Find the center and radius of the circle represented by the equation below.
x² + y² - 20x - 14y + 100 = 0

The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.

A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.

The formula for calculating the confidence interval for the population mean is:

Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)

Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.

Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.

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Answer: Correct answer is -1

Step-by-step explanation:

Answer:

B. -9

Step-by-step explanation:

The equation would be f(-3)=-3^2

3*3 is 9

Add the - back on, and you get -9

I hope this helps!

Answer: 2/3

Step-by-step explanation: use scratch work and compare the shaded amounts.

When a point falls outside of control limits in statistical process control, the probability is quite high that the process is experiencing special cause variation.

In statistical process control (SPC), control limits are used to define the range within which a process is expected to operate under normal or common cause variation. Common cause variation refers to the inherent variability of a process that is predictable and expected.

On the other hand, special cause variation, also known as assignable cause variation, refers to factors or events that are not part of the normal process variation. These are typically sporadic, non-random events that have a significant impact on the process, leading to points falling outside of control limits.

When a point falls outside of control limits, it indicates that the process is exhibiting a level of variation that cannot be attributed to common causes alone. Instead, it suggests the presence of specific, identifiable causes that are influencing the process. These causes may include equipment malfunctions, operator errors, material defects, or other significant factors that introduce variability into the process.

Therefore, when a point falls outside of control limits in statistical process control, it is highly likely that the process is experiencing special cause variation, which requires investigation and corrective action to identify and address the underlying factors responsible for the out-of-control situation.

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Answer:

40000

Step-by-step explanation:

800 millimeters x 50 bottles = 40000 millimeters total

The amount of money Rony earn in dollars will be (p/2) – 17. Then the correct option is C.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

Rony earns 17 dollars, less than half of what John earns.

If John earns p dollars.

Then the amount of money Rony earn in dollars will be

Then the expression can be written as in the mathematical form. Then we have

⇒ (p/2) – 17

Then the correct option is C.

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The formula for calculation of circumference of the circle = d π or 2πr where d is diameter of circle and r is the radius of circle

As given in the question the circumference of the circle whose diameter is 2 cm is 6.28cm and we come to know that value of π used here is 3.14 and not 22/7

So, the circumference of the circle whose diameter is 1cm = d π

              = 1 π

            = 1 3.14

                                                                                          = 3.14 cm

Hence the circumference of the circle whose diameter is 1cm using the value of pi as 3.14 comes out to be pi that is 3.14 cm

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Multiply the numerator and denominator by the conjugate.

Exact Form:

−10−5√3

Decimal Form:

−18.66025403...

The measure of angle A is 85^o.

A quadrilateral is any form of plane figure which is bounded by four straight sides. Examples include: square, rhombus, rectangle trapezium etc. Each example of quadrilateral has differentiating properties.

The given quadrilateral ABCD inscribed in the circle has the shape of a rhombus. So we have:

the measure of opposite internal angles of a rhombus are congruent, so that;

x + (2x + 1) + 148 + (2x + 1) = 360

5x + 150 = 360

5x = 360 - 150

5x = 210

x = 210/ 5

  = 42

x = 42^o

Thus measure of angle A = (2x + 1)

                              = 2*42 + 1

                              = 85^o

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To find the length of a line segment with endpoints Q(8, 2) and R(5, 7), we can use the distance formula. The measurement closest to the length of the line segment can be determined by calculating the distance between the two points using the formula and comparing the result to other given measurements.

The distance formula is used to find the length of a line segment between two points in a coordinate plane. The formula is given as:

d = √[(x2 - x1)² + (y2 - y1)²]

where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

In this case, the coordinates of the endpoints are Q(8, 2) and R(5, 7). We can substitute these values into the distance formula and calculate the distance between the points.

d = √[(5 - 8)² + (7 - 2)²]

  = √[(-3)² + 5²]

  = √[9 + 25]

  = √34

The length of the line segment QR is approximately √34 units. To determine which given measurement is closest to this length, you would compare the value of √34 to the other given measurements and select the one that is closest in value.

