A bag contains 9 green marbles, 6 purple marbles, 4 red marbles, 10 blue marbles, and 7 orange marbles. One marble is randomly selected from the bag.

What is the probability that the marble selected is blue or purple?

Answer as a Fraction, not simplified.

Answer: Using the formula i = prt, we have:

i = (104292.12 - 80040) = 24252.12

p = 80040

t = 3

Substituting these values, we get:

24252.12 = 80040 * r * 3

Solving for r, we get:

r = 0.101 or 10.1%

Therefore, the interest rate is 10.1%.

Step-by-step explanation:

The answer of the given question based on the  twelve-tone technique is This is equivalent to 479,001,600 possible tone rows.

The twelve-tone technique is a method of musical composition developed by Arnold Schoenberg and his disciples in the Second Viennese School in the early 20th century. It is also known as dodecaphony, which means "twelve sounds" in Greek. The technique involves arranging the twelve notes of the chromatic scale in a specific order called a tone row or series, and then using that row as the basis for the composition.

Using the twelve-tone technique, we can create a tone row of 12 pitches from the chromatic scale in any order, but with no pitch repeated in the row. Since there are 12 pitches to choose from for the first note, 11 pitches for the second note (since we can't repeat the first pitch), 10 pitches for the third note (since we can't repeat either the first or second pitch), and so on, the total number of possible tone rows is:

12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

which simplifies to:

12!

This is equivalent to 479,001,600 possible tone rows.

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Answer:

2 yards or 6 feet long

Step-by-step explanation:

Each yard is 3 feet long.

If Tanya shortens the leash by 6 feet, that is 2 yards.

4-2=2

The leash is 2 yards (or 6 feet) long.

Answer:

6 foot

Step-by-step explanation:

1 yards = 3 foot

4 yards = 12 foot

We take

12 - 6 = 6 foot

So, the length of the shortened least is 6 foot.

Kyd's expected value is positive and North's expected value is negative, Kyd has the advantage in this game

What is expected value?

Expected value is a concept used in probability theory to describe the average value or outcome of a random variable over many trials. It is calculated by multiplying each possible outcome of a variable by its probability, and then summing all of the products. This can help to estimate the most likely outcome or value of an uncertain event or situation.

The probability of selecting a face card from a standard 52-card deck is 12/52 or 3/13. The probability of selecting any other type of card is 1 - 3/13 or 10/13.

Kyd's expected value for this game can be calculated as follows:

(3/13) x (-$3) + (10/13) x $6 = $3.38

Therefore, Kyd's expected value for this game is $3.38.

North's expected value for this game can also be calculated as follows:

(3/13) x $6 + (10/13) x (-$3) = -$0.92

Therefore, North's expected value for this game is -$0.92.

Since Kyd's expected value is positive and North's expected value is negative, Kyd has the advantage in this game.

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Answer:

[tex]x^2+(y-5)^2=49[/tex]

Step-by-step explanation:

Recall the formula for the graph of a circle:

[tex](x-h)^2+(y-k)^2=r^2\\[/tex]

Where h is the x-coordinate of the vertex, k is the y-coordinate of the vertex, and r is the radius.

We are given the vertex and the length of the radius.

Substitute the values:

[tex](x-0)^2+(y-5)^2=7^2=\\x^2+(y-5)^2=49[/tex]

Thus, the standard form is:

[tex]x^2+(y-5)^2=49[/tex]

Answer: Option A:

To calculate the total amount Owen will spend on Option A, we need to calculate the monthly payment and then multiply it by the number of months:

First, we need to calculate the total amount of the loan. Owen is making a down payment of $3200, so he will be borrowing $28,820 (the price of the car minus the down payment).

Next, we can use the formula for calculating the monthly payment for a loan:

P = (r * A) / (1 - (1 + r)^(-n))

where P is the monthly payment, r is the monthly interest rate, A is the total amount of the loan, and n is the number of months.

