Question 2 (1 point)
Which equation BEST represents the line of best fit for the scatterplot?
0000
a y=-3x - 2
b
y=x-3
y=-3x + 2
с
d y = x + 3

The system of equations that has a solution of (5,-3) is y +  3 = m (x-5).

or

We have the points (5, -3).

Now, The point-slope form of a linear equation is:

(y - y₁) = m (x - x₁)

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

y +  3 = m (x-5)

Now, let the slope m = -2 then

y + 3 = -2(x-5)

y + 3 = -2x + 10

y + 2x + 3 -10 = 0

y + 2x - 7 = 0

Or we can also form the equation as

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The accrued value of the account in 14 years is $4967.89

From the question, we have the following parameters that can be used in our computation:

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

Amount = P * (1 + 0.25r)ᵗ

Where

P = Principal = 4200

r = Rate = 5.2% = 0.052

t = time = 13

Substitute the known values in the above equation, so, we have the following representation

Amount = 4200 * (1 + 0.25 * 0.052)¹³

Evaluate

Amount = 4967.89

Hence, the amount is 4967.89

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Answer:

5.6

Step-by-step explanation:

180/50 is 5.6

Controlled destruction, also known as selective demolition or deconstruction, involves carefully dismantling a building or structure in order to salvage and reuse as many materials as possible. This process can make it easier to build new buildings in several ways:

Minimizes waste: By salvaging and reusing materials from the old building, controlled destruction minimizes the amount of waste generated during the demolition process. This can reduce the need for new materials, which can be costly and time-consuming to source and transport.

Reduces environmental impact: Controlled destruction can also be more environmentally friendly than traditional demolition methods, as it produces less waste and pollution. This can help to minimize the impact on the local environment and reduce the carbon footprint of the construction project.

Provides access to reusable materials: Salvaging materials from the old building can also provide access to high-quality, durable materials that can be used in the construction of the new building. This can save time and money on sourcing new materials, and can also provide an opportunity to incorporate unique and interesting architectural features.

Helps to preserve historical buildings: In some cases, controlled destruction can be used to preserve historical buildings or structures by carefully dismantling them and reusing the materials in a new context. This can help to maintain the cultural and historical significance of the original building, while still allowing for new development and construction in the area.

