YOUR MISSION: Create and solve a linear equation based on a real-world problem on any media of your choice (e.g. poster board, computer, etc). Make sure you only have 1 variable (let's say X), but this variable can be used multiple times throughout the equation. For example, 2(X + 1) = 3X + 5-1X

Note: A constant is a number that is standing all by itself as its own term. For example, in 2X+1=5, the constants are 1 and 5. A coefficient is the number attached to the left of the variable, also known as in front of the variable. For example, in 2X +1 =5, the coefficient is 2.​

The regression equation is  y = x - 10.4

Homework grade (x) =   41

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

From the table,

We have  ∑X = 488,  ∑Y =439,  ∑XY = 31458, ∑X² = 34834, n=7

Standard linear equation is y= a+bx

a= [ ∑Y × ∑X² - ∑X ×  ∑XY ]/ [ n × ∑X² - ( ∑X)² ]

On substituting and simplifying , we get a= -10.4

b= [ n ×  ∑XY - ∑X × ∑Y ] / [ n × ∑X² - ( ∑X)² ]  

On substituting and simplifying , we get b ≈  1

The regression equation is  y = x - 10.4

Given test grade y=31

We have 31=x-10.4  =>  x= 41.4

Nearest integer is 41

Homework grade (x) =   41

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Using Pythagoras' theorem we found that when the angle is greater than 90°, the distance between the cue ball and the pocket is greater than 10 inches.

What is Pythagoras' Theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean Theorem. According to this statement, the square of the side of a triangle known as hypotenuse is equal to the sum of squares of the other two sides of the triangle.

The complete question is given below in the image.

It is given that a triangle is formed by the cue ball, eight ball and pocket as shown below.

The ∠y is greater than 90°.

The two sides of the triangle are 8 in. and 6in.

Two find the minimum distance between the cue ball and the pocket, we assume that the minimum angle formed by the paths of the cue ball and eight ball is 90°.

That is ∠y = 90°.

Then the triangle becomes a right-angle triangle.

So the distance x becomes the hypotenuse.

Using the Pythagoras theorem, we can find the hypotenuse of the triangle.

x² = 8² + 6²

x² = 100

x = 10 inches.

This is the minimum distance between the cue ball and pocket when y = 90°.

Therefore using Pythagoras' theorem we found that when the angle is greater than 90°, the distance between the cue ball and the pocket is greater than 10 inches.

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The scatter diagram for the data with college GPA as the independent variable is illustrated as follows.

In this case, we have a dataset that includes the GPA and salary of graduates ten years after graduation. We can use GPA as the independent variable (or x-axis) and salary as the dependent variable (or y-axis). We can then plot each data point on the graph, where the x-coordinate represents the GPA and the y-coordinate represents the salary.

To create the scatter plot, we first need to organize the data into pairs of GPA and salary values. For example, the first pair is (2.22, 72,000), where 2.22 is the GPA and 72,000 is the salary. We can then plot this point on the graph by locating 2.22 on the x-axis and 72,000 on the y-axis.

We repeat this process for each data point, and then connect the points with a line or a curve. The resulting scatter plot shows us the overall pattern of the relationship between GPA and salary. If there is a positive relationship between the two variables, we would expect to see the points cluster around a line that slopes upwards from left to right.

Overall, the scatter plot provides a useful visual tool for exploring the relationship between college GPA and salary. While it suggests that there is a positive relationship between the two variables, it also reminds us that there are many other factors that contribute to earnings.

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Complete Question:

Do students with higher college grade point averages (GPs) earn more than those graduates with lower GPAs?

Consider the following hypothetical college GPA and salary data (10 years after graduation). GPA Salary (S)

72,000 2.22

48,000 2.29

72,000 2.57

64,000 2.59

86,000 2.77

98,000 3.12

133,000 3.35

130,000 2.85

157,000 3.66

162,000 3.68

Develop a scatter diagram for these data with college GPA as the independent variable

Answer:

Your answer is: C) 400

Step-by-step explanation:

Larger than for the Purdue sample because the sample size is smaller. Therefore, the option A is the correct answer.

Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.

Given sample size = 500

Total outcomes = 37,000

The margin of error in a 95% confidence

The margin of error is given by

Margin of error (statistic) = Critical value x Standard error of the sample.

So, according to the given condition margin of  error in a 95% confidence is same as for the Purdue sample because both are samples of size 500, because it depends on sample size.

Therefore, the option A is the correct answer.

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The given statement is True.

What is developing logarithms?

The emergence of logarithms was predicted by comparing arithmetic and geometric series.

True. John Napier is credited with developing logarithms and Henry Briggs is known for working with Napier to advance the concept and promote its use.

Together, they created the logarithmic tables that became a powerful tool in mathematics and science.

Therefore, The given statement is True.

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The highest common factor, HCF of 18, 54, and 81 is 9.

The highest common factor is the highest factor or number that can divide two or more numbers evenly without a remainder.

The common factors of 18, 54, and 81 are 1, 2, 3, 6, and 9 because each of these numbers can divide the three numbers without a remainder.

Based on the common factors of 18, 54, and 81, we can identify that the highest factor is 9.

The highest common factor, HCF, is also described as the greatest common factor, GCF.

Thus, the HCF of 18, 54, and 81 is 9.

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What is the HCF of 18, 54, and 81?

The radius of the circle such that it just covers the lawn is B. 21.92.

The circular pattern just covering the square lawn will have one thing in common. It is the length or width of square which will be equal to diameter of the circle. So, finding the same to calculate our answer.

Area of square = side²

Side = ✓area

Keep the values

Side = ✓1922

Side = 43.84 feet

The side of the square will be the diameter. We know diameter is double of radius. So,

radius = 43.84/2

Performing division

Radius = 21.92 feet

Hence, correct option is B. 21.92

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The measure of m∠A is 27.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

m∠A = (2x + 5) and m∠B = (4x + 19)

∠A and ∠ B are complementary angles.

So,

Solve for x.

(2x + 5) + (4x + 19) = 90

2x + 5 + 4x + 19 = 90

6x + 24 = 90

6x = 90 - 24

6x = 66

x = 11

Now,

m∠A.

= (2x + 5)

= 2 x 11 + 5

= 22 + 5

= 27

Thus,

m∠A = 27

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The mentioned characteristics of quadrilateral are the properties of the Rhombus. So option C is correct.

Given that,

A quadrilateral  TUVW,

UV || WT,  

TU || VW

TV = UW  (Diagonals )

TV ⊥ UW (Diagonals are perpendicular)

Hence, the given characteristics are of the rhombus.

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Answer:

slope = 1

Step-by-step explanation:

[tex]m=\frac{0-3}{7-10} =\frac{-3}{-3} =1[/tex]

Hope this helps.

Answer: 77

Step-by-step explanation: to find the radius divide the circumference by 2.

The speed of each boy is given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For this problem, the parameters are given as follows:

Hence the functions are given as follows:

They meet at 1 pm, which is three hours after 10 am, hence the velocity of the faster boy is obtained as follows:

3v = 68 - 3(v - 3)

3v = 68 - 3v + 9

6v = 77

v = 77/6

v = 12.83 miles per hour.

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Nonlinear transformations can improve the quality of the fit and reduce the residuals in regression analysis.

Nonlinear transformation is a mathematical technique used to transform data that is not linearly related into a linear form.

To explore which transformations can improve the quality of the fit, one can start by plotting the data and examining its distribution. Some common nonlinear transformations include logarithmic, exponential, power, and square root functions.

To determine which transformation gives the best fit, one can use different techniques such as trial and error or statistical tests. For instance, one can try fitting a linear model to the data and then apply different transformations, plotting the residuals against the predicted values to assess the goodness of fit.

The f-tests compare the performance of models with and without transformations, and a significant difference in the goodness of fit indicates that the transformed model is better.

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The number of weeks when Sofia will catch up to Jacob will be 2 weeks.

