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The equation of the circle is (x - 2)² + (y + 3)² = 100.

We have,

To find the equation of a circle given its diameter endpoints, we can use the formula:

(x - h)² + (y - k)² = r²

Where (h, k) represents the center of the circle and r is the radius.

Given the diameter endpoints at (-6, 3) and (10, -9), we can find the center of the circle by finding the midpoint of the diameter.

Midpoint coordinates:

x-coordinate = (x1 + x2) / 2

= (-6 + 10) / 2

= 4 / 2

= 2

y-coordinate = (y1 + y2) / 2

= (3 + (-9)) / 2

= -6 / 2

= -3

Therefore, the center of the circle is (2, -3).

To find the radius, we can use the distance formula between one of the diameter endpoints and the center of the circle.

Radius = √((x2 - x1)² + (y2 - y1)²)

= √((10 - 2)² + (-9 - (-3))²)

= √(8² + (-6)²)

= √(64 + 36)

= √100

= 10

Now we have the center (h, k) = (2, -3) and the radius r = 10.

Substituting these values into the equation formula, we get:

(x - 2)² + (y - (-3))² = 10²

(x - 2)² + (y + 3)² = 100

Therefore,

The equation of the circle is (x - 2)² + (y + 3)² = 100.

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I hope this can help you out some

Answer:

y=1/4x-25/4

Step-by-step explanation:

Lines that are parallel from an equation have the same slope, so your slope is 1/4.

Use point slope formula to solve for slope intercept form.

y-y1=m(x-x1)

m= 1/4

x= 1

y= -6

y-(-6)=1/4(x-1)

y+6=1/4x-1/4

y=1/4x-25/4

The confidence interval is the range of values while the level of confidence is the probability that the true population parameter falls within that range of values.

The correct answer is: the confidence interval is a range of values, the level of confidence is the probability for that range of values. A confidence interval is a range of values that is likely to contain the true value of a population parameter based on a sample of data. It is calculated from the sample statistics and provides a range of values that is likely to contain the true value of the population parameter with a certain level of confidence. For example, a 95% confidence interval for the population mean would provide a range of values that is likely to contain the true population mean with 95% confidence. On the other hand, the level of confidence is the probability that the true population parameter falls within the confidence interval. It is expressed as a percentage and represents the degree of confidence we have in the interval estimate. For example, a 95% level of confidence would mean that if we were to take many samples and calculate a 95% confidence interval for each sample, we would expect 95% of these intervals to contain the true population parameter.

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533/100 then simplify

5 and 33/100

But that isn't an option and none of those options convert into 5.33, and I haven't been able to solve 3.75 repeating yet nor think it would convert into 5.33 anyhow. Please correct me if I'm solving this wrong.

The equation that represents h(x) is h(x) = (f(x))(g(x)).

To determine which equation represents h(x), we need to analyze the given table and understand the relationship between the functions f(x), g(x), and h(x).

Since h(x) represents the output values obtained by multiplying f(x) and g(x), we should look for values in the table where h(x) is the product of the corresponding values of f(x) and g(x).

Let's examine the table and compare the values:

x | f(x) | g(x) | h(x)

1 | 3 | 4 | 12

2 | 5 | 2 | 10

3 | 2 | 6 | 12

From the table, we can see that the values in the h(x) column are the products of the corresponding values in the f(x) and g(x) columns. Therefore, the equation that represents h(x) is h(x) = (f(x))(g(x)).

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Answer:

It's B.

Step-by-step explanation:

Edge 2020.

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The value of x is 1 & y is 2 (a).

Steps are attached.

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The inequalities that represent the given word problem is;

1.2x + 2y ≤ 20    

x + y ≤ 16

We are given;

The cost of each apple = $1.25

The cost of each mango = $2

The maximum number of apples = 20

The maximum number of mangoes = 3

The minimum selling amount of chairs and tables = $ 4800

Let the number of apples purchased be x

Let the number of mangos purchased be y

Thus, we can form the inequalities as;

1.2x + 2y ≤ 20         .......(1)

x + y ≤ 16   -----(2)

x ≤ 13     -----(3)

y ≤ 3     ------(4)

Now, from the inequality graph attached the point where the two graphs meet is a solution to the simultaneous inequalities which is;

x ≤ 11.67 and y ≤ 3

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Answer:

Sarah earned $10 per hour for babysitting

Step-by-step explanation:

The surface area of a conical grain storage tank that has a height of 42 meters and a diameter of 24 meters is 1,670.5 square meters.

The surface area of a cone is calculated using the following formula:

Surface area = πr² + πrl, where π is approximately equal to 3.14, r is the radius of the base of the cone, and l is the slant height of the cone.

