Work out 15:
6
Give your answer as an integer or as a
fraction in its lowest terms.


PLEASE HELP

Answer:

7

Step-by-step explanation:

The table which represents a linear function is answer B. By calculating the slope between any two points on the table.

A linear function is a mathematical function that produces a straight line when graphed. It is a type of function where the input variable (x) and output variable (y) are related in a way that can be represented by a straight line.

To determine which table represents a linear function, we need to check whether the change in the output variable (y) is proportional to the change in the input variable (x) for any two points on the table.

Answer A:

When we compare the difference between each value of y, we see that each subsequent value of y is multiplied by 2. For example, 2 x 2 = 4, 4 x 2 = 8, and so on. This means that there is a constant rate of change between each pair of x and y values, but the rate of change is not constant. Therefore, the function is not linear.

Answer B:

When we compare the difference between each value of y and x, we see that the difference between any two values of y is proportional to the difference between the corresponding x values. Specifically, when x increases by 1, y increases by 1, except for the first two values. This means that the rate of change between each pair of x and y values is constant, and the function is linear.

Answer C:

When we compare the difference between each value of y, we see that the difference between any two values of y is not proportional to the difference between the corresponding x values. Specifically, the rate of change is not constant. Therefore, the function is not linear.

Answer D:

When we compare the difference between each value of y, we see that the rate of change is not constant. Specifically, the rate of change from x = 1 to x = 2 is different from the rate of change from x = 2 to x = 3. The function is not linear.

Therefore, only answer B represents a linear function.

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Using Simple interest, savings account for her needed to deposit $1,842.82 each year.

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

t can also be computed using the annuity factor of 5% for 17 years to divide the total sum of $50,000.

The 529 plan, according to available data, is a tax-advantaged or tax-qualified savings plan designed to encourage individuals to save for future education costs of their relations or for themselves.

Data and Calculations:

N (number of intervals) = 17 years

Interest every year is equal to 5%.

Present Value = $0 PV

FV (Future Value) = $50,000 ($31,327.88 + $18,672.12)

Results: PMT = $1,842.82

Sum of all periodic payments = $31,327.88 ($1,842.82 x 17)

Total Interest = $18,672.12

Hence, in order to save $50,000 in 17 years at a 5% return for his granddaughter, the man who wanted to open a 529 college savings account for her needed to deposit $1,842.82 each year.

Hence the interest the bank will collect will be $117.53.

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Using the method of undetermined coefficients, the particular solution is:

[tex]\mathrm{y_p(t) = 6e^{2t} \times cos(9t) + 3^{2t} \times sin(9t)}[/tex]

To use the method of undetermined coefficients, we assume that the particular solution has the same form as the forcing term, but with undetermined coefficients.

Let's start by finding a particular solution for the equation:

y′′ − 4y′ + 81y = 48[tex]e^{2t}[/tex]cos(9t) + 80[tex]e^{2t}[/tex]sin(9t) + 3[tex]e^{(-t)[/tex]

Since the forcing term contains both exponential and trigonometric functions, we'll assume that the particular solution is of the form:

[tex]y_p[/tex](t) = A*[tex]e^{2t}[/tex]cos(9t) + B[tex]e^{2t}[/tex]*sin(9t) + C[tex]e^{(-t)[/tex]

where A, B, and C are undetermined coefficients that we need to determine.

Let's find the first and second derivatives of [tex]y_p[/tex](t):

[tex]y'_p[/tex](t) = (2A + 9B)*[tex]e^{2t}[/tex]*sin(9t) + (2B - 9A)*[tex]e^{2t}[/tex]*cos(9t) - C[tex]e^{(-t)[/tex]

[tex]y''_p[/tex](t) = (4A - 81B)*[tex]e^{2t}[/tex]*cos(9t) + (4B + 81A)*[tex]e^{2t}[/tex]*sin(9t) + C[tex]e^{(-t)[/tex])

Substituting these expressions into the differential equation, we get:

(4A - 81B)*[tex]e^{2t}[/tex]*cos(9t) + (4B + 81A)*[tex]e^{2t}[/tex]*sin(9t) + C[tex]e^{(-t)[/tex]