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Answer:

In geometry, point, line, and plane are considered undefined terms because they are only explained using examples and descriptions. that lie on the same line. that lie in the same plane.

The point, line, and plane are undefined words in geometry. Parallel lines are explained using one of the undefined terms "line".

Parallel lines are coplanar straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space and also the distance between these two lines is always constant.

The point, line, and plane are undefined words in geometry since they are only described by examples and explanations. Identify the points, lines, and planes. Collinear points are those that are located on the same line.

Parallel lines are explained using one of the undefined terms "line". The Parallel lines are coplanar straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space and also the distance between these two lines is always constant.

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Answer:

\(D = 0.42m\)

Step-by-step explanation:

Given

Force = 0.052 N when Distance = 1.6 m

Required

Find Force; when distance = 0.74 N

The question says force is inversely proportional to square of distance;

Let F represent Force and D represent Distance;

Mathematically;

\(F\alpha \frac{1}{D^2}\)

Convert proportion to equation

\(F = \frac{k}{D^2}\)

Where k is the proportionality constant; This means that k is always constant

Make k the subject of formula

\(F * D^2 = \frac{k}{D^2} * D^2\)

\(FD^2 = k\)

When F = 0.052 and D = 1.6; the value of k is as follows

\(0.052 * 1.6^2 = k\)

\(0.13312 = k\)

\(k = 0.13312\)

When F = 0.74;

Recall that k is always constant; so \(k = 0.13312\)

To solve for D, we'll make use of \(F = \frac{k}{D^2}\)

Substitute \(k = 0.13312\) and F = 0.74;

\(0.74 = \frac{0.13312}{D^2}\)

Multiply both sides by D²

\(0.74 * D^2 = \frac{0.13312}{D^2} *D^2\)

\(0.74 * D^2 = 0.13312\)

Divide both sides by 0.74

\(\frac{0.74 * D^2}{0.74} = \frac{0.13312}{0.74}\)

\(D^2 = \frac{0.13312}{0.74}\)

\(D^2 = 0.17989189189\)

Take square roots of both sides

\(D = \sqrt{0.17989189189}\)

\(D = 0.42413664294\)

\(D = 0.42m\) (Approximated)

Roman has a certain amount of money. if he spends 15, then he has 14 of the original amount left. Roman had originally 20.

To find out how much money Roman had originally, you can follow these steps:
Step 1: Let the original amount of money be "x".
Step 2: According to the problem, if Roman spends $15, he has 1/4 of the original amount left.

So, after spending 15, he has (1/4)x left.
Step 3: Since he spent $15, we can write the equation as: x - 15 = (1/4)x.
Step 4: To solve for x, first multiply both sides of the equation by 4 to get rid of the fraction:

4(x - 15) = 4(1/4)x => 4x - 60 = x.
Step 5: Subtract "x" from both sides:

4x - x - 60 = 0 => 3x - 60 = 0.
Step 6: Add 60 to both sides:

3x = 60.
Step 7: Divide both sides by 3 to find the value of x:

x = 60 / 3 => x = 20.

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the matches are

-2(2x+5) ≤ -7(x+4)         x<=-6

4x-3x-1                          x<=-1

5(x-3)9(x+1)                   x>=-6

3(x-4)+5 2x-9                x>=-2

Generally, Inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not equal, or which one is greater or smaller. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For example, 5 < 8 is an inequality that indicates that 5 is less than 8, and x + 3 ≥ 7 is an inequality that indicates that the value of x plus 3 is greater than or equal to 7.

Inequalities are commonly used in algebra and other branches of mathematics to represent relationships between quantities.

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The correct matching of the inequalities can be shown from the calculations below

Inequalities are an important tool in mathematical modeling and optimization problems, where they are used to express constraints and objective functions.