In this problem, we are given that the height of the cone is 42 meters and the diameter of the base is 24 meters. The radius of the base is half of the diameter, so the radius is 12 meters. The slant height of the cone can be calculated using the Pythagorean theorem.

l² = 12² + 42²

l² = 1764

l = 42.01 meters

The surface area of the cone is then calculated as follows:

Surface area = πr² + πrl

Surface area = 3.14 * 12² + 3.14 * 12 * 42.01

Surface area = 1,670.5 square meters

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P = 90 is the solution for the given equation.

Given: Qd=95−4

PQs=5+P

To find Qd if P=5:

Put P = 5 in the equation

Qd=95−4P

Qd = 95 - 4 x 5

Qd = 75

So, Qd = 75.

To find P if Qs = 20:

Put Qs = 20 in the equation

Qs = 5 + PP

= Qs - 5P

= 20 - 5P

= 15

So, P = 15.

To solve Qd=Qs, substitute Qd and Qs with their respective values.

Qd = Qs

95 - 4P = 5 + P

Subtract P from both sides.

95 - 4P - P = 5

Add 4P to both sides.

95 - P = 5

Subtract 95 from both sides.

- P = - 90

Divide both sides by - 1.

P = 90

Thus, P = 90 is the solution for the given equation.

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The lower bound of the series solution for the radius of convergence about the point x0 = −1 is -2 < x < 0, about the point x0 = 0 is -1 < x < 1, and about the point x0 = 1 is 0 < x < 2.

To determine a lower bound of the series solution for the radius of convergence about the point x0 = −1, x0 = 0, and x0 = 1, we can use the formula for the radius of convergence:
\(R = 1/lim sup (|an|^{(1/n)})\)
where an is the nth coefficient of the power series.

For x0 = -1, we consider the power series centered at x0 = -1.

Let the power series be:
∑an(x+1)ⁿ

Then, we can use the ratio test to find the lim sup:
lim sup |an(x+1)ⁿ / a(n-1)(x+1)ⁿ⁻¹| = |x+1|

Therefore, the radius of convergence is:
\(R = 1/lim sup (|an|^{(1/n)}) = 1/lim sup (|x+1|^{(1/n)}) = 1\)

So the series converges for all x such that |x+1| < 1, or -2 < x < 0.

For x0 = 0, we consider the power series centered at x0 = 0.

Let the power series be:
∑anxⁿ

Then, we can use the ratio test to find the lim sup:
lim sup |anxⁿ / a(n-1)xⁿ⁻¹| = |x|

Therefore, the radius of convergence is:
\(R = 1/lim sup (|an|^{(1/n)}) = 1/lim sup (|x|^{(1/n)}) = 1\)

So the series converges for all x such that |x| < 1.

For x0 = 1, we consider the power series centered at x0 = 1.

Let the power series be:
∑an(x-1)ⁿ

Then, we can use the ratio test to find the lim sup:
lim sup |an(x-1)ⁿ / a(n-1)(x-1)ⁿ⁻¹| = |x-1|

Therefore, the radius of convergence is:
\(R = 1/lim sup (|an|^{(1/n)}) = 1/lim sup (|x-1|^{(1/n)}) = 1\)

So, the series converges for all x such that |x-1| < 1, or 0 < x < 2.

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The probability of a student completing the final examination in less than 65 minutes is 13.45%.

The time it takes to complete a final examination in a particular college course is normally distributed with a mean of 77 minutes and a standard deviation of 12 minutes. This can be expressed mathematically as X~N(77, 12).

The probability of a student completing the final examination in less than 65 minutes can be calculated by using the Z-score formula:

Z = (x - μ) / σ

Where x = 65 minutes, μ = 77 minutes, and σ = 12 minutes.

Plugging these values into the formula, we get:

Z = (65 - 77) / 12 = -1.17

Using a Z-score table, we can find the probability of a student completing the final examination in less than 65 minutes, which is equal to 0.1345, or 13.45%. Therefore, the probability of a student completing the final examination in less than 65 minutes is 13.45%.

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The coordinate points on the first quadrant represent the possible dimensions of the rectangle with an area of 32 m².

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

Given is that the area of a rectangle is 32 m².

Assume that the length and breadth of the rectangle are {x} m and {y} m respectively. We can write the area of the rectangle as -

xy = 32

We can write -

y = 32/x                                    .... Eq { 1 }

The dimensions cannot be negative. So, the coordinate points on the first quadrant represent the possible dimensions of the rectangle.

Therefore, the coordinate points on the first quadrant represent the possible dimensions of the rectangle with an area of 32 m².