4[(2A + 9B)*[tex]e^{2t}[/tex]*sin(9t) + (2B - 9A)*[tex]e^{2t}[/tex]*cos(9t) - C[tex]e^{(-t)[/tex]

81[A*[tex]e^{2t}[/tex]cos(9t) + B[tex]e^{2t}[/tex]*sin(9t) + C[tex]e^{(-t)[/tex]]

= 48[tex]e^{2t}[/tex]cos(9t) + 80[tex]e^{2t}[/tex]sin(9t) + 3[tex]e^{(-t)[/tex]

Simplifying and grouping terms, we get:

[(4A + 18B)cos(9t) + (18A - 4B)sin(9t)][tex]e^{2t}[/tex]+ (81C + 3)[tex]e^{(-t)[/tex] = 48[tex]e^{2t}[/tex]cos(9t) + 80[tex]e^{2t}[/tex]sin(9t) + 3[tex]e^{(-t)[/tex]

Since the two sides of the equation must be equal for all values of t, we can equate the coefficients of the exponential and trigonometric functions on both sides:

4A + 18B = 48 => A = 6

18A - 4B = 80 => B = 3

81C + 3 = 3 => C = 0

Therefore, the particular solution is:

[tex]y_p[/tex](t) = 6[tex]e^{2t}[/tex]*cos(9t) + 3[tex]e^{2t}[/tex]*sin(9t)

Thus, the general solution of the differential equation is:

[tex]\mathrm{y(t) = y_h(t) + y_p(t)}[/tex]

where [tex]y_h[/tex](t) is the complementary solution. Since the characteristic equation of the differential equation is r² - 4r + 81 = 0, it has two complex conjugate roots: r = 2 ± 9i. Therefore, the complementary solution is:

[tex]y_h[/tex](t) = [tex]c_1[/tex]*[tex]e^{2t}[/tex]cos(9t) + [tex]c_2[/tex][tex]e^{2t}[/tex]*sin(9t).

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The domain is the set of all x-values greater than or equal to 1, and the range is the set of all y-values greater than or equal to -2.

A coordinate plane is a two-dimensional graph that is used to locate points in a given space. The two axes intersect at a point called the origin, which is located at the coordinates (0, 0). Points on the coordinate plane can be labeled using their x and y coordinates, which are written in the form (x, y).

The graph below shows a function in the coordinate plane, which is made up of a curved line that begins at the point (1, -2) and rises as it moves to the right. The domain of the function is all x-values, or inputs, which are greater than or equal to 1. The range of the function is all y-values, or outputs, which are greater than or equal to -2.

When determining the domain and range of a function, it is important to remember that the domain is the set of all possible inputs, while the range is the set of all possible outputs. In the case of the graph below, the domain is the set of all x-values greater than or equal to 1, and the range is the set of all y-values greater than or equal to -2.

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The mean and standard deviation for Brett Favre's per game pass completions were 21.4 and 6.47, respectively, and all measurements fall within two standard deviations of the mean.

What is standard deviation ?

Standard deviation is a measure of the amount of variation or dispersion in a set of data. It is a statistic that indicates how much the individual data points deviate from the mean or average of the dataset.

a. Here's a stem-and-leaf plot for the number of passes completed by Brett Favre for each of the 16 regular season games in the fall of 2006:

Each stem represents the tens digit of the number of passes completed, and each leaf represents the ones digit.

b. To calculate the mean and standard deviation for Brett Favre's per game pass completions, we can use the following formulas:

mean = (sum of all values) / (number of values)

standard deviation = sqrt[(sum of (each value minus the mean) squared) / (number of values - 1)]

Using these formulas, we get:

mean = (15 + 31 + 25 + 22 + 22 + 19 + 17 + 28 + 24 + 5 + 22 + 24 + 22 + 20 + 26 + 21) / 16 = 21.4

standard deviation = [tex]sqrt[((15-21.4)^2 + (31-21.4)^2 + (25-21.4)^2 + (22-21.4)^2 + (22-21.4)^2 + (19-21.4)^2 + (17-21.4)^2 + (28-21.4)^2 + (24-21.4)^2 + (5-21.4)^2 + (22-21.4)^2 + (24-21.4)^2 + (22-21.4)^2 + (20-21.4)^2 + (26-21.4)^2 + (21-21.4)^2) / (16-1)] = 6.47 \\ \\= 6.47[/tex] (rounded to two decimal places)

