6 - Which statement best explains whether the following table represents a linear or nonlinear function?

x −2 −1 0 1 2
y −4 −2 0 2 −2

The table represents a nonlinear function because there is not a constant rate of change in the output values.

The table represents a nonlinear function because there is not a constant rate of change in the input and output values.

The table represents a linear function because there is a constant rate of change in the input and output values.

The table represents a linear function because there is not a constant rate of change in the input and output values.

Gabriel is 19 years old and Caroline is 14 years old

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Aaron has two children, Gabriel and Caroline. Gabriel is older than Caroline. The difference of their ages is 5. The sum of their ages is 33.

Let C represent Caroline's age and G represent Gabriel's age.

Hence, We can formulate;

The difference of their ages is 5.

⇒ G - C = 5  .. (i)

The sum of their ages is 33.

⇒ G + C = 33 .. (ii)

Add (i) and (ii);

⇒ 2G = 38

⇒ G = 19 years

And, From (i);

⇒ G - C = 5

⇒ 19 - C = 5

⇒ 19 - 5 = C

⇒ C = 14 years

Thus, Gabriel is 19 years old and Caroline is 14 years old.

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The amount of time in which the simple interest on Rs7560 be Rs1102.50 at 25/4% per annum, 5 years

Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).

Every time we calculate simple interest the principal values will be the same unlike compound interest.

Formula;    Simple Interest(I) =  P × R × T/100

To find the time it takes for the simple interest on Rs. 7560 to be Rs. 1102.50 at 25/4% per annum, we can use the formula for simple interest:

We are given I = 1102.50 and P = 7560, and the interest rate is 25/4% per annum, which we can convert to a decimal:

r = 25/4% ÷ 100

 = 0.25/4

 = 0.0625

Now, we can substitute the known values into the formula and solve for t:

1102.50 = 7560 x r x t

1102.50 / 7560 = r x t

t = 1102.50 / (7560 x 0.0625)

t = 5 years

So, it will take 5 years for the simple interest on Rs. 7560 to be Rs. 1102.50 at 25/4% per annum.

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Answer:

= 43.

Step-by-step explanation:

[tex] \frac{5}{18} + \frac{11}{12} \\ = 36 \times \frac{5}{18} + 36 \times \frac{11}{12} \\ = 2(5) + 3(11) \\ = 10 + 33 \\ = 43[/tex]

Note// the LCM for 18 and 12 is 36.

Hence, the three numbers are 8, 1, and 3

Answer:

Here is my original puzzle problem:

* * *

There are three coins, each with a different value. The sum of the three coins is 10. The value of the first coin is twice the value of the second coin. The value of the third coin is 1 more than the value of the first coin.

What are the values of the three coins?

_________________

To solve this puzzle, you can use the following steps:

1. Let X be the value of the first coin.

2. Let Y be the value of the second coin.

3. Let Z be the value of the third coin.

4. Set up equations to represent the given information.

5. Solve the equations for X, Y, and Z.

The equations for this puzzle are as follows:

X + Y + Z = 10

X = 2Y

Z = X + 1

Solving these equations, we find that the values of the three coins are X = 4, Y = 2, and Z = 5.

I hope you enjoy this puzzle!

The approximate measure of the slide is 20 feet.

Heights and Distances is a study about the applications of Trigonometry. It has many real-life applications, such as measuring the object’s height, depth of the object, the distance between two celestial objects etc. The formulas and the ratios of trigonometry are helpful in the study of heights and distances.

Given that, a slide is 15 feet high and the slides makes a 50° angle with the ground.

Let the length of the slide be x.

Now, sin50° =15/x

0.766=15/x

x=15/0.766

x=19.58

≈ 20 feet

Therefore, the approximate measure of the slide is 20 feet.

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There are 2 balls on the side length 3 layers down in the pyramid.

A pyramid is a three-dimensional figure. It has a flat polygon base. All the other faces are triangles and are called lateral faces.

Given that, Ms. Ryan is making a pyramid of kick-balls, the bottom layer has a side length of 5 balls, each layer going down the side length is one less than the previous one,

We need to find the number of balls 3 layers down,

Since, it is given that, there is reducing one balls as going down,

Therefore,

When we will go 3 layers down it will be 3 balls reduced, the layer from where we started is having 5 balls and after coming 3 layers down, the side layer will have = 5-3 = 2 balls.

Hence, there are 2 balls on the side length 3 layers down in the pyramid.

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7/13 as a decimal rounded to the nearest hundredth.

Answer: 0.54

Answer: The answer is 0.54

The line plots that represent the data sets are:

Mean = 6, standard deviation = 2 → image 1

Mean = 10, standard deviation = 2 → image 2

Mean = 10, standard deviation = 6 → image 4

A line plot is a simple way to display data along a number line. It is used to show the distribution of a set of data by plotting each data point as a dot above its value on the number line. The dots are then connected with a line to create a plot.