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Answer:

\(10 \frac{2}{5}\)

Step-by-step explanation:

Using BODMAS

\(6\frac{1}{2} \times (\frac{8}{9} \div\frac{13}{18}) + ( \frac{3}{4} )\ of \ 3\frac{1}{5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ solving \ expression \ inside \ bracket \ ]\\\\\frac{13}{2} \times (\frac{8}{9} \times \frac{18}{13}) + (\frac{3}{4}) \ of \ \frac{16}{5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} \ ]\\\\\frac{13}{2} \times (\frac{16}{13}) + (\frac{3}{4}) \ of \frac{16}{5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ solving \ of \ ] \\\\\)

\(\frac{13}{2} \times (\frac{16}{13} ) + (\frac{3}{4} \times \frac{16}{5} )\\\\\frac{13}{2} \times (\frac{16}{13} ) + \frac{12}{5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ solving \ \times \ expressions \ ] \\\\(\frac{13}{2} \times \frac{16}{13}) + \frac{12}{5}\\\\8 + \frac{12}{5}\\\\\frac{40 + 12}{5}\\\\\frac{52}{5}\\\\10\frac{2}{5}\)

Answer:

The answer would be B

Step-by-step explanation:

the y-intercept would be a postive 4 and because it's a negative slope, it would rule out all of them except B.

Answer:

y = -1/2x +4

Step-by-step explanation:

We have two points so we can find the slope

m = (y2-y1)/(x2-x1)

   = ( 0-4)/(8-0)

   = -4/8

   = -1/2

We know the y intercept is 4

The slope intercept form of the line is

y = mx+b where m is the slope and b is the y intercept

y = -1/2x +4

Kim performs to create rectangle A'B'C'D' Transformation, ''Rotation of 270 degrees counterclockwise about the origin'' and it can be determined by using the rules of transformation.

Kim performed a transformation on rectangle ABCD to create rectangle A'B'C'D', as shown in the figure below:

Rectangles ABCD and A prime B prime C prime and D prime are shown.

What transformation did Kim perform to create rectangle A'B'C'D'?

Kim performed a transformation on rectangle ABCD to create rectangle A'B'C'D', as shown in the figure below:

Rectangles ABCD and A prime B prime C prime and D prime are shown.

Transformation involves changing the position of the given shape.

A (1, -2),

B (-1, 5)

C (-3, 5)

D (-3, 2)

A (2, 1),

B (5, 1)

C (5, 3)

D (2, 3)

The transformation from ABCD to A'B'C'D is 270 degrees counterclockwise about the origin.

And the proof is as follows.

The rule of 270 degrees counterclockwise about the origin is:

The given coordinates;

A (2, 1) - (-1, 2)

B (5, 1) - (-1, 5)

C (5, 3) - (-3, 5)

D (2, 3) - (-3, 2)

Hence, Kim performs to create rectangle A'B'C'D' Transformation, ''Rotation of 270 degrees counterclockwise about the origin''.

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Answer:

Step-by-step explanation:

The question is not properly structured. Here is the complete question.

For cones with radius 6 units, the equation V=12\pi h relates the height h of the cone, in units, and the volume V of the cone, in cubic units. Sketch a graph of this equation on the axes.

The formula for calculating the volume of a cone is expressed as shown;

\(V = \frac{1}{3} \pi r^{2} h\) where r is the radius and h is the height.

Given radius r = 6units, on substituting;

\(V = \frac{1}{3}*\pi *6^{2}*h\\ V = \frac{36\pi h}{3}\\V = 12\pi h... (1)\)

It can be seen from the derived volume of the cone that it is linear in nature. The volume of the cone has a linear relationship with its height. As the volume increases, the height also increases and vice versa.

Generally for a direct variation

\(if\ y\ \alpha x \ \\y = kx\)

where k is the constant of proportionality. comparing to equation 1, k = 12π.

Find the graph attached

The maximum distance from the origin of the polar curve \(r = e^{-\theta sin\theta}\) for 0 ≤ θ ≤ π is approximately 2.143 units.

To find the maximum distance from the origin of the polar curve \(r = e^{-\theta sin\theta}\) for 0 ≤ θ ≤ π, we need to evaluate the value of r at critical points and determine the maximum value.

To find critical points, we look for values of θ where the derivative of r with respect to θ is equal to zero or is undefined.

First, let's find the derivative of r with respect to θ:

\(dr/d \theta=e^{-\theta sin\theta} (sin\theta+ \theta cos\theta)\)

Now, let's set this derivative equal to zero and solve for θ:

\(0=e^{-\theta sin\theta} (sin\theta+ \theta cos\theta)\)

This equation will be satisfied if either \(e^{-\theta sin\theta}=0\) or (sinθ + θcosθ) = 0.

Since \(e^{-\theta sin\theta}\)   is never zero for any value of θ, we focus on the second condition: (sinθ + θcosθ) = 0.