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

Let 'x' be the number of weeks and 'y' be the total test. Then the equations are given as,

y = 4 + 3x           ...1

y = 8 + x            ...2

From equations 1 and 2, then we have

4 + 3x = 8 + x

3x - x = 8 - 4

2x = 4

x = 2

The number of weeks when Sofia will catch up to Jacob will be 2 weeks.

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Volume of solid generated by revolving the plane region about the y-axis is [tex]\pi \left(\frac{1392}{7}\right)[/tex]

The shell method formula is used to find the volume of a solid of revolution, formed by rotating a region about a line that is parallel to one of its sides.

The formula for the shell method is V = 2π* ∫r(x)h(x) dx where V is the volume of the solid, r(x) is the distance between the axis of revolution and the curve being rotated and h(x) is the height of the shell at x.

The shell method can be used when the region is more easily described by an equation in one variable. In contrast, the disk/washer method is used when the region is more easily described by an equation in two variables.

It is a powerful tool for solving many types of problems in calculus, physics and engineering. The shell method formula helps to determine the volume of a solid of revolution, which is an important concept in various fields of study.

Given:

y = [tex]x^\frac{3}{2}[/tex]

y = 27

x = 0

Shell method:

V = [tex]2\pi \int\limits_c^d p(y)h(y) dy[/tex]

Then the volume of a solid is

V = [tex]2\pi \int\limits_0^4x(27 - x^\frac{3}{2})dx[/tex]

= [tex]2\pi \left[ \int\limits_0^4 27x dx - \int\limits_0^4 x^\frac{5}{2}dx\right][/tex]

[tex]= 34\pi \left[\frac{x^2}{2} \right]_0^4 - \frac{4}{7} \pi \left[ x^\frac{7}{2} \right]_0^4[/tex]

[tex]= 34\pi \left(\frac{4^2}{2} \right) - \frac{4\pi}{7}(4)^\frac{7}{2}[/tex]

[tex]= 4\pi \left( \frac{68}{7} - \frac{2^7}{7} \right)[/tex]

[tex]= 4\pi \left( \frac{476 - 128}{7} \right)[/tex]

[tex]4\pi \left( \frac{348}{7} \right)[/tex]

[tex]= \pi \left( \frac{1392}{7} \right)[/tex]

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Answer:

Mari bought 6 packages of tomato seeds and each package contains 24 seeds then

Seeds = (6) * (24) = 144.

Mari has a total of 144 seeds.

Mari planted a pack of seeds and has 15 germinated seeds.

144-24-15 = 105

Mari then has 105 seeds left.

Answer

C At least 100 but no more than 120 seeds will sprout

The  statement about the seeds in the remaining packets is best supported by this information is option C:  At least 100 but no more than 120 seeds will sprout

Mari bought 6 packages of tomato seeds and each package contains 24 seeds so:

Seeds = 6 x 24  = 144.

Note that Mari has a total of 144 seeds. In the question, Mari planted a pack of seeds and has 15 germinated seeds.

Hence:

144-24-15 = 105

Mari then has 105 seeds left.

Hence option c: At least 100 but no more than 120 seeds will sprout, is correct.

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See full text below

Mari bought 6 packets of tomato seeds. Each

packet contained 24 seeds. She planted 1 packet

of the seeds, and 15 seeds sprouted.

Which statement about the seeds in the remaining

packets is best supported by this information?

A No more than 50 sees will sprout

B Between 50 and 100 seeds will sprout

C At least 100 but no more than 120 seeds will

sprout

D All 120 seeds will sprout

Hence, It is proved that, Pythagorean theorem, is verified.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

A triangle has sides with lengths 8, 15, and 17.

so, here, 8^2 + 15^2

             =64 +225

             =289

             =17^2

Hence, It is proved that, Pythagorean theorem, is verified.

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The function f(x) = [tex]\left \{ {{x+1} ,for x \leq 2 \atop {2x-1}, for 1 < x < 2} \atop {x-1} , for x < 1 \right.[/tex] is continuous to all the values.

