that f(-1) = g(1) = 5. Therefore, the solution to the system of equations is x = -1.

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Answer:

$140.70

Step-by-step explanation:

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Answer:

68/25

Step-by-step explanation:

Answer:

57.8°

Step-by-step explanation:

SohCahToa

use sin^1 to get angle

sin^1(11/13)=57.7957725

to the nearest tenth=57.8°

We need a sample size of at least 154 subjects to estimate the mean HDL cholesterol within 3 points with 95% confidence.

Dcreasing the confidence level from 99% to 95% reduces the required sample size. This is because a higher confidence level requires a larger z-value, which increases the sample size needed to achieve the desired margin of error.

The standard deviation is a measure of the amount of variation or dispersion of a set of data values. It is calculated as the square root of the variance, which is the average squared difference between each value and the mean.

The mean is a measure of central tendency that represents the average value of a set of data. It is calculated by summing up all the values in the set and dividing by the number of values.

According to the given information:

To estimate the required sample size, we can use the formula:

n = (z-value)² × s² / E²

where:

z-value = the z-score corresponding to the desired level of confidence

s = the population standard deviation (given as 14)

E = the desired margin of error (3 points)

For a 99% confidence level, the z-value is 2.576 (obtained from a standard normal distribution table). Plugging in the given values, we get:

n = (2.576)² × 14² / 3²

n = 267.89

We need a sample size of at least 268 subjects to estimate the mean HDL cholesterol within 3 points with 99% confidence.

For 95% confidence, the z-value is 1.96. Using the same formula, we get:

n = (1.96)² × 14² / 3²

n = 153.44

We need a sample size of at least 154 subjects to estimate the mean HDL cholesterol within 3 points with 95% confidence.

As we can see, decreasing the confidence level from 99% to 95% reduces the required sample size. This is because a higher confidence level requires a larger z-value, which increases the sample size needed to achieve the desired margin of error.

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Answer: $624.24.

Step-by-step explanation:

To find the total amount of interest paid on the loan, we first need to find the total amount of money repaid over the course of 36 months.

The total amount repaid is the monthly payment multiplied by the number of months:

Total amount repaid = Monthly payment x Number of months

Total amount repaid = $79.84 x 36 = $2,874.24

To find the total amount of interest paid, we need to subtract the original amount borrowed from the total amount repaid:

Total interest paid = Total amount repaid - Original amount borrowed

Total interest paid = $2,874.24 - $2,250 = $624.24

Therefore, the total amount of interest paid on the loan is $624.24.

Answer: The type of probability illustrated here is theoretical probability, and option A correctly identifies it as such.

Theoretical probability is based on mathematical reasoning and analysis of possible outcomes. In this case, we know that there are 52 cards in a deck, and 13 of them are hearts. So, the probability of drawing a heart on the first card is 13/52. After the first card is drawn, there are 51 cards remaining in the deck, including 12 hearts. So, the probability of drawing a heart on the second card is 12/51. Continuing this process, we find the probability of drawing five hearts in a row to be:

P(heart) = (13/52) x (12/51) x (11/50) x (10/49) x (9/48) = 0.0104 or about 1.04%

This probability is based purely on mathematical reasoning and analysis of possible outcomes, and does not involve any actual experimentation. Therefore, it is an example of theoretical probability.

Step-by-step explanation:

Therefore, it is not even chance, but it is also not very unlikely. It is moderately likely that a yellow marble will be selected on the first draw.

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurring. It is a measure of the likelihood or chance of an event happening. Probability is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.

In other words, probability is a way of quantifying uncertainty. It is used in various fields, such as statistics, physics, finance, engineering, and more, to help make predictions and decisions based on uncertain information. Probability theory provides a set of rules and tools for analyzing and manipulating random variables and events, and for calculating the probability of complex events.

The likelihood of a yellow marble being selected on the first draw can be calculated by dividing the number of yellow marbles by the total number of marbles in the bag:

likelihood of selecting a yellow marble = number of yellow marbles / total number of marbles

So, in this case, the likelihood of selecting a yellow marble on the first draw is:

likelihood of selecting a yellow marble = 2 / (3 + 2 + 1) = 2/6 = 1/3

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Answer:

[tex]f(x) = \frac{(x - 1)(x - 2)(x - 6)}{(x - 1)(x - 3)(x - 5)} [/tex]

We need to collect 46 newspapers to be certain that at least two newspapers have the same number of pages.