For Option A, the monthly interest rate is 1.3% / 12 = 0.01083, the total amount of the loan is $28,820, and the number of months is 36. Plugging these values into the formula, we get:

P = (0.01083 * 28,820) / (1 - (1 + 0.01083)^(-36)) = $860.45

Therefore, the total amount Owen will spend on Option A is:

36 * $860.45 = $30,975.98

Option B:

For Option B, we need to take into account the $1500 cash back that Owen will receive as part of the down payment. This means that the total amount of the loan will be $32,020 - $3200 - $1500 = $27,320.

To calculate the monthly payment, we can use the same formula as before:

P = (r * A) / (1 - (1 + r)^(-n))

For Option B, the monthly interest rate is 5.2% / 12 = 0.04333, the total amount of the loan is $27,320, and the number of months is 36. Plugging these values into the formula, we get:

P = (0.04333 * 27,320) / (1 - (1 + 0.04333)^(-36)) = $825.53

Therefore, the total amount Owen will spend on Option B is:

36 * $825.53 + $1500 = $30,316.08

Therefore, Option A will cost Owen a total of $30,975.98, and Option B will cost him a total of $30,316.08. Therefore, Option B is the cheaper option for Owen.

Step-by-step explanation:

Becky can afford a car with a price of $20,858.33 or less, given her monthly payment of $530, and assuming an annual interest rate of 6% for 4 years.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To calculate the price that Becky can afford for the car, we need to use the present value formula for an annuity:

PV = PMT x [tex]((1 - (1 + r/n)^{(-nt))}[/tex] / (r/n))

where:

PV = present value of the car

PMT = monthly payment

r = annual interest rate

n = number of compounding periods per year

t = number of years

In this case, PMT = $530, r = 6% (or 0.06 as a decimal), n = 12 (since monthly payments are being made), and t = 4. Plugging in these values, we get:

PV = $530 x[tex]((1 - (1 + 0.06/12)^{(-12*4)})[/tex] / (0.06/12))

PV = $20,858.33

Therefore, Becky can afford a car with a price of $20,858.33 or less, given her monthly payment of $530, and assuming an annual interest rate of 6% for 4 years.

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if we change the value of 523 to 424 in the list of numbers, then the mean decreases by approximately 3.22 and the median stays the same.

How to calculate the mean?

To calculate the mean, we add up all the numbers in the list and divide by the total number of values. Before the change, the sum of the numbers is:

164 + 225 + 227 + 250 + 261 + 268 + 277 + 379 + 523 = 2494

And there are 9 numbers in the list. So the mean is:

2494 / 9 ≈ 277.11

If we change the value of 523 to 424, then the sum becomes:

164 + 225 + 227 + 250 + 261 + 268 + 277 + 379 + 424 = 2465

And there are still 9 numbers in the list. So the new mean is:

2465 / 9 ≈ 273.89

So the mean decreases by approximately 3.22.

To calculate the median, we find the middle value of the list. If the list has an odd number of values, then the median is the middle value. If the list has an even number of values, then the median is the average of the two middle values. In this case, the list has an odd number of values, so the median is:

261

If we change the value of 523 to 424, then the list becomes:

164, 225, 227, 250, 261, 268, 277, 379, 424

And the median is still:

261

So the median stays the same.

In summary, if we change the value of 523 to 424 in the list of numbers, then the mean decreases by approximately 3.22 and the median stays the same.

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The range of the 98% confidence interval for the percentage of faulty components that differ between machines A and B is about between -0.2448 and 0.1305. (rounded to 4 decimal places).