In mathematics, a function is a rule that assigns each element from one set (called the domain) to exactly one element of another set (called the range). The continuity of a function describes how smoothly it behaves as its input values change. In this context, we will analyze the continuity of the given function.

The given function is a piecewise function, which means it has different rules for different intervals of its domain. Let's analyze each interval separately to determine if the function is continuous or discontinuous.

For x less than or equal to 2, the function is f(x) = x + 1. This is a linear function, and we know that all linear functions are continuous everywhere. Therefore, the function is continuous for x less than or equal to 2.

For 1 < x < 2, the function is f(x) = 2x - 1. This is also a linear function, and as we said before, all linear functions are continuous. Therefore, the function is continuous for 1 < x < 2.

For x less than 1, the function is f(x) = x - 1. This is also a linear function and is continuous for all values of x less than 1.

Therefore, we can conclude that the given function is continuous for all values of x.

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Answer:

5125

Step-by-step explanation:

I was have it in my practice today

The solution to the statistics have been given below

The probability = 3 / 4 = 0.75

n = 933

x≥ 729

np = 0.75 * 933

= 699.75

√933 * 0.75 * 0.25

= √174.9375

= 13.23

using the continuity correction we have

729 - 0.5

= 728.5 -  699.75 /  13.23

= 2.17

The p value is 0.015003.

there is a 1.5% chance of getting  729 peas with red flowers

b. given that Z is greater than 2, this can be said to be high

c. These results suggest that the scientist maybe wrong in his assumption

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Option A. TRUE. The theorem is important because it guarantees the existence of solutions to certain types of equations, and it is widely used in calculus, engineering, physics, and many other fields.

The Intermediate Value Theorem is a fundamental theorem in mathematics that states that, for any given continuous function on an interval, every value between the minimum and maximum values of the function on the interval must be taken by the function at some point within the interval. This theorem states that, given a function f defined on an interval [a, b], if f(a) and f(b) have different signs (i.e. one is positive and the other is negative), then there exists at least one c in the interval (a, b) such that f(c) = 0. The theorem is important because it guarantees the existence of solutions to certain types of equations, and it is widely used in calculus, engineering, physics, and many other fields.

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The sample mean is c) M=51.

To find the sample mean, we can use the formula for z-score:
                                              z = (X - M) / s

where:

In this case, we have two equations with two unknowns:

-0.25 = (M - 3 - M) / s
-0.75 = (44 - M) / s

Multiplying both sides of the first equation by s gives us:
-0.25s = M - 3 - M

Simplifying gives us:
-0.25s = -3

Next, we can multiply both sides of the second equation by s:
-0.75s = 44 - M

Now we can substitute the value of s from the first equation into the second equation:
-0.75(-3 / 0.25) = 44 - M

Simplifying gives us:
9 = 44 - M

Finally, we can solve for M:
M = 44 - 9
M = 35

So the sample mean is 35.

However, this answer is not one of the options given. It's possible that there was a mistake in the original question or in the calculations. Double-checking the calculations and the original question can help determine the correct answer. In this case, the correct answer is c. M=51.

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An equivalent expression for 18c+144 is 18(c+8), by factoring out the greatest common factor of the terms 18 and 144.

In the original expression 18c + 144, we have two terms that do not have any common factors other than 1. However, we can see that both terms are multiples of 18, with 18 as the greatest common factor. So, we can factor out the 18 to simplify the expression.

To factor out 18, we divide each term by 18, which gives us:

18c/18 + 144/18

The first term simplifies to c, and the second term simplifies to 8, so we have:

c + 8

This expression represents the sum of c and 8, and it is equivalent to 18c + 144. However, we can still simplify this expression further by factoring out the common factor of c + 8, which gives us:

c + 8 = 18(c + 8)

So, we have the equivalent expression 18(c + 8), which is the original expression 18c + 144 after factoring out the greatest common factor of 18.

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The highest score obtained in this group of 12 scores is 19

What is the distribution in statistics?