According to the Pigeonhole Principle, if we have n+1 pigeons and n holes, then there must be at least one hole with two or more pigeons. Similarly, if we have n+1 newspapers with n possible page counts, then there must be at least one page count that appears in two or more newspapers.

In this case, we have a range of 38 possible page counts (46 - 9 + 1), so we need at least 39 newspapers to guarantee that each possible page count appears in at least one newspaper.

However, to guarantee that at least two newspapers have the same number of pages, we need one more newspaper than the number of possible page counts, so we need a total of 46 newspapers. Therefore, if we collect 46 newspapers, we can be certain that at least two of them have the same number of pages.

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Answer:

Definitely 4 always 4!!!

Answer: Let the experienced one help you out! Read the explanation down below! Brainliest?

Step-by-step explanation:

The sample space for rolling a 4-sided die twice consists of all possible pairs of outcomes, where each outcome is a number from 1 to 4. To find which outcome is not part of the sample space, we can list all the possible outcomes and then look for a number pair that does not appear.

Possible outcomes:

(1,1), (1,2), (1,3), (1,4)

(2,1), (2,2), (2,3), (2,4)

(3,1), (3,2), (3,3), (3,4)

(4,1), (4,2), (4,3), (4,4)

There are 16 possible outcomes, so one of the numbers from 1 to 16 is not part of the sample space. The missing outcome is (3,4) or (4,3), depending on the order in which the dice are rolled.

if 4-sided die, labeled 1–4 is rolled twice then 5,3 is not part of the sample space because the outcomes 5 and 3 are not part of the sample space.

It is a branch of mathematics that deals with the occurrence of a random event.

A sample space is a collection or a set of possible outcomes of a random experiment.

The sample space of rolling a 4-sided die twice can be represented by all possible ordered pairs of the outcomes, which can be listed as follows:

{(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}

Therefore,  if  4-sided die, labeled 1–4 is rolled twice then 5,3 is not part of the sample space because the outcomes 5 and 3 are not part of the sample space.

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Expressions for the square footage of the tile Dining area, Considering only the tile floor, and not the cabinets shown in black will be (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11)

The area of a rectangle is a measure of the amount of space it occupies in two-dimensional (2D) space. It is calculated by multiplying the length of the rectangle by its width. Mathmatically,

                                     [tex]Area=length*width[/tex]

Now, Solving given problem,

The total area of the grid will be:Length of grid = 16 ft, Width of grid = 13 ft

Total area of grid = Length x Width = 16 ft x 13 ft = 208 sq ft

The area of the rectangle in the top right :Length of rectangle = 12 ft, Width of rectangle = 2 ft

Area of rectangle = Length x Width = 12 ft x 2 ft = 24 sq ft

To remove the top right rectangle from the tile dining area, subtract its area from the total area of the grid:

(Total area of grid) - (Area of rectangle in top right) = (208 sq ft -24 sq ft )= 184 sq ft

So, the expression for this calculation will be: (16 x 13) - (12 x 2) = 184 sq ft

The area of the vertical rectangles on the far left and right sides is calculated as follows:Width of vertical rectangles = 4 ft, Length of grid = 13 ft

Area of vertical rectangles = Width of vertical rectangles x Length of grid = 4 ft x 13 ft = 52 sq ft

The area of the rectangle in the top right:Length of rectangle = 12 ft, Width of rectangle = 11 ft

Area of rectangle = Length x Width = 12 ft x 11 ft = 132 sq ft

Add the areas of the vertical rectangles and the rectangle in the top right to get the total area of the tile dining area:

Area of vertical rectangles + Area of rectangle in top right = 52 sq ft + 132 sq ft = 184 sq ft

So, the expression for this calculation is: (4 x 13) + (12 x 11) = 184 sq ft

Hence, both of these expressions- (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11) gives the square footage of the tile dining area based on the given information.

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