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Coordinate of circumcenter of the given triangle = (3, 2)

What is circumcenter of a triangle?

Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.

Let the coordinate of circumcenter be (x , y)

Distance of Circumcenter from (4,2) =

\(\sqrt{(x - 4)^2 + (y-2)^2\)

Distance of Circumcenter from (3, 3) =

\(\sqrt{(x - 3)^2 + (y-3)^2\)

Distance of Circumcenter from (2,2) =

\(\sqrt{(x - 2)^2 + (y-2)^2\)

By the problem,

\(\sqrt{(x - 2)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 2)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 4x + 4 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\6x - 4x +6y -4y = 18-8\\2x +2y = 10\\x+ y = 5\\\)..... (1)

Again,

\(\sqrt{(x - 4)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 4)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 8x + 16 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\8x - 6x +4y -6y = 20-18\\2x -2y = 2\\x- y = 1\\\)...... (2)

Adding (1) and (2)

\(2x = 6\\x = \frac{6}{2}\\x = 3\)

Putting the value of x in (1),

3 + y = 5

y = 5 - 3

y  = 2

Coordinate of circumcenter = (3, 2)

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Answer:

42

Step-by-step explanation:

If you add all the number in the stem and leaf plot it equals 336 and you divide by how many numbers there are and there are 8 numbers so 336/8=42

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The rate of change of the area of a square with respect to its side length when s = 5 is 10.

The given equation represents the area of a square as a function of its side length, A(s) = s^2.

To find the rate of change of the area with respect to the side length, we differentiate the area function with respect to s:

dA/ds = 2s.

Substituting s = 5 into the derivative, we have:

dA/ds = 2(5) = 10.

Therefore, the rate of change of the area of a square with respect to its side length when s = 5 is 10. This means that for every unit increase in the side length, the area of the square increases by 10 units.

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Answer:

Slope of line M= -5

Step-by-step explanation:

Perpendicular lines have opposite reciprocals for slope.

For ex: 1/2x=y is perpendicular to -2x=y

For this one simplify the first equation:

x+1=5y

x/5+1/5=y

The slope of the original equation is 1/5.

So the slope of the perpendicular line would be -5.

The actual equation would be:

-5x+19=Y

Answer:

60 cents

Step-by-step explanation:

1. The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The Probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

1. The outcomes in the sample space of choosing a letter from the word THANKS are: T, H, A, N, K, S.

  The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. To find the number of outcomes in the sample space, we multiply the number of outcomes for each word.

  Number of outcomes in the sample space = Number of outcomes for the first word × Number of outcomes for the second word

  Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The probability of choosing the letters AA would be the number of favorable outcomes (which is 0 in this case) divided by the total number of outcomes in the sample space.

  Probability of choosing AA = Number of favorable outcomes / Total number of outcomes

  Probability of choosing AA = 0 / 30 = 0.

Therefore, the probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

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The solution to the absolute value inequality 3|x-9|+9<15 is option d. (1,17).

To solve the absolute value inequality 3|x-9|+9<15, we need to isolate the absolute value expression and consider both the positive and negative cases.

First, subtract 9 from both sides of the inequality:

3|x-9| < 6

Next, divide both sides by 3:

|x-9| < 2

Now, we consider the positive and negative cases:

Positive case:

For the positive case, we have:

x-9 < 2

Solving for x, we get:

x < 11

Negative case:

For the negative case, we have:

-(x-9) < 2

Expanding and solving for x, we get:

x > 7

Combining both cases, we have the solution:

7 < x < 11

Expressing the solution in interval notation, we get option d. (1,17), which represents the open interval between 1 and 17, excluding the endpoints.

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Using Poisson distribution formula;

a. The probability of receiving exactly ten request with a 2 hour period is 9.9%.

b. The probability the operator does not miss any call for assistance is 13/5%

c. We expect 2 calls during the break.

d. The probability that 10 of them arrived within that period is 10.4%

(a) To compute the probability of receiving exactly ten requests during a particular 2-hour period, we can use the Poisson probability formula. For a Poisson process with rate λ, the probability of observing exactly k events in a given time interval is given by:

\(P(X = k) = (e^(^-^\lambda^) * \lambda^k) / k!\)

In this case, the rate λ is 4 requests per hour, and the time interval is 2 hours. Therefore, the average number of requests in a 2-hour period would be λ = 4 * 2 = 8.