Therefore, Brett Favre's per game pass completions had a mean of 21.4 and a standard deviation of 6.47.

c. To find the proportion of the measurements that lie within two standard deviations of the mean, we need to find the range of values that fall within two standard deviations above and below the mean. We can use the following formula:

range = mean ± (2 × standard deviation)

Plugging in the values we calculated in part b, we get:

range = 21.4 ± (2 × 6.47) = 8.46 to 34.34

Therefore, the mean and standard deviation for Brett Favre's per game pass completions were 21.4 and 6.47, respectively, and all measurements fall within two standard deviations of the mean.

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The area of the complex figure is 178 square meters.

Option (A) is correct.

What is an area?

In geometry, area is the measure of the amount of surface enclosed by a two-dimensional shape or a planar figure. It is typically measured in square units such as square centimeters, square inches, or square meters.

To find the area of a rectangle, we can multiply its length by its width.

Given width = 8 m and length = 16 m, the area of the rectangle is:

Area = length x width = 16 m x 8 m
Area = 128 cm^2 ------(I)

To find the area of a rectangle, we can multiply its length by its width.

Given width = 5 m and length = 6 m, the area of the rectangle is:

Area = length x width = 6 m x 5 m
Area = 30 m^2 -----(II)

The area of a triangle is given by the formula A = 1/2 x b x h, where A is the area, b is the base of the triangle, and h is its height.

Given that the height of the triangle is 8 m and its base is 5 m, the area of the triangle is:

A = 1/2 x b x h = 1/2 x 5 m x 8 m
Area = 20 square m  ---------(III)

Adding (I), (II) and (III), we get

Area = 128 + 30 + 20

Area = 178 sq.m

Hence, the area of the complex figure is 178 square meters.

Option (A) is correct.

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Answer:

The area of the complex figure is 178 square meters. Thus, Option (A) is correct.

The value of the given function for x=4 is 82.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is y+√x=5x+(x+4)².

Here, y=5x+(x+4)²-√x

f(x)=5x+(x+4)²-√x

Substitute x=4 in the function, we get

f(4)=5(4)+(4+4)²-√4

= 20+64-2

= 82

Therefore, the value of function is 82.

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The volume of the box is a function of x, given by:[tex]V(x) = 4x^3 - 32x^2 + 64x[/tex]

What is volume ?

Volume is a physical quantity that measures the amount of three-dimensional space that a substance or object occupies. It is usually measured in cubic units, such as cubic meters, cubic centimeters, cubic feet, or cubic inches.

To construct the box, we start with a square piece of cardboard that is 8 inches by 8 inches. We will cut out squares from each corner with side length x inches. This will leave us with a rectangular piece of cardboard with dimensions 8-2x by 8-2x, and we can fold up the sides to form the open box.

The height of the box will be x inches, and the length and width of the base of the box will be 8-2x inches. Therefore, the volume of the box will be:

Volume = Length x Width x Height

Volume = (8-2x) x (8-2x) x x

[tex]Volume = x(64-32x+4x^2)[/tex]

Therefore, the volume of the box is a function of x, given by: [tex]V(x) = 4x^3 - 32x^2 + 64x[/tex]

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The probability is approximately 0.8185 or 81.85%.

Normal distribution, also known as Gaussian distribution, is a probability distribution that is commonly used in statistics, mathematics, and the natural sciences to describe real-valued random variables whose distributions are not known.

To find the probability that a randomly selected x-value from a normal distribution with a mean of 48 and a standard deviation of 7 is between 34 and 55, we need to standardize the values using the z-score formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

For x = 34:

z = (34 - 48) / 7 = -2

For x = 55:

z = (55 - 48) / 7 = 1

We can use a standard normal distribution table or a calculator to find the area under the standard normal distribution curve between z = -2 and z = 1. This area represents the probability that a randomly selected x-value from the given normal distribution is between 34 and 55.

Using a standard normal distribution table, we can find the probabilities as follows:

P(z < -2) = 0.0228 (from the table)

P(z < 1) = 0.8413 (from the table)

Therefore, the probability that a randomly selected x-value from the given normal distribution is between 34 and 55 is:

P(-2 < z < 1) = P(z < 1) - P(z < -2) = 0.8413 - 0.0228 = 0.8185

So, the probability is approximately 0.8185 or 81.85%.

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The 1-dimensional space can be identified using the point x= 3, that is the x-coordinate of the point. This depicts the complexity of the space in 1-dimension.

The link between the number of dimensions and the complexity of the space is shown by the fact that just one integer is required to identify a specific location in a 1-dimensional space. The complexity of the space increases as the number of coordinates required to identify a point increases in higher dimensions.

Hence, the 1-dimensional space can be identified using the point x= 3, that is the x-coordinate of the point. This depicts the complexity of the space in 1-dimension.

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Therefore, the correct answer is option 4: 5x + 3y = 80.

A mathematical statement that shows the equivalence of two formulas is what an equation through algebra means. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.

Let the number of 3-point questions answered correctly be x, and the number of 5-point questions answered correctly be y. Then, we can form two equations based on the information given:

3x + 5y = 80 (total score equation)

x + y = ?? (number of questions answered equation)

We cannot determine the exact value of x + y from the given information, so we will leave it as an unknown.

The correct equation that represents the number of 33-point questions, x, and the number of 5-point questions, y, he answered correctly is:

5x + 3y = 80

This equation comes from the fact that the student only answered 3-point and 5-point questions correctly. Therefore, the only way for the student to get a score of 80 is if the number of 3-point questions he answered correctly is a multiple of 3 and the number of 5-point questions he answered correctly is a multiple of 5. Thus, we can write:

x = 33n, where n is a non-negative integer (since the number of 3-point questions he answered correctly must be a multiple of 33)

y = 5m, where m is a non-negative integer (since the number of 5-point questions he answered correctly must be a multiple of 5)

Substituting these expressions into the total score equation, we get:

3(33n) + 5(5m) = 99n + 25m = 80

Simplifying this equation, we get:

5x + 3y = 80

Therefore, the correct answer is option 4: 5x + 3y = 80.

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Answer:42

Step-by-step explanation:took the quiz

The DRD for Jazz Corporation on the dividend it received from Williams Corp. is $4,000.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To calculate the dividends received deduction (DRD) for Jazz Corporation on the dividend it received from Williams Corp., we need to determine the taxable income limit for the deduction.

The taxable income limit is based on the percentage of ownership in the company. Since Jazz Corporation owns 10% of Williams Corp. stock, the taxable income limit is 50% of its taxable income, or $4,000 ($8,000 x 50%).

The DRD is then calculated as the lesser of the dividend received or the taxable income limit. In this case, Jazz Corporation received a dividend of $12,900, which exceeds the taxable income limit of $4,000.

Therefore, the DRD for Jazz Corporation on the dividend it received from Williams Corp. is $4,000.

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The solution of the inequality is x > -4. In the interval notation is (-4,∞).

What is inequality?

In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equal. But various inequalities are used to compare the values, whether it is less than or greater than.

An inequality exists when two real numbers or algebraic expressions are connected by the symbols “>”, “<”, “≥”, “≤”.

The given inequality is:

6x + 8 > - 16

Subtract 8 from both sides:

6x + 8 - 8 > - 16 - 8

6x  > - 24

Divide both sides by 6:

x > -24/6

x > -3

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We have no control over our cravings, affection, passion, or avarice. Humans and plants have many characteristics. You eat human flesh because you are a plant. Our way of life is represented by the plant.

Whether by hunting or scavenging, an animal or plant that consumes meat gets its food and energy needs from animal tissues (primarily muscle, fat, and other soft tissues).

The majority of the member species of the order Carnivora are known by the technical term "carnivoran," although confusion is often caused by the resemblance between the name of the order and the name of the diet.

So, in the given situation as the grows and as the money grows, it demonstrates that we are all looking out for one another.

In some ways, we are all carnivorous plants.

We all commit murder.

We are powerless against our hunger, love, passion, and greed. Plants and humans are similar in many ways.

What we desire is to live, and to exist in this world. You are a plant that consumes human flesh.

The plant represents our way of life.

Therefore, we have no control over our cravings, affection, passion, or avarice. Humans and plants have many characteristics. You eat human flesh because you are a plant. Our way of life is represented by the plant.