Given:

Sample proportion from machine A ([tex]p_1[/tex]) = 5/35 = 0.14285714285714285

Sample proportion from machine B ([tex]p_2[/tex]) = 7/35 = 0.2

Sample size from machine A ([tex]n_1[/tex]) = 35

Sample size from machine B ([tex]n_2[/tex]) = 35

Standard error (SE) = [tex]\sqrt{ [(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}[/tex]

= [tex]\sqrt{[0.14285714285714285 * (1 - 0.14285714285714285) / 35] + [0.2 * (1 - 0.2) / 35] }[/tex]

= 0.07058061453775912 (rounded to 11 decimal places)

Margin of error (ME) = Critical value * Standard error

= 2.660 * 0.07058061453775912 (using z-score for a 98% confidence level)

= 0.18765117789861733 (rounded to 11 decimal places)

Confidence interval (CI) = Sample statistic ± Margin of error

= [tex](p_1 - p_2) \pm ME[/tex]

= (0.14285714285714285 - 0.2) ± 0.18765117789861733

= -0.05714285714285715 ± 0.18765117789861733

The 98% confidence interval for the difference in proportions of defective parts between machine A and machine B is approximately -0.2448 to 0.1305 (rounded to 4 decimal places).

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When X = 5, Y is approximately equal to 27.34.

What is proportion?

The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.

We are given that "Y varies directly as the cube of X", which can be written as:

Y = kX³

where k is a constant of proportionality. We need to find the value of k to solve for Y when X = 5.

Using the values given in the problem, we can write:

7 = k(4³)

Simplifying this equation, we get:

7 = 64k

Dividing both sides by 64, we get:

k = 7/64

Now that we know the value of k, we can solve for Y when X = 5:

Y = (7/64)(5³) = 27.34 (rounded to two decimal places)

Therefore, when X = 5, Y is approximately equal to 27.34.

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Answer: ∡1 = 153°

∡2 = 27°

Step-by-step explanation:

Answer:

angle 2=27°

angle 1= 153°

Step-by-step explanation:

6x-9+x=180

7x-9=180

7x=189

x=27

angle 2=27°

angle 1= 27×6-9=153°

angle 1= 153°

Answer:

x = √17

y = 10.1

Step-by-step explanation:

x² + 8² =  9²

x² = 81 - 64 = 17

x = √17

sin∅ = √17/9

∅ = 27.27°

9/y = cos(27.27)

y = 9/cos(27.27) = 10.13

y = 10.1

If the the a is greater than 1, compared to the parent function the C. Stretched vertically.

The equation y = ax^2 + c represents a quadratic function where "a" is the coefficient of the x^2 term and "c" is a constant term. The parent function of this quadratic function is y = x^2.

If the equation of a quadratic function is given in the form y = ax^2 + c and "a" is greater than 1, then the graph of the function will be stretched vertically and the vertex will be shifted up or down depending on the value of "c".

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The statement that (sin 2x) / (1 + cos 2x) = tan x can be proven.

To prove that (sin 2x) / (1 + cos 2x) = tan x, we will use trigonometric identities.

(sin 2x) / (1 + cos 2x)

(2sin x × cos x) / (1 + (cos²x - sin²x))

(2sin x × cos x) / (cos²x + 2sin x × cos x + sin²x)

We can rewrite the denominator using the Pythagorean identity sin²x + cos²x = 1:

(2sin x × cos x) / (1 + 2sin x × cos x)

(2sin x × cos x) × (1 - 2sin x × cos x) / (1 - (2sin x × cos x)²)

((2sin x × cos x) - (4sin²x × cos²x)) / (1 - 4sin²x × cos²x)

(2sin x - 4sin²x) / (1/cos²x - 4sin²x)

Since tan x = sin x / cos x, we can rewrite the expression:

(2tan x - 4tan²x) / (sec²x - 4tan²x)

(2tan x - 4tan²x) / (1 + tan²x - 4tan²x)

(2tan x - 4tan²x) / (1 - 3tan²x)

2tan x × (1 - 2tan²x) / (1 - 3tan²x)

tan x

So, we have proved that (sin 2x) / (1 + cos 2x) = tan x.