Using k = 10 and λ = 8 in the formula, we have:

P(X = 10) = (e⁻⁸ * 8¹⁰) / 10!

Calculating this expression, we find the probability of exactly ten requests during the 2-hour period.

P(X = 10) = 0.099

P(X = 10) = 9.9%

(b) If the operators take a 30-minute lunch break, the probability that they do not miss any calls for assistance can be calculated by considering the probability that no calls occur during that 30-minute period.

The average number of requests in a 30-minute interval would be λ = 4 * 0.5 = 2. Therefore, using the Poisson probability formula, we can find the probability of no requests during this interval:

P(X = 0) = (e⁻² * 2⁰) / 0!

P(X = 0) = 0.135 = 13.5%

This probability represents the likelihood that no calls occur during the 30-minute lunch break.

(c) To determine the expected number of calls during the operators' 30-minute lunch break, we can use the average rate of requests per hour and adjust it for the 30-minute duration. The average rate is 4 requests per hour, which corresponds to 4/2 = 2 requests per 30 minutes. Therefore, we can expect approximately 2 calls during their break.

(d) If 30 requests were received between 10 a.m. and 5 p.m., and we want to determine the likelihood that 10 of them arrived between 2 p.m. and 5 p.m., we can use the Poisson distribution again.

First, we need to calculate the average number of requests during the 3-hour period from 2 p.m. to 5 p.m. The average rate is 4 requests per hour, so the average number of requests during this period would be λ = 4 * 3 = 12.

Using k = 10 and λ = 12 in the Poisson probability formula, we can find the probability of exactly 10 requests during the 3-hour period.

P(X = 10) = (e⁻¹² * 12¹⁰) / 10!

P(X = 10) = 0.105 = 10.5%

This probability represents the likelihood that 10 requests arrived between 2 p.m. and 5 p.m.

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The probability of randomly choosing a 5-letter password for an internet web site that consists of only vowels is approximately 0.00026 (or 0.026%).

There are 5 vowels in the English alphabet (a, e, i, o, u). To create a 5-letter password using only vowels, we have 5 choices for each letter in the password. Therefore, the total number of possible 5-letter passwords made up of only vowels is 5^5 = 3125.

To find the total number of possible 5-letter passwords, we need to consider all 26 letters of the English alphabet. Since there are 26 choices for each letter in the password, the total number of possible 5-letter passwords is 26^5 = 11,881,376.

The probability of randomly choosing a 5-letter password for an internet web site that consists of only vowels is the number of possible 5-letter passwords made up of only vowels divided by the total number of possible 5-letter passwords:

P(password consists of only vowels) = 3125 / 11,881,376

Therefore, the probability of randomly choosing a 5-letter password for an internet web site that consists of only vowels is approximately 0.00026 (or 0.026%).

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Answer:

B. 31.4

Step-by-step explanation:

To find x, the hypotenuse, we need to use sin because we have been given the opposite (the side opposite the angle 35°) and we need to work out the hypotenuse (the longest or slanted side):

SOH, CAH, TOA

sin(θ) = opposite ÷ hypotenuse

Sub in the values (we don't know the hypotenuse so i've called it x):

sin(35) = 18 ÷ x (multiply both sides by x)

x × sin(35) = 18 (divide both sides by sin(35))

x = 18 ÷ sin(35) = 31.38204...

x ≈ 31.4

Hope this helps!

