(a) An angle measures 111°. What is the measure of its supplement?

Answer: y=−1/7x+13/7

Step-by-step explanation: m=x2-x1/y2-y1, then put it in slope formula

The linear regression equation that represents the correlation between homework grade (x) and test grade (y) is y = 0.6x + 18.5. Using this equation, the estimated homework grade for a student with a test grade of 32 is 38.

To find the linear regression equation, we need to calculate the slope and the y-intercept using the given data:

1: Calculate the mean of the homework grades (x) and test grades (y) from the table.

  Mean of x: (50 + 70 + 80 + 90) / 4 = 72.5

  Mean of y: (60 + 85 + 95 + 100) / 4 = 85

2: Calculate the differences between each homework grade (x) and the mean of x, and each test grade (y) and the mean of y.

  Difference for x: (50 - 72.5), (70 - 72.5), (80 - 72.5), (90 - 72.5) = -22.5, -2.5, 7.5, 17.5

  Difference for y: (60 - 85), (85 - 85), (95 - 85), (100 - 85) = -25, 0, 10, 15

3: Calculate the sum of the product of the differences for x and y, as well as the sum of the squared differences for x.

  Sum of (x - mean of x) * (y - mean of y): (-22.5 * -25) + (-2.5 * 0) + (7.5 * 10) + (17.5 * 15) = 162.5

  Sum of (x - mean of x)^2: (-22.5)^2 + (-2.5)^2 + (7.5)^2 + (17.5)^2 = 1050

4: Calculate the slope (b) using the formula:

  b = Sum of (x - mean of x) * (y - mean of y) / Sum of (x - mean of x)^2

  b = 162.5 / 1050 ≈ 0.155

5: Calculate the y-intercept (a) using the formula:

  a = mean of y - (b * mean of x)

  a = 85 - (0.155 * 72.5) ≈ 85 - 11.24 ≈ 73.76

6: Write the linear regression equation by rounding the coefficients to the nearest tenth:

  y = 0.2x + 73.8

7: Substitute the given test grade (y = 32) into the equation to estimate the homework grade (x):

  32 = 0.2x + 73.8

  0.2x = 32 - 73.8

  0.2x = -41.8

  x ≈ -209 (rounded to the nearest integer)

Therefore, the estimated homework grade for a student with a test grade of 32 is 38.

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Answer:

See below.

Step-by-step explanation:

A(x) = x^2 + 5x

A(x) = x^2 + 5x = 14

x^2 + 5x - 14 = 0

(x + 7)(x - 2) = 0

x + 7 = 0  or  x - 2 = 7

x = -7 or x = 2

x is the height of a rectangle.

The only viable solution is x = 2 because the height of a rectangle cannot be a negative number such as -7.

The only viable solution for the height is x= 2, because height cannot be a negative value.

A rectangle is a quadrilateral with four right angles.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is \(ax^{2} +bx+c=0\)

Given,

Area of the rectangle = \(x^{2} +5x\) = 14

Then,

\(x^{2} +5x-14=0\\(x+7)(x-2)=0\)

Therefore x = -7 and 2

But the Height cannot be negative therefore x = 2

Hence, only viable solution for the height is x= 2, because height cannot be a negative value.

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To find the derivatives of the given expressions, we can apply the chain rule, which states that the derivative of a composition of functions is equal to the derivative of the outer function multiplied by the derivative of the inner function.

(a) To find the derivative of f(g(x)), we start by differentiating the outer function f with respect to the inner function g(x), and then multiply it by the derivative of the inner function g(x) with respect to x.

df/dx = df/dg * dg/dx

df/dx = cos(g(x)) * (2x)

(b) To find the derivative of g(f(x)), we differentiate the outer function g with respect to the inner function f(x), and then multiply it by the derivative of the inner function f(x) with respect to x.

dg/dx = dg/df * df/dx

dg/dx = 2f(x) * cos(x)

Hence, the derivatives are:

(a) d/dx(f(g(x))) = cos(g(x)) * (2x)

(b) d/dx(g(f(x))) = 2f(x) * cos(x)

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A consumer's optimal consumption bundle represents the best possible combination of goods and services that a consumer can purchase given their budget constraint and the prices of those goods. In this scenario, the utility function given is a(f, g) = 2√f + g

The price of good f is 2 and the price of good g is 1.

The consumer's income is 3/4 and 1/4 respectively. Using these, we can solve for the optimal consumption bundle for the consumer using the utility function.

a) To calculate the optimal consumption bundle when the income is 3/4, we can use the following method:

Let the optimal consumption bundle be represented as (x, y).

Here, x represents the quantity of good f consumed, and y represents the quantity of good g consumed.

The consumer's budget constraint can be given as follows:

2x + y = 3/4

The consumer's goal is to maximize their utility, which can be represented as:

a(f, g) = 2√f + g = 2√x + y

The consumer's optimization problem can be represented as follows:

Maximize 2√x + y subject to 2x + y = 3/4

To solve this optimization problem, we can use the Lagrangian function:

L(x, y, λ) = 2√x + y - λ(2x + y - 3/4)

To find the optimal consumption bundle, we must solve for the following set of equations:

∂L/∂x = 0,

∂L/∂y = 0, and

∂L/∂λ = 0

Solving for the first two equations yields the following:

x/√x = λ2y - λ

= 1

The third equation can be used to solve for λ:

2x + y - 3/4 = 0

Solving for x and y using the first two equations and the value of λ yields:

x = 1/2 and y = 1/4

Therefore, the optimal consumption bundle is (1/2, 1/4)

b) To calculate the optimal consumption bundle when the income is 1/4, we can use a similar method to the one used in part a.

Using the same budget constraint of 2x + y = 1/4 and the same utility function of 2√x + y, we can solve for the optimal consumption bundle by using the Lagrangian function L(x, y, λ) = 2√x + y - λ(2x + y - 1/4).

Solving for the same set of equations, we get:

x = 1/8 and y = 0

Therefore, the optimal consumption bundle is (1/8, 0)

Utility functions are mathematical representations of the satisfaction a consumer derives from consuming goods and services. A consumer's optimal consumption bundle represents the best possible combination of goods and services that a consumer can purchase given their budget constraint and the prices of those goods.In this question, we were given a specific utility function and the prices of two goods. We used this information to solve for the optimal consumption bundle when the consumer's income was 3/4 and 1/4 respectively.To solve for the optimal consumption bundle, we used the Lagrangian method to optimize the consumer's utility function subject to their budget constraint. The Lagrangian method involves creating a Lagrangian function that includes the consumer's utility function and their budget constraint. We then solve for the first-order conditions of the Lagrangian function, which are a set of equations that yield the optimal values of the goods consumed.This method is useful for solving for optimal consumption bundles because it takes into account both the consumer's preferences and their budget constraint. By solving for the optimal consumption bundle, we can determine how much of each good the consumer should consume to maximize their satisfaction given their budget constraint

Utility functions and optimal consumption bundles are important concepts in microeconomics. They allow us to understand how consumers make choices and how they allocate their resources. By solving for the optimal consumption bundle, we can determine the best combination of goods and services that a consumer can purchase given their budget constraint and the prices of those goods.

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The two methods which can be used to solve the quadratic equation are; The completing the square method and the factor method.

Although, not limited to the aforementioned methods of solving quadratic equations, the two methods are major methods of solving quadratic equations.

The completing the square method (also used in expressing quadratic equations in vertex form) and the factor method are very efficient method of solving quadratic equations.

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Answer:

Step-by-step explanation:

At home depot

Price of Christmas tree = $149.00

Discount = 15%

Amount discounted = 15% of $149

Amount discounted = 15/100 * $149

Amount discounted = 15 * 1.49

Amount discounted = $22.35

Amount she paid = $149-$22.35

Amount she paid = $126.65

At Lowe's:

Price of Christmas tree = $175.00

Discount = 260%

Amount discounted = 20% of $175

Amount discounted = 20/100 * $175

Amount discounted = 0.2 * 175

Amount discounted = $35

Amount she paid = $175-$35

Amount she paid at Lowe's = $140

From the prices above, it can be seen that Home Depot has a better deal since the price after removing discount is lower than that of Lowe's.

Amount she will save will be $140 - $126.65 = $13.35

Answer:Factor the polynomial

3(a−4b)2

The one that is a step used in the construction of an equilateral triangle inscribed in a circle  is:

B. draw two line segments connecting the points where the arc intersects the circle and an endpoint of the diameter

The steps to construct an equilateral triangle inscribed in a circle are:

1. Draw a point that will be the center of the circle. Label this "point O". Technically, it doesn't matter which character you use to represent a point.

2. Draw a perfect circle centered at point O using a compass.

3. Use a ruler to draw a straight vertical line through point O. Extend this line beyond the boundaries of the circle. 4) Draw a point where the line and the circle intersect. Label the bottom point "Point W" and the top point "Point X".

5) Draw a second circle. The center of this circle is point W and the radius extends to point O.

6) Mark both places where the two circles intersect. Label the left point "Point Y" and the right point "Point Z".

7) Connect the points X, Y and Z with a ruler or straightedge. 

Looking at the options, the only correct step is:

B. draw two line segments connecting the points where the arc intersects the circle and an endpoint of the diameter

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The inverse Laplace transform of the function G(s) = 4(\(s^2\) - 2s + 2)/s(s + 2)(s + 1) can be expressed as f(t) = (2 - \(e^(-t)cos(t)\) - \(2e^(-t)sin(t)\)).

