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We have shown that the left-hand side simplifies to 1, which is equal to the right-hand side. Therefore, the identity cos θ sec θ = 1 is verified.

To verify the identity cos θ sec θ = 1, we can simplify the left-hand side and show that it equals the right-hand side.

Starting with the left-hand side:

cos θ sec θ = cos θ * (1 / cos θ)   [using the reciprocal identity for secant]

Simplifying further:

cos θ sec θ = cos θ * (1 / cos θ) = 1.

The domain of validity for this identity is all real numbers except for the values of θ where cos θ = 0. In other words, the identity holds true for any angle θ as long as cos θ is not equal to zero. This is because the reciprocal of zero is undefined, and we cannot divide by zero in mathematics.

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The greatest amount of sap collected from any one tree is two times.

The maximum amount of sap that can be gathered from a single tree is two times greater than the minimum amount. SAP enables businesses to innovate on anything from cancer therapies to flood mitigation. We support life-saving research and are deeply committed to social responsibility and sustainability. At SAP, we collaborate to create innovations.

Work in a stimulating and rewarding environment by joining us. Minerals and nutrients can be found in tree sap. In the spring, when new buds are growing, a sticky substance that travels through the tree and out onto the branches helps the tree produce energy. Sugars are created as a result of photosynthesis and sent back into the tree, where they serve as sustenance for the tree's growth.

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Correct Question:

The greatest amount of sap collected from any one tree is _____________

Answer:

\((6x + 3)\degree = 81\degree \\ \{{ \sf{corresponding \: angles \}}} \\ 6x = 78 \\ { \boxed{ \boxed{x = 13}}}\)

Answer:

Its 5

Step-by-step explanation:

When measuring wind speed with a cup anemometer on a sailboat trip across the Atlantic Ocean, there are a few situations that may arise, as shown below:1. When the bearing of the axle is old, the type of error that occurs is systematic error. To reduce or overcome this error, you would need to replace the bearing to avoid it.

2. When there is turbulent flow, the type of error that occurs is random error. To overcome this error, you would have to wait for the wind to stabilize or take an average of many measurements.  3. When there is icing on the cups, the type of error that occurs is also random error.

To overcome this error, you would need to remove the ice or wait for it to melt before continuing the measurement.4. When there is strong tumbling of the sailboat, the type of error that occurs is systematic error. To overcome this error, you would need to find a way to stabilize the boat or take measurements when the boat is less unstable.

It is not well posed to use a cup anemometer to measure in-cabin air flow in a quiet environment because the device is not sensitive enough. The device needs a minimum wind speed to provide accurate readings, and it is not designed to measure low wind speeds. Therefore, it may not be the right tool for the job, and a different instrument may be more appropriate.

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No, negative decimals are not considered integers.

An integer is simple defined as a whole number, cannot be a fraction,  that is either positive, negative, or zero.

It can also be described as the number zero, a natural positive number or a negative integer, that is, one with a minus sign.

The negative numbers are seen as the additive inverses of their corresponding positive numbers.

The three types of integers are;

Hence, decimals are not integers

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Therefore , the solution of the given problem of unitary method comes out to be  the composite shape's overall size is 30  square units.

Utilizing previously well-known variables, this uniform convenience, or all crucial elements from a prior flexible study that followed a particular methodology event can all be used to achieve the goal. It will be possible to contact the entity again if the anticipated assertion outcome actually happens; if it doesn't, both important systems will surely miss the statement.

Here,

We must divide the composite shape into smaller shapes and sum up their areas in order to determine the area of the composite shape.

We can see that the composite form is made up of a triangle with a base of four and a height of three, and a rectangle with dimensions of six by four.

=> length times breadth equals six by four, or 24 square units, for a rectangle.

Triangle's area is equal to

=>  (1/2) x base times height, or (1/2) x 4 times 3, or 6 square units.

As a result, the composite shape's overall size is:

=> 24 + 6 = 30  square units.

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Answer:

1.

R= Number of orange juice cases.

G = Number of greapefruit juice cases.

T = Number of tomato juice cases.

Equations:

9R+10G+12T=398

6R+4G+4T=164

R+2G+T=58

2.

R=6

G=20

T=12

Step-by-step explanation:

1.

The problem is talking about three types of products and it wants us to find how many of each the factory prepares. Since this is the data we need to know, then we set them to be our variables:

R= Number of orange juice cases.

G = Number of greapefruit juice cases.

T = Number of tomato juice cases.

Next, we can use the provided information to build our equations. First, we start with the Sterilizing machine equation: 9 minutes for orange juice, 10 minutes for grape juice and 12 minutes for tomato juice. So we use the sterilizing values for each of the product, to build our first equation:

9R+10G+12T=398

next, we build the filling machine equation, so like on the previous equation, we use the provided data for filling to build the second equation:

6R+4G+4T=164

and finally we build the labeling machine equation so we get:

R+2G+T=58

so we need to solve the following system of equations:

9R+10G+12T=398

6R+4G+4T=164

R+2G+T=58

2.

The very first thing we need to do in order to solve this problem by using the Gauss-Jordan elimination method is to build our matrix based on the system of equations we got on the previous part.

\(\left[\begin{array}{cccc}9&10&12&398\\6&4&4&164\\1&2&1&58\\\end{array}\right]\)

The idea is to end up with an identity matrix on the first three columns, that will directly give us the answer to the system of equations. So we can start by dividing the first row into 9: \(\frac{R_{1}}{9}\) So we get:

\(\left[\begin{array}{cccc}1&\frac{10}{9}&\frac{4}{3}&\frac{398}{9}\\6&4&4&164\\1&2&1&58\\\end{array}\right]\)

Next, we can multiply the first row by -6 and add it to the second row to get the new second row. \(-6R_{1}+R_{2}\)

so we get:

-6   -20/3   -8   -796/3

6     4          4      164

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

0    -8/3    -4    -304/3

our matrix now looks like this:

\(\left[\begin{array}{cccc}1&\frac{10}{9}&\frac{4}{3}&\frac{398}{9}\\0&-\frac{8}{3}&-4&-\frac{304}{3}\\1&2&1&58\\\end{array}\right]\)

Next, we can subtract R3 from R1 so we get:

1   10/9   4/3   398/9

-1   -2     -1       -58

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

0    -8/9   1/3   -124/9

So the matrix looks like this now:

\(\left[\begin{array}{cccc}1&\frac{10}{9}&\frac{4}{3}&\frac{398}{9}\\0&-\frac{8}{3}&-4&-\frac{304}{3}\\0&-\frac{8}{9}&\frac{1}{3}&-\frac{124}{9}\\\end{array}\right]\)

Now, we can multiply the second row by -3/8 so we get:

\(\left[\begin{array}{cccc}1&\frac{10}{9}&\frac{4}{3}&\frac{398}{9}\\0&1&\frac{3}{2}&38\\0&-\frac{8}{9}&\frac{1}{3}&-\frac{124}{9}\\\end{array}\right]\)

Now, we can subtract: \(R_{1}-\frac{10}{9}R_{2}\) so we get:

0   -10/9   -5/3  -380/9

1      10/9    4/3   398/9

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

1        0       -1/3   2

So the matrix will now look like this:

\(\left[\begin{array}{cccc}1&0&-\frac{1}{3}&2\\0&1&\frac{3}{2}&38\\0&-\frac{8}{9}&\frac{1}{3}&-\frac{124}{9}\\\end{array}\right]\)

Next, we do the following operation: \(R_{3}+\frac{8}{9}R_{2}\)

0      8/9      4/3 304/9

0      -8/9     1/3   -124/9

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

0       0         5/3   20

So our matrix will now look like this:

\(\left[\begin{array}{cccc}1&0&-\frac{1}{3}&2\\0&1&\frac{3}{2}&38\\0&0&\frac{5}{3}&20\\\end{array}\right]\)

We next multiply R3 by 3/5 so we get:

\(\left[\begin{array}{cccc}1&0&-\frac{1}{3}&2\\0&1&\frac{3}{2}&38\\0&0&1&12\\\end{array}\right]\)

and now we do: \(\frac{R_{3}}{3}+R_{1}\)