Using the principle of inequalities we have;

1) -2(2x + 5) ≤ - 7(x + 4)

-4x -10 ≤ -7x -28

-4x +7x ≤ -28 + 10

3x ≤ -18

x ≤ -6

2) 4x - 6/2 ≥ 3x - 1

4x - 6 ≥ 6x - 2

4x - 6x ≥ -2 + 6

-2x ≥ 4

x  ≤ -2

3) 5(x - 3) ≤ 9(x + 1)

5x - 15  ≤ 9x + 9

5x - 9x  ≤ 9 + 15

-4x  ≤ 24

x ≥ -6

4) 3(x - 4) + 5 ≥ 2x - 9

3x - 12 + 5≥ 2x - 9

3x - 2x ≥ -9 + 12 -5

x ≥ -2

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Answer:

\(a) \: y = \frac{4}{ {x}^{2} }\)

\(b) \: x = \frac{2}{5} \)

Step-by-step explanation:

Please see the attached pictures for the full solution.

The number of hours to breakeven will be 5 hiurs

The breakeven is the point at which the cost and the revenue are equal.

Since Mitch sells thingamabobs. His revenue is modeled by the function R(h) = 5h+ + 8 for every h hours he spends working and his overhead cost is modeled by the function C'′(h) = h² + 7h − 16.

This wll be:

Revenue = Cost

5h + 8 = h² + 7h - 16

Collect like terms

h² + 7h - 5h - 16 = 0

h² - 2h - 16 = 0

Solving the equation will give h as 5.

The number of hours will be 5 hours.

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Using the simplex method, the optimal solution for the given linear programming problem is x = 2, y = 2, z = 0, with the maximum objective value of P = 10.



a. To rewrite the formulation in standard form, we need to replace the inequalities with equality constraints and introduce non-negative variables. Let's assume x, y, and z as the non-negative variables:

Maximize P = 3x + 2y + 4z

Subject to:2x + y + z + s1 = 8

x + 2y + 3z + s2 = 10

x, y, z ≥ 0

b. Utilizing the linear programming simplex method, we can solve the above formulation. After setting up the initial tableau, we perform iterations by selecting a pivot element and applying the simplex algorithm until an optimal solution is reached. The algorithm involves row operations to pivot the tableau until all coefficients in the objective row are non-negative. This ensures the optimality condition is satisfied, and the maximum value of P is obtained.

To provide a brief solution within 120 words, we determine the optimal solution by applying the simplex method to the above formulation. After performing the necessary iterations, we find that the maximum value of P occurs when x = 2, y = 2, z = 0, with P = 10. Therefore, the maximum value of P is 10, and the solution for the given problem is x = 2, y = 2, and z = 0.

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Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

The upper limit of the 99% confidence interval for the mean net worth of all university graduates in Australia is $2.356 million (correct to three decimal places).

A study was conducted to determine the average net worth of university graduates in Australia. The data was based on a random sample of 201 graduates, with an average net worth of $1.90 million and a standard deviation of $1.57 million. In case it is known that the net worth is normally distributed, then the upper limit of the 99% confidence interval for the mean net worth of all university graduates in Australia can be calculated as follows:

The critical value of z when the level of confidence is 99% is: z = 2.576

Using the formula for the confidence interval, we get: Upper limit = X + z x (σ/√n)

Upper limit = $1.90 million + 2.576 x ($1.57 million/√201)

Upper limit = $1.90 million + $0.456 million

Upper limit = $2.356 million

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Greetings from Brasil...

Let's apply rule of 3:

  cups             oz

     2     -------   48

     5     -------    X

2 · X = 48 · 5

2X = 48 · 5

X = (48 · 5)/2

48 is the volume of soda, so just multiply that volume by 2/5 to get the new amount of soda...

Answer:

The answer is 63 miles per hour.

The distance (d) is multiplication of speed x and time (t):

d = x * t

d = 1,764 mi

t = 28 h

x = ?

