The line graph shows the poluution rate of a certain lake from 1950 to 2000. Use the graph to answer the question. Percentage of pollution by Volume (+ SP) 4.0% 3.0% 2.0% 1.0% 0.0% 1950 1960 1970 1980 1990 2000 Find an estimate for the percent of pollution by volume of the lake in 1960. A. 3% OB. 2.5% OC. 2% D. 1%

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The relations we notice between the variables we examined is the relationship linear or quadratic or inverse or logarithmic or something else.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables.

To correctly interpret a statistical study, it is crucial to comprehend the relationships between the variables. How the factors interact impacts how the correct conclusions are drawn. Without knowing this, you run the risk of getting caught in one of the many traps that come with statistical analysis and drawing incorrect conclusions from your data.

Before making decisions based on relationships between variables, it is necessary to research and understand those relationships. Natural science and engineering typically make this easier because you can research how one parameter influences the result being studied while holding all other parameters constant.

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i. The side of ΔNMQ that corresponds to side Y is NQ.

ii. The length of MP is 21.

Similar triangles are two or more triangles that have common properties of their corresponding sides. Though the triangles are not congruent.

From the given question,

i. The side of ΔNMQ that corresponds to side Y is NQ.

ii. Comparing ΔNMQ and ΔOPM, we have;

NM/ OM = QM/ MP

20/ 30 = 14/ (14+ x)

20 (14 + x) = 30 *14

280 + 20x = 420

20x = 420 -280

      = 140

x = 140/ 20

  = 7

x = 7

So that,

MP = (14 + x)

     = 14 + 7

     = 21

MP = 21

The length of MP is 21.

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The required value of the upper limit for both the integral are,
4. a = -1 or a = 1/2
5. b = 1

The limit of a sum can be used to express the definite integral of any function, or if the interval [a, b] has an antiderivative F, the definite integral of the function is the difference of the values at points a and b.

Here,

4.
Given expression,
[tex]= \int _{-2}^{a}x^2dx = 7/3\\= [x^3]_{-2}^a = 7 / 3\\= a^3 + 8 / 3 = 7/3\\a=-1,\:a=\frac{1}{2}-\frac{\sqrt{3}}{2}i,\:a=\frac{1}{2}+\frac{\sqrt{3}}{2}i[/tex]

Since as mentioned that a must be greater than -2 so the considered value of a is, a = -1 and a = 1/2, and a graph of the area of the expression is shown,

Similarly,
5.
b = 1
A graph of the area under the given integration has been shown.

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         A + (100 +4.5A) = 1675

Now, According to the question:

The given data is:

The area of the playground section is 1,675 square feet.

It is 100 square feet more than 4. 5 times the area of the sandbox section.

To write an equation the area, A, of the sandbox section.

The area of the sandbox and playground together is 1675 square feet. Using A as the area of the sandbox section, the playground section is said to be (100 +4.5A).

Then the total area is :

A + (100 +4.5A) = 1675  

Subtract 100 on both sides, we get

5.5A = 1575

Now, The area of the sandbox section is:

A = 1575/5.5 = 286 4/11.

Hence, The area of the sandbox section is about 286.4 square feet.

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The solution of the given system of equations is x = -2.25, y = 8.25 and z = 4.75. This was obtained by using Gauss Jordan method by solving the equations one by one.

The given system of equations is,

x + y + z = 9

x - 2y + 3z = 8

2x + y - z = 3

We will add the first equation to the third equation to get,

3x + 2y = 12

We will subtract the second equation from the first equation to get,

-y + 4z = 1

We will divide the second equation by 4 to get,

z = 0.25

We will substitute the value of z in the third equation to get,

2x + y = 3

We will divide the third equation by 2 to get,

x + 0.5y = 1.5

We will substitute the value of x and y from the third equation in the first equation to get,

1.5 + 0.5y + z = 9

We will substitute the value of z from the second equation to get,

1.5 + 0.5y + 0.25 = 9

We will solve the above equation for y to get,

y = 8.25

We will substitute the value of y in the third equation to get,

2x + 8.25 = 3

We will solve the above equation for x to get,

x = -2.25

We will substitute the value of x and y in the second equation to get,

-2.25 - 2(8.25) + 3z = 8

We will solve the above equation for z to get,

z = 4.75

Hence, the solution of the given system of equations is,

x = -2.25

y = 8.25

z = 4.75

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The product of the circle's radius and the point's distance from the origin determines the distance between the circle and the point.

Straight lines are the shortest path between any two places. The formula for measuring distance can be used to get this distance.

In geometry, distances are always positive unless the points are exactly adjacent. The distance between A and B is equal to the distance between B and A. We consider two points A(a, b) and B to get the formula for the distance between two points in the plane (c, d).