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Complete question:

Carnivorous plants have some unique and amazing characteristics. What do these characteristics suggest about life and the world that we live in? In other words, what can carnivorous plants teach us about the world?? Make a point and support it with an example from the text. Explain what your support shows.

Answer:

Side PQ is the same as RQ

Angle QRS is the same as QPS

Step-by-step explanation:

The slope of the secant line  PQ is -11.6

To find the slope of the secant line PQ, we need to find the coordinates of point Q, and then calculate the slope using the formula:

slope of PQ = (yQ - yP)/(xQ - xP)

where (xP, yP) = (0, 9) and (xQ, yQ) = (0.1, y(0.1)).

First, we need to find y(0.1) by substituting x = 0.1 into the equation y = (3 - 2x)^2:

y(0.1) = (3 - 2(0.1))^2 = (2.8)^2 = 7.84

Therefore, point Q is (0.1, 7.84).

Now we can calculate the slope of PQ:

slope of PQ = (yQ - yP)/(xQ - xP) = (7.84 - 9)/(0.1 - 0) = -11.6

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Using basic arithmetic operation, Ann's stock investment has increased in value more, by $331.25, compared to her bond investment, which has increased in value by $378.66.

The current value of Ann's bond investment can be calculated using the following formula:

Current Value of Bonds = Par Value x Market Rate

Since Ann has 7 bonds with a par value of $500 each, the total par value of her bond investment is:

$500 x 7 = $3,500

Using the market rate of 106.384, we can calculate the current value of Ann's bond investment as:

Current Value of Bonds = $3,500 x 1.06384 = $3,725.44

The current value of Ann's stock investment can be calculated by multiplying the number of shares she owns by the current stock price:

Current Value of Stock = Number of Shares x Stock Price

Since Ann owns 125 shares of Cilla Shipping stock and the current stock price is $30.65, the current value of her stock investment is:

Current Value of Stock = 125 x $30.65 = $3,831.25

To determine which investment has increased in value more, we need to compare the difference between the current and original values of each investment. The original value of Ann's bond investment is:

Original Value of Bonds = Par Value x Market Rate = $500 x 7 x 0.95626 = $3,346.78

The difference between the current and original value of Ann's bond investment is:

$3,725.44 - $3,346.78 = $378.66

The original value of Ann's stock investment is:

Original Value of Stock = Number of Shares x Stock Price = 125 x $28.00 = $3,500

The difference between the current and original value of Ann's stock investment is:

$3,831.25 - $3,500 = $331.25

Hence, Ann's stock investment has increased in value more, by $331.25, compared to her bond investment, which has increased in value by $378.66.

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The value of probability that they have pulse rates with mean less than 78 beats per min would be; 0.5948

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Given that If 16 female are randomly selected the Mean is 75 beats per min And, Standard deviation is, 12.5

Hence, We get;

z = (78 - 75) / 12.5

z = 3/12.5

z = 0.24

Hence, The probability is, 0.5948

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Answer:

B, C

Step-by-step explanation:

360 - 90 - 15 = 255

-90 - 15 = -105

The value of the given expression √8/81 = 2√2/81.

The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number may be found by looking for a number that, when squared, yields the original value. The equation a a = b is true if 'a' is the square root of 'b'. Every integer has two square roots, one of a positive value and one of a negative value, because the square of any number is always a positive number. For instance, the square roots of 4 are both 2 and -2.

Given that,

√8/81

We can write the value of √8 = √(2)(2)(2) = 2√2.

Thus, we have the value of √8/81 = 2√2/81.

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By rewriting the 3 given systems, we will see that:

1) Independent and consistent.

2) Independent and inconsistent.

3) Dependent.

What is the system of equations?

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Let's look at the first one, we can rewrite it as:

y = 2x + 3

y = -x - 3

So, the slopes are different, meaning that we have one solution, so this system is consistent and independent.

Now let's look at the second system, we can rewrite it as:

y = 3x - 2

y = 3x + 2

Here both lines have the same slope, so the lines never do intersect, meaning that the system is inconsistent and independent.

For the final system, we have:

y = (-1/2)×x + 2

y = (-1/2)×x + 2

Hence, we have two equal lines, so this system is dependent.

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The measure of angle x in the hexagon is 140 degree.