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Answer:

B is the answer

Step-by-step explanation:

The expression that is not equal to the others is B [[2/−5]] The other expressions are A −[[2/5]], C [[−2/5]], and D [[2/5]].

For all x, P(x) (using universal quantifier ∀) and  It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)

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 the event is impossible and 1 means the event is certain to happen.

Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:

1. For all x in S, P(x) (using universal quantifier ∀)

2. It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)

If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:

For all x, P(x) (using universal quantifier ∀)

It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:

For all x in S, P(x) (using universal quantifier ∀)

It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)

If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:

1. For all x, P(x) (using universal quantifier ∀)

2. It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)

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The surface area of the triangular prism with rectangular base is 736 cm².

Surface area refers to the total area that the surface of an object covers. It is a measure of how much exposed area there is on the outside of an object. The surface area of an object is usually expressed in square units, such as square meters, square centimeters, or square feet.

Here,

The formula for the surface area of a triangular prism with rectangular base is:

SA = 2lw + lh + wh

where l is the length of the rectangular base, w is the width of the rectangular base, h is the height of the triangular prism.

Given:

Side of triangle = 16 cm and 12 cm

Side of rectangle = 20 cm and 10 cm

Since we are not given the height of the triangular prism, we cannot calculate the exact surface area. However, we can give a general formula for the surface area in terms of the height h:

SA = 2(20)(10) + (16)(h) + (12)(h)

SA = 400 + 28h

So the surface area of the triangular prism with rectangular base is 400 + 28h, where h is the height of the triangular prism in cm.

h=12 cm

400+28h=400+28*12

=736 cm²

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After calculation we get

11) d. m/JML = 90 degrees, a. m/GMH = 45 degrees, b. mLH = 90 degrees, c. m/LKH = 45 degrees

12) a. AGKH is an isosceles triangle, b. Another triangle formed by two radii is an equilateral triangle.

13) a. m/GKH = 33.4 degrees, c. m/KHJ = 33.4 degrees, e. mJL66.8 degrees, b. m/KGH = 66.8 degrees, d. m/JKL = 113.2 degrees

A quadrilateral is a geometric shape with four straight sides and four angles. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and kites.

According to the given information:

a. Since m/LGH and m/GHJ are both 45°, GH is a bisector of ∠JGL. Therefore, m/GMH = 90° - 45° = 45°.

b. Since GH is a bisector of ∠JGL, m/LGH = m/HGL = 45°. Also, since LH is a straight line, m/LGH + mLH + m/HGL = 180°. Thus, mLH = 90° - 45° = 45°.

c. Since GH is a bisector of ∠LJK, m/GHK = m/JHK = 45°. Also, since LK is a straight line, m/LKH + m/JHK + m/LJK = 180°. Thus, m/LKH = m/LJK = (180° - 2*45°)/2 = 45°.

d. Since GH is a bisector of ∠JGL and JML is a straight line, m/JML = m/JGH + m/HGL = 45° + 45° = 90°.

a. AGKH is a quadrilateral with two sides that are radii of the circle. Since all radii of a circle are equal, AGKH is a kite. Furthermore, since the two radii AG and KH are perpendicular to each other, AGKH is also a rectangle.

b. Another triangle formed by two radii is AKJ, where AK and AJ are radii of the circle and KJ is a chord.

a. Since GH is a diameter of the circle and GKH is a right triangle with ∠GHK = 90°, m/GKH = 180° - 90° = 90°.

b. Since GH is a diameter of the circle and KJ is a chord, m/KGH = m/KJ = 1/2 * m/KHJ = 1/2 * (180° - 113.2°) = 33.4°.

c. Since GH is a diameter of the circle and KHJ is a right triangle with ∠KHJ = 90°, m/KHJ = 180° - m/GKH = 180° - 90° = 90°.

d. Since GH is a diameter of the circle and JKL is a right triangle with ∠JKL = 90°, m/JKL = 180° - m/KJ - m/JKH = 180° - 33.4° - 45° = 101.6°.

e. Since JL is a chord of the circle and ∠JGL is an inscribed angle that intercepts it, m/JGL = 1/2 * m/JL = 1/2 * (180° - m/JKL) = 1/2 * (180° - 101.6°) = 39.2°. Also, since GH is a diameter of the circle and GJL is a right triangle with ∠GJL = 90°, m/GJL = 90° - m/GHL = 90° - 45° = 45°. Therefore, m/JLH = m/JGL - m/GLH = 39.2° - 45° = -5.8°. Note that the negative value indicates that ∠JLH is a reflex angle.

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Answer:

b)

Step-by-step explanation:

Answer: The answer is, y=18x

Step-by-step explanation: This is going up by 18 as the y axis increases by 9. Hope this helped :)

This sentence relating to the quotient can be expressed mathematically as:

(30 / x) - 2

This sentence can be expressed mathematically as:

(30 / x) - 2

where x represents the unknown number.

The word "quotient" indicates that we are dividing 30 by the unknown number x. The phrase "is decreased by 2" means that we need to subtract 2 from the quotient.

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Sin 7π/4 is the value of sine trigonometric function for an angle equal to 7π/4 radians. The value of sin 7π/4 is -(1/√2) or -0.7071 (approx).

315° is comparable to 7 / 4 radians. In general, we multiply the angle measurement in radians by 180/ to translate an angle measurement given in radians to degrees. Therefore, we multiply 7 / 4 by 180 / to convert to radians. We discover that 7/4 radians equals 315 degrees.

We can first convert the angle to degrees as follows:

7π/4 radians = (7/4) × 180 degrees/π ≈ 315 degrees

The trigonometric ratios for 315 degrees (or 7/4 radians) can therefore be calculated using the reference angle of 45 degrees (which is /4 radians), as shown below.

sin(7π/4) = -sin(π/4) = -1/√2

cos(7π/4) = -cos(π/4) = -1/√2

tan(7π/4) = tan(π/4) = 1

csc(7π/4) = csc(-π/4) = -√2/2

sec(7π/4) = sec(-π/4) = -√2/2

cot(7π/4) = cot(-π/4) = 1

Therefore, the trigonometric ratios for the angle 7π/4 radians are:

sin(7π/4) = -1/√2

cos(7π/4) = -1/√2

tan(7π/4) = 1

csc(7π/4) = -√2/2

sec(7π/4) = -√2/2

cot(7π/4) = 1

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Therefore, the wire Ryan wants to walk is approximately 107.9 ft long.

Trigonometric functions are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The most commonly used trigonometric functions are sine, cosine, and tangent, often abbreviated as sin, cos, and tan respectively.

The sine function (sinθ) gives the ratio of the length of the side opposite an angle θ in a right triangle to the length of the hypotenuse (the longest side). The cosine function (cosθ) gives the ratio of the length of the adjacent side to θ to the length of the hypotenuse, while the tangent function (tanθ) gives the ratio of the length of the opposite side to θ to the length of the adjacent side.

Other trigonometric functions include cosecant (cscθ), secant (secθ), and cotangent (cotθ), which are the reciprocals of the sine, cosine, and tangent functions, respectively.

A represents the top of the tower, B represents the point where the wire is attached 30 ft away from the tower, and the wire itself is represented by the line segment AB. The angle between the wire and the ground is θ, and we want to find the length of the wire, which is represented by y.

We can use the trigonometric function tangent to relate the angle θ to the sides of the triangle:

tan(θ) = y/x

Solving for y, we get:

y = x * tan(θ)

We know that x = 30 ft, and θ = 74º, so we can plug those values in and calculate y:

y = 30 ft * tan(74º) = 107.9 ft (rounded to the nearest tenth)

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0.685 is a decimal that equals 68.5%.