Answer:

the answer isosceles

Step-by-step explanation:

well, an isosceles triangle as two equal angles

hope this was helpful

Answer:

The constant of a proportionality in a graph of a proportional relationship is the constant ratio of y to x (the slope of the line

Answer: 4th box

Step-by-step explanation:

Answer: the answer is A), normal is 28 + 4fee, but if she buys LOTS its 22 +8

contact me through discord Acathia#0103, its easier to help, I can help with multiple questions aswell

Step-by-step explanation:

Answer:

Orange per pound= $4.86

Step-by-step explanation:

Giving the following information:

Decrease rate= 20%

Price this week= $3.89 per pound

To calculate the price of oranges last week, we need to use the following formula:

Orange per pound= price this week / (1 - decrease rate)

Orange per pound= 3.89 / (1 - 0.8)

Orange per pound= $4.86

Answer:

\(\huge\boxed{x=\frac{W}{3y}}\)

Step-by-step explanation:

If we have the equation \(3xy=W\) and we want to solve for x, our goal is to isolate x one one side of the equation.

The question we have to ask ourself is ”What’s stopping x from being isolated?”

That would be the 3 and the y.

Since we’re multiplying x by the 3 and the y, we can divide both sides by the 3 and the y to get x isolated.

\(3xy \div 3y = w \div 3y\)

\(x = \frac{W}{3y}\)

Hope this helped!

Gross margin is calculated by subtracting the cost of goods sold from the total revenue.

To understand this calculation more comprehensively, let's break it down:

1. Total Revenue: Total revenue represents the total amount of money generated from the sales of goods or services.

It includes the selling price of the products or services and any additional income related to sales, such as shipping charges or discounts.

2. Cost of Goods Sold (COGS): Cost of Goods Sold refers to the direct costs incurred in producing or acquiring the goods that were sold.

It includes expenses such as the cost of raw materials, manufacturing costs, labor costs directly associated with production, and any other expenses directly tied to the production of goods.

By subtracting the COGS from the total revenue, we arrive at the gross margin, which represents the amount of money remaining after accounting for the direct costs associated with the production or acquisition of the goods sold.

Gross margin reflects the profitability of the core business operations before considering other indirect expenses such as overhead costs, marketing expenses, or administrative costs.

The formula for calculating gross margin can be represented as follows:

Gross Margin = Total Revenue - Cost of Goods Sold

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Roger has enough stainless steel pipe to replace the chimney liner, with a slight surplus remaining.

To determine if Roger has enough stainless steel pipe for the chimney liner, we need to convert the given measurements to a consistent unit of measurement. Since the length of the liner required is given in feet, we need to convert the 400 inches of stainless steel pipe to feet.

There are 12 inches in a foot, so 400 inches is equal to 400/12 = 33.33 feet (approximately).

Comparing this converted length of the stainless steel pipe (33.33 feet) with the length of the liner required (33 feet), we can see that Roger does indeed have enough pipe. In fact, he has slightly more than required.

Since the length of the liner required is 33 feet and Roger has 33.33 feet of stainless steel pipe available, there is a surplus of approximately 0.33 feet (about 4 inches) of pipe. This additional length is more than enough to cover any potential measurement errors or adjustments needed during the installation process.

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Answer:

89.25

Step-by-step explanation:

because:

it just is

The number of pattern block rhombuses that would create a hexagons is 3.

A hexagon is a six-sided polygon or 6-gon creating the outline of a cube.

A hexagon can be divided into a minimum of three rhombuses, each of which can be further divided into four rhombuses. With n being a positive integer, the result is 3n.

The total number of rhombuses that can fit in a hexagon is not limited to multiples of three, given that the total number of rhombuses dividing a hexagon can be raised by three by quartering a single component rhombus. The amount might actually be any integer larger than 7.

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The NBA Hall of Famer you are referring to is Michael Jordan. Michael Jordan is a retired professional basketball player widely considered to be one of the greatest basketball players of all time.

During his career, Jordan won six NBA championships, five NBA Most Valuable Player awards, 10 scoring titles, and was named an NBA All-Star 14 times. He is also known for his numerous signature sneakers and his successful career off the court, including his ownership of the Charlotte Hornets NBA team.

The NBA stands for the National Basketball Association, which is a professional basketball league in North America. It is composed of 30 teams, 29 in the United States and one in Canada, and is considered to be the premier men's basketball league in the world.

