Find the value of each variable show proofs

The equations of the lines in slope-intercept form are:

22. y = -1/2x + 3.

23. y = 2x - 3.

24. y = -x

25. y = -2x + 4.

26. y = 3/2x - 2.

27. y = 5/2x - 1/2

28. y = x + 3

29. y = -x + 2

30. y = -1/4x + 9/4

The equation of a line is y = mx + b, in slope-intercept form, where:

m = slope = rise/run = change in y / change in x

b = y-intercept or the point where the graph intercepts the y-axis.

22. Slope (m) = rise/run = -1/2

y-intercept (b) = 3

Substitute m = -1/2 and b = 3 into the equation, y = mx + b:

y = -1/2x + 3.

23. Slope (m) = rise/run = 4/2 = 2

y-intercept (b) = -3

Substitute m = 2 and b = -3 into the equation, y = mx + b:

y = 2x - 3.

24. Slope (m) = rise/run = -2/2 = -1

y-intercept (b) = 0

Substitute m = -1 and b = 0 into the equation, y = mx + b:

y = -x + 0

y = -x

25. Slope (m) = rise/run = -2/1 = -2

y-intercept (b) = 4

Substitute m = -2 and b = 4 into the equation, y = mx + b:

y = -2x + 4.

26. Slope (m) = rise/run = 3/2

y-intercept (b) = -2

Substitute m = 3/2 and b = -2 into the equation, y = mx + b:

y = 3/2x - 2.

27. Slope (m) = rise/run = 5/2

y-intercept (b) = -0.5 = -1/2

Substitute m = 5/2 and b = -1/2 into the equation, y = mx + b:

y = 5/2x - 1/2

28. Slope (m) = change in y / change in x = (5 - 3) / (2 - 0) = 2/2 = 1

y-intercept (b) = 3

Equation is, y = x + 3

29. Slope (m) = change in y / change in x = (-1 - 4) / (3 -(-2)) = -5/5 = -1

Substitute (x, y) = (3, -1) and m = -1 into y = mx + b, to find b:

-1 = -1(3) + b

-1 = -3 + b

-1 + 3 = b

2 = b

b = 2

The equation would be: y = -x + 2

30. Slope (m) = change in y / change in x = (3 - 2) / (-3 - 1) = 1/-4 = -1/4

Substitute (x, y) = (1, 2) and m = -1/4 into y = mx + b, to find b:

2 = -1/4(1) + b

2 = -1/4 + b

b = 2 + 1/4

b = 9/4

The equation would be: y = -1/4x + 9/4

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The solution to the two simultaneous linear equations are;

x = -2 and y = -2

There are three main ways of solving simultaneous linear equations and they are;

Elimination method

Substitution method

Graphical Method

The two simultaneous equations are;

y = 2x + 2   -----(1)

y = x    -----(2)

Plug in eq 2 into eq 1 to get;

x = 2x + 2

x - 2x = 2

-x = 2

x = -2

Thus, y = -2

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If a residual is negative, then that data point lies below the regression line. In a regression analysis, the goal is to find the line that best describes the relationship between two variables.

The line is determined by finding the values of the slope and intercept that minimize the sum of the squared errors between the observed data points and the predicted values on the line.

The difference between the actual value of the dependent variable and the predicted value on the line is known as the residual. A residual represents the vertical distance between the observed data point and the regression line.

If the residual is positive, it means that the observed value is above the regression line, and if the residual is negative, it means that the observed value is below the regression line.

When a residual is negative, it means that the predicted value on the regression line is higher than the actual value of the dependent variable for that particular data point. In other words, the observed data point is lower than what we would expect based on the relationship described by the regression line.

This situation indicates that the regression line may not fit the data very well at that point, and it may be worth investigating further to see if there are other factors that may be affecting the relationship between the two variables.

In summary, a negative residual means that the observed data point lies below the regression line, and it indicates that the regression line may not be the best fit for that particular data point.

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The proper combined percentage, Pc, for the disparity in population proportions between the two cities' support for the candidate (J minus K) is: 0.65−0.60 / √(0.62) (0.38) (1/100 + 1/125)

Therefore, the correct answer is  0.65−0.60 / √(0.62) (0.38) (1/100 + 1/125)

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Answer: look at the image for the answers and solutions

Step-by-step explanation:

For the given data, the best measure of variability is the interquartile range (IQR) and its value is 18.5.

