Find the circumcenter of the triangle ABC.
A(8,-8), B(-4, 4), C(8.4).
The circumcenter is
(Type an ordered pair.)

According to the concept of inverse function, the domain of the function is explained below.

The term inverse function is defined as a function which is a square of a linear function.

Here we have know that we will restrict the domain of the function so that the function is one to one.

And then we will find the inverse and then we will find the domain of the inverse function.

Here we have given that the function is not one-to-one and then delete part of the domain so that the function that remains is one-to-one.

As we all know that a function is the set of inputs accepted by the function.

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12 tons of gravel has been used for the driveway.

Weight of first load = 7 tons

Weight of second load = 8000 pounds

There are 2000 pounds (lb) in one US customary ton (t). Both tons and pounds are measurements of mass/weight in the US customary and imperial systems of measurement. However, the definitions of the ton vary in both systems. For example, there are 2240 pounds in an imperial ton, and 2204.6226 pounds in a metric ton.

The US ton is mostly used in the United States and Canada. The imperial ton was mostly used in the UK, and still is to a degree, but since the UK began the process of metrication, the metric ton is also used in the UK.

Convert pounds to tons:

1 pound = 0.0005 ton

8000 pounds = 4 ton

Then,

Weight of second load = 4 ton

Total weight of the gravel, in tons = Weight of first load + Weight of second load

= 8 tons + 4 tons

= 12 tons

Thus, 12 tons of gravel has been used for the driveway.

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Given the facts, the percentage of the left brick is 7/12.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.

Total Bricks = 12

Use Brick = 5

Left Brick = 12-5

                = 7

fraction of left brick = 7/12

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Answer:

see explanation

Step-by-step explanation:

(a)

x - 9y = 10 ( add 9y to both sides )

x = 9y + 10 → (1)

3y² = 4x + 7 → (2)

substitute x = 9y + 10 into (2)

3y² = 4(9y + 10) + 7

3y² = 36y + 40 + 7

3y² = 36y + 47 ( subtract 36y + 47 from both sides )

3y² - 36y - 47 = 0 ← as required

(b)

solving using the method of completing the square

add 47 to both sides

3y² - 36y = 47 ← factor out 3 from each term in the left side

3(y² - 12y) = 47

to complete the square on the left

add/subtract ( half the coefficient of the y- term)² to y² - 12y

3(y² + 2(- 6)y + 36 - 36) = 47

3(y - 6)² - 3(36) = 47

3(y - 6)² - 108 = 47 ( add 108 to both sides )

3(y - 6)² = 155 ( divide both sides by 3 )

(y - 6)² = [tex]\frac{155}{3}[/tex] ( take square root of both sides )

y - 6 = ± [tex]\sqrt{\frac{155}{3} }[/tex] ≈ ± 7.2 ( to 1 decimal place )

add 6 to both sides

y = 6 ± 7.2

then

y = 6 - 7.2 = - 1.2

y = 6 + 7.2 = 13.2

substitute these values into ( 1) for corresponding values of x

x = - 1.2 : x = 9(- 1.2) + 10 = - 10.8 + 10 = - 0.8 ⇒ (- 1.2, - 0.8 )

x = 13.2 : x = 9(13.2) + 10 = 118.8 + 10 = 128.8 ⇒ (13.2, 128.8 )

Answer:

  (x, y) ≈ (-0.7, -1.2) or (128.7, 13.2)

Step-by-step explanation:

You want the solution to the simultaneous equations ...

Solving the first equation for x, we can substitute into the second equation to get a quadratic in y.

  x = 9y +10 . . . . . . . add 9y to the first equation

  3y² = 4(9y +10) +7 . . . . . substitute for x

  3y² = 36y +47 . . . . . . . eliminate parentheses

  3y² -36y -47 = 0 . . . . subtract the right-side expression

The equation can be written in vertex form as ...

  3y² -36y = 47

  3(y² -12y +36) = 47 +3(36)

  3(y -6)² = 155

  y -6 = ±√(155/3)

  y = 6 ± (√465)/3 ≈ -1.19, 13.19

  x = 9y +10 ≈ -0.69, 128.69

The approximate solutions are ...

  (x, y) ≈ (-0.7, -1.2), (128.7, 13.2)

__

Additional comment

The attached graph confirms these solution points.