The length of the perpendicular drawn from a point to a line is the distance, or more particularly, the shortest distance of a point from a line, as previously stated.

The distance between the circle and the point is equal to the product of the radius of the circle and the distance the point is from the origin.

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Using the concept of place value, the numbers in ascending order are 0.005 < 0.01 < 0.1 < 1/2

Place value is a system used to represent numbers in which the position of a digit determines its value. It is a way of identifying the value of a digit in a number based on its position in the number.

In the decimal system, which is the system most commonly used in everyday life, the place value of a digit is determined by its position in relation to the decimal point. The digit furthest to the left of the decimal point represents the largest place value, while the digit furthest to the right represents the smallest place value.

In this problem, we have to arrange the numbers in ascending order and that will start from the smallest to the largest.

0.005 < 0.01 < 0.1 < 1/2

The answer to this is option A

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Answer:1

Step-by-step explanation:

The equation 5(2x – 3) = 5  has one solution.

The solution of the equation is x = 2.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, let's solve the equation as follows:

5(2x – 3) = 5

open the brackets

5(2x – 3) = 5

10x - 15 = 5

add 15 to both sides of the equation

10x - 15 = 5

10x - 15 + 15 = 5 + 15

10x  = 20

divide both sides by 10

x = 20 / 10

x = 2

Hence, the solution of the equation is x = 2.

The equation has only one solution.

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A linear function is a function that represents a straight line when plotted on a coordinate plane.

A linear function is a function that has a constant rate of change and can be represented by a straight line when plotted on a coordinate plane. The equation for a linear function is usually written in the form y = mx + b, where m is the slope and b is the y-intercept. The slope indicates how much the y-value changes when the x-value increases by one unit, and the y-intercept indicates the value of y when x is equal to zero.

When we imply that a linear function has a constant rate of change, we also mean that the rate of change of the output (y-value) with respect to the input (x-value) is always the same.

Linear functions can be used to model many everyday situations such as population growth, speed, distance, and temperature. Linear functions are also used in mathematics to solve equations, calculate slopes, and determine the area under a curve.

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Answer:

No, because the remainder is not equal to zero.

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Now, According to the question:

What is horizontal line?

A horizontal line is a straight line that is parallel to the x-axis and where all the points on the line have the same y-coordinate. Are all horizontal lines in 2-D shapes parallel? Yes, all horizontal lines are parallel to each other. Horizontal lines, when extended, never intersect with one another.

Hence, The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

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The sample space is 18. The probability of getting a 2 or a b is 8/18 = 4/9.

The sample space is the set of all possible outcomes of the experiment. In this case, the sample space is all the possible combinations of a die being tossed and a spinner being spun.

There are 6 possible outcomes for the die (1,2,3,4,5,6) and 3 possible outcomes for the spinner (a,b,c). Therefore, the sample space consists of 6x3=18 possible outcomes.

Now, to calculate the probability of getting a 2 or a b, we can count the number of outcomes in which this occurs. There are 4 outcomes that satisfy this condition (2a, 2b, 2c, b). Therefore, the probability of getting a 2 or a b is 4/18 = 8/18 = 4/9.

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Answer:

C.

Step-by-step explanation:

Answer:

-1g + -7

Step-by-step explanation:

(-5g+-6) + (4g+-1)

(-5g + 4g) + (-6+-1)

-1g + -7

(posible answer)

Logarithmic functions are inverse of exponential functions and describe the relationship between two variables when one increases or decreases at a constant rate. Exponential functions are functions where the variable increases or decreases at a rate that is proportional to its current value.

Logarithmic functions are inverse of exponential functions and describe the relationship between two variables when one increases or decreases at a constant rate. This means that the logarithm of a number is equal to the exponent to which another fixed number, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 10 to the power of 3 is equal to 1000. Exponential functions are functions where the variable increases or decreases at a rate that is proportional to its current value. An example of this is a population growth function, where the population size increases exponentially with time. The equation for an exponential function is y=ab^x, where a is the initial value, b is the base and x is the exponent. The exponential function can also be written in logarithmic form, which is log_b(y)=x. In this form, the base number is fixed, and the exponent is being found. This can be used to solve for x.

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The formula is base*height. measure of angle MNQ in the parallelogram <MNQ is 100 degrees.

The formula is base*height.

This is because in a parallelogram (a slanted one), you can multiply base*height and the triangle from the other side can be moved.

Which is why it's also the formula for rectangle and squares since they are also parallelograms.

The measure of angle MNQ in the parallelogram<MNQ is 100 degrees

From the diagram, we have the following parameters

Angle MNQ = 100 degrees

Also, from the diagram, angles MNQ are alternate interior angles

This means that,  angles are congruent

This gives

<MNQ =100 degree

Hence, the measure of angle MNQ in the parallelogram <MNQ is 100 degrees.