What is variability?

The extent to which data points in a statistical distribution or data collection diverge or vary from the average value, as well as the extent to which these data points differ from one another, is practically by definition the concept of variability.

The given stem and leaf plot is:

stem          leaf

0                 5

1                   0, 3,7

2                  4,6,8

3                   2

5                    8

The value in the stem is the ten's place and the value in the leaf is the one's place.

So the scores are 05, 10, 13, 17, 24, 26, 28, 32 and 58.

Because extreme values and outliers have a smaller impact on the interquartile range than the complete data range, statisticians prefer using them to measure variability. To understand the centre and spread of your data, utilise the IQR along with a measure of central tendency, like the median.

Range for this data = 58 - 5 = 53.

To find the Inter Quartile Range (IQR), we first find the median.

Median = 24

So Q1 is the first quartile.

This is the median of the first half of the scores(5,10,13,17).

Q1 = 10+13 / 2 = 11.5

Q3 is the third quartile.

This is the median of the second half of the scores (26, 28, 32 58).

Q3 = 28+32 / 2 = 30

Now,

IQR = Q3 - Q1 = 30 - 11.5 = 18.5

Therefore for the given data, the best measure of variability is the interquartile range (IQR) and its value is 18.5.

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Answer:

Step-by-step explanation:

For the given data, the best measure of variability is the interquartile range (IQR) and its value is 18.5.

What is variability?

The extent to which data points in a statistical distribution or data collection diverge or vary from the average value, as well as the extent to which these data points differ from one another, is practically by definition the concept of variability.

The given stem and leaf plot is:

stem          leaf

0                 5

1                   0, 3,7

2                  4,6,8

3                   2

5                    8

The value in the stem is the ten's place and the value in the leaf is the one's place.

So the scores are 05, 10, 13, 17, 24, 26, 28, 32 and 58.

Because extreme values and outliers have a smaller impact on the interquartile range than the complete data range, statisticians prefer using them to measure variability. To understand the centre and spread of your data, utilise the IQR along with a measure of central tendency, like the median.

Range for this data = 58 - 5 = 53.

To find the Inter Quartile Range (IQR), we first find the median.

Median = 24

So Q1 is the first quartile.

This is the median of the first half of the scores(5,10,13,17).

Q1 = 10+13 / 2 = 11.5

Q3 is the third quartile.

This is the median of the second half of the scores (26, 28, 32 58).

Q3 = 28+32 / 2 = 30

Now,

IQR = Q3 - Q1 = 30 - 11.5 = 18.5

Therefore for the given data, the best measure of variability is the interquartile range (IQR) and its value is 18.5.

I totally didnt copy   - 0                                  

Answer:

  3.0549 MJ

Step-by-step explanation:

You want to know the work done to empty a half-full spherical tank of radius 3 m containing liquid of density 900 kg/m³ through a 2 m spout at the top of the tank.

The mass of the liquid is the product of its volume and its density. The volume of the hemisphere is ...

  V = 2/3πr³ = 2/3π(3³) = 18π . . . . . . cubic meters

Then the mass of the liquid is ...

  m = ρV = (900 kg/m³)(18π m³) = 16200π kg

The centroid of the liquid is 3/8r below the center of the tank. The mass of liquid must be moved from that location to a point 2 m above the top of the tank. The total height the liquid must be moved is ...

  3/8(3 m) + 3m + 2m = 6.125 m

The work done to lift the liquid is ...

  W = Fd = (m·g)d = (16200π kg)(9.8 m/s²)(6.125 m) = 972405π J

  W ≈ 3,054,900.4 J ≈ 3.0549 MJ

The work required is about 3.0549 megajoules.

__

Additional comment

We could find the incremental work to move a layer of liquid dy thick to the necessary height, then integrate over the depth of liquid. It is much easier to look up the centroid location for a hemisphere, and use that in the calculation.

We have used "m" to represent both mass and meters. We trust you can determine which is which from the context.

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Answer:

that these angles are inclusive of 0° and 360° because the question states that 0° ≤ Θ ≤ 360°.