Overall, controlled destruction can make it easier to build new buildings by minimizing waste, reducing environmental impact, providing access to reusable materials, and helping to preserve historical buildings.

~~~Harsha~~~

Answer:

A. They are one-dimensional

B. They connect two endpoints

Both statements A and B are true about line segments. Line segments are one-dimensional figures that have two endpoints and connect them with a straight path.

Statement C is not true. Line segments do not have a unit of measure on their own, but their length can be measured using a unit of measure such as inches, centimeters, or meters.

Statement D is not true either. Line segments are flat, one-dimensional objects and cannot grow to become three-dimensional objects. However, multiple line segments can be connected to form a three-dimensional object, such as a cube or pyramid.

The probability that a randomly selected point within the circle falls in the red-shaded circle is 0.25

We have,

The area of the whole circle.

= πr²

Where r = 8

So,

= 3.14 x 8 x 8

= 200.96

Now,

Area of the red shaded circle = πr²

Where r = 4

So,

= 3.14 x 4 x 4

= 50.24

Now,

The probability that a randomly selected point within the circle falls in the red-shaded circle.

= Area of the red shaded circle / Area of the whole circle

= 50.24 / 200.96

= 1/4

= 0.25

Thus,

The probability that a randomly selected point within the circle falls in the red-shaded circle is 0.25

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Answer:

From the picture,

∠ABC + ∠DBC = ∠ABD

Substituting with data,

x + (3x + 10) = 90

4x + 10 = 90

4x = 90 - 10

4x = 80

x = 80/4

x = 20

Step-by-step explanation:

The area of the shaded region = 30.903 in²

From the attached figure we can observe that the radius of the circle R is r = 6 in.

Using the forula for the area of circle, the area of circle R would be,

A₁ = πr²

A₁ = π × 6²

A₁ = 36π

A₁ = 113.097 in²

So, the diameter would be d = 6 × 2 = 12 in.

The circle R is inscribed in a square.

So, the side length of square is equal to the diameter of the circle.

This means the side length 'a' os square = 12 in.

Using the formula of the area of square,

A₂ = side²

A₂ = a²

A₂ = 12²

A₂ = 144 in²

so, the area of the shaded region would be,

A = A₂ - A₁

A = 144 -113.097

A = 30.903 in²

This is the required area.

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The rate at which her daily revenue is currently changing and the direction of the change is; Her revenue is currently increasing at $12 per day

The rate of change of a function is the rate at which the output of the function changes per unit change in the input of the function.

Let x represent the number of days, therefore;

The number of T-shirts Dorothy sells, y = 40 - 4·x

The price at which she sells the T-shirts = 7 + x

Therefore, Dorothy's daily revenue, R(x) = (40 - 4·x) × (7 + x) = 12·x - 4·x² + 280

The rate of change of her daily revenue can be obtained from the derivative of the revenue function as follows;

The rate at which her daily revenue is therefore;

R'(x) = d(R(x))/dx = 12 - 8·x

The rate at which her revenue is changing currently can be obtained from the rate function by plugging in x = 0, as follows;

R'(0) = 12 - 8×0 = 12

Her revenue is changing at a rate of $+12 per day.

The positive value of the rate, 12, indicates that her revenue is increasing at $12 per day

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Answer:160

formula:y=kx

16=(16)(10)

=160

Step-by-step explanation:

Step-by-step explanation:

the area of a right-angled triangle is

leg1 × leg2 / 2 =

sin(angle)×baseline × cos(angle)×baseline / 2 =

sin(angle)×cos(angle) × baseline² / 2

4 = sin(30)×baseline = 0.5 × baseline

baseline = 4/0.5 = 8 units

Pythagoras gives us the third side = cos(30)×baseline :

8² = 4² + side²

64 = 16 + side²

48 = side²

side = sqrt(48) = sqrt(16×3) = 4×sqrt(3) units

so, the area of the triangle is again

sin(30)×baseline × cos(30)×baseline / 2 =

= 4 × 4×sqrt(3) / 2 = 2×4×sqrt(3) = 8×sqrt(3) units² =

= 13.85640646... units²

Answer:

B is the correct answer

Step-by-step explanation:

The general form of the equation for a circle centered at the origin (0, 0) is x^2 + y^2 = r^2, where r is the radius of the circle. The radius can be calculated as the distance between the center O (0, 0) and point B (4, 5) on its circumference using the distance formula: r = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((4 - 0)^2 + (5 - 0)^2) = sqrt(16 + 25) = sqrt(41). Therefore, the equation for the given circle centered at O (0, 0) is x^2 + y^2 = 41. The correct answer is B. x^2 + y^2 − 41 = 0.

The break-even point for the division is as follows:

The break-even point is the unit or dollar value where the total revenue equals the total costs.

The total costs consist of the fixed and variable costs.

Selling price per unit of the income tax app = $8

The variable cost per unit = $3

Contribution margin per unit = $5 ($8 - $3)

Contribution margin ratio = 62.5% ($5 ÷ $8 x 100)

Fixed cost per month = $20,000

Break-even point in units = Fixed Costs/Contribution margin per unit

= 4,000 units ($20,000 ÷ $5)

Break-even point in dollars = Fixed Costs/Contribution margin ratio

= $32,000 ($20,000 ÷ 62.5%)

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Find the break-even point for the division.

A)By applying permutation and combination we can select committee in  1782 ways.

B) The probability cannot be determined with the given information, as the calculated probability is greater than 1, which is not possible.

Permutation and combination are two concepts in mathematics that deal with counting the number of possible outcomes or arrangements in a given situation. Permutation refers to the arrangement of objects in a specific order, while combination refers to the selection of objects without regard to the order in which they are chosen.

