In the drawing, A, C, and D are collinear and AB is



tangent to the circle B. Using the values shown, what



is the measure of CD?

The number of birds at the Bronx Zoo is 139. There are 139 birds at the Bronx Zoo, based on the information provided by Maggie's animal count and leg count.

Let's use algebraic equations to solve for the number of birds at the Bronx Zoo.

Let's assume that the number of mammals is represented by the variable "m" and the number of birds is represented by the variable "b."

From the given information, we know that the total number of animals counted, whether mammals or birds, is 200. This can be expressed as:

m + b = 200 (Equation 1)

Additionally, we know that the total number of legs counted is 522. Mammals have 4 legs each, while birds have 2 legs each. Therefore, the total number of legs can be calculated as:

4m + 2b = 522 (Equation 2)

To solve this system of equations, we can use substitution or elimination method.

Let's solve using the elimination method:

Multiply Equation 1 by 2 to make the coefficients of "b" in both equations the same:

2m + 2b = 400 (Equation 3)

Now subtract Equation 3 from Equation 2:

4m + 2b - (2m + 2b) = 522 - 400

Simplifying:

2m = 122

Divide both sides by 2:

m = 61

Now substitute the value of "m" back into Equation 1 to solve for "b":

61 + b = 200

Subtract 61 from both sides:

b = 200 - 61

b = 139

Therefore, the number of birds at the Bronx Zoo is 139.

By solving the given algebraic equation, we determined that there are 139 birds at the Bronx Zoo, based on the information provided by Maggie's animal count and leg count.

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Answer:

To find out how long it will take before Jaclyn and Pedro have saved the same amount of money, we need to calculate the monthly savings for both of them.

Jaclyn earns $40 each month in allowance and saves the entire amount, so her monthly savings is $40.

Pedro's monthly savings can be calculated by subtracting his monthly expenses from his monthly allowance. Pedro writes a check for $20 for his cable bill and $42.50 for his phone bill each month. Therefore, his monthly expenses are $20 + $42.50 = $62.50.

Pedro earns $40 each month in allowance, so his monthly savings is $40 - $62.50 = -$22.50 (negative amount).

Since Pedro's monthly savings is negative, it means he is spending more than his allowance, and he won't be able to catch up with Jaclyn's savings. Therefore, they will never save the same amount of money.

Answer:  Since both the LHS and RHS simplify to undefined, we can conclude that the equation √sec²0-1+√cosec²0-1 = sec0cosec0 is true when evaluated using trigonometric identities.

Step-by-step explanation:

To prove the equation √sec²0-1+√cosec²0-1 = sec0cosec0, we can simplify both sides of the equation separately and show that they are equal.

Starting with the left-hand side (LHS):

√sec²0-1+√cosec²0-1

Using trigonometric identities, we know that sec²θ - 1 = tan²θ and cosec²θ - 1 = cot²θ. Substituting these identities, we have:

√tan²0 + √cot²0

Since tan0 = 0 and cot0 is undefined, we can simplify further:

√0 + √undefined

The square root of 0 is 0, and the square root of undefined is also undefined. Therefore, the LHS simplifies to:

0 + undefined = undefined

Now, let's simplify the right-hand side (RHS):

sec0cosec0

Using the definitions of secant and cosecant in terms of cosine and sine:

1/cos0 * 1/sin0

Recall that sin0 = 0, so the RHS simplifies to:

1/cos0 * undefined = undefined

Answer:

Here is a possible text using the given keywords:

The given equation is √sec²0-1+√cosec²0-1 = sec0cosec0.​ To prove this equation, we will use some trigonometric identities and algebraic manipulations. First, we will rewrite the equation as follows:

√(sec²0-1)+√(cosec²0-1) = sec0cosec0

Next, we will use the identity sec²0 = 1+tan²0 and cosec²0 = 1+cot²0 to substitute for sec²0-1 and cosec²0-1:

√(1+tan²0)+√(1+cot²0) = sec0cosec0

Then, we will use the identity tan0 = sin0/cos0 and cot0 = cos0/sin0 to substitute for tan0 and cot0:

√(1+(sin0/cos0)²)+√(1+(cos0/sin0)²) = (1/cos0)(1/sin0)

Now, we will simplify the expression by multiplying both sides by cos0sin0:

√(cos²0+sin²0)+√(sin²0+cos²0) = 1

Finally, we will use the identity cos²0+sin²0 = 1 to simplify the expression further:

√1+√1 = 1

Hence, we have proven that √sec²0-1+√cosec²0-1 = sec0cosec0.​

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The height of the Eiffel Tower is approximately 290 meters. Michael and Layla are standing 21.2 meters apart, and from their respective positions, The height of the Eiffel Tower is approximately 290 meters.