Step-by-step explanation:

If csc Θ is undefined, that means that the sine of the angle is zero, because csc Θ is the reciprocal of the sine function, and division by zero is undefined.

So we need to find all the angles where sin Θ = 0.

The sine function is equal to zero at multiples of 180 degrees, so the solutions to sin Θ = 0 are:

Θ = 0°, 180°, 360°

Note that these angles are inclusive of 0° and 360° because the question states that 0° ≤ Θ ≤ 360°.

Answer:

90 buttons

Step-by-step explanation:

the ratio of yellow : blue = 2 : 3 = 2x : 3x ( x is a multiplier )

after buying 27 more blue buttons

2x : 3x + 27 = 4 : 9

expressing the ratios in fractional form

[tex]\frac{2x}{3x+27}[/tex] = [tex]\frac{4}{9}[/tex] ( cross- multiply )

18x = 4(3x + 27)

18x = 12x + 108 ( subtract 12x from both sides )

6x = 108 ( divide both sides by 6 )

x = 18

number of buttons at first = 2x + 3x = 5x = 5 × 18 = 90

The partial tax bracket is the 24% tax bracket.

To determine your tax bracket, you need to know your taxable income, which is your gross pay minus any applicable deductions and exemptions. Based on the information provided, your taxable income is $68,282.

In the United States, the federal tax brackets for the tax year 2022 (for taxes filed in 2023) are as follows:

Based on these tax brackets, you would be in the 24% tax bracket, since your taxable income is between $86,376 and $164,925.

However, it's important to note that the marginal tax rate, which is the rate applied to your last dollar of income, does not reflect the average tax rate you will pay on your entire taxable income. Your actual tax liability will depend on the total amount of your taxable income and any other applicable tax credits or deductions.

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Answer:

Step-by-step explanation: the answer is 50000.

The slope-intercept form of the equation of the given line which passes through the points ( – 8,9) and ( – 2, – 9) is:

     y = -3x - 15

What is meant by slope-intercept form of the line equation?

The slope (m) and the y-intercept (b) of a line are highlighted in the slope-intercept form of linear equations (y=mx+b). One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis) are known, the slope-intercept formula can be used to determine the equation of a line. The equation of a line is the equation that each point on the line fulfils.

Given the line passes through the points  (– 8,9) and ( – 2, – 9).

When only two points on the line are given,  the equation of the line is:

y - y₁ = m ( x - x₁)

m = slope = [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex] = (-9 - 9)/ ( -2 -(-8)) = -18/ 6 = -3

Substituting,

y - 9 = -3 ( x - ( -8))

y - 9 = -3x -24

y = -3x - 15

Therefore the slope-intercept form of the equation of the given line is:

     y = -3x - 15

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Using division, we know that Leo replaces 6 new strings from 3 guitars which are a total of 18 strings.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction.

On a fundamental level, counting the instances in which one number is included within another is one interpretation of the division of two natural numbers.

When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with a remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.

So, we know that:

6 new strings are put on each guitar.

He uses 18 strings.

Then, the number of guitars:

⇒ 18/6 = 3

Therefore, using division, we know that Leo replaces 6 new strings from 3 guitars which are a total of 18 strings.

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The area in square km of a square field 4 cm² is given as follows:

1 km².

The area is obtained applying the proportions in the context of the problem.

The scale is of:

1 cm : 50000 cm -> 1 cm = 0.5 km, as 1 cm = 10^-5 km.

Hence, for the areas, in square units, the scale is obtained squaring both sides, as follows:

(1 cm)² = (0.5 km)²

1 cm² = 0.25 km².

Meaning that the area of the square field is of:

4 x 0.25 = 1 km².

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The expression S÷7 when s = 4 is simplified to 4/7

A fraction can be described as the part of a whole variable, number or element

There are several types of fractions which includes;

From the information given, we have that;

S÷7 is the given expression as a quotient.

For s = 4, we have to substitute the value of s as 4 in the expression, we have;

4/7

Hence, it is an example of a proper fraction where the denominator is greater than the numerator.