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The value of A in the given situation would be 3√2 which would calculate the distance to 5.

The total velocity of an object defines its distance regardless of direction.

Regardless of where it started or ended, distance is the amount of space that an object has covered.

We can estimate an object's actual size by knowing how far it is from us.

The following equation is frequently used to calculate the separation between two points: d=((x2 - x1)2 + (y2 - y1)2)

So, the points are as follows:

(2, 3) and (5, A)

Now, calculate using the formula d=((x2 - x1)2 + (y2 - y1)2) as follows:

d=((x2 - x1)2 + (y2 - y1)2)

d=((2 - 5)2 + (A - 3)2)

d=((-3)2 + (A - 3)2)

d=9 + A² + 9

d = 18 + A²

A² = 18

A = √18

A = √2*3*3

A = 3√2

Therefore, the value of A in the given situation would be 3√2 which would calculate the distance to 5.

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An operation that fills in the blank to make the equation a true statement is addition (+).

In order to determine the required mathematical operation that would make the equation a true statement, we would apply the distributive property of multiplication to the left-hand side (LHS) of the given equation.

By applying the distributive property of multiplication to the given mathematical expression, we have the following:

Left-hand side (LHS) = 5(1/2q + 3r - 4s) - 9r

Left-hand side (LHS) = 5/2q + 15r - 20s - 9r

By collecting like terms, we have the following mathematical expression:

Left-hand side (LHS) = 5/2q + (15r - 9r) - 20s

Left-hand side (LHS) = 5/2q + 6r - 20s

In conclusion, we can reasonably infer and logically deduce that the required mathematical operation is addition (+).

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There are three basic methods of graphing linear functions. The first is by plotting points and then drawing a line through the points. The second is by using the y-intercept and slope. The third is applying transformations to the identity function f(x)=x f ( x ) = x .

Now, According to the question :

What is linear function ?

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.

Hence, There are three basic methods of graphing linear functions. The first is by plotting points and then drawing a line through the points. The second is by using the y-intercept and slope. The third is applying transformations to the identity function f(x)=x f ( x ) = x .

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The equation of an ellipse with x-intercepts at (4, 0) and (-4, 0), y-intercepts at (0, 9) and (0, -9), and center at (0, 0) is [tex]$\frac{x^2}{16}+\frac{y^2}{81}=1$$[/tex].

As per the given data the ellipse with x-intercepts at (4, 0) and (-4, 0), y-intercepts at (0, 9) and (0, -9), and center at (0, 0).

If the ellipse has its x-intercepts at points (4, 0) and (-4, 0) and y-intercepts at points (0, 9) and (0, -9), then it's symmetric across the y- axis and the x-axis.

The equation of an ellipse where the major axis 2a is greater than the minor 2b.

When 2b > 2a , then the equation becomes [tex]$\frac{(y-h)^{2} }{b^{2} } + \frac{ (x-k)^{2} }{a^{2} } =1[/tex]

Moreover h = 0 and k = 0 because the center is on the origin, so the equation becomes:

[tex]$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

Moreover,

a = 4

b = 9

The equation of the such ellipse is

[tex]$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

Hence, the equation of the ellipse is

[tex]$\frac{x^2}{4^2}+\frac{y^2}{9^2}=1[/tex]

[tex]$\frac{x^2}{16}+\frac{y^2}{81}=1$$[/tex]

Therefore the equation of an ellipse is  [tex]$\frac{x^2}{16}+\frac{y^2}{81}=1$$[/tex].

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Find the equation of the ellipse with the following properties. The ellipse with x-intercepts at (4, 0) and (-4, 0), y-intercepts at (0, 9) and (0, -9), and center at (0, 0).

The solution for the given system of linear equations is (-1, 4).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are 3x-3y=-21 ----(i) and 3x+3y=15 ----(ii).

Add equation (i) and (ii), we get

3x-3y+(3x+3y)=-21+15

6x=-6

x=-1

Substitute x=-1 in equation (i), we get

3(-3)-3y=-21

-9-3y=-21

-3y=-12

y=4

Therefore, the solution for the given system of linear equations is (-1, 4).

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The true statements about the system of equations are:

"They have different y-intercepts"

"he substitution method results in the false statement, 8 = –1"

Here we have the following system of equations:

y = 4x + 8

y = 4x - 1

Remember that the general linear equation is:

y = a*x +b

Where a is the slope and b is the y-intercept.

Notice that both equations have the same slope and different y-intercepts, this means that the lines are parallel.

Then the true statements are:

"They have different y-intercepts"

"he substitution method results in the false statement, 8 = –1"

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By adding up all the positive real numbers, one may determine the domain of a logarithmic expression.

A logarithm is a measurement of the amount that a fixed number (the base) must be increased in order to create a particular number.