Line plots are often used to visualize the frequency distribution of a dataset, particularly when the data is discrete or categorical. They are also useful for identifying outliers and patterns in the data.

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Answer:

Step-by-step explanation:

a + 2a + 6 = 180

3a = 174

a = 58

2(58) + 6 = 122

The solution to the equation is x = 0 or x = 2πn, where n is an integer.

Starting with the given equation:

sec(x) + tan(x) = 1

We know that sec(x) is equal to 1/cos(x), so we can substitute that in:

1/cos(x) + sin(x)/cos(x) = 1

Combining the two fractions on the left side:

(1 + sin(x))/cos(x) = 1

Cross-multiplying to eliminate the fraction:

1 + sin(x) = cos(x)

Now, we can use the Pythagorean identity to substitute in for sin(x)^2:

1 + (1 - cos(x)^2) = cos(x)

Simplifying:

2 - cos(x)^2 = cos(x)

Rearranging:

cos(x)^2 + cos(x) - 2 = 0

This is a quadratic equation in terms of cos(x), so we can use the quadratic formula:

cos(x) = (-1 ± sqrt(1 + 8))/2

cos(x) = (-1 ± 3)/2

cos(x) = -2 or cos(x) = 1

Since cos(x) can't be negative, we can discard the -2 solution, leaving us with cos(x) = 1. This means that x must be 0 or a multiple of 2π. Checking our work, we can see that when x = 0:

sec(0) + tan(0) = 1 + 0 = 1

So x = 0 is indeed a valid solution.

Therefore, the solution to the equation is x = 0 or x = 2πn, where n is an integer.

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The measure of angle m is,

⇒ m = 43°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle PQR is shown in figure.

Now, We know that;

An exterior angle of a triangle is sum of two opposite angle of that triangle.

⇒ m + 68° = 111°

Solve for m;

⇒ m = 111° - 68°

⇒ m = 43°

Thus, The measure of angle m is,

⇒ m = 43°

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1. a. The graph for the g(x) = -4x - 5 is mentioned in the image below.

1. b. The graph for the h(x) = - 4x - 12 is mentioned in the image below.

1. c. The graph for the j(x)= -4x -15 is mentioned in the image below.

2. The equation for the linear function with a gradient of - 4 and an unknown y-intercept of k is y = -4x + k.

A slope-intercept form is an equation that represents a straight line and is written as y = mx + c, where m is the gradient and c is the y-intercept. If c becomes zero, it passes through the origin.

1. a.

The function g(x) = -4x - 5 represents a straight line that has a slope of -4 and a y-intercept of -5.

When x = 0, g(x) = -5. The point is (0,-5).

When x = 1, g(x) = -9. The point is (1,-9).

When x = -1, g(x) = -1. The point is (-1,-1).

The graph of the function is given below.

1. b.

The function h(x) = -4x - 12 represents a straight line that has a slope of -4 and a y-intercept of -12.

When x = 0, h(x) = -12. The point is (0,-12).

When x = 1, h(x) = -16. The point is (1,-16).

When x = -1, h(x) = -8. The point is (-1,-8).

The graph of the function is given below.

1. c.

The function j(x) = -4x - 15 represents a straight line that has a slope of -4 and a y-intercept of -15.

When x = 0, j(x) = -15. The point is (0,-15).

When x = 1, j(x) = -15. The point is (1,-19).

When x = -1, j(x) = -11. The point is (-1,-1).

The graph of the function is given below.

2.

The slope-intercept form of a line is y = mx + c. On substituting m = -4 and c = k into the equation, it gets reduced to y = -4x + k.

Therefore, the obtained answer is y = -4x +k.

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Yall are some cheaters. Quit looking it up on this website like, dang....

Answer:

kg = gal × 3.7854 × density.

Step-by-step explanation:

The t-test assuming equal variances means Pooled t-test in which variances of the two sample populations are equal.

The pooled t-test is the statistical procedure that assumes that population variances are equal. Finding a weighted average of the two independent sample variances is referred to as pooling. By combining data from samples from populations 1 and 2, we may estimate the common variance when there is solid evidence that population 1's variance is equal to population 2's variance.

Compare the ratio of the two sample standard deviations as a quick way to verify this. The ratio would be compared as: S1/S2. The ratio would be 1, or, in the event that the two are equal.

However, we cannot anticipate the ratio to be exactly 1, as they are samples and as a result, there will be some errors. Thus, the pooled t-test implies whether the null-hypothesis should be accepted or rejected.

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Answer:

Step-by-step explanation:

Continuous variables are variables that can take on any value within a specified range. Some common examples of continuous variables include:

Height: Height can be measured in inches, centimeters, or any other unit of length and can take on any value within the range of human heights.

Weight: Weight can be measured in pounds, kilograms, or any other unit of weight and can take on any value within the range of human weights.

Age: Age can be measured in years, months, or days and can take on any value within the range of human ages.

Time: Time can be measured in seconds, minutes, or hours and can take on any value within the range of time that can be measured.

Temperature: Temperature can be measured in degrees Celsius, Fahrenheit, or any other unit of temperature and can take on any value within the range of temperatures that can be measured.

Income: Income can be measured in dollars, euros, or any other currency and can take on any value within the range of human incomes.

These are just a few examples of continuous variables. In general, any variable that can take on an infinite number of values within a specified range can be considered a continuous variable.

Answer:

Therefore, the height of the pole is approximately 20.79 feet.

Step-by-step explanation:

the person is standing at point A, which is 36 ft away from the base of the telephone pole. The angle of elevation from the ground to the top of the pole is 30 degrees. We want to find the height of the pole, which is represented by "h" in the diagram.

To solve for "h", we can use the tangent function, which relates the opposite side (height) to the adjacent side (distance from the pole to the person) of a right triangle:

tan(30°) = h / 36

We can solve for "h" by multiplying both sides by 36 and taking the tangent of 30 degrees:

h = 36 * tan(30°)

h = 36 * 0.5774 (rounded to four decimal places)

h ≈ 20.79

Therefore, the height of the pole is approximately 20.79 feet.

Answer:

20.78460969082652752232935609807

Step-by-step explanation:

;)

Integer: 12

Irrational numbers: -2√10 and √20

Rational numbers: 17/4, 0.25, and -77/11.

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

There are rational and irrational numbers in the image.

The numbers can be written in the form of p/q, where q is never zero is rational numbers.

And rest of the numbers are irrational numbers.

So, the solutions are given in the image below.

√144 = 12

0.25 = 25/100 = 1/4

Therefore, the solutions are given in the image below.

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The Marginal product is equal to the difference between the output and the input.

The term "marginal product" refers to the extra output that is created when one more unit of a specific input (such as labour or capital) is added to the manufacturing process while keeping other inputs constant.

The marginal product equation is:

Marginal Product is equal to the difference between the output and the input.

Where:

Change in Total Product (CTP) is the term used to describe how the firm's overall output changes when an additional unit of input is added during the manufacturing process.

The term "change in input" describes how much of an input is changed during the manufacturing process.

To put it another way, the marginal product method calculates the extra output brought on by a unit increase in input.

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The true response would be 15,488/7 square centimeters based on the information provided.

Square offers businesses a range of goods and services to help them complete sales transactions, use marketing strategies, and control their finances, inventory, and workforce.

The lateral surface (the curved portion of the cylinder) is added to the areas of a round top and bottom to figure out the surface surface of the cylindrical cheese wheel. The perimeter of the base (2πr, where r is the radius) as well as the height can be used to compute the lateral surface area. Each round top and bottom's surface area is πr².

Hence, the cheese wheel's overall surface area is:

(2πr × h) + (2πr²)

Inputting the values provided yields:

(2 × 22/7 × 22 × 16) + (2 × 22/7 × 22 × 22)

When we simplify and find the total area of the surface, we obtain:

15,488/7 square centimeters

As a result, 15,488/7 square centimeter of the cheese wheel are covered by the label.

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Sin 2 is the integral of -cos 2 plus c, where c is a constant integration equation sin2x dx = -cos2x + c.

1. Calculate sin 2 integral.

2. Apply the integration equation sin2x dx = -cos2x + c.

3. Increase the outcome by the constant C.

Sin 2 is the integral of -cos 2 plus c, where c is a constant. This integral must be calculated in several steps. Take the integral of sin 2 first. Use the integration formula sin2x dx = -cos2x + c to do this. According to this equation, the integral of sin 2 is equal to cos -2/c plus a certain constant. The next step is to add the constant c to the outcome after using this formula. This will result in the integral of sin 2 having a final value of -cos 2 + c. Any actual number may be used as the constant c, and the value will vary depending on the circumstances. It's crucial to keep in mind that the constant c must always be a part of the outcome.

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The point 3/4th of the way from point A to point B is (3.25, -1.25).

What is the coordinate geometry?

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements

To determine the point 3/4th of the way from point A to point B, we can use the midpoint formula to find the coordinates of the midpoint M of the line segment AB, and then use those coordinates to find the point 3/4th of the way from point A to point B.

The midpoint M of the line segment AB can be found using the midpoint formula:

M = ((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.

Substituting the given coordinates, we get:

M = ((3 + 4)/2, (2 - 3)/2) = (3.5, -0.5)

Now we can find the point 3/4th of the way from point A to point B by starting at point A and moving 3/4th of the way towards point B. To do this, we can use the following formula:

P = ((1 - 3/4)*x1 + (3/4)*x2, (1 - 3/4)*y1 + (3/4)*y2)

Substituting the coordinates of points A and B, we get:

P = ((1 - 3/4)*3 + (3/4)*4, (1 - 3/4)2 + (3/4)(-3)) = (3.25, -1.25)

Hence, the point 3/4th of the way from point A to point B is (3.25, -1.25).

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A procedure for using sample data to find the estimated regression equation is (c) the least squares method.

The least squares method is a commonly used statistical procedure for finding the estimated regression equation by minimizing the sum of the squared differences between the observed and predicted values.

The goal of this method is to find the line of best fit that closely represents the relationship between the independent and dependent variables in the sample data. The regression equation obtained from the least squares method can be used to make predictions about the dependent variable based on the values of the independent variable.

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C. The probability of the type I error best defines the notion of the significance position of a thesis test.

The significance position, denoted by alpha( α), is the probability of rejecting the null thesis(H_o) when it's actually true. This is also known as a type I error, which occurs when we inaptly reject a true null thesis.

Option a isn't correct because the probability of rejecting H_o, whether it's true or not, isn't fixed and depends on the sample and the chosen significance position.

Option b isn't correct because it describes the p- value, which is a affiliated conception but not the significance position. The p- value is the probability of observing a sample statistic as extreme or more extreme than the one actually attained, assuming the null thesis is true.

Option d is also not correct because it describes the probability of a type II error, which occurs when we fail to reject a false null thesis. The probability of a type II error is denoted by beta( β) and is told by factors similar as sample size and effect size.

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An algebraic expression to represent how much Xavier will have in his savings account after w weeks is; y = 15w + 43

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are given that Xavier has $43 in his savings account. Thus;

y-intercept = $43

He plans to save $15 each week. Thus;

Slope = $15

Now, after w weeks, the total savings is expressed as;

y = 15w + 43

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It is not possible to make a ratio between 2kg and 3m, as the measures have different units of measurement.

The ratio between two amounts a and b is obtained applying a proportion, dividing the amount a by the amount b.

The division can only be calculated if the two amounts have the same unit of measurement, for example, if both are kg or if both are m.

As 2 kg and 3 m have different units of measurement, a ratio cannot be calculated between these two units.

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the shape is bimodal and symmetric and  histogram have 38 to 40 and 44 to 46.

If the two peaks are mirror reflections of one another, the bimodal distribution may be symmetrical. symmetrical Cauchy distributions exist. These are not likely to be found in basic statistics. These distributions belong to a family where the anticipated value is hypothetical. the long tails of the logistic distribution. If the data is symmetric but contains more extreme values than one would anticipate from a normal distribution, the logistic and Cauchy distributions are utilized. these different distribution types. It is symmetric for the uniform distribution. Since the odds are same at every location, the distribution is essentially a straight line. The distribution is bimodal and nearly symmetric. There are two modes in the distribution, from 38 to 40 and 44 to 46. The existence of data for both men and women may account for this. Women may prefer the lower mode, whereas males may prefer the upper.

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Since an adult ticket costs $13, a child ticket is $8, and expression 3a+5c indicates the price in dollars for a family to attend the game, the total cost is $79 for the event.

Increasing, partitioning, adding, or reducing are all doable in mathematics. As an example, take this expression: Function is defined, equation, and number The components that compose an algebraic equations are numbers, variables, but rather functions (such as addition, subtraction, multiplication or division etc.) One can differentiate two terms or sentences. The terms "expression" or "algorithmic expression" refer to any detailed estimate that suitable parameter, numbers, or an arithmetic action among both them. For instance, the phrase 4m + 5 consists of the terms 4m but also 5, as well as the number m from the given expression, which are all separated by that of the arithmetic symbol +.

given

expression 3a+5c represents the cost

3a + 5c

=  5 * 8 +  3 * 13

= 39 + 40

= 79

Since an adult ticket costs $13, a child ticket is $8, and expression 3a+5c indicates the price in dollars for a family to attend the game, the total cost is $79 for the event.

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The angle of elevation is 61.34°.

An angle of elevation is defined as an angle between the horizontal plane and line of sight from the observer's eye to some object above.

here, we have,

Given here, ramp 18 ft long rises to a platform.

The bottom of the platform is 13 ft from the foot of the ramp.

Let the angle be x then angle of elevation is

      tanx =22/12

     x   = tan⁻¹(22/12)

    x   =61.34°

Hence, the angle of elevation is  61.34°

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