The formula for calculating the sum of interior angles of a polygon is ( n − 2 ) × 180 degree.

where is the number of sides

Since the number of sides of the polygon in the diagram is 6, we can find the sum of the interior angle.

Sum of interior angle = ( n − 2 ) × 180

Plug in n = 6

Sum of interior angle = ( 6 − 2 ) × 180

Sum of interior angle = ( 4 ) × 180

Sum of interior angle = 720°

Next, we sum up the interior angles given in the diagram equate to 720 degree and solve for x.

108 + 155 + 123 + 104 + 90 + x = 720

Collect and add like terms

580 + x = 720

Subtract 580 from both sides

580 - 580 + x = 720 - 580

x = 720 - 580

x = 140°

Therefore, the value of x is 140 degree.

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The cost of Shai's haircut is $25 and the cost of his shave is $30, so the subtotal before tax and tip is:

$25 + $30 = $55

The sales tax is 8.25%, so the tax amount is:

$55 * 0.0825 = $4.54

The total cost before tip is:

$55 + $4.54 = $59.54

If Shai tips 25% on the subtotal, the tip amount is:

$55 * 0.25 = $13.75

So the total cost including tax and tip is:

$59.54 + $13.75 = $73.29

Therefore, Shai must pay a total of $73.29 if he gets his hair cut and beard shaved and he tips the barber 25%. The answer is option (B).

Part a: Compounded Semiannually: A = 20,771.75.

Part b: Compounded quarterly: A = 20817.66.

Part c: Compounded monthly: A = 20848.76

Part d: Compounded continuously :A = 407,538.49

Compound interest formula:

A = P[tex](1 + \frac{r}{n} )^{nt}[/tex]

And

A = P[tex]e^{rt}[/tex]

Principal P : $15,000

Time t = 6 years

Rate of interest r = 5.5%

number of time compounded - n

Part a: Compounded Semiannually:

r --> r/2

n = 2

A = 15,000[tex](1 + \frac{0.055}{2} )^{2*6}[/tex]

A = 20,771.75

Part b: Compounded quarterly:

r --> r/4

n = 4

A = 15,000[tex](1 + \frac{0.055}{4} )^{4*6}[/tex]

A = 20817.66

Part c: Compounded monthly:

r --> r/12

n = 12

A = 15,000[tex](1 + \frac{0.055}{12} )^{12*6}[/tex]

A = 20848.76

Part d: Compounded continuously

A = Pe∧(rt)

A = 15,000(2.72)∧(0.55*6)

A = 407,538.49

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Answers:

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Explanation:

Problem 1

Each time x goes up by 1, y goes down by 5. This constant rate of change leads to the equation being linear. The slope is m = -5/1 = -5. You can use the slope formula for any two points in the table to confirm this is the correct slope.

The y intercept is b = 15 because we have x = 0 lead to y = 15.

Therefore, we go from y = mx+b to y = -5x+15

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Problem 2

Each time x goes up by 3, the y coordinate goes down by 3. Therefore, we have another linear equation here. The slope is m = -3/3 = -1.

The y intercept is b = 4 because x = 0 leads to y = 4.

y = mx+b turns into y = -x+4

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Problem 3

Each time x goes up by 1, y is NOT going up the same amount. The jump from 10 to 20 is +10. The jump from 20 to 40 is +20. And so on.

Therefore, this equation isn't linear. Instead it's exponential. Each y term doubles when x increases by 1, so that's why the b term is b = 2.

The initial term is a = 80 because x = 0 leads to y = 80.

We go from y = a*b^x to y = 80*2^x

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You can use a tool like Desmos or GeoGebra to visually confirm each of the answers. Both also offer support for function tables.

Answer:

1.  y = -5x + 15.

2. y = -x + 4.

3. y = 80(2^(x/3))

Step-by-step explanation:

1.

From the given data, we can see that as x increases by 1, y decreases by a fixed amount of 5. This means that the relationship between x and y is linear, specifically a decreasing linear relationship.

To write the equation for a linear relationship, we need to find the slope (m) and y-intercept (b).