To explain further, let's consider the triangle formed by the base of the Eiffel Tower, Michael's position, and the top of the tower. In this triangle, the angle of elevation from Michael's position is 40°, and the opposite side is the height of the tower. Similarly, in the triangle formed by the base of the tower, Layla's position, and the top of the tower, the angle of elevation from Layla's position is 38.5°, and the opposite side is also the height of the tower.

Using trigonometric ratios, we can set up the following equations:

For Michael's triangle:

tan(40°) = height of the tower / 21.2

For Layla's triangle:

tan(38.5°) = height of the tower / 21.2

By solving these equations, we find that the height of the Eiffel Tower is approximately 290 meters.

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The denominator remains the same, so multiplying 1/6 by 2 gives 2/6. But we can simplify this fraction further by dividing both the numerator and denominator by their highest common factor, which is 2. This gives us the simplest fraction 1/3 equivalent to 2 copies of 1/6.

To write a fraction for the given statement "2 copies of 1/6 is", we need to multiply the given fraction by 2. When we multiply a fraction by a whole number, we just multiply the numerator by that number. The denominator remains the same, as shown below:2 copies of 1/6= 2 × 1/6= 2/6or, 2/6 is the required fraction for the given statement.

We can simplify this fraction by dividing both the numerator and denominator by their highest common factor, which is 2. This gives us:2/6= 1/3Thus, 1/3 is the simplest fraction equivalent to 2 copies of 1/6. In more than 100 words, we can say that to write a fraction for the given statement "2 copies of 1/6 is", we have multiplied the given fraction by 2. As we know that when we multiply a fraction by a whole number, we just multiply the numerator by that number.

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To advise school leavers on stress management techniques to deal with the psychological impact of unemployment, it is essential to encourage self-care practices, maintain a positive mindset, seek support from others, develop new skills, and explore alternative opportunities.

1. Self-care practices: Emphasize the importance of self-care activities such as exercise, proper sleep, healthy eating, and engaging in hobbies or activities that bring joy and relaxation. These practices help reduce stress and promote overall well-being.

2. Positive mindset: Encourage school leavers to maintain a positive outlook by focusing on their strengths, setting realistic goals, and maintaining a sense of optimism. Remind them that unemployment is a temporary phase and that opportunities will arise in the future.

3. Seek support: Encourage school leavers to reach out to family, friends, or mentors for emotional support and guidance. Sharing their concerns and feelings with others can help alleviate stress and provide valuable perspectives.

4. Develop new skills: Suggest utilizing the free time to learn new skills or enhance existing ones. This could involve taking online courses, volunteering, or participating in community projects. Skill development increases confidence and expands future job prospects.

5. Explore alternative opportunities: Encourage school leavers to explore alternative paths such as entrepreneurship, freelancing, internships, or part-time work. Encouraging them to think creatively and consider different options can help them find fulfilling opportunities.

By adopting these stress management techniques, school leavers can proactively cope with the psychological impact of unemployment, maintain a positive mindset, and continue developing themselves for future opportunities.

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Let's assume that x represents the number of child tickets sold and y represents the number of adult tickets sold.Based on the given information, we can set up the following equations:

Equation 1: x + y = 88 (total number of tickets sold)

Equation 2: 4x + 7y = 553 (total revenue from ticket sales)

To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method: Multiplying Equation 1 by 4, we get: 4x + 4y = 352

Subtracting Equation 2 from this modified Equation 1:

[tex](4x + 4y) - (4x + 7y) = 352 - 553[/tex]

[tex]-3y = -201[/tex]

[tex]y = 67[/tex]

Substituting the value of y into Equation 1:

x + 67 = 88

x = 88 - 67

x = 21

Therefore, 21 child tickets and 67 adult tickets were sold. Let's assign variables to the unknowns in the problem. We'll let x represent the number of child tickets sold and y represent the number of adult tickets sold. According to the problem, the total number of tickets sold is 88. This can be represented by the equation x + y = 88. This equation states that the sum of the number of child tickets (x) and the number of adult tickets (y) equals 88.

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Equation: x^2 + 4y^2 = 16

Conic Section: Ellipse

The equation represents an ellipse because both the x and y terms are squared with positive coefficients, indicating a horizontally stretched ellipse centered at the origin.

Equation: 3x^2 - 2y^2 = 12

Conic Section: Hyperbola

The equation describes a hyperbola because the x term is squared with a positive coefficient while the y term is squared with a negative coefficient.

Equation: y = 2x^2 + 4x + 3

Conic Section: Parabola

The equation represents a parabola because it is a quadratic equation in the form of y = ax^2 + bx + c, where a ≠ 0. The positive coefficient of the x^2 term indicates an upward-opening parabola.

Equation: x^2 - 9y^2 = 36

Conic Section: Hyperbola

The equation represents a hyperbola because the x term is squared with a positive coefficient while the y term is squared with a negative coefficient.

Equation: y = 6

Conic Section: Line (Degenerate case)

The equation represents a degenerate conic section, specifically a line, because there are no squared terms involved, resulting in a straight line parallel to the x-axis with a constant y-value of 6.

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The solution that can be eliminated is -0.2 s. The reason for eliminating this solution cannot be a negative value in this context. The height of football at t is modeled by quadratic equation h(t) = -16t^2 + 40t + 7,

When solving the equation h(t) = 0 to find the times when the height of the football is zero, we obtain two solutions: -0.2 s and 2.7 s (rounded to the nearest tenth). We need to determine which solution is valid and which one should be eliminated.

In this case, the solution -0.2 s can be eliminated because time cannot be negative. Time represents the duration after the ball is thrown, and it cannot go back in time before the throw occurred. Therefore, -0.2 s does not make sense in the context of this problem.

On the other hand, 2.7 s is a valid solution as it represents the time when the football reaches a height of zero during its trajectory. This solution indicates that after approximately 2.7 seconds, the football has landed or reached its lowest point in its flight path.Thus, the solution -0.2 s can be eliminated because time cannot be negative in this situation.

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The ages are: Natalie is 15 years old and Fred is 31 years old.

Let's assign variables to represent Natalie's age (N) and Fred's age (F).

From the given information, we can create a system of equations:

Equation 1: N + F = 46  (The sum of Natalie's age and Fred's age is 46)

Equation 2: F + 4N = 91  (The sum of Fred's age and four times Natalie's age is 91)

To solve this system of equations, we can use the method of substitution or elimination.

Let's solve it using the method of substitution:

From Equation 1, we can express F in terms of N:

F = 46 - N

Substituting this into Equation 2:

(46 - N) + 4N = 91

46 + 3N = 91

3N = 91 - 46

3N = 45

N = 45 / 3

N = 15

Now, substitute the value of N back into Equation 1 to find F:

15 + F = 46

F = 46 - 15

F = 31

Therefore, Natalie is 15 years old and Fred is 31 years old.

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Phylea can repackage the candy into smaller bags, each containing 6 fireballs and 6 Jolly Ranchers.

To repackage the candy into smaller bags with an equal number of fireballs and Jolly Ranchers, we need to find the greatest common divisor (GCD) of 30 and 24. The GCD represents the largest number that divides both 30 and 24 evenly.

The prime factorization of 30 is 2 * 3 * 5, and the prime factorization of 24 is 2 * 2 * 2 * 3. To find the GCD, we take the common factors with the lowest exponent: 2 * 3 = 6.

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The probability that Anji goes to the cinema on a particular Friday is (2 - √3) / √3. Let's denote the event of Anji going to the cinema as A and the event of Katrina going to the cinema as K.

We are given the following probabilities:

P(A and K) = 1/3 (probability of both Anji and Katrina going to the cinema)

P(A or K) = 5/6 (probability of at least one of them going to the cinema)

We can use the principle of inclusion-exclusion to find the probability of Anji going to the cinema (P(A)).

P(A or K) = P(A) + P(K) - P(A and K)

Since P(A and K) = 1/3, we have:

5/6 = P(A) + P(K) - 1/3

Now, let's consider that Anji and Katrina decide independently, so the events A and K are independent. Therefore, P(A and K) = P(A) * P(K).

Since P(A and K) = 1/3, and assuming equal probabilities for Anji and Katrina going to the cinema (P(A) = P(K) = x), we have: 1/3 = x * x

Solving this equation, we find: x = 1/√3

Now, substituting this value of x into the equation:

5/6 = P(A) + P(K) - 1/3

5/6 = 2x - 1/3

5/6 = 2(1/√3) - 1/3

5/6 = 2/√3 - 1/3

To find P(A), we can subtract P(K) from both sides: P(A) = 2/√3 - 1/3 - P(K)

Since P(K) = x = 1/√3, we have: P(A) = 2/√3 - 1/3 - 1/√3

Simplifying this expression, we get: P(A) = (2 - √3) / √3

Therefore, the probability that Anji goes to the cinema on a particular Friday is (2 - √3) / √3.

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Answer:

the 12th term of the geometric sequence is approximately 9,559,938.

Step-by-step explanation:

Given that a₄ = 54 and a₇ = 1,458, we can use these values to find the common ratio:

a₇ = a₄ * r³

1,458 = 54 * r³

r³ = 1,458 / 54

r³ ≈ 27

Taking the cube root of both sides:

r ≈ ∛27

r ≈ 3

Now that we have the common ratio (r = 3), we can find the 12th term using the formula for the nth term of a geometric sequence:

aₙ = a₁ * r^(n-1)

In this case, we have a₁ = 54, n = 12, and r = 3:

a₁₂ = 54 * 3^(12-1)

a₁₂ = 54 * 3^11

Calculating this expression:

a₁₂ = 54 * 177,147

a₁₂ ≈ 9,559,938.