Probability is a measure of the likelihood or chance that an event will occur. It is a number between 0 and 1.

According to the given information:

A) To find the number of ways to select a committee of 5 members, where exactly one of Mr Lan and Mrs Lan must be on the committee, we can use the principle of inclusion-exclusion i.e. Permutation and combination:

First, we find the total number of ways to select a committee of 5 members from 14 members (6 men and 8 women), which is given by:

C(14,5) = 2002

Next, we find the number of ways to select a committee of 5 members that includes both Mr Lan and Mrs Lan, which is given by:

C(12,3) = 220

Note that we choose 3 members from the remaining 12 members after Mr and Mrs Lan have been chosen.

Finally, we subtract the number of committees that include both Mr Lan and Mrs Lan from the total number of committees, since we only want committees that include exactly one of them:

2002 - 220 = 1782

Therefore, there are 1782 different ways to select a committee of 5 members where exactly one of Mr Lan and Mrs Lan must be on the committee.

B) To find the probability that there are more women than men on the committee, given that Mrs Lan was selected, we need to consider the number of committees that satisfy this condition and divide by the total number of committees that include Mrs Lan.

If Mrs Lan is selected, there are two cases to consider:

Case 1: The committee has more women than men.

In this case, we need to select 4 members from the 8 women and 1 member from the 5 men, which can be done in C(8,4) x C(5,1) = 560 ways.

Case 2: The committee has an equal number or more men than women.

In this case, we need to select 3 members from the 8 women and 2 members from the 5 men, which can be done in C(8,3) x C(5,2) = 560 ways.

Therefore, the total number of committees that include Mrs Lan and have more women than men or an equal number of women and men is 560 + 560 = 1120.

The total number of committees that include Mrs Lan is C(13,4) = 715, since we choose 4 members from the remaining 13 members after Mrs Lan has been chosen.

Therefore, the probability of selecting a committee with more women than men or an equal number of women and men, given that Mrs Lan was selected, is:

1120/715 = 1.5664

Note that this probability is greater than 1, which is not possible. Therefore, there is an error in the calculation, and the correct probability cannot be determined with the given information.

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You have to find what 0.2 of 132 is

132 x 0.2 = 26.40

The answer [tex]\boxed{\bold{\$26.40}}[/tex]

A line plot for the data is shown in the image attached below.

In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a line plot as shown in the image attached below.

In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 3.5 or 3 1/2 because it has the highest frequency of 5.

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Symbol notation

A negative real number is any real number that is less than zero.

A positive real number is any real number that is greater than zero.

Zero is neither positive nor negative.

(a)  The negative of z is not greater than 6

If the negative of z is not greater than 6, then it is less than or equal to 6.

-z ≤ 6.

(b)  The negative of m is not less than -6

If the negative of z is not less than -6, then it is greater than or equal to -6.

-m ≥ -6.

The property of equality that the statement m(n-p) = mn - mp illustrates is (d) the distributive property

Given that

m(n-p) = mn - mp

The above property is the distributive property

The distributive property states that

a(b - c) = ab - ac

This case

a = m

b = n

p = c

Substitute the known values in the above equation, so, we have the following representation

m(n-p) = mn - mp

Hence, the property of equality that the statement illustrates is the distributive property

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The best description of the figure would be that it is a C. a square.

To find out the type of figure that we have, it would be best to find the lengths of the sides of the figure. We should find AB, BC, CD, and AD.

We can use the distance formula which is:

D=√ ( x 2 - x1 ) ² + ( y2 - y1) ²

Using this formula, we find that AB, BC, CD, and AD are all a distance of 6 units. This therefore means that this figure is a square because all the sides are equal.

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Full question is:

Which best describes the figure that is represented by the following coordinates?

A(-3, 4), B(3, 4), C(3,-2) and D(-3,-2)

a rectangle

a trapezoid

a square

Answer:

5.1

Step-by-step explanation:

x = x+10

6. 42

cross multiply

42x= 6x + 60

42x-6x =60

36x=60

x=1.7

3x= 3×1.7

=5.1

To graph the two lines, we can plot two points on each line and connect them with a straight line. For y = 3x + 2, we can choose x = 0 and x = 1 to get the points (0, 2) and (1, 5), respectively. For y = x - 2, we can choose x = 0 and x = 1 to get the points (0, -2) and (1, -1), respectively.

In the graph: The red line represents y=3x+2 and the blue line represents y=x-2

Explain the term straight line

A straight line is a geometric figure that extends infinitely in both directions and has no curvature or bends. It is the shortest distance between two points and can be described using various mathematical equations, such as y = mx + b, where m is the slope and b is the y-intercept. Straight lines are used in various fields, including geometry, physics, and engineering, to represent and analyze the relationships between objects or points.

According to the given information

To graph the system of equations y = 3x + 2 and y = x - 2, we can plot the two lines on the same coordinate plane and find the point where they intersect.

First, we can find the point of intersection by setting the two equations equal to each other:

3x + 2 = x - 2

Simplifying, we get:

2x = -4

x = -2

Substituting this value of x back into one of the equations, we get:

y = (-2) - 2 = -4

So the solution to the system of equations is the point (-2, -4).

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The population of Westville increased by approximately 99.95 people from 2015 to 2016.

To find the increase in population from 2015 to 2016 in Westville, we need to use the formula:

Increase in population = (Population density in 2016 - Population density in 2015) x Land area

First, we need to find the population density in 2016. To do that, we can divide the population of 2,000 people by the land area of 84.4 square miles:

Population density in 2016 = 2,000/84.4 ≈ 23.69 people per square mile

Next, we can plug in the values into the formula:

Increase in population = (23.69 - 22.5) x 84.4 ≈ 99.95 people

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The function is defined piecewise, and 4 does not fall under any of the conditions where the function is defined. Therefore, the function is not defined for x=4.

So the answer is C, "function is not defined for this value."

Answer:

9

Step-by-step explanation:

The calculated degrees of freedom for the t-test is 18

The degrees of freedom (df) for an independent t-test with two samples can be calculated using the following formula:

df = (n1 + n2) - 2

Where n1 is the sample size of the first group and n2 is the sample size of the second group.

In this case, the first sample has N = 8 and the second sample has N = 12.

Therefore, the degrees of freedom for the t-test will be:

df = (8 + 12) - 2

df = 18

So the t-test for this experiment will have 18 degrees of freedom.

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Step 1:  Order from least to greatest

51, 56, 62, 72, 79, 81, 82, 85, 89, 95, 97, 98

Step 2:  Determine the median of the lower half of the data

There are 12 numbers which means that there is going to be 6 numbers on both sides of the data. So using the first 6 numbers we will be able to determine the median of the lower half of the data.

51, 56, 62, 72, 79, 81

Since there is an even amount of numbers, that means that we will need to find the middle between the 3rd and 4th number.  We can do that by adding them up together and dividing by 2.

[tex](62 + 72) \div 2 = \bold{67}[/tex]

Step 3:  Determine the median of the upper half of the data

So using the first 6 numbers we will be able to determine the median of the upper half of the data.

82, 85, 89, 95, 97, 98

Since there is an even amount of numbers, that means that we will need to find the middle between the 3rd and 4th number.  We can do that by adding them up together and dividing by 2.

[tex](89 + 95) \div 2 = \bold{92}[/tex]

Answer: The median of the lower half of the data was determined to be 67 while the median of the upper half of the data was determined to be 92.

The definite integral of ∫ 2t⁻⁴ dt is -2/3 * t^(-3) + C, where C is the constant of integration.

To find the definite integral of ∫ 2t⁻⁴ dt, we can use the power rule of integration. The power rule states that the integral of t^n with respect to t is (t^(n+1))/(n+1), where n is a constant not equal to -1.

Applying the power rule, we have:

∫ 2t⁻⁴ dt = 2 * (t^(-4 + 1))/(-4 + 1) + C

= -2/3 * t^(-3) + C

where;

Thus, the definite integral of ∫ 2t⁻⁴ dt is -2/3 * t^(-3) + C, where C is the constant of integration.

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Answer:

Step-by-step explanation:

To find the result when the number 59 is decreased by 3.9%, we need to first calculate what 3.9% of 59 is.

To do this, we can multiply 59 by 3.9% (or 0.039), which gives us:

59 x 0.039 = 2.301

This tells us that 3.9% of 59 is 2.301.

Next, we need to subtract 2.301 from 59 to get the final result:

59 - 2.301 = 56.699

Therefore, the result when the number 59 is decreased by 3.9% is 56.699.  we could say that if you take 3.9% of 59 and subtract that amount from 59, the answer is 56.699.

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Here, we want to get the final volume

From the general gas equation, we have it that:

[tex]\dfrac{P_1V_1}{T_1} =\dfrac{P_2V_2}{T_2}[/tex]

From the question, we have it that:

P1 is the initial pressure which is 475 torr

V1 is the initial volume which is 296 mL

T1 is the initial temperature which we have to convert to absolute value by adding 273.15 K ([tex]68 + 273.15 = 341.15 \ \text{K}[/tex])

P2 is the final pressure that is the same as the initial which is 475 torr

V2 is the final volume that we want to calculate

T2 is the final temperature which is 273.15 K (0 degrees Celsius is 273.15 K)

Substituting the values, we have:

            [tex]\dfrac{475\times296}{341.15}=\dfrac{475\times V_2}{273.15}[/tex]

[tex]V_2=\cfrac{475\times296\times273.15}{341.15\times475} =\boxed{\bold{237 \ mL}}[/tex]

We could have solved this by using Charles' law that relates temperature to volume (volume is directly proportional to temperature)

Applying the properties of a rhombus, we have:

AB = BD = CD = AC = 11

A rhombus is a type of quadrilateral, which is a four-sided polygon with four angles. A rhombus is a special type of parallelogram in which all four sides are equal in length.

Therefore, we would create an equation to find the value of  using the properties of rhombus:

2x - 3 = x + 4

2x - x = 3 + 4

x = 7

AB = 2x - 3 = 2(7) - 3 = 11

All sides are equal, therefore:

AB = BD = CD = AC = 11

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