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The second post is 30 feet tall because the ratio of the shadows is 2:1, meaning that for every 2 feet of shadow, the post is 1 foot tall.

1. ratio of shadows is 2:1, so for every 2 feet of shadow, the post is 1 foot tall

2. 60 feet of shadow divided by 2 is 30 feet tall

3. 24 feet of shadow divided by 2 is 12 feet tall

4. 30 feet tall is the second post

The goal post that casts a 60-foot shadow is 20 feet tall, and the ratio of the shadows is 2:1, meaning that for every 2 feet of shadow, the post is 1 foot tall. To find the height of the second post, we divide the length of the shadow by 2. The second post casts a 24-foot shadow, so when we divide it by 2, the post is 12 feet tall. Therefore, the second post is 30 feet tall. This is because for every 2 feet of shadow, the post is 1 foot tall, so for the 60-foot shadow, the post was 20 feet tall, and for the 24-foot shadow, the post is 12 feet tall. Therefore, the second post is 30 feet tall.

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The probability that Onex will have an EBIT that is below $0 is 0.38%. The correct answer is C.

The first step in solving this problem is to calculate the z-score, which is a measure of how many standard deviations a value is from the mean. In this case, the mean EBIT is $240,000, and the standard deviation is $90,000.

To find the z-score for an EBIT of $0, we subtract the mean from the value and divide by the standard deviation as follows:

This gives us a z-score of -2.67. Next, we use Table V, which is a table of standard normal distribution values, to find the probability that a value with a z-score of -2.67 will fall below 0. The probability is 0.38%, which means there is a very low chance that Onex's EBIT will be below $0.

This question should be provided with answer choices, which are:

The correct answer is C.

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This fraction can be simplified to P(woman) = 21/49 or approximately 0.428.

What is probability ?

Probability is a measure of the likelihood of an event occurring, represented as a number between 0 and 1. 0 indicates that an event is impossible, and 1 indicates that an event is certain to happen. It is the ratio of number of favorable outcomes to the total number of possible outcomes.

In this case, the number of favorable outcomes is the number of women in the class, which is 63. The total number of possible outcomes is the total number of students in the class, which is 63 women + 86 men = 149 students. Therefore, the probability of selecting a woman is,

P(woman) = 63/149

So , This fraction can be simplified to P(woman) = 21/49 or approximately 0.428.

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Simple interest is p15612.12 and compound interest is p16500.If I was were Mr. henry ,I will choose offer of 2%.

1.To calculate simple interest, multiply the principal (initial amount) by the number of years, the interest rate, and the interest rate.

Contrarily, compound interest is computed by first adding the interest from earlier periods to the principal, and then computing the interest for the subsequent period on the updated sum.

Consider Mr. Henry investing P150,000 in ABC Bank at an annual simple interest rate of 2%:

Year 1: Interest earned is P3,000 (P150,000 x 2%).

Year 2: Interest earned is P3,000 ($150,000 x 2%).

Year 3: Interest earned is P3,000 ($150,000 x 2%).

Year 4: Interest earned is P3,000 ($150,000 x 2%).

Year 5: Interest earned is P3,000 ($150,000 x 2%).

Interest earned overall: P15,000

After five years, the total will be P150,000 plus P15,000, or P165,000.

Let's imagine Mr. Henry makes a P150,000 investment in Union Bank at a 2% yearly compound rate:

Year 1: P150,000 multiplied by 2% yielded P3,000 in interest, for a total of P153,000.

Year 2: P153,000 multiplied by 2% to be P3,060 in interest, for a total of P156,060.

Year 3: P156,060 multiplied by 2% to equal P3,121.20 in interest, for a total of P159,181.20.

Year 4: P159,181.20 multiplied by 2% yielded P3,183.624 in interest, for a total of P162,364.824.

Year 5: P162,364.824 multiplied by 2% yields P3,247.29696 in interest, for a total of P165,612.12096.

Interest earned in whole was P15,612.12096.

2 .If I were Mr. Henry, I would pick the 2% compounded annual offer from Union Bank. This is so that after five years, the total sum will be larger due to compound interest. Compound interest increases the amount on which interest is computed in the following period by adding the interest from prior periods to the principal. Due to this, the interest earned during the subsequent period will increase, and so on. As a result, after a certain amount of time, interest accrues more quickly and the overall amount is higher.

  Therefore , simple interest is p15612.12 and compound interest is p16500.If I was were Mr. henry ,I will choose offer of 2% .

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Answer:

----------------------------

Parallel lines divide transversals proportionally.

Set proportions and solve for x:

x 2, and the second side is expressed by  2x-25 , The value of x is 5.

What is isosceles triangles ?

An isosceles triangle is a triangle with two sides of equal length. These two sides are called the legs and they are congruent. The third side is called the base and it is not necessarily congruent to the legs. The angle opposite to the base is called the vertex angle.

To solve for x, we can start by isolating x on one side of the equation.

We can do this by subtracting x^2 from both sides ,

x^2 - x^2 = 2x-25 - x^2

we get 0 = 2x - 25 - x^2

Now we can add x^2 to both sides ,

x^2 = 2x - 25

Now we can move the -25 to the other side of the equation ,

x^2 - 2x + 25 = 0

Now we can factor the left side of the equation ,

(x-5)(x-5) = 0

Now we can solve for x by setting each factor equal to zero ,

x-5 = 0 , x = 5

x 2, and the second side is expressed by  2x-25 , The value of x is 5.

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The given quadratic equation 4x^2 - 4x + 1 = 0 has one real solution

by its discriminant.

The discriminant of a quadratic equation ax^2 + bx +c = 0 is given by

            D = b^2- 4ac

Now from the equation that we have 4x^2 - 4x +1 = 0

             a = 4

             b = -4   and

             c = 1

Hence the discriminant (D) is given by :

             D = b^2- 4ac

                 = (-4)^2- 4(4)(1)

                 = 0

Now check for discriminant D, (D=0)

Therefore the discriminant of a given equation is 0.

So the roots of given equation are real and equivalent.

Hence the equation given 4x^2 - 4x + 1 =0 has only one real solution.

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There are 26 rows and 34 seats per row in the movie theater.

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x represent the number of seats per row and y represent the number of rows.

The number of seats in a row is 8 greater than the number of rows, hence:

x = y + 8    (1)

The total number of seats in the theater is 884, hence:

xy = 884

but x = y + 8. Substituting:

(y + 8)(y) = 884

y² + 8y - 884 = 0

y = 26

x = y + 8 = 26 + 8 = 34

There are 26 rows

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Answer: The answer to part a is the same if you eat 5 cookies from each batch as you are baking because the number of cookies you have is the product of the number of batches times the number of cookies per batch minus the number of cookies you eat.

In the expression 14(5) + 2 = 3(24)

14(5) represents the total number of cookies you put in 14 bags. (14 x 5) = 70

2 represents the number of cookies left after you have put 5 cookies in each of the 14 bags.

3(24) represents the total number of cookies you made from the 3 batches of cookies. (3 x 24) = 72

So the equation can be read as:

The total number of cookies you put in bags (70) plus the number of cookies left (2) is equal to the total number of cookies made from the 3 batches (72).

Step-by-step explanation:

The range of the function, considering the context of this problem, is given as follows:

[0.5, 8].

The range of a function is the set that contains all the possible output values for the function.

The output variable in this context is given as follows:

Amount of water into the 8 ounce glass.

The y-intercept of the graph is obtained as follows:

y - 3 = 2.5(0 - 1)

y = -2.5 + 3

y = 0.5.

Hence the lower bound of the range is of 0.5.

The maximum capacity of the glass of water is of 8 ounces, hence the upper bound of the range is of 8.

The range is composed by a closed interval, as the amounts of 0.5 ounces and 8 ounces can be assumed by the function.

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An answer is- More information is needed before t can be found.  So, option(D) is the correct answer.

Here initial rotation speed is given, the final rotation speed is given, and the asking for time( in a sec) is.

If we use,

A) θ=θ0+ω0t+(1/2)αt2

For this equation, we don't have any details about the value of angular displacement and angular acceleration, so it is not useful.

B) We use,

ω=ω0+αt

For this equation, we don't have any details about angular acceleration, so it is not useful.

C) We know that,

ω2=ω02+2α(θ−θ0)

In this equation, time is not included, hence it is not useful.

D) So, more information is needed.

Thus, option (D) is the correct answer.

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The complete question is:

Suppose you are asked to find the amount of time t, in seconds, it takes for the turntable to reach its final rotational speed. Which of the following equations could you use to directly solve for the numerical value of t?

A) θ=θ0+ω0t+(1/2)αt2

B) ω=ω0+αt

C) ω2=ω02+2α(θ−θ0)

D) More information is needed before t can be found.

The expression for the t1 with the tension in cable 1 that does not depend on t2 is T1sinθ1 + T2sinθ2 = mg

While we looking into the given diagram we have identified that the angle made by strings 1 and 2 are 01 and 02 respectively.

Here we also know that the tension made by strings 1 and 2 are T1 and T2 respectively.

Here let us considering that the diagram shown is the following tension components are available

And the weight of the block mg acting on the body directing the force downwards then the components are written as,

Here the Vertical component of T1 is T1 sinθ1 which acts upwards and the horizontal component of T1 is T1cosθ1 which acts to the left

Where as the another vertical component of T2 is T2sinθ2 which acts upwards then the horizontal component of T2 is T2cosθ2 acting towards right

Here we have to maintain a state of equilibrium, then the upward forces and downwards forces must be equal even as the forces on the right and left hand side must balance

According to this details the balancing the vertical components we obtain

=> T1sinθ1 + T2sinθ2 = mg

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Therefore , the solution of the given problem of ratio comes out to be

there are 32 fauvists .

Ratios show how often one number is contained in another in mathematics. For instance, the ratio of oranges to lemons in a fruit dish is 8 to 6 if there are 8 oranges and 6 lemons present. In a similar vein, the proportion of oranges to whole fruit is 8, while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. The ratio can be expressed as 1:3, for instance, if there is 1 boy and 3 girls (for every boy she has 3 girls) 3/4 are girls, while 1/4 are boys.

Here,

Given :

the ratio is 13:4

and there were 104 impressionists

Let x be the fauvisits

=> 13:4 = 104/x

=>  13 /4  = 104/x

=> x = 104 *4 /13

= >x  = 32

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After five decades, the amount is worth to the nearest hundredth is 607.54

Any decimal number is rounded to the nearest hundredth by the term "to the nearest hundredth." A hundredth is 1/100 or 0.01 in decimal form. For instance, 2.17 is the result of rounding 2.167 to the nearest tenth.

Look at the next place value to the right in order to round a number to the closest hundredth (the thousandths this time). The same applies: Simply eliminate all the digits to the right if the number is 4 or fewer. Add 1 to the digit in the hundredths place if the number is five or above, and then eliminate all the digits to the right.

The equation below can be used to describe this amount at intervals of 2t decades. where r is the rate of increase and Q(0) is the initial quantity. A 510-valued quantity increases exponentially at a rate of 7% every 20 years. After five decades, the amount is worth 607.54

Q(t)=Q(0)[tex]e^{xt}[/tex]

Q(2.5)= 510e^(0.07*2.5)

= 607.54

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Answer:

Step-by-step explanation: Applying BODMAS rule,

[tex](8a-6a^2 +9)+(-10a-8+8a^2)-(-3)\\=8a-6a^2+9-10a-8+8a^2+3\\=2a^2-2a+12[/tex]

The circumference of a circle is the distance encircling its edge. The length measured through the centre of a circle is its diameter. The radius of a circle is the distance from the centre to any point on the edge. The diameter and radius are identical in size, or 2r=d2 r=d.

Circumference =2×227×21=132 cm. Q.

Another way to think about the circle's circumference curve is to look at its 360-degree arc. As a result, a circle's diameter is equal to its 360-degree arc's length.

(a) Circumference of the circle = 2πr

= 2 × 22/7 × 14 cm

= 2 × 22 × 2 cm

= 88 cm

(b) Circumference of the circle = 2πr

= 2 × 22/7 × 28 mm

= 2 × 22 × 4 mm

= 176 mm

© Circumference of the circle = 2πr

= 2 × 22/7 × 21 cm

= 2 × 22 × 3 cm

= 132 cm

Therefore, 176 mm and 132 cm is the circumference of a circle.

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Answer:

1.96

Step-by-step explanation:

Answer: Based on the histogram, it is not possible to determine the exact number of people who travel more than 30 miles to work. However, we can estimate the number of people by using the histogram.

Step-by-step explanation: The histogram shows the frequency density of people traveling different distances to work.

The Y-axis shows the frequency density, and the X-axis shows the distance in miles.

The histogram is divided into bars, each representing a range of distances.