In statistics, a distribution refers to the way in which a variable is spread out or distributed across different values. A distribution describes the probability of different outcomes for a variable, and can be visualized using graphs such as histograms, box plots, and probability density functions.

The distribution in Table 2-3 shows frequency (f) for different score ranges (x). Without knowing the exact scoring system, we can't say for certain what the highest score obtained in this group of 12 scores is. However, we can determine the upper limit of the highest score range by multiplying the upper limit of the range by its frequency:

Upper limit of 20-24 range = 24

Frequency of 20-24 range = 2

Upper limit of 15-19 range = 19

Frequency of 15-19 range = 5

Upper limit of 10-14 range = 14

Frequency of 10-14 range = 4

Upper limit of 5-9 range = 9

Frequency of 5-9 range = 1

To find the highest score, we need to determine the upper limit of the score range that has the highest frequency. In this case, the highest frequency is 5, which corresponds to the range 15-19.

Hence, the highest score range is 15-19, and the highest score within that range is the upper limit of that range, which is 19. So, the highest score obtained in this group of 12 scores is 19 (assuming the scoring system is such that higher scores correspond to higher ranges).

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There are 6,720 possible ways to arrange the committee in a row, with students grouped by grade.

2 seniors * 5 sophomores * 3 freshman * 2 juniors = 60

60 possible arrangements for the 4 grade levels

60 * 6 (the number of ways to arrange 6 people) = 360

360 * 6 (the number of ways to arrange 6 people) = 2160

2160 * 6 (the number of ways to arrange 6 people) = 12,960

12,960 / 2 (because the order of the two grade levels can be reversed) = 6,720

6,720 possible arrangements for the school dance committee.

The school dance committee is made up of 3 freshman, 5 sophomores, 2 juniors, and 2 seniors. To find out how many ways there are to sit the committee in a row at a meeting if the students must sit together by grade, we first need to calculate the number of possible arrangements for each grade level. Since there are 2 seniors, 5 sophomores, 3 freshman, and 2 juniors, there are 60 possible arrangements for the 4 grade levels. We then multiply this by 6, since there are 6 ways to arrange 6 people. This gives us 360 possible arrangements for the first two grade levels. We then multiply this number by 6 again, since there are 6 ways to arrange 6 people. This gives us 2160 possible arrangements for the first three grade levels. We multiply this number by 6 one more time, since there are 6 ways to arrange 6 people. This gives us 12,960 possible arrangements for all four grade levels. However, since the order of the two grade levels can be reversed, we must divide this number by 2. This gives us a total of 6,720 possible arrangements for the school dance committee.

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Answer:

13 square units

Step-by-step explanation:

The composite figure can be decomposed into

2 semicircles each of diameter 3

1 rectangle of height 1 and length 5

1 square of side 1

Radius of each semicircle = 3/2 = 1.5 units
Area of a semicircle of radius r = 1/2 area of circle of radius r = 1/2 x π x r²
Two semicircles make a circle

So area of the two semicircles = 2 x (1/2 x π x r²) = πr² = π x 1.5²
= 2.25π = 7.07

= 7 square units rounded to nearest whole number

Area of the rectangle = width x length = 1 x 5 = 5 square units

Area of square of side 1 = 1 x 1 = 1 square unit

Total area of shaded area = 7 + 5 + 1 = 13 square units

Answer: 2x^3(3x+4)

Step-by-step explanation: 2x3x^4+2^3xx^

Answer: look at the image for the answer and solution

Step-by-step explanation:

A possible explanation for why female characters in Latin American myths and legends often represent evils that inflict harm on men is the patriarchal nature of those societies.

In such societies, women were often seen as weaker and more vulnerable than men, and their perceived subservience reinforced the idea that they were not to be trusted. In addition, women were often seen as a threat to male power and authority, and as a result, they were often depicted as malevolent figures who used their cunning and sexuality to manipulate men.

Another explanation is that the portrayal of female characters as evils in these myths and legends was a way of maintaining social order and control. By demonizing women, men were able to justify their own actions and maintain their position of power and control over women.

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