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Answer:

MQ=4... sides are equal

PQ=MQ+MP

=4+4

=8

Answer:

(x - 8) + 3x + x = 107

x - 8 + 3x + x = 107

5x - 8 = 107

5x = 115

x = 23, SO...

The first number is 23-8, which is 15

The second number is 3 x 23, which is 69

The third number is 23

15 + 69 + 23 = 107 CHECK!

Step-by-step explanation:

We want to find the perimeter of the fifth square in the given sequence.

The perimeter of the fifth square is 1cm.

Let's see how to get that:

The perimeter of the first square is 16cm.

Remember that the perimeter of a square of side length S is:

P = 4*S

Then the side length of the first square is given by:

16cm = 4*S

16cm/4 = S = 4cm

Then she connects the midpoints of the sides to form another square (actually four equal squares).

The midpoint would be at half of the side length of the square, then the side length of the new squares is 4cm/2 = 2cm.

For the third square, the side length is divided by two again, to get 2cm/2 = 1cm

For the fourth square this happens again: 1cm/2 = 0.5cm

For the fift square this happens again: 0.5cm/2 = 0.25cm

Then we have a square of side length equal to 0.25cm, the perimeter will be:

p' = 4*0.25cm = 1cm

The perimeter of the fifth square is 1cm.

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The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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To evaluate the integral ∫(\(x^{2}\) - \(a^{2}\))/\(x^{4}\) dx, where a is a constant, we can use the substitution x = a sec(θ) in order to simplify the expression.

Let's apply the substitution x = a sec(θ) to the integral. We have dx = a sec(θ) tan(θ) dθ and \(x^{2}\) -\(a^{2}\) = \(a^{2}\) sec^2(θ) - \(a^{2}\) = \(a^{2}\) (sec^2(θ) - 1).

Substituting these expressions into the integral, we get:

∫(x^2 - a^2)/x^4 dx = ∫(\(a^{2}\) (sec^2(θ) - 1))/(\(a^{4}\)sec^4(θ)) (a sec(θ) tan(θ) dθ)

= ∫(1 - sec^2(θ))/\(a^{2}\) sec^3(θ) tan(θ) dθ.

Simplifying further, we have:

= (1/a^2) ∫(1 - sec^2(θ))/sec^3(θ) tan(θ) dθ

= (1/a^2) ∫(1 - sec^2(θ))/(sec^3(θ)/cos^3(θ)) (sin(θ)/cos(θ)) dθ

= (1/a^2) ∫(cos^3(θ) - 1)/(sin(θ) cos^4(θ)) dθ.

Now, we can simplify the integrand further by canceling out common factors:

= (1/a^2) ∫(cos^2(θ)/cos(θ) - 1/(cos^4(θ))) dθ

= (1/a^2) ∫(1/cos(θ) - 1/(cos^4(θ))) dθ.

At this point, we have transformed the integral into a form that can be evaluated using standard trigonometric integral formulas.

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They support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let denote the proportion of adults in the sample who say they support the increase. Suppose that 40% of all adults in Ohio support the increase. the correct answer is (d) 0.40.

Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data

set.  The mean, median and mode are the three commonly used measures of central tendency.

To calculate the mean, we need to add the total values given in a datasheet and divide the sum by the total number of

values.

The mean, μ, of the sampling distribution of p can be found using the formula

μ = p,

where p is the proportion of adults in the entire population who support the increase.

In this case, 40% of all adults in Ohio support the increase, so p = 0.40.

Therefore, the mean of the sampling distribution of p is:

μ = 0.40

So the correct answer is (d) 0.40.

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Answer:

Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height.So the volume of the cube having side 15 mm is 3375 cubic inches.

Different Ways to Find Volume

Solve for Volume by Space. All physical objects occupy space, and you can find the volume for some of them by measuring their physical dimensions. ...

Solve for Volume by Density and Mass. Density is defined as an object's mass per a given unit of volume. ...

Solve for Volume by Displacement.

Step-by-step explanation:

Answer:

56

Step-by-step explanation: