Question 3 of 10
A construction worker needs to put a rectangular window in the side of a
building. He knows from measuring that the top and bottom of the window
have a width of 9 feet and the sides have a length of 12 feet. He also
measured one diagonal to be 15 feet. What is the length of the other
diagonal?
A. 12 feet
B. 9 feet
C. 15 feet
D. 21 feet

x² + 2 + 6x: The quadratic expression can be factorized as (x + 2)(x + 3).

The factorization of the given expressions is as follows:

+1/3 + 2: This is a simple addition and cannot be factorized.

x² + 2 + 6x: The quadratic expression can be factorized as (x + 2)(x + 3).

a(2 − ¹)(2 + 6)/(a - x/6)(x - 1): This expression cannot be factorized further due to the presence of variables in the denominator.

(2 + √2)(2 + √6)/x: This expression cannot be factorized further due to the presence of variables in the denominator.

(x + 1)² (x + 6): This expression is already fully factorized.

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The complete question

a) Factorize the expression: x² + 6x + 8

b) Factorize the expression: x² - 1

c) Factorize the equation: x² + 2x - 3 = 0

Answer:

the graph represents the average heights of the girls in mrs.hills class.

Step-by-step explanation:

Half of the swans are black, the  fraction of the swans are black is 4/8

There are eight swans swimming on a pond and four of those swans are

black.

We have to find the fraction of the swans are black

The fraction of black swans is given by:

4 (number of black swans)

8 (total number of swans)

Simplifying the fraction 4/8 = 1/2

Therefore, half of the swans are black, the  fraction of the swans are black is 4/8

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Measure of angle E is, 25 degree

And, Measure of side FG is,

FG = 10 units

We have to given that;

In parallelogram EFGH,

EF = 3y

EH = 2 (y + 1)

HG = y + 8

Hence, We can formulate;

∠ E = ∠G

⇒ (7x - 15) + (7x - 15)  = 90°

⇒ 14x - 30 = 90

⇒ 14x = 60

⇒ x = 30/7

Hence., ∠ E = (7x - 5) = (7 x 30/7 - 5)

                                 = (30 - 5)

                                 = 25

Since, Opposite sides are equal in parallelogram.

Hence, We get;

3y = y + 8

2y = 8

y = 4

Hence, Measure of side FG is,

FG = 2 (y + 1)

FG = 2 (4 + 1)

FG = 10 units

Thus, Measure of angle E is, 25 degree

And, Measure of side FG is,

FG = 10 units

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The statements that are true about the area of the figure is that the area can be found by multiplying 3 by 2 1/2 and adding the product of 1/2 and 1/2 .

Recall that In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle

Also, the area of a rectangle can be found by multiplying the length of the rectangle by its width and using the formula, where is the base and is the height of the triangle.

Area of the rectangle - LB

Area = (1/2 * 1/2) + (7/2*7/2)

Area = 1/4 + 35/4

Simplifying the fraction to get

36/4

Area of the figure is 9 square units

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The times are 2.5 sec and 3.75 sec

* Lets explain the projectile formula

- The ball thrown vertically in the air with initial velocity 100 ft/sec

- the projectile formula is h = -16 t² + vo t, where h is the height of the

ball after thrown it in t seconds and vo is the initial velocity

∵ The initial velocity is 100 ft/sec

- substitute vo by 100

∴ The projectile formula is h = -16 t² + 100 t

- To find the time that the ball is at a height of 150 ft substitute

 h by 150 in the projectile formula

∵ h = - 16 t² + 100 t

∵ h = 150 ft

∴ 150 = -16 t² + 100 t

- Subtract 150 from both sides

∴ 0 = -16 t² + 100 t - 150

- Multiply the both sides by -1

∴ 16 t² - 100 t + 150 = 0

* Lets factorize it to find the value of t

∵ 16 t² = 4t × 4t ⇒ first terms in the 2 bracket

∵ 150 = 15 × 10 ⇒ second terms in the two brackets

∵ 4t × 15 = 60 t ⇒ nears

∵ 4t × 10 = 40 t ⇒ extremes

∵ 6t + 40 t = 100 t ⇒ middle term

∴ 16 t² - 100 t + 150 = (4t - 15)(4t - 10)

∵ 16 t² - 100 t + 150 = 0

∴ (4t - 15)(4t - 10) = 0

- Equate each bracket by 0

∴ 4t - 15 = 0 ⇒ add 15 to both sides

∴ 4t = 15 ⇒ divide both sides by 4

∴ t = 3.75

- OR

∴ 4t - 10= 0 ⇒ add 10 to both sides

∴ 4t = 10 ⇒ divide both sides by 4

∴ t = 2.5

- The ball will be at height 150 ft in 2.5 seconds we the ball goes up

 and again ate 3.75 seconds when the ball goes down after it

 reached its maximum height

* The times are 2.5 sec and 3.75 sec.

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The correct interpretation of the slope and y-intercept of the equation

y = 50 is:

A. The slope predicts a temperature increase of about 50° for every increase of 1 chirp per minute. The y-intercept shows that when the crickets are not chirping (x = 0), the temperature is 0°.

In the given equation y = 50, the slope of 50 indicates that for every increase of 1 chirp per minute (x), the temperature (y) increases by approximately 50° Fahrenheit.

The positive slope suggests a positive correlation between the number of chirps per minute and temperature.

The y-intercept of 0 in this equation represents the temperature when the crickets are not chirping (x = 0). It implies that when there are no chirps per minute, the temperature is at 0° Fahrenheit.

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The surface area of the second shape, denoted as b, is 9.3 cm².

To find the surface area of the second shape, we need to determine the relationship between the lengths and surface areas of the two shapes. Since the shapes are similar, the ratio of their surface areas will be equal to the square of the ratio of their lengths.

Let's denote the surface area of the second shape as B and the length of the second shape as L. We can set up the following proportion based on the given information:

(Surface area of the first shape)/(Surface area of the second shape) = (Length of the first shape)/(Length of the second shape)

Substituting the given values:

3.1 cm²/B = 2 cm/L

To find B, we can rearrange the equation:

B = (L * 3.1 cm²) / 2 cm

Now, we're given that the length of the second shape is 6 cm. Substituting this value:

B = (6 cm * 3.1 cm²) / 2 cm

Calculating:

B = (18.6 cm³) / 2 cm

B = 9.3 cm²

Therefore, the surface area of the second shape, denoted as b, is 9.3 cm².

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Using Cramer's rule for first-order condition:

Using Hessian for the second-order condition, critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

(a) Using Cramer's rule for the first-order condition:

To optimize the function y, find the critical points where the gradient is equal to zero. The gradient of y is given by:

∇y = [6x₁ - x₂ - 3x₃ - 5, -x₁ + 12x₂ + 2x₃ - 4, 2x₂ + 8x₃ + 2 - 3x₁]

Setting the gradient equal to zero:

6x₁ - x₂ - 3x₃ - 5 = 0 (1)

-x₁ + 12x₂ + 2x₃ - 4 = 0 (2)

2x₂ + 8x₃ + 2 - 3x₁ = 0 (3)

Using Cramer's rule to solve this system of linear equations, the determinant of the coefficient matrix is:

|A| =

| 6 -1 -3 |

|-1 12 2 |

|-3 2 -3|

|A| = 444

The determinant of the matrix obtained by replacing the first column of A with the constants on the right-hand side of the equations is:

|A₁| =

| 5 -1 -3 |

| 0 12 2 |

| 0 2 -3|

|A₁| = -149

The determinant of the matrix obtained by replacing the second column of A with the constants is:

|A₂| =

| 6 5 -3 |

|-1 0 2 |

|-3 0 -3|

|A₂| = -138

The determinant of the matrix obtained by replacing the third column of A with the constants is:

|A₃| =

| 6 -1 5 |

|-1 12 0 |

|-3 2 2|

|A₃| = -278

Therefore, using Cramer's rule:

x₁ = |A₁|/|A| = -149/444

x₂ = |A₂|/|A| = -69/222

x₃ = |A₃|/|A| = 139/444

(b) Using the Hessian for the second-order condition:

To check whether the critical point found in part (a) is a maximum, minimum or saddle point, we need to use the Hessian matrix evaluated at the critical point. The Hessian of y is given by:

(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

Evaluating H(y) at the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444):

H(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

The eigenvalues of H(y) are 2, 6, and 18, which are all positive. Therefore, H(y) is positive definite, and the critical point is a minimum.

Therefore, the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

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The equivalent exponential function is given as follows:

[tex]S(t) = 79(1.25)^t[/tex]

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The function for this problem is defined as follows:

[tex]S(t) = 79(2)^{4t}[/tex]

Considering the growth rate as 1 + r = 2 -> r = 1, with a period of n = 4, the equivalent exponential function can be written as follows:

[tex]S(t) = 79(1 + \frac{1}{4})^{t}[/tex]

[tex]S(t) = 79(1.25)^t[/tex]

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Answer:

FG is y = -0.5x - 5.5. circle is (x - 1)² + (y + 1)² = 20. Length FA = 7

Step-by-step explanation:

please see attached

only 5 attachments/pics allowed

so FA² = (√69)² - (√20)²

            = 69 - 20

           = 49

FA = √49 = 7

Answer:

Step-by-step explanation:

You want an equation and its solution to tell you the number of $5 books that were purchased for $58 with a $7 discount coupon.

The cost of b books at $5 each is 5b.

After a $7 discount is subtracted, the cost is 5b -7.

That cost is said to be $58, so an appropriate equation is ...

  5b -7 = 58

Adding 7 gives ...

  5b = 65

Dividing by 5 tells the number of books:

  b = 13

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Answer:

a) 2nd form: 5b-7=58

b) 13 books

Step-by-step explanation:

Equation:

5b-7=58

b) 5b=65

b=13

The two villages farthest from one another are E and F.

To determine which two villages are the farthest from one another, we need to analyze the given information and calculate the distances between all possible pairs of villages.

Let's start by visualizing the locations of the villages based on the given information:

           B ---- F

          /       |

         /        |

        A         |

        |         C ---- D

        |                |

        |                |

        E -------------- G

Using the information provided, we can calculate the distances between the villages:

Distance between E and F: Since E is 2 km to the west of B and F is 2 km to the north of B, we can calculate the distance between E and F using the Pythagorean theorem. The distance is approximately √(2^2 + 2^2) = √8 ≈ 2.83 km.

Distance between E and C: E is exactly in the middle of B and E, which means the distance between E and C is half the distance between B and C. Using the Pythagorean theorem, the distance between B and C is √(2^2 + 1^2) = √5 ≈ 2.24 km. Therefore, the distance between E and C is 2.24 km / 2 = 1.12 km.

Distance between E and D: Since D is 2 km to the south of A, and A is the same as E, the distance between E and D is the same as the distance between A and D, which is 2 km.

Distance between E and G: Since G is 2 km to the east of C, the distance between E and G is the same as the distance between C and G, which is 2 km.

Now, let's compare the distances between all possible pairs of villages:

E and F: 2.83 km

E and C: 1.12 km

E and D: 2 km

E and G: 2 km

From the above calculations, we can see that the farthest distance is between E and F, which is approximately 2.83 km.

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Answer:

Step-by-step explanation:

The answer is 360.

Explanation: each pillow is $3 and you have $960.

You need to figure out how many times $3 can go into $960 and you do that by dividing.

960 divided by 3 is 360.

The hotel can buy 360 pillows.

Answer:

D. Most immigrants started in the lowest-paying jobs when they came to America.

In a case whereby Sound travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echo in  1650 feet away.

In a case whereby you want to hear the echo, the sound will have had to gone out to the wall  which will later return , then The sound's speed, in feet/second is:

(750 mi/hour)*(1 hour/3600 seconds)*(5280 feet/mile)

= 1100 ft/sec

However in 3 seconds, the sound will have traveled 3300 feet. Since the sound's movement is a round trip, the canyon wall can be exressed

3300/2

= 1650 feet away.

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The measure of the missing arc in this problem is given as follows:

? = 159º

We have two secants in this problem, and point C is the intersection of the two secants, hence the angle measure of 50º is half the difference between the angle measure of the unknown far arc by the near arc of 59º.

Hence the measure of the missing arc in this problem is obtained applying the two-secant theorem as follows:

(? - 59)/2 = 50

? - 59 = 100

? = 159º.

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Step-by-step explanation:

y = 4 ^(x+1)    by inspection

Answer:

1)  23.4 km²

2)  403.1 mi²

Step-by-step explanation:

The formula for the area of a regular polygon is half the product of its apothem and perimeter.

[tex]\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{1}{2}aP$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the apothem.\\ \phantom{ww}$\bullet$ $P$ is the perimeter.\\\end{minipage}}[/tex]

From inspection of the given regular polygons, we have been given the perimeter or side length only. Therefore, we need to calculate the apothem.

The formula for the length of the apothem of a regular polygon is:

[tex]\boxed{\begin{minipage}{5.5cm}\underline{Length of apothem}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

The given polygon has 6 sides, and its perimeter is 18 km. Therefore:

Substitute the values of s and n into the apothem formula and solve for a:

[tex]\begin{aligned}\implies a&=\dfrac{3}{2 \tan\left(\dfrac{180^{\circ}}{6}\right)}\\\\&=\dfrac{3}{2 \tan\left(30^{\circ}\right)}\\\\&=\dfrac{3}{\left(\dfrac{2\sqrt{3}}{3}\right)}\\\\&=\dfrac{3\sqrt{3}}{2}\end{aligned}[/tex]

To find the area of the polygon, substitute the found value of a, along with the perimeter, P = 18, into the area formula:

[tex]\begin{aligned}\implies A&=\dfrac{1}{2} \cdot\dfrac{3\sqrt{3}}{2}\cdot 18\\\\&=\dfrac{54\sqrt{3}}{4} \\\\&=23.382685...\\\\&=23.4\; \sf km^2\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the area of the regular polygon is 23.4 km² to the nearest tenth.

[tex]\hrulefill[/tex]

The given polygon has 12 sides, and the length of one side is 6 miles. Therefore:

Substitute the values of s and n into the apothem formula and solve for a:

[tex]\begin{aligned}\implies a&=\dfrac{6}{2 \tan\left(\dfrac{180^{\circ}}{12}\right)}\\\\&=\dfrac{6}{2 \tan\left(15^{\circ}\right)}\\\\&=\dfrac{3}{\tan\left(15^{\circ}\right)}\\\\&=\dfrac{3}{2-\sqrt{3}}\\\\&=6+3\sqrt{3}\end{aligned}[/tex]

The perimeter of the polygon is n · 2 = 12 · 6 = 72 miles.

To find the area of the polygon, substitute the found value of a, along with the perimeter, P = 72, into the area formula:

[tex]\begin{aligned}\implies A&=\dfrac{1}{2} \cdot (6+3\sqrt{3})\cdot 72\\\\&=36 (6+3\sqrt{3})\\\\&=216+108\sqrt{3}\\\\&=403.061487...\\\\&=403.1\; \sf mi^2\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the area of the regular polygon is 403.1 mi² to the nearest tenth.

Answer:

1.23.38 km^2

2.402.84 mi^2

Step-by-step explanation:

Note:
The area of a polygon can be found using the following formula:

[tex]\boxed{\bold{Area = \frac{Perimeter*apothem}{2}}}[/tex]

where:

Perimeter is the total length of all the sides of the polygon

Apothem is the distance from the center of the polygon to a point on any side

To find , use this formula

[tex]\boxed{\bold{Apothem = \frac{ length\:of\:side }{ 2 *tan(\frac{180}{n})}}}[/tex]

where:

n is the number of sides of the polygon

For question:

1.

Perimeter(p)=18km

no. of side (n)=6

length of one side= [tex]\frac{p}{n}=\frac{18}{6}=3[/tex] km

Now finding apothem(a),

by substituting value, we get,

[tex]Apothem = \frac{ 3 }{ 2 *tan(\frac{180}{6})}\\Apothem = \frac{ 3 }{ 2 *tan(30)}\\Apothem = \frac{ 3 }{ 2 * \frac{\sqrt{3}}{3}}}\\Apothem =\frac{3\sqrt{3}}{2}} \: or\: 2.598km\\[/tex]

Now, we have

[tex]A=\frac{1}{2}*a*P[/tex]

substituting value:

[tex]A=\frac{1}{2}*2.598*18=23.38 km^2[/tex]

2.

no. of side (n)=12

length of one side(l)=6 mi

Perimeter(p)=n*l=12*6=72 mii

Now finding apothem(a),

by substituting value, we get,

[tex]Apothem = \frac{ 6}{ 2 *tan(\frac{180}{12})}\\Apothem = \frac{ 6 }{ 2 *tan(15)}\\Apothem = \frac{ 3 }{ 2*0.27}}\\Apothem =\frac{6}{0.54}=11.19mi[/tex]

Now, we have

[tex]A=\frac{1}{2}*a*P[/tex]

substituting value:

[tex]A=\frac{1}{2}*11.19*72=402.84 mi^2[/tex]

The option 1 is a more suitable and preferred option because the deductible is the option2 are more as per the break-even analysis.

Option 1 is preferable if no claims are filed. Let's now think about how long it would take someone to go without a claim for Option 2 to become profitable. The deductible on the option 2 are more as compared to option 1. For each year they don't make a claim, they must save $250 in premiums in order to break even.

The annual premium difference between the two plans is $1000 – $800, or $200. As a result, Option 2 would not become profitable until 1.25 years (or 15 months) in the absence of a claim.

$200 in premium differences divided by $250 in savings from a higher deductible is 1.25 years. So, if the buyer expects to go more than 1.25 years without making a claim, then they should choose Option 2 with the higher deductible.

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After considering the given data we conclude that the most suitable and preferred option will be option 1,in comparison to option 2 due to its deductibility.

Break-even analysis is a imperative tool for making financial decisions. It helps describe how long it would take for a higher deductible option to break-even with a lower deductible option.
For the given  case,
$250 deductibility comes with a $1000 annual premium. -  Option 1
$500 deductibility comes with a $800 annual premium. - Option 2

To evaluate how long someone would have to go without a claim for the higher deductible option to break-even, we can apply the following formula:

Break-even point = (Higher deductible - Lower deductible) / (Lower premium - Higher premium)

Placing in the values from our example:

Break-even point = (500 - 250) / (1000 - 800)
Break-even point = 250 / 200
Break-even point = 1.25 years

Then, someone would have to go without a claim for 1.25 years for the higher deductible option to break-even with the lower deductible option. Hence Option 1
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Answer:

33/7

Step-by-step explanation:

7x4=28

28+5=33

Jacquie's prediction of 500 heads in 1,000 trials is actually correct based on the assumption of a fair coin.

Jacquie used an app to simulate a coin flip 40 times, and it landed on heads 20 times. From these results, Jacquie predicts that the expected number of times the coin will land on heads in 1,000 trials is 500 times.

Jacquie's prediction is not correct. The expected number of times the coin will land on heads in 1,000 trials can be estimated using the concept of probability. For a fair coin, the probability of landing on heads in a single flip is 0.5 (assuming the coin is unbiased).

In a large number of trials, the expected number of heads can be calculated by multiplying the probability of heads by the total number of trials. Therefore, the expected number of heads in 1,000 trials would be:

Expected number of heads = Probability of heads × Total number of trials

Expected number of heads = 0.5 × 1000

Expected number of heads = 500

Thus, Jacquie's prediction of 500 heads in 1,000 trials is actually correct based on the assumption of a fair coin. However, we cannot conclude the fairness of the coin based on her previous 40 flips, as this sample size is too small to accurately represent the expected outcome. The Law of Large Numbers suggests that as the number of trials increases, the observed results should converge towards the expected probabilities. Therefore, it would require a larger number of trials to validate the fairness of the coin and provide a more accurate estimation of the expected number of heads.

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Given statement solution is :- The Sketch Graph is a straight line with a negative slope. It passes through the points (-3, 2.5), (-2, -2.5), (-1, -2.5), and (0, -5). The line is interrupted at x = 1 .