Answer: $80

Step-by-step explanation:

If Tyrone's savings account earns a simple 10% annual interest and is not compounded, then the interest for one year can be calculated using the formula:

Interest = Principal × Rate × Time

where:

Principal = $800

Rate = 10% = 0.1

Time = 1 year

Interest = $800 × 0.1 × 1 = $80

Tyrone will earn $80 in interest in 1 year. To find the total amount in his account after 1 year, we add the interest to the principal:

Total amount = Principal + Interest

Total amount = $800 + $80 = $880

In 1 year, Tyrone will have $880 in total in his savings account.

Answer:

$880

Step-by-step explanation:

10% = .1

800 x .1 = 80

80 + 800= 880

The domain restrictions on the function [tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex] are the x values -9, 0, 3, 4 and 9

From the question, we have the following function that can be used in our computation:

[tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex]

Next, we set the denominator to 0 and solve for x

So, we have

81 - x²: x = ±9

2x² - 6x: x = 0 and x = 3

x² + 2x - 6x: x = 0 and x = 4

Hence, the domain restrictions are the x values -9, 0, 3, 4 and 9

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So, the area of triangle DEF is 312.5 square feet, using the scale factor of 5/2.

the context of mathematics and geometry, dilation is a transformation that changes the size of an object. It is a type of transformation that scales an object by a certain factor, without changing its shape or orientation.

In other words, dilation involves multiplying the coordinates of a geometric figure by a fixed constant, which results in an enlarged or reduced version of the original figure. The constant is known as the dilation factor or the scale factor, and it can be any real number greater than zero.

For example, if we dilate a circle by a scale factor of 2, every point on the circle will be moved twice as far away from the center, resulting in a new circle with a diameter twice as large as the original.

Let's start by using the formula for the perimeter of a triangle:

[tex]Perimeter of triangle ABC = AB + BC + AC = 65.5 feet[/tex]

We can also use Heron's formula to find the area of triangle ABC:

[tex]Area of triangle ABC = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]

where s is the semi perimeter of the triangle:

[tex]s = (AB + BC + AC) / 2[/tex]

We can use these equations to solve for the side lengths of triangle ABC:

[tex]AB + BC + AC = 65.5[/tex]

[tex]s = (AB + BC + AC) / 2[/tex]

[tex]25 = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]

Solving for AB, BC, and AC gives us:

AB = 15

BC = 20

AC = 30.5

Now, let's dilate triangle ABC by a factor of 5/2 to create triangle DEF. This means that each side of triangle ABC will be multiplied by 5/2 to get the corresponding side length of triangle DEF.

DE = AB * (5/2) = 37.5

EF = BC * (5/2) = 50

DF = AC * (5/2) = 76.25

Now we can use Heron's formula again to find the area of triangle DEF:

s = (DE + EF + DF) / 2 = 81.875

Area of triangle DEF = sqrt(s(s-DE) (s-EF) (s-DF)) = 312.5 square feet

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===================================================

Explanation:

Focus on triangle BDH

The three inside angles of any triangle always add to 180 degrees.

B+D+H = 180

47+31+H = 180

78+H = 180

H = 180-78

H = 102

Angle BHD is 102 degrees.

It adds to angle x, aka angle BHC, to get 180 degrees. These two adjacent angles combine to a straight line.

(angle BHD) + (angle BHC) = 180

102 + x = 180

x = 180-102

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

Shortcut:

Focus on triangle BDH.

Use the remote interior angle theorem to add the given interior angles.

B+D = 47+31 = 78

This is equal to the exterior angle that is not adjacent to either interior angle mentioned. This refers to angle BHC, aka angle x.

The function evaluated in x = 2 is:

3f(2) =12

Here we know that:

f(x) = x^2

And we want to evaluate the expression:

3f(2)

To do that replace x by 2.

3f(2) = 3*(2^2) = 3*4 = 12

That is the value of the expression.

Learn more about evaluating functions at:

https://brainly.com/question/1719822

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