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An octant's main features are :

An octant is formed by three perpendicular axes, labeled X, Y, and Z. These axes intersect at a common point called the origin. Each octant contains both positive and negative values along the X, Y, and Z axes. The positive region is located on one side of each axis, while the negative region is on the other side.

Each of the three axes divides an octant into two quadrants. These quadrants are numbered from 1 to 8, with quadrant 1 being in the positive X, Y, and Z regions and quadrant 8 being in the negative X, Y, and Z regions.

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Answer: 189

Step-by-step explanation:

for every 45 minnow there will be 27

315 minnow is 7 times 45 minnow 27*7 is 189

The requried difference between the perimeters of the two gardens would be, 12x + 20 - 4s.

Perimeter is the measure of the figure on its circumference.

Here,
Let's assume that Shawn's garden is also a square with side lengths. Therefore, the perimeter of Shawn's garden would be 4s.
The perimeter of Charlie's garden would be 4(3x + 5), which simplifies to 12x + 20.

The difference between the perimeters of the two gardens would be,

12x + 20 - 4s

We can't simplify this expression any further without knowing the value of s.

Therefore, we can conclude that the difference between the perimeters of the two gardens depends on the side length of Shawn's garden.

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Correct numerical expression is G. 6(18)2 – 27(6)(12).

In mathematics, an expression is a combination of numbers, symbols and operations such as addition, subtraction, multiplication and division that may be evaluated to produce a single number, a variable or a set of numbers.

This expression calculates the number of cubic inches of the box filled with packing material by subtracting the volume of the cylinder from the volume of the cube. The volume of the cube is 6(18)2, and the volume of the cylinder is 27(6)(12). Thus, the number of cubic inches of the box filled with packing material is 6(18)2 – 27(6)(12).

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Answer:

[tex]7y {}^{2} = 0[/tex]

Answer:

the correct answer is y = -1/2x + 6

Step-by-step explanation:

P-value of a hypothesis test is an important measure of the strength of evidence against the null hypothesis and helps us make informed decisions about rejecting or failing to reject the null hypothesis.

A hypothesis test is a statistical method used to test the validity of an assumption or a hypothesis about a population based on a sample data.

The correct answer is b. The P-value of a hypothesis test is the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true.

In hypothesis testing, we start with a null hypothesis, which is usually denoted as H_0, that represents the status quo or the default assumption. The alternative hypothesis, denoted as H_a, represents the opposite of the null hypothesis.

The P-value is the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true. A low P-value indicates that the sample data provides strong evidence against the null hypothesis, and we reject the null hypothesis.

A high P-value indicates that the sample data does not provide strong evidence against the null hypothesis, and we fail to reject the null hypothesis.

In mathematical terms, the P-value is calculated as the probability of observing a test statistic Z that is more extreme than the one actually obtained, assuming the null hypothesis is true.

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Answer:

Step-by-step explanation:

Cost = 0.85 x $7.90

Cost = $6.72

Answer:

Skip it bro this  fin be hard and i can do the next one i tryed to do this and it hard

Step-by-step explanation:

Answer:

$5155

Step-by-step explanation:

We know

A car salesman earns 5% on the sale of a BMW sold for $103,100.

5% = 0.05

What is his take-home pay that day?

We take

103,100 times 0.05 = $5155

SO he takes home $5155.

Step-by-step explanation:

Looks like we're trying to find out what 5% of 103,100 is. We first need to convert the percent into a decimal and then multiply.

[tex]5\% = 0.05[/tex]

Now we can multiply

[tex](0.05)(103100) = 5155[/tex]

Answer: (0,4), (1,6), (2,8), (3,10)

Step-by-step explanation:

you can plug this equation into a graphing calculator (if you don't have a physical one, you can use desmos online graphing calculator) or just graph it on paper.

If you graph it on paper, start at (0,4) because that is the y-intercept. Then go up 2 and right 1 and plot a point there. Up 2 and right 1 and plot a point, etc.

Some points on this line are (0,4), (1,6), (2,8), (3,10)

Answer: y = mx+b

              y = -1x+1/4

Step-by-step explanation:

Answer:

Two-Sample Z-Test. The Two-Sample Z-test is used to compare the means of two samples to see if it is feasible that they come from the same population. The null hypothesis is: the population means are equal.

Step-by-step explanation:

have a nice day.