We can see that the majority of people travel less than 30 miles to work, with the highest frequency density being around 20 miles.

However, the histogram does not provide the exact number of people for each bar. Therefore, we cannot determine the exact number of people who travel more than 30 miles to work.

b) Sam travels around 20 miles to work.

Explanation:

205 people out of 550 people is approximately 37% of the total number of people surveyed.

The closest bar on the histogram to 37% is the one around 20 miles.

Therefore, it can be estimated that the distance that Sam travels is around 20 miles.

53 dollar t is the cost of goods if manufacturing costs equal $50 each ,packaging equals $1.00 each, delivery equals $2.00 each, and advertising equals $1,000

what is cost ?

Definition: A cost function is a mathematical formula used to used to chart how production expenses will change at different output levels. In other words, it estimates the total cost of production given a specific quantity produced.

50$ + 1$ + 2$ = 53$

50 for the production

1$ for packaging

2$ for delivery

Hence 53 dollar t is the cost of goods if manufacturing costs equal $50 each ,packaging equals $1.00 each, delivery equals $2.00 each, and advertising equals $1,000

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The probability that a randomly selected student plays basketball, given that they run track is 0.38.

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability.

Assume that events A and B are two independent occurrences with probabilities P(A) and P(B), respectively, such that the probability that event B will occur given that event A is given by: P(B|A) = P(A∩B)/P (A)

Given:

Percentage of the students who play basketball, P(A) = 31%

Percentage of the students who run track, P(B)= 29%

Percentage of the students who participate in both sports, P(A∩B) = 11%

The probability that a randomly selected student plays basketball, given that they run track is:

P(A|B) = P(A∩B)/P(B)

          = 11/29

          = 0.38

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Answer:

y-1=3(x-2)

Step-by-step explanation:

This is the equation you have to fill in y-y1=m(x-x1) to fill in this you have to lable the points (2,1)

x,y

Determining if the method of randomization is either appropriate or not for each given situation includes:

A.           Inappropriate

B.           Appropriate

C.          Appropriate.

Randomization is what?

The technique of randomly assigning study participants to various treatment groups is known as randomization.

Randomization can take the form of selecting names at random to place people in groups or flipping a fair coin to place participants in the experimental or control groups.

In contrast to experiments B and C, the randomization strategy used in experiment A is incorrect.

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Answer:

2.45%

Step-by-step explanation:

(2.86 - 2.79) / 2.86 = 0.0245

0.0245 x 100 = 2.45%

One possible solution of the inequality x + y ≤ 18 and 0.1x + 0.05y ≥ 1.20 is 12 dimes and 4 nickels

An equation is a expression that shows the relationship between numbers and variables.

Let y represent the nickels and x represent the dimes

1 nickel = $0.05, 1 dime = $0.1

She has a maximum of 18 coins worth at least $1.20 combined. Hence:

x + y ≤ 18    (1)

Also;

0.1x + 0.05y ≥ 1.20    (2)

One possible solution is 12 dimes and 4 nickels

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The probability that exactly one of the 4 players has exactly one ace and one king is 4/221.

What is probability ?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means that an event is impossible and 1 means that an event is certain. Events with a probability of 0.5 or greater are considered likely to happen, while events with a probability of less than 0.5 are considered unlikely to happen.

There are 4 players and each player receives thirteen cards. Each player has 4 aces and 4 kings out of the 52 cards.

The probability that exactly one of the 4 players has exactly one ace and one king ,

There are 4 ways to choose the player who gets the ace and king.

The probability that the chosen player gets an ace is 4/52.

The probability that the chosen player gets a king after getting an ace is 3/51.

so the probability that exactly one of the 4 players has exactly one ace and one king is ,

4*(4/52)*(3/51) = 4/221

Therefore, the probability that exactly one of the 4 players has exactly one ace and one king is 4/221.

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Answer:

A quadrilateral is a parallelogram if and only if opposite angles are equal.

So, to make the quadrilateral a parallelogram, we can set the following equalities:

(4x + 13) deg = (5x - 12) deg

(4y + 7) deg = (3x - 8) deg

Solving the first equation,

4x + 13 = 5x - 12

x = -5

Solving the second equation,

4y + 7 = 3(-5) - 8

4y + 7 = -17

4y = -24

y = -6

So, the values of x and y that make the quadrilateral a parallelogram are x = -5 and y = -6