1,764 mi = x * 28 h

x = 1,764 mi / 28 h

x = 63 miles per hour

Step-by-step explanation:

There's a 0.0465 probability that a customer will have to wait more than 11.3 minutes

To find the probability that a customer will have to wait more than 11.3 minutes, we need to calculate the area under the normal distribution curve to the right of 11.3 minutes.

First, we need to standardize the value 11.3 using the formula z = (x - mean) / standard deviation.

Substituting the given values into the formula, we get z = (11.3 - 18) / 4 = -6.7 / 4 = -1.675.

Next, we can use a standard normal distribution table or a calculator to find the probability corresponding to the z-score of -1.675.

Looking up the z-score of -1.675 in the standard normal distribution table, we find that the probability is approximately 0.0465.

Therefore, the probability that a customer will have to wait more than 11.3 minutes is 0.0465 or 4.65%.

In other words, there is a 4.65% chance that a customer will have to wait more than 11.3 minutes for a Micron representative to become available.

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The domain and the range of the piecewise function for this problem are given as follows:

For this problem, the piecewise function is defined for all values of x, hence the domain is all real values.

The range is obtained as follows:

Hence the range is given as follows:

[-2, ∞).

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Answer:

Step-by-step explanation:

The probability of a success is 0.2, as there are 5 possible outcomes (0 to 4), and one of them is a success (3). Therefore, the probability of a success is 1/5, or 0.2.

The sum of first seven terms of the given series is 89.4.

The given series is 6.4+8+10+12.5+. . . . . ;

n=7.

We need to determine whether the series is arithmetic or geometric and evaluate the finite series for the specified number of terms.

We can observe that the common difference or ratio of the series is not constant. Hence the series is neither arithmetic nor geometric.

Therefore, the series is neither arithmetic nor geometric. The series does not belong to any of the two categories and can be considered an irregular sequence.

In order to evaluate the finite series for n=7, we need to find the sum of first seven terms. So, adding the first seven terms of the given series,

we have,6.4+8+10+12.5+. . . . . +nth term

= 6.4 + 8 + 10 + 12.5 + . . . . . (to 7 terms)         

= 6.4 + 8 + 10 + 12.5 + 15 + 17.5 + 20           

= 89.4

Therefore, the sum of first seven terms of the given series is 89.4.

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The benefit-cost ratio (B/C) for Option A is 0.9085, while for Option B it is 0.9553. Since a B/C ratio greater than 1 indicates a favorable investment, Option B is recommended as it has a higher B/C ratio. Option A is recommended based on the B/C analysis.

Explanation:
To calculate the benefit-cost ratio (B/C) for both options, we need to consider the cash flow diagrams (CFDs) and the given data:
Option A:
First cost = $500
Annual revenue = $138.70
Option B:
First cost = $200
Annual revenue = $58.30

Step-by-step calculation:
1. Calculate the net present value (NPV) for each option:
NPV_A = Annual revenue * (1 - (1 + MARR)^(-life span)) / MARR
NPV_A = $138.70 * (1 - (1 + 0.10)^(-5)) / 0.10 = $454.26
NPV_B = $58.30 * (1 - (1 + 0.10)^(-5)) / 0.10 = $191.06
2. Calculate the benefit-cost ratio (B/C) for each option:
B/C_A = NPV_A / First cost_A
B/C_A = $454.26 / $500 = 0.9085
B/C_B = NPV_B / First cost_B
B/C_B = $191.06 / $200 = 0.9553

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IT is found that the value of x is 4 and value of y is 5.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given system of equations are

2x-6y=22

-5x+y=1

The matrix form is

\(\left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}22\\1\end{array}\right]\)

Let as assume

\(A = \left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right]\\ \\X = \left[\begin{array}{ccc}x\\y\end{array}\right] \\B = \left[\begin{array}{ccc}22\\1\end{array}\right]\)

WE know that AX = B

Then we have;

\(\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}4\\5\end{array}\right]\)

Therefore, the value of x is 4 and value of y is 5.

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