To sketch the graph of the equation 2y + 5x + 10 = 0 within the given range of x, we first need to rearrange the equation to solve for y:

2y = -5x - 10

Dividing both sides by 2:

y = (-5/2)x - 5

Now, let's plot the graph:

Choose some x-values within the range [-3, 1) to find their corresponding y-values.

Let's choose x = -3, -2, -1, 0.

For x = -3:

y = (-5/2)(-3) - 5

= (15/2) - 5

= 7.5 - 5

= 2.5

For x = -2:

y = (-5/2)(-2) - 5

= 5/2 - 5

= 2.5 - 5

= -2.5

For x = -1:

y = (-5/2)(-1) - 5

= 5/2 - 5

= 2.5 - 5

= -2.5

For x = 0:

y = (-5/2)(0) - 5

= 0 - 5

= -5

Plot the points (-3, 2.5), (-2, -2.5), (-1, -2.5), and (0, -5) on the graph.

Draw a straight line passing through these points. Since the range for x is (-3, 1), the line should be dotted or interrupted at x = 1.

The resulting graph should look like this:

yaml

Copy code

       |    

   *   |    

       |   *  

       |      

-------+-------

       |      

       |

Note: The Sketch Graph is a straight line with a negative slope. It passes through the points (-3, 2.5), (-2, -2.5), (-1, -2.5), and (0, -5). The line is interrupted at x = 1 since it is not included in the given range.

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Answer:

1. The Answer is a 2. The answer is c and 3. the answer is b

Step-by-step explanation:

Answer:

19 (D)

20(A)

Step-by-step explanation:

you just put those values you given into the expression and punch the calculator for confirmation

The real zeros of the function f(x) = x³ - x² - 68x + 186 are x = 3, x = -1 + 3√7 and x = -1 - 3√7

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

f(x) = x³ - x² - 68x + 186

To find the real zeros of the function, we set the function to 0

Using the above as a guide, we have the following:

x³ - x² - 68x + 186 = 0

Next, we solve by graphing (see attachment for graph)

With the use of a graph, the real zeros of the function are

x = 3, x = -1 + 3√7 and x = -1 - 3√7

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Complete questions

Find all real zeros of f(x)=x3-x2-68x+186.x=(Enter the zeros as a list, e.g. 1,2,3. Use exact forms, not decimal approximations.)

Answer:To find the value of k such that 156k is a perfect square, we need to determine the factors of 156 and look for a common factor that can be squared to obtain a perfect square.

The prime factorization of 156 is [tex]2^2[/tex] * 3 * 13. A perfect square must have an even exponent for each prime factor in its prime factorization. Thus, for 156k to be a perfect square, k must have an even exponent for each prime factor in the prime factorization of 156.

Analyzing the prime factorization, we can see that the exponent of 2 in 156 is 2, the exponent of 3 is 1, and the exponent of 13 is 1. To make each exponent even, we need to multiply 156 by another 2. Therefore, k should be equal to 2.

Let's verify this by calculating 156 * [tex]2^2:[/tex]

156 * [tex]2^2[/tex] = 156 * 4 = 624

624 is a perfect square since it can be expressed as [tex]24^2.[/tex] Hence, the value of k that makes 156k a perfect square is 2.

In summary, the value of k that makes 156k a perfect square is 2.

Step-by-step explanation:

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To find the annual rate of interest as a percent on the musician's loan for the trumpet, we can use the simple interest formula:

$$\sf\:I = P \cdot r \cdot t \\$$

Where:

We can rearrange the formula to solve for r :

$$\sf\:r = \frac{I}{P \cdot t} \\$$

Substituting the given values:

$$\sf\:r = \frac{792}{2200 \cdot 3} \\$$

Now, we can calculate the value of r :

$$\sf\:r = \frac{792}{6600} \\$$

Simplifying the fraction:

$$\sf\:r = 0.12 \\$$

To express this as a percentage, we multiply by 100:

$$\sf\:r = 0.12 \times 100 \\$$

Therefore, the annual rate of interest on the musician's loan for the trumpet is 12%.[tex][/tex]