0         0      1/3       4

1           0     -1/3      2

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

1       0          0        6

So our matrix will now look like this:

\(\left[\begin{array}{cccc}1&0&0&6\\0&1&\frac{3}{2}&38\\0&0&1&12\\\end{array}\right]\)

and now we do the following: \(R_{2}-\frac{3}{2}R_{3}\)

so we get:

0         0      -3/2     -18

0         1       3/2      38

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

0        1          0        20

for our final matrix to be:

\(\left[\begin{array}{cccc}1&0&0&6\\0&1&0&20\\0&0&1&12\\\end{array}\right]\)

so now we can retrieve the corresponding answers:

R=6

G=20

T=12

Answer:

9

Step-by-step explanation:

hi I'm pretty sure this is really wrong but just kinda guessing

+2 is just a positive 2 so it's just known as 2

2+1+6 = 9

Answer: 9

Step-by-step explanation:because if its 2+1+6 then u get 2 and 6 add thats 8 then your 1 and its 9.

There are a total of 12 possible outcomes in the sample space.

The possible outcomes of Brittany wearing a skirt and a top can be determined by considering all the combinations of skirts and tops.

Skirts: Black, Violet, White, Red

Tops: Yellow, Pink, Green

The possible outcomes are as follows:

Black skirt and yellow top

Black skirt and pink top

Black skirt and green top

Violet skirt and yellow top

Violet skirt and pink top

Violet skirt and green top

White skirt and yellow top

White skirt and pink top

White skirt and green top

Red skirt and yellow top

Red skirt and pink top

Red skirt and green top

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Given:

The set is:

\(\{2,3,5,7,11\}\)

To find:

The set builder notation for the given set.

Solution:

Consider the given set:

\(S=\{2,3,5,7,11\}\)

The element of given set are 2, 3, 5, 7, 11 and so on. These area the prime numbers.

If x defines each element of the set then x must belongs to P which is the set of prime numbers. So, the given set can be written as

\(S=\{x|x\in P\}\)

Therefore, the set builder notation for the given set is \(\{x|x\in P\}\).

Answer:

3.2768 feet

Step-by-step explanation:

The situation can be model by h(x)=8*(4/5)^(n-1). For the 5th jump, n=5. The height will be 8*(4/5)^4=3.2768

Answer:

Step-by-step explanation:
I need more explanation to answer

Answer:

4.2 miles per/hour

Step-by-step explanation:

we know

speed  total distance covered/ total time taken to cover that distance.

Time from 9:00 Am to 11:30 Am is 2 hours 30 minutes

time = 2 1/2 hours = 5/2 hours

for distance\

By 11:30 AM, he was 13 miles from the start.

so he covered a total distance of 12 miles

At 9:00 AM, a person running a race was 2 1/2 miles from the start

until 9 am he had already ran 2 1/2 miles = 5/2 miles

since we have to take distance travelled from 9 to 11 :30 Am

we need to subtract distance travel until 9 am from total distance traveled until 11:30 pm

Distance travlled from 9:11:30 am = distance traveled from start till 11:30AM -  distance traveled from start till 9 AM

Distance traveled from 9:11:30 am =  13 - 5/2 = (26-5)/2 = 21/2

Thus, speed = 21/2 / 5/2 = 21/5 = 4 1/5 miles/hour = 4.2 miles/hour

Thus, he was running with 4.2 miles per/hour.

The volume of a hemisphere with a radius of 44.9 m is approximately 189582.2 cubic meters, rounded to the nearest tenth.

To calculate the volume of a hemisphere, you can use the formula

V = (2/3)πr^3

where V is the volume, π is pi (approximately 3.14), and r is the radius. In this case, r = 44.9 m.

So, (2/3)π(44.9)^3 = 189582.234 cubic meters.

This is the exact volume, but since the question asked for the volume rounded to the nearest tenth, the final answer would be 189582.234 cubic meters. It's worth mentioning that a hemisphere is half of a sphere, thus, the volume of a full sphere with a radius of 44.9 m would be double of this value.

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Rounded to 1 decimal place, the wholesaler's in-stock probability during a normal week is approximately 89.2%.

To calculate the wholesaler's in-stock probability during a normal week, we need to consider the number of items that are available for the entire week and divide it by the total demand.

Total demand = 4,800 items

Items not available for the entire week = 250 items

Items available for only part of the week = 270 items

Therefore, the number of items available for the entire week can be calculated as follows:

Items available for the entire week = Total demand - Items not available for the entire week - Items available for only part of the week

                                = 4,800 - 250 - 270

                                = 4,280 items

The in-stock probability can be calculated by dividing the number of items available for the entire week by the total demand and then multiplying by 100 to convert it to a percentage:

In-stock probability = (Items available for the entire week / Total demand) * 100

                   = (4,280 / 4,800) * 100

                   = 89.1666...

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To determine the time it will take for $10,000 to grow to $17,100 when invested at 5.50% compounded continuously, we can use the continuous compound interest formula:It will take approximately 9.22 years for $10,000 to grow to $17,100 when invested at 5.50% compounded continuously.

A = P * e^(rt),

where A is the final amount, P is the principal amount, e is the base of the natural logarithm (approximately 2.71828), r is the interest rate, and t is the time in years.

In this case, we have:

A = $17,100,

P = $10,000,

r = 5.50% = 0.055 (expressed as a decimal).

Substituting these values into the formula, we get:

$17,100 = $10,000 * e^(0.055t).

Dividing both sides of the equation by $10,000, we have:

1.71 = e^(0.055t).

To solve for t, we can take the natural logarithm (ln) of both sides:

ln(1.71) = 0.055t.

Now, divide both sides by 0.055:

t = ln(1.71) / 0.055.

Using a calculator, we find:

t ≈ 9.22 years.

Therefore, it will take approximately 9.22 years for $10,000 to grow to $17,100 when invested at 5.50% compounded continuously.

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Answer:

Step-by-step explanation:

have you gotten the answer yet or found out how to resolve this problem?

Answer:

2

Step-by-step explanation:

Hardest question ever.

Hence option 1, 2, 3 are the right angle triangle.

The given triangles can be classified according to the Pythagorean theorem.

If the longest side of the triangle is c, and the other two sides are a and b, then the Pythagorean theorem states that

a² + b² = c².

1. Triangle 1: 6, 12, and 13.

The length of sides of the first triangle is 6, 12, and 13.

This triangle is a right triangle as a² + b² = c² can be applied here.

where a = 6, b = 12, and

c = 13.6² + 12²

= 36 + 144 = 18013²

= 169

Hence the triangle is a right triangle.

2. Triangle 2: 5, 12, and 13.

The length of sides of the second triangle is 5, 12, and 13.

This triangle is a right triangle as a² + b² = c² can be applied here

where a = 5, b = 12, and

c = 13.5² + 12²

= 25 + 144 = 16913²

= 169

Hence the triangle is a right triangle.

3. Triangle 3: 3, 4, and 5.

The length of sides of the third triangle is 3, 4, and 5.

This triangle is also a right triangle as a² + b² = c² can be applied here where a = 3, b = 4, and c = 5.

3² + 4² = 9 + 16 = 255² = 25.

Hence the triangle is a right triangle.

4. Triangle 4: 2, 4, and 6.

The length of sides of the fourth triangle is 2, 4, and 6.

This triangle is not a right triangle as a² + b² = c² cannot be applied here where a = 2, b = 4, and c = 6.2² + 4² = 4 + 16 = 20 (not equal to 6² = 36)

Hence the triangle is not a right triangle.

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Answer:

the reflection would be (5,2)

Step-by-step explanation:

According to the question we have found the values of fxy(x, y) and fyy(x, y).