To solve this equation, we can use numerical methods or graphical analysis. The solutions to this equation are approximately θ ≈ 0.852 and θ ≈ 2.685.

Next, we evaluate the value of r at the critical points and the endpoints of the given interval:

\(r(0) = e^{-0sin0} = 1\)

r(0.852) ≈ 0.423

r(2.685) ≈ 2.143

\(r(\pi ) = e^{-\pi sin\pi } = 1\)

The maximum distance from the origin occurs at either r(0.852) or r(2.685), whichever is larger. In this case, r(2.685) ≈ 2.143 is the maximum distance.

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The value of (a)  125 / 78125 and  (b)  1296 / 7776.

What is exponential power?

In mathematics, power defines a base number raised to the exponent, where the base number is the factor that is multiplied by itself and the exponent denotes the number of times the same base number is multiplied.

To solve 5³ * 5⁻⁷, we can simplify the exponents first:

5³ = 125

5⁻⁷ = 1 / 5⁷

So, the expression simplifies to:

125 * (1 / 5⁷) = 125 / 78125

To solve 6⁴ * 6⁻⁵, we can simplify the exponents first:

6⁴ = 1296

6⁻⁵ = 1 / 6⁵

So, the expression simplifies to:

1296 * (1 / 6⁵) = 1296 / 7776

Hence, The value of (a)  125 / 78125 and  (b)  1296 / 7776.

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Answer:

x=-5

Step-by-step explanation:

First distribute:

10x+30=5x+15+2x

Then combine like-terms:

10x+30=7x+15

Subtract 30 from both sides:

10x=7x-15

Subtract 7x from both sides:

3x=-15

divide both by 3

x=-5

\(\frac{j^{3}k }{h^{0} }=1\)

An algebraic expressions is an expressions in which it contains the variables and constants, along with algebraic operations (addition, subtraction, multiplication, etc.). Expressions are made up of terms.

Given, h=8, j = -1 and k=-12.

To find :

\(\frac{j^{3}k }{h^{0} }\)

The given is the expressions made up of variables as j, k, h and constants as 3,0 and operations as exponents and division.

To find the value of the given term we have to substitute the given values.

\(\frac{j^{3}k }{h^{0} }\) = \(\frac{(-1)^3*-12}{8^0}\)

Solve the denominator we get, \(8^{0} = 1\)

Then the above term becomes,

\(\frac{(-1)^3*-12}{8^0} = \frac{(-1)^3*12}{1}\)

Evaluate all exponents we get, \(-1^{3} =-1\)

, \(\frac{-1*-12}{1}\) = 12

Hence,\(\frac{j^{3}k }{h^{0} } =1\)

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The cost function is composed of various pieces of information that relate to the costs of the production process.

Ashley's cost function includes the cost of her grandma's heat and cable TV and Yam price to make toys.The cost function of Ashley is the economic relationship between the costs incurred by Ashley and the production of her products. It is a mathematical function that helps her analyze the production process to make her product profitable. The cost function is composed of various pieces of information that relate to the costs of the production process.Here are the pieces of information included in Ashley's cost function:- The cost of her grandma's heat and cable TV- Yam price to make toysTherefore, the correct answer is B and E.

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Answer:

5

Step-by-step explanation:

10 - 2 + 3- 7 = 5

Answer:

5........................

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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The probability that someone who buys 3 packages will return exactly 1 of them is approximately 0.2448, or 24.48%.

Let's start by calculating the probability of finding at most 1 defective diskette in a single package. We can use the binomial distribution formula for this:

P(X ≤ 1) = P(X = 0) + P(X = 1) = (0.99)¹⁰ + 10(0.01)(0.99)⁹

The first term represents the probability of finding 0 defective diskettes in the package, and the second term represents the probability of finding exactly 1 defective diskette in the package. We can use the formula for combinations to calculate the second term: 10 choose 1.

Using a calculator, we can simplify this expression to:

P(X ≤ 1) = 0.9044

Now, let's consider the three packages. We want to find the probability that exactly one of them will be returned. This means that two of the packages will have at most 1 defective diskette, and one of them will have more than 1 defective diskette.

We can use the binomial distribution again to calculate this probability. Let's define a success as a package with at most 1 defective diskette, and a failure as a package with more than 1 defective diskette. The probability of success is 0.9044, as we calculated earlier, and the probability of failure is 1 - 0.9044 = 0.0956.

Using the binomial distribution formula, we can calculate the probability of exactly one failure in three trials:

P(X = 1) = (3 choose 1)(0.0956)¹(0.9044)²

Using a calculator, we can simplify this expression to:

P(X = 1) = 0.2448 or 24.48

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Answer:

connotative meaning

Step-by-step explanation:

Answer:

connotative meaning

Step-by-step explanation: