two vertices of an obtuse triangle are $(6,4)$ and $(0,0)$. the third vertex is located on the negative branch of the $x$-axis. what are the coordinates of the third vertex if the area of the triangle is 30 square units?

Answer:

x = -6

Step-by-step explanation:

3x + 8 = -10

3x = -10-8

3x=-18

divide both sides by the coefficient of x which is 3

3x/3 = -18/3

x = -6.

The probability that all the people will get their own coats back is 1/7.

Likelihood is the part of science concerning mathematical depictions of how likely an occasion is to happen, or how likely it is that a suggestion is valid. The likelihood of an occasion is a number somewhere in the range of 0 and 1, where, generally talking, 0 shows difficulty of the occasion and 1 demonstrates sureness. The higher the likelihood of an occasion, the almost certain it is that the occasion will happen. A basic model is the throwing of a fair coin. Since the coin is fair, the two results are both similarly plausible; the likelihood of "heads" rises to the likelihood of "tails"; and since no different results are conceivable, the likelihood of all things considered "heads" or "tails" is 1/2.

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The given statement is a descriptive statistic.

So, the statement "Robin expects to serve 12% fewer meals this year than last year" is a descriptive statistic.

Therefore, the given statement is a descriptive statistic.

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The value of the domain for f(2x) is 2 * 4 to 2 * 18 or 8 to 36.

The set of inputs that a function will accept is referred to as the domain of the function in mathematics. It is sometimes represented by the symbol dom(f), where f is the function.

The function f can be graphed in the Cartesian coordinate system in the specific case where X and Y are both subsets of R. In this instance, the graph's x-axis shows the domain as a projection of the function's graph there. It is a partial function in this instance, and the set of real numbers on which the formula may be evaluated to a real number is known as the natural domain or domain of definition of f.

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Answer:

  16

Step-by-step explanation:

You want the middle of three consecutive even integers that have a sum of 48.

We can let x represent the middle of the three integers. Then the other two are (x -2) and (x +2), and their sum is ...

  (x -2) +x +(x +2) = 48

  3x = 48  . . . . . simplify

  x = 16 . . . . . . divide by 3

The middle integer of the three is 16.

__

Additional comment

As we see here, the average of the three integers is their sum divided by their number: 48/3 = 16. The middle of an odd number of consecutive integers will be equal to their average value. Hence, the middle integer must be 16.

The dimensions of the carpet are 73 x 43. = 3139.

In mathematics, a dimension is a way to quantify the size or separation of an area, an object, or a space inside one direction. In simpler terms, It is just the measurements of an object's length, width, and height.

Geometric figures can be created using any configuration of points, lines, or planes. Depending on their dimensions, geometric figures can be categorized as either a space figure, a surface figure, a line, another line segment, a ray, or a point.

The perimeter of the carpets = is 232.

The length of the carpet = 30 in.

In a rectangle, the edge is P = 2W + 2L

In this case 232 = 2W + 2L

Also, the 2nd sentence says L = W + 30

This length variable can be changed in the perimeter formula:

232 = 2W + 2(W+30)

232 = 2W + 2W + 60

232 = 4W + 60

172 = 4W

43 = W

Then, since L = W+30

L = 43+30 = 73

So the dimensions of the carpet are 73 x 43. = 3139.

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Given hats are forming a conical shape and the volume of the cone will be 27.28 inches³.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

Given that,

4 inches in diameter, 6.5 inches tall, slant height of 6.8 inches

So,

D = 4 inches

Now radius r = D/2

r = 4/2 = 2 inches.

Height h = 6.5 inches.

The volume of the conical bar is given as ;

(1/3)πr²h

So,

Volume = (1/3)π(2)²6.5

Volume = 27.28 inches³

Hence "The volume of the given conical-shaped hat will be 27.28 inches³".

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the red point represents the moment when you return to your house, 8 time units after you originally left.

Let's assume that the graph represents the distance to your home as a function of time. (The x-axis represents time in time units and the y-axis represents the distance in distance units)

Then you can see how in the first 3 units of time you travel a certain distance from your home.

Then for the 3 next time units your position does not change, so you are in a fixed place.

In the next 3 time units you return to your house, here we reached the red point, which represents the moment when you return to your house, 8 time units after you originally left.

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8 is the least number of main courses that the restaurant should offer so that a customer could have a different dinner each night in the year 2003.

What are Integers in Math?

Let m be the number of main courses the restaurant serves, so 2m is the number of appetizers.

Then the number of dinner combinations is 2m *  m * 3=6m².

Since the customer wants to eat a different dinner in all $365$ days of 2003, we must have

                     6m² ≥ 365

                     m²   ≥   60.83

Also, year 2003 is not a leap year, because 2003 divided by 4 does not equal an integer. The smallest integer value that satisfies this is E = 8.

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According to given triangle the value of cos A = 3/5

We know that cos theta = Adjacent Side / Hypotenuse Side

According to the question given that Adjacent side = 3

And Hypotenuse Side  = 5

Then cos A = 3/5

Hence, option 3 is correct

Each geometrical shape has unique side and angle characteristics that enable us to recognize it. The following is a list of a triangle's key characteristics.

Three vertices, three internal angles, and three sides make up a triangle.

According to the triangle's "angle sum property," a triangle's three inner angles can never add up to more than 180 degrees. Take note of the triangle PQR shown above, where the angles P, Q, and R all add up to 180 degrees.

A closed triangle has three vertices, three sides, and three angles. The symbol for a triangle with the three vertices P, Q, and R is PQR. Sandwiches and signboards in the shape of triangles are the most prevalent triangle-shaped objects.

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In the picture there is a triangle with ABC angles. Sides AB=5, BC=3, CA=4. The ratio of CosA=4/5.

Given that,

In the picture there is a triangle with ABC angles.

Sides AB=5, BC=3, CA=4

Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.

The right triangle's three sides are as follows:

Hypotenuse (the longest side)

Perpendicular (opposite side to the angle)

Base (Adjacent side to the angle)

According to the cos theta formula, the cos of an angle in a right-angled triangle is equal to the ratio of the Adjacent side to the hypotenuse.

Cos A = Adjacent side / hypotenuse

CosA=4/5

Therefore, CosA=4/5.

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The basic unit of mass of the ball in the metric system is the gram.

The base units of length (distance), capacity (volume), and weight (mass) in the metric system are the meter, liter, and gram, respectively. We utilize units that are derived from metric units to measure smaller or greater quantities.

Mass is a physical body's total amount of matter. Inertia, or the body's resistance to acceleration when a net force is applied, is also measured by this term. The strength of an object's gravitational pull to other bodies is also influenced by its mass.

Therefore, the basic unit of mass of the ball in the metric system is the gram.

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Answer:

A=10. D=_3

Step-by-step explanation:

Start from 10 and make minus 3 every time

Answer:

0.72 or 18/25

Step-by-step explanation:

Multiply -(-31/50)

0.1 + 31/50

To write 0.1 as a fraction with a common denominator, multiply by 50/50.

0.1*50/50+31/50

Combine 0.1 and 50/50.

0.1+50/50 + 31/50

Combine the numerators over the common denominator.

0.1*50+30/50

Simplify the numerator.

36/50

Cancel the common factor of 36 and 50.

Results are 18/25 and 0.72.

Hope this helps.

Thus coordiante of point H is(4,6)

The Midpoint Formula: The midpoint of two points,

(x1,y1) and (x2,y2) is the point

M=(x1+x2)/2 and (y1+y2)/2

(2+x2)/2=3

(6+y2)/2=6

solving above equation

x2=4

y2=6

Thus coordiante of point H is(4,6)

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Answer: 13.5

Step-by-step explanation:

First arrange the scores in order:

5, 5, 9, 12, 15, 23, 26, 27

**remove 1st and last number in the set of scores every time**

Median of 5, 5, 9, 12, 15, 23, 26, 27=

Median of 5, 9, 12, 15, 23, 26=

Median of 9, 12, 15, 23=

Median of 12, 15 =

**Take mean of remaining two numbers**

(12+15)/2=

27/2=13.5

Answer:

y = 5/2 √6x

Solution.

Rewrite

y = 5/2a√6x

y = 5a√6x

----------

2

Cross multiply

2y = 5a√6x

Swap both sides

√6x = 2y

-----

5a

Take the square of both sides

6x = 2y²

------

5a²

Divide both sides by 6

x = 2y² 6

----- ÷ -----

5a². 1

x = 2y² 1

---- × ----

5a². 6

x = 2y²

-----

75a²

Imani painted the wall most

Mary painted 3/4 of the wall

3/4 = 0.75

Tonya painted 5/4 of the wall

5/7 = 0.71

Imani painted 11/13 of the wall

11/13 = 0.84

Luz painted 11/17 of the wall

11/17 = 0.64

Imani painted the wall most

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Since a negative number's exponent is always positive, [(-4)⁴]⁵ will always be greater than -[(4¹²)³].

What is number system?

The Number System covers any of the several sets of symbols and usage guidelines for indicating numbers, which are used to indicate how many items are present in a particular group. Thus, the Roman numeral I, the Greek letter alpha, the first letter used as a numeral, the Hebrew letter aleph, or the modern number 1, which is nothing more than Hindu-Arabic in origin, can all be used to express the idea of "oneness."

A mathematical representation of the numbers in a given set is called a number system.

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Answer:

The number is 15.

Step-by-step explanation:

Let n be the number.

[tex] \frac{1}{5} n + 21 = 2(n - 3)[/tex]

[tex]n + 105 = 10(n - 3)[/tex]

[tex]n + 105 = 10n - 30[/tex]

[tex]9n = 135[/tex]

[tex]n = 15[/tex]

We are to calculate the value of 4p. The value of 4p will be π / 4.

Let's give the numbers we get from the calculator the names x and y. Independent random variables with a uniform[0,1] distribution are x and y.

Let's take notice that since x and y are both between 0 and 1, 1 is the triangle's longest side.

Let's start by interpreting geometry. If the triangle were a rectangle, the side with length 1 would be the hypotenuse, and x and y would then need to meet the following criteria:

x²+y² = 1

Keep in mind that we are supposing the triangle to be a rectangle in this instance. However, the task requires us to create an acute triangle.

To do that, we must widen the angle formed by the sides of length x and y. We can do that by 'growing' the triangle, but if we do so while maintaining the x and y values, the length of side 1 should rise, which is not what we want.

Therefore, if we enlarge the triangle, we should likewise decrease the value of x and/or y so that the length of the first side may be maintained. This insight allowed us to conclude that

x²+y² < 1

Let's now employ a more mathematical strategy. The Cosine Theorem states that a triangle with three sides of length a, b, and c is satisfying.

A2 is equal to b2+c2 - 2bc* cos(), where is the angle formed by the lengths of b and c's sides.

The result of applying this formula to our triangle is that

[tex]1+x^{2} +y^{2} - 2bc * cos\alpha[/tex] , where aplha is the angle between x and y.

Let's call the figures we obtain from the calculator x and y. X and Y are independent random variables with uniform[0,1] distribution.

Consequently, we must ascertain P(x2+y2 1). This likelihood may be calculated using integration. You need polar coordinates.

(X, Y) = (r*cos, r*sen), where r is an integer between 0 and 1, and (that way, the numbers are positive).

Because the Jacobian matrix has determinant r, X2 + Y2 = 1.

On integrating, we get out answer as π / 4

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Yes, I would play the game, because the probability of winning is 13/18.

Probability:

Probability refer the possible occurrence of any particular event.

Given,

A game where two players each throw two dice each. if any one die matches the other, you win a dollar. if there is no match, you lose a dollar.

Here we need to find whether we able to play this one or not.

To find that one, first, we have to identify the winning scenarios,

Let us consider five winning scenarios. Lets represent the dice outcomes as A, B, C, and D, where your dice are A and B and the other player's are C and D. The five scenarios are:

1) A = B

2) A = C

3) A = D

4) B = C

5) B = D

We know that the total possible outcomes is 6^4. We can go through each scenario and count the possible outcomes. We must be careful to avoid overcounting.

Based on this,

The probability that none match is

=> 6*5*4*3/6^4

=> 360 / 1296

=> 5 / 18

So, probability of winning is,

=> 1 - 5/18

=> 13/18.

So, based on the probability the chance of winning is high. So, we can play it.

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The MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.

For given question,

In 2001 there were 738,114 departures.

As we can see, 2001 was not a leap year.

So, the number of days in 2001 = 365

We find the number of departures per day in 2001.

738,114 / 365 = 2,022.23

So, approximately 2,022 departures per day.

Now we find the number of departures in an hour.

2,022 / 24 = 84.25

This means, approximately 84 departures per hour

We know that, 1 hour = 3,600 seconds

Now we find the mean number of seconds between departure time.

3,600 / 84 = 42.8

                  ≈ 43 seconds

Therefore, the MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.

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The area of the sheet of paper in correct metric units is 602.6c[tex]m^{2}[/tex].

A region's size on a plane or curved surface is expressed by the term "area," which is a mathematical concept. As opposed to surface area, which refers to the area of an open surface or the boundary of a three-dimensional object, plane region or plane area refers to the area of a form or planar lamina. Area can be thought of as the volume of material, at a particular thickness, required to create a model of the shape, or as the volume of paint required to paint the surface in a single coat. It is equivalent to the volume of a solid or the length of a curve in two dimensions (a three-dimensional concept).

Calculations:

The length of a 8 X 11 paper in metric unit is 27.9 cm and width of 8 X 11 paper in metric unit is 21.6 cm.

Area of sheet of paper=length*width

               =27.9*21.6

               =602.6 c[tex]m^{2}[/tex]

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​

Answer: 250/43

Step-by-step explanation

Answer:

he would need seven weeks, i believe.

The true statements are,

⇒ If the price is marked up 25%, the selling price will be $50.

⇒ If the selling price is $70, the price is marked up 75%.

What is the Cost price?

Cost price is the total amount of money that it costs a manufacturer to produce a given product or provide a service.

Given that:-

A Store bought jeans at a cost of $40 a pair.

If the price is marked up 25%, the selling price will be $50

⇒ 40 x 25 / 100 = 10

Selling Price = $50

Hence, This is true statement.

And, If the selling price is $70, the price is marked up 75%.

P = 70 - 40 = $30

40 x 75  / 100 = $30

Hence, This statement is true.

Therefore, the true statements are;

⇒ If the price is marked up 25%, the selling price will be $50.

⇒ If the selling price is $70, the price is marked up 75%.

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The complete question is this,

A store bought jeans at a cost of $40 a pair. Select all the statements that are true.

A. If the price is marked up 20%, the selling price will be $60.

B. If the price is marked up 25%, the selling price will be $50.

C. If the selling price is $65, the price is marked up 50%.

D. If the selling price is $70, the price is marked up 75%.

Rich has to pay an interest of $1525.10  during the 4.5 year non payment period.

In the question

it is given that the Amount of loan taken by Rich = $7900

non payment time period = 4.5years

Interest charged during the non payment time = 4.29%

Interest charge for the first year = 4.29% of 7900

= 0.0429 * 7900                       ...(as 4.29% = 0.0429)

= 338.91

So , the interest charge for first non payment year = $338.91

to find the interest for 4.5 years , multiply the first year interest by 4.5.

So the interest charge for 4.5 years = 4.5*338.91

=1525.095

≅1525.10

Therefore , Rich has to pay an interest of $1525.10  during the 4.5 year non payment period.

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Answer:

b

Step-by-step explanation:

To find the percent of Cara's gross pay, divide what was deducted for Medicare tax by what her bi-weekly gross pay is.

So,

13.97 ÷ 735.18 = 0.019

Which means 1.9%