To find the inverse Laplace transform of G(s), we first need to decompose the function into partial fractions. The denominator can be factored as s(s + 2)(s + 1), and by applying partial fraction decomposition, we can express G(s) as A/s + B/(s + 2) + C/(s + 1).

By equating the numerators of the partial fractions and finding the values of A, B, and C, we obtain the expression G(s) = 2/s - 2/(s + 2) + 2/(s + 1).

Next, we use the linearity property of the inverse Laplace transform to find the inverse transforms of each term separately. The inverse Laplace transform of 2/s is simply 2, the inverse Laplace transform of -2/(s + 2) is -2\(e^(-2t)\), and the inverse Laplace transform of 2/(s + 1) is \(2e^(-t)\).

Finally, combining these inverse transforms, we get the expression f(t) = (2 -\(e^(-t)cos(t)\) - \(2e^(-t)sin(t)\)), which represents the inverse Laplace transform of G(s).

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The highest level of detailed information about social scientific findings can typically be found in academic journals. These journals publish peer-reviewed research articles written by experts in the field, ensuring a rigorous review process and a high level of quality and accuracy.

Academic journals provide detailed information about the methodology, data analysis, and results of social scientific studies. They often include statistical analyses, charts, and graphs to support the findings. Additionally, these journals may also provide in-depth discussions of the implications and limitations of the research, as well as suggestions for future studies.

Accessing academic journals can sometimes require a subscription or payment, but many universities, libraries, and research institutions provide access to these resources. Some journals also offer open access options, allowing anyone to read and download their articles free of charge.

It's important to note that when using information about social scientific findings from academic journals, it is crucial to properly cite and reference the original source to avoid plagiarism. Academic integrity is a fundamental principle in research and scholarly writing.

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This can be rounded to the nearest tenths place, giving us a final answer of V = 4πSin in³, rounded to the nearest tenths place.

Area is the size of a two-dimensional surface or shape. It is usually measured in square units such as square feet, square meters, or acres. Area can be used in a variety of ways, such as for measuring the size of a garden or calculating the amount of paint needed for a wall. Area can also be used to measure the area of a circle, triangle, or other shapes. Area is an important concept in mathematics, as it is used in a variety of formulas and equations.

The volume of a cylinder is calculated by multiplying the base area with the height. The base area is calculated by multiplying pi (π) with the square of the radius. Therefore, the volume of a cylinder with a height of h and a base radius of r is calculated by the formula V = πr2h. In this case, the height is h = Sin and the base radius is r = 2in. Applying these values to the formula, we get V = π(2in)2(Sin) = 4πSin in². This can be rounded to the nearest tenths place, giving us a final answer of V = 4πSin in3, rounded to the nearest tenths place.

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Answer:

D

Step-by-step explanation:

-9x-27+12 = -6x-15-3x

0=0

D) the equation has infinitely many solutions

Answer:

224

Step-by-step explanation:

i2+161+64

=224

The pair of equations whose lines are perpendicular is (d) y = 1/6x + 3; y = -6x - 3

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

The pair of equations

By definition;

The slopes of perpendicular lines are opposite reciporcals

So, we have

(a) -1/3 and -3 false

(b) -3 and -6 false

(c) 3 and 3 false

(d) 1/6 and -6 true

Hence, the equations are (d) y = 1/6x + 3; y = -6x - 3

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Answer:

−\(x^{2}\) + 9x + 1

Step-by-step explanation:

Step-by-step explanation:

Ans 6 Use Pythagoras theorem...

Hypotneuse²=Base²+Height²

6²=4²+H²

36-16=H²

20=H²

√20=H

√2×2×5=H

2√5 = H....

hope it helps

Problem 4

Draw a diagonal to connect the opposite non-right angles as shown below. This forms two right triangles. As you can probably guess, we'll use the pythagorean theorem to find the length of this segment. We'll call it x.

a^2+b^2 = c^2

7^2+24^2 = x^2

49+576 = x^2

x^2 = 625

x = sqrt(625)

x = 25

The hypotenuse of each right triangle is 25 units long.

Move your focus to the upper right triangle. We can use the pythagorean theorem again in a slightly different way to find y.

a^2+b^2 = c^2

15^2+y^2 = 25^2

225+y^2 = 625

y^2 = 625-225

y^2 = 400

y = sqrt(400)

y = 20

====================================================

Problem 6

The largest triangle, ignore segment x for now, is isosceles because we have two congruent sides.

As with any isosceles triangle, the vertex angle is bisected by the perpendicular bisector as shown in the diagram. This produces two identical right triangles. Most importantly, it means that horizontal side 4 is cut in half to 4/2 = 2 units.

In short, each smaller right triangle has a horizontal leg of 2, vertical leg x, and hypotenuse 6. Let's focus on just one of those right triangles.

Like the previous problem, we'll use the pythagorean theorem to find x.

a^2+b^2 = c^2

x^2+2^2 = 6^2

x^2+4 = 36

x^2 = 36-4

x^2 = 32

x = sqrt(32)

x = sqrt(16*2)

x = sqrt(16)*sqrt(2)

x = 4*sqrt(2)

Answer:

A coeffient is the first number at the beginning of a problem

Ex.

2Na+3H ---> 4O+5S

2 would be the coeffient of Na

3 would be the coeffient of H

4 would be the coeffient of O

5 would be the coeffient of S

Step-by-step explanation:

Answer:

1) sixty-eight million, six hundred and thirty-four thousand

2) acute triangle

3) 6

4) either 4 inches if it is one inch long or 8 inches if 2 long

5) 162

I really need brainliest please

Answer:

X=50

Step-by-step explanation:

If you algebraically plug in 50 you come to an answer of X=50

Answer:

x=4

Slove it 3x-5=x+3

3x-5=x+3

3x-x-5=3

2x-5=3

2x=3+5

2x=8

x=4

Answer:

x=4

Step-by-step explanation:

3x-5=x+3

-x +5 -x +5

2x=8

next you divide 2 from 8

x=4

Answer:

7 and -8

Step-by-step explanation:

Based on the density and the given parameters, the density of the sheet of glass in kg per m cubed is 2500 kg/m cubed

The density of the sheet of glass  is given as

Density = 2.5g/cm cubed

Start by converting grams (g) to kilogram (kg)

This is done by dividing 2.5 by 1000

So, we have:

Density = 2.5/1000 kg/cm cubed

Evaluate the quotient

Density = 0.0025 kg/cm cubed

Next, we then convert cm cubed (cm^3) to meter cubed (m^3)

This is done by dividing the volume by 1000000

So, we have:

Density = 0.0025 kg/(1/1000000) m cubed

Express as product

Density = 1000000 * 0.0025 kg/m cubed

Evaluate the product

Density = 2500 kg/m cubed

Based on the density and the given parameters, the density of the sheet of glass in kg per m cubed is 2500 kg/m cubed

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Answer:

See below

Step-by-step explanation:

Are you wanting to convert density of   gm/ cm^3   to    kg/m^3 ??

    there are 100 x 100 x 100  cm^3 =  1,000,000  cm^3/ m^3

2.5 gm / cm^3   *  1 000 000 cm^3 / m^3   =  2, 500 000 gm / m^3

   now 1 kg is   1000 gm

2, 500 000 gm / m^3   *  1 kg / 1000 gm  = 2500 kg / m^3

such pair of equation that have only one pair of solutions which satisfy both equation is linear equation

Answer:

y = 1x + 9

Step-by-step explanation:

This is probably a form of y = mx + b.

m = the slope of a line, which is up one over one (rise/run)

b = y-intercept, or what point is the line crossing at on the y axis.

This formula is very important and it's very helpful when plotting lines. So remember: y = mx + b  !!

Hopefully this helps! Leave a comment wether it does or not. :)

y=mx+b

y=x+9

choose any x coordinates

x = 0,1,2

y is equal to the x coordinate plus 9

in this case y will be

y = 9,10,11

respectively

graph the points:

(0,9)

(1,10)

(2,11)

Answer:

eq of a line= (y-y1)=m(x-x1)

y-1=1/2(x-3)

2(y-1)=x-3

2y-2=x-3

x-2y-1=0

x-2y=1

The given data is,A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers.

Of the 60 subjects who participate in the study, 21 prefer the instant coffee. We need to find the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee, let's say p. The formula to calculate the proportion of the population is:

p = (n1 + n2) / (x1 + x2)n1 and n2 are the sample sizes of two categories and x1 and x2 are the number of favorable outcomes from the respective categories. Here, n1 = n2 = 60 and x1 = 39 (since 21 out of 60 prefer instant coffee, the remaining 39 must prefer fresh-brewed coffee).Now, p = (60 + 60) / (39 + 21) = 1.2. Since p is a probability, it must be between 0 and 1. But here, p is greater than 1, which is not possible. Therefore, there is an error in the given data and we cannot proceed with the calculation.

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The equation to determine the length and width of the rug is

28 = w² + 12w

Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.

What is a rectangle?

Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We are given a rectangular rug with an area of 28 square feet.

Also, the rug is 12 feet longer than it is wide.

So,

Let 'l' be the length of the rug and 'w' be the width of the rug

As given, Length is 12 feet longer than its width

Therefore, l = w + 12

We know Area of rectangle = Length * Width and area is given to be 28 square feet.

So,

⇒28 = (w + 12)w

⇒28 = w² + 12w

Hence, the equation to determine the length and width of the rug is

28 = w² + 12w.

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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.

Create an equation to determine the length and the width of the rug.