Given f(x, y) = 5x^8 cos(y^6), we are to find fxy(x, y) and fyy(x, y).
Let's start with the partial derivative of f(x, y) with respect to x.∂f(x, y)/∂x = 5.8x^7 cos(y^6) = 40x^7 cos(y^6)
Now, the partial derivative of f(x, y) with respect to y is∂f(x, y)/∂y = -5x^8 sin(y^6).
Differentiating ∂f(x, y)/∂x with respect to y gives the mixed partial derivative fxy(x, y).∂²f(x, y)/∂y∂x = 40.7x^6 cos(y^6) - 30x^8 sin(y^6) = 280x^6 cos(y^6) - 30x^8 sin(y^6)
Therefore, fxy(x, y) = 280x^6 cos(y^6) - 30x^8 sin(y^6).
Now, let's differentiate ∂f(x, y)/∂y with respect to y to obtain the second partial derivative of f(x, y) with respect to y.fyy(x, y) = -5x^8 cos(y^6)
Therefore, fyy(x, y) = -5x^8 cos(y^6).
Thus, we have found the values of fxy(x, y) and fyy(x, y).

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The answer would be 7.5

The proportion of those surveyed who chose basketball as their favorite sport is 34.149 (option a)

Let's denote the proportion of adults who chose basketball as their favorite sport as P(Basketball). To calculate P(Basketball), we need to divide the total number of adults who chose basketball by the total number of surveyed adults. Mathematically, it can be represented as:

P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)

To calculate the number of adults who chose basketball, we sum up the values from the age range categories:

Number of adults who chose basketball = Number of adults (18-30) who chose basketball + Number of adults (31-50) who chose basketball + Number of adults (51 and above) who chose basketball

Looking at the table, we find that the number of adults (18-30) who chose basketball is 15, the number of adults (31-50) who chose basketball is 8, and the number of adults (51 and above) who chose basketball is 11. Adding these values together, we get:

Number of adults who chose basketball = 15 + 8 + 11 = 34

Now, let's calculate the total number of surveyed adults. We can sum up the values from the age range categories:

Total number of surveyed adults = Total number of adults (18-30) + Total number of adults (31-50) + Total number of adults (51 and above)

From the table, we find that the total number of adults (18-30) is 49, the total number of adults (31-50) is 48, and the total number of adults (51 and above) is 52. Adding these values together, we get:

Total number of surveyed adults = 49 + 48 + 52 = 149

Now, we have the values we need to calculate the proportion:

P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)

= 34 / 149

Hence the correct option is (a).

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We have the next information

48000 represent the 100%

8640 represent the ?

ANSWER

8640 represent the 18%

Answer:

anser is D.

Step-by-step explanation:

have a nice day

The difference quotient for the function f(x) is given by f(x+h)-f(x)/h. We are required to find the difference quotient for f(x) = 2x² - 4x + 5.

Let's find the difference quotient by substituting the given values into the formula:difference quotient = f(x + h) - f(x) / hdifference quotient = [2(x + h)² - 4(x + h) + 5] - [2x² - 4x + 5] / hdifference quotient = [2(x² + 2xh + h²) - 4x - 4h + 5] - [2x² - 4x + 5] / hdifference quotient = [2x² + 4xh + 2h² - 4x - 4h + 5 - 2x² + 4x - 5] / hdifference quotient = [4xh + 2h² - 4h] / hdifference quotient = 2x + 2h - 2 Simplifying the expression, we get the difference quotient as 2x - 2 + 2h. Therefore, the difference quotient for f(x) = 2x² - 4x + 5 is 2x - 2 + 2h.A difference quotient is a method of calculating the derivative of a function.

The difference quotient formula is [f(x + h) - f(x)] / h, where h is the change in x and f(x + h) - f(x) is the change in y.

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The given function is f(x) = 2x² - 4x + 5. To find the difference quotient, we will use the formula as given:Difference quotient= [f(x+h)-f(x)]/h Now, substitute the values in the above formula:

\(f(x) = 2x² - 4x + 5f(x+h) = 2(x+h)² - 4(x+h) + 5= 2(x²+2xh+h²) - 4x - 4h + 5[As x²\) remains x²,

but the other terms contain x and h]Therefore,

Difference quotient

\(= [f(x+h)-f(x)]/h= [2(x²+2xh+h²) - 4x - 4h + 5 - (2x² - 4x + 5)]/h= [2x² + 4xh + 2h² - 4x - 4h + 5 - 2x² + 4x - 5]/h= [4xh + 2h² - 4h]/h= 2x + 2h - 4\)

Thus, the difference quotient for f(x) = 2x² - 4x + 5 is 2x + 2h - 4, and this is the simplified answer.In more than 100 words:

Difference quotient is used in calculus to describe how a function changes as it is evaluated over two points. Given a function, f(x), the difference quotient can be found by using the formula (f(x+h) - f(x))/h.

This gives us

\(f(x+h) = 2(x²+2xh+h²) - 4(x+h) + 5 andf(x) = 2x² - 4x + 5.\)

Then, we simplify the formula by expanding and combining like terms.

This gives us the difference quotient 2x + 2h - 4.

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The inradius of the triangle of the given dimensions will be equal to the value 2.

To find the inradius of a triangle, we need to know the semi perimeter of the triangle, which is half of the perimeter. The perimeter of a triangle is the sum of the lengths of its sides. So, the semi perimeter of triangle ABC is (6+8+10)/2 = 12.

Now that we know the semi perimeter, we can use the formula for the inradius of a triangle:

inradius = √(s-a)(s-b)(s-c)/s

where a, b, and c are the lengths of the sides of the triangle and s is the semi perimeter.

Plugging in the values for a, b, c, and s, we get:

inradius = √(12-6)(12-8)(12-10)/12 = √(6)(4)(2)/12 = √48/12} = √4 = 2

Therefore, the inradius of triangle ABC is 2.

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a. The function f(x₁, x₂, x₃, x₄) is homogeneous of degree 1.

b. The function f(x, y, z) is not homogeneous.

a. To determine if the function f(x₁, x₂, x₃, x₄) is homogeneous, we need to check if it satisfies the definition of homogeneity. According to the definition, a function f is homogeneous of degree k if f(tx₁, tx₂, tx₃, tx₄) = t^k * f(x₁, x₂, x₃, x₄) for all values of t.

For the given function f(x₁, x₂, x₃, x₄) = (x₁ + 2x₂ + 3x₃ + 4x₄) / (x₁² + x₂² + x₃² + x₄²), let's test the condition. If we replace each variable xᵢ with txᵢ, we get:

f(tx₁, tx₂, tx₃, tx₄) = (tx₁ + 2tx₂ + 3tx₃ + 4tx₄) / (t²x₁² + t²x₂² + t²x₃² + t²x₄²)

                        = t(x₁ + 2x₂ + 3x₃ + 4x₄) / t²(x₁² + x₂² + x₃² + x₄²)

                        = (x₁ + 2x₂ + 3x₃ + 4x₄) / (x₁² + x₂² + x₃² + x₄²)

We can see that the function satisfies the condition, as the expression simplifies to the original function. Therefore, the function f(x₁, x₂, x₃, x₄) is homogeneous of degree 1.

b. To determine if the function f(x, y, z) is homogeneous, we apply the same definition of homogeneity. Let's test the condition by replacing each variable with tx, ty, and tz:

f(tx, ty, tz) = (tx²y)(2tz) + 2txz

                  = t³xyz + 2txz

We can see that the term t³xyz does not cancel out, which means the condition of homogeneity is not satisfied. Therefore, the function f(x, y, z) is not homogeneous.

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The final elevation of the AUV is \(-31 \frac{5}{12}\) feet.

Given that, AUV is at an elevation of -8.25 ft. It dives down \(6\frac{2}{3}\) ft to collect a specimen. Then the AUV dives another \(15\frac{3}{4}\) ft.

The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".

Here, the mixed fraction can be written in improper fraction

\(6\frac{2}{3} = \frac{20}{3}\) and \(15\frac{3}{4}=\frac{63}{4}\)

Now, 8.25 = 825/100 = 33/4

The final elevation = -33/4-20/3-63/4

= -99/4 - 20/3

= -297/12 -80/12

= - 377/12

= \(-31 \frac{5}{12}\)

Therefore, the final elevation of the AUV is \(-31 \frac{5}{12}\) feet.

To learn more about an elevation visit:

https://brainly.com/question/481548.

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