Basically,

if y=ax

So, logₐ(y) = x

The base of the logarithm in this instance is a. The following two bases are frequently employed: base-10 and Base-e

'e' is a mathematical constant having a value of around 2.718.

If the base is "e," we use a specific expression: ln(x)

Fundamentally,

ln(x)=loge(x)  

Here, e is the base.

Base-10 will be used if no base is provided, as in the formula

log(x)=log10(x)

Here 10 is the base

The domain of a function is the set of all input values (sometimes referred to as independent variables) for which the function is defined and produces an acceptable result (also called dependent variable). Most often, the domain is represented by a collection of numbers or a range of numbers.

The term "range" refers to the entire set of potential output values (dependent variable) that a function can produce for any set of valid input values inside its domain. Usually, a group of numbers or a range of numbers is used to represent the range.

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The direct variation equation is a linear equation in two variables and is given by y = kx where k is the constant proportionality. The direct variation graph in a coordinate plane is a straight line. The ratio of two quantities in a direct variation is a constant.

Now, According to the question:

What is Direct Variation?

Direct variation exists between any two variables when one quantity is directly dependent on the other i.e. if one quantity increases with respect to the other quantity and vice versa. It is the relationship between two variables where one of the variables is a constant multiple of the other. Since the two variables are directly related to each other it is also termed as directly proportional.

Hence, The direct variation equation is a linear equation in two variables and is given by y = kx where k is the constant proportionality. The direct variation graph in a coordinate plane is a straight line. The ratio of two quantities in a direct variation is a constant.

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the distance between the given points will be 10 units.

What is the distance in math?

As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, Using the coordinates of any two locations in a two-dimensional plane, the distance between them may be determined. the separation between two parallel lines, the separation between two parallel planes, etc. The distance between two given point A(x1,y1) and B(x2,y2) is √((y2-y1)² +(x2-x1)²).

Given points are: (-5,2) and (1,-6)

So the distance between them = √(-8²+-6²)

=√64+36

=√100

=10

Hence the distance between the given points will be 10 units.

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There is a 6.7 percent probability that you are making a mistake by failing to reject the null hypothesis. Hence, option C is the correct answer to this question.

The p-value is a measure of the evidence against a null hypothesis. A smaller p-value means that there is stronger evidence against the null hypothesis. A common threshold for rejecting the null hypothesis is a p-value of less than 0.05, which corresponds to a confidence level of 95%. In this case, the p-value of 0.067 is greater than 0.05, meaning that there is not enough evidence to reject the null hypothesis and conclude that there is a statistically significant difference between the two experimental groups. Therefore, there is a 6.7% probability that you are making a mistake by failing to reject the null hypothesis, which means that the two experimental groups may be statistically identical.

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The complete question is -

As a statistician, you conducted an experiment and obtained a t-test value for the two experimental groups. At a confidence level of 5 percent, the corresponding statistical p-value of 0.067 would suggest that:

a. The inherent error of the experiment is calculated to be 6.7 percent.

b. There is probably a statistically significant difference between the two groups of interest.

c. There is a 6.7 percent probability that you are making a mistake by failing to reject the null hypothesis.

d. There is a 6.7 percent probability that you are making a mistake in accepting the experimental hypothesis.

e. The two experimental groups are statistically identical.

The probability of all heads occurring at the end of the sequence is 1/2^100, or approximately 0.00000000079.

Probability is the branch of mathematics that deals with the likelihood or chance of an event occurring. It is a value between 0 and 1 (or 0% to 100%), where 0 represents an impossible event and 1 (or 100%) represents a certain event.

The probability of each outcome in the sequence is 1/2 (i.e. heads or tails). The total number of possible outcomes is 2^100. This means that the probability of all heads occurring at the end of the sequence is 1/2^100. This can be expressed as 1/2 * 1/2 * 1/2 * ... (100 times), which simplifies to 1/2^100, or approximately 0.00000000079.

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The maximum power of the variable present in the equation is equal to the degree of the polynomial. The variable in this case is x, and the term 4x2 has x to its maximum power of 2.

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On solving the provided question, we can say that in the parallel lines we have 14x +21 = 87 - 2x +> 12x = 66 =>. x = 10.5

Parallel lines in geometry are coplanar infinite lines that don't intersect anywhere. In a given three-dimensional space, parallel planes are those that never cross. Curves with a constant minimum distance between them and no points of contact or intersection are said to be parallel. Two lines that are in the same plane, equally spaced apart, and never intersect are referred to as parallel lines in geometry. Either horizontal or vertical can apply. Parallel lines can be noticed in everyday objects like railroad tracks, rows of notebooks, and pedestrian crossings.

here,

14x +21 = 87 - 2x

12x = 66

x - 22/4

x = 11/2

x = 10.5

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