Using the formula for slope:

m = (change in y) / (change in x)

m = (0 - 30) / (3 - (-3))

m = -5

Using the point-slope form of a linear equation:

y - y1 = m(x - x1)

y - 30 = -5(x - (-3))

y - 30 = -5x - 15

y = -5x + 15

So the equation for this linear relationship is y = -5x + 15.

2.

From the given data, we can see that as x increases by 3, y decreases by a fixed amount of 3. This means that the relationship between x and y is linear, specifically a decreasing linear relationship.

To write the equation for a linear relationship, we need to find the slope (m) and y-intercept (b).

Using the formula for slope:

m = (change in y) / (change in x)

m = (-5 - 13) / (9 - (-9))

m = -18 / 18

m = -1

Using the point-slope form of a linear equation:

y - y1 = m(x - x1)

y - 13 = -1(x - (-9))

y - 13 = -1(x + 9)

y = -x + 4

So the equation for this linear relationship is y = -x + 4.

3.

From the given data, we can see that as x increases by 1, y doubles. This means that the relationship between x and y is exponential.

To write the equation for an exponential relationship, we can use the general form of an exponential function:

y = ab^x

where a is the initial value, b is the base, and x is the exponent.

To find a and b, we can use the first and fourth data points since they have the smallest and largest values of y, respectively.

When x = -3, y = 10, so we have:

10 = ab^(-3)

When x = 0, y = 80, so we have:

80 = ab^(0)

From the second equation, we can see that a = 80. Substituting this into the first equation, we get:

10 = 80b^(-3)

Simplifying, we get:

b = 2^(1/3)

So the equation for this exponential relationship is:

y = 80(2^(1/3))^x

Simplifying further:

y = 80(2^(x/3))

The symmetry of the functions are

In mathematics, the symmetry of a function refers to the property that the function remains unchanged under a certain transformation

Using the above as a guide, we have the following:

Graph 1

Under any transformation, the function would not remain the same when transformed

Graph 2

This function is a circle equation and it would remain the same when reflected or rotated across the axes and the origin

Graph 3

This function would only remain the same when reflected across the x-axis

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Answer: Let's use variables to represent the three digits of the number. We can use d1 for the first digit, d2 for the second digit, and d3 for the third digit. Based on the given information, we can write the following equations:

d1 > d2 + 4 (the first digit is greater than the second by 4)

d3 > d1 + 2 (the third digit is greater than the first by 2)

We also know that the three digits combine to form a three-digit number. We can write this number as:

100d1 + 10d2 + d3

To solve for the digits, we can use the information we have to write expressions for d1, d2, and d3 in terms of a single variable, and then use that to find the digits. Let's start with the first equation:

d1 > d2 + 4

Subtracting 4 from both sides, we get:

d1 - 4 > d2

Now we can substitute this expression for d2 in the second equation:

d3 > d1 + 2

d3 > (d1 - 4) + 2

d3 > d1 - 2

So we have the following inequalities:

d1 > d2 + 4

d3 > d1 - 2

We can use these to write expressions for d1, d2, and d3 in terms of a single variable, say x:

d1 = x + 4

d2 = x

d3 = x + 2 + 4 = x + 6

Now we can substitute these expressions into the equation for the three-digit number:

100d1 + 10d2 + d3 = 100(x+4) + 10x + (x+6) = 111x + 406

So the three-digit number can be written as 111x + 406. To find the digits, we need to choose a value of x that satisfies the inequalities we derived. Let's start with the first inequality:

d1 > d2 + 4

x + 4 > x + 4

x > 0

So x must be greater than 0. Now let's check the second inequality:

d3 > d1 - 2

x + 6 > x + 2

6 > 2

This inequality is always true, so we don't need to worry about it. Therefore, any value of x greater than 0 will satisfy the given conditions. For example, if we choose x = 1, then the digits are:

d1 = 5

d2 = 1

d3 = 7

And the three-digit number is:

100d1 + 10d2 + d3 = 500 + 10 + 7 = 517

So the number is 517.

Step-by-step explanation:

The value of a is given as follows:

a = 2.4.

Similar polygons are polygons that share these two features presented as follows:

As the two polygons are similar for this problem, the proportional relationship for the lengths is given as follows:

3/5 = a/4 = (b - 6)/2.

Hence the value of a is obtained as follows:

3/5 = a/4

5a = 12

a = 12/5

a = 2.4.

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