Answer:

The 12th term is 354294

Step-by-step explanation:

A geometric sequence has the from,

f(n) = f(n-1)(r)

where r is the common ratio

in our case, f(4) = 54

and f(7) = 1458

we have to find f(12)

now, since f(4) = 54, then f(5) must be,

[tex]f(5) = r(f(4))\\so,\\f(5) = r(54)\\similarly,\\f(6) = r(f(5))\\but f(5) = r(54) \ so,\\f(6) = r(r(54))\\f(6) = r^{2} (54)\\finally, \\f(7) =rf(6)\\f(7)=r(r^{2} (54))\\but f(7) = 1458\\so\ we \ get\\1458=r^{3}(54)\\ == > \ 1458/54=r^{3}\\ 27=r^{3}\\so,\\r=3[/tex]

Hence we have found the ratio,

now we just keep going till we get to the 12th term

[tex]f(8) = 3(f(7))\\f(8) = 3(1458)\\f(8) = 4374\\f(9) = 3(4374)\\f(9) = 13122\\\\Similarly,f(10) = 39366\\f(11) = 118098\\f(12) = 354294[/tex]

Hence the 12th term is f(12) = 354294

or a sub 12 = 354294

A rocket launched into the air reaches a height of 720 feet after 5 seconds. After 10 seconds, the rocket lands. Let the x-axis be the ground and the y-axis be at the starting point of the rocket. Equation modeling the path of the rocket where h is the height of the rocket and t is the time in seconds after the rocket is launched is:

a. H(t) = -16t² + vt + h

Where: H(t) = Height of rocket at time t (in feet)

h = Initial height (in feet) = 0

v = Initial velocity (in feet/sec) = 0

Gravity = 32 ft/s²

(Since the rocket is going upward)So the equation for the path of the rocket is:

H(t) = -16t² + 0t + 0

H(t) = -16t²b.

The height of the rocket 7 seconds after it was launched can be determined by using the formula derived above:

H(t) = -16t² + 0t + 0

H(7) = -16(7)²

= -784

b. The height of the rocket after 7 seconds of launch is 784 feet.

c. Time duration the rocket is in the air is given by the formula:

H(t) = -16t² + 0t + 0

We can determine the time at which the rocket lands by equating the height of the rocket to 0:

H(t) = -16t² + 0t + 0

= 0

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Therefore, Sarah has 20p left after paying for the fruit.

Sarah wants to buy 3 oranges at 30p each, which totals to 3 x 30p = 90p. She also wants to buy 1/2 kg of apples at £1.20 per kg, which is 0.5 kg x £1.20/kg = 60p. In total, the cost of the fruit is 90p + 60p = 150p.

Sarah has one 50p coin and six 20p coins, which amounts to 50p + (6 x 20p) = 170p.

To find out how much money Sarah has left, we subtract the cost of the fruit from the total amount of money she has.

170p - 150p = 20p

Therefore, Sarah has 20p left after paying for the fruit.

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The total number of people who take the elevator is 19.

Based on the given two-way table, the number of people who take the elevator is found in the "Elevator" column, which includes both athletes and non-athletes.

Looking at the "Elevator" column, we can see that the number of athletes who take the elevator is 3, and the number of non-athletes who take the elevator is 16.

To find the total number of people who take the elevator, we add the number of athletes and non-athletes who take the elevator:

3 (athletes) + 16 (non-athletes) = 19

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Answer:

π(10²) = 100π = about 314.2 ft²

The area of a square with side length 3xy^2 can be expressed as a monomial, which is 9x^2y^4.

The area of a square is calculated by multiplying the length of its side by itself. Given a side length of 3xy^2, we can express the area as a monomial by simplifying the expression. First, we square the side length: (3xy^2)^2. Applying the exponent to each term within the parentheses, we get 9x^2y^4. This monomial represents the area of the square with a side length of 3xy^2. It indicates that the area is the product of the coefficient, 9, and the variables raised to their respective exponents, x^2 and y^4. Therefore, the monomial expression for the area of the square is 9x^2y^4.

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The probability that a randomly chosen club member will not be a 7th grader is 13/20.

To find the probability that a randomly chosen club member will not be a 7th grader, we need to consider the probability of selecting any member other than a 7th grader from the given probability model.

Given information:

There are 6 6th graders, 7 7th graders, and 8 8th graders among the 40 club members.

Probability of selecting a 6th grader: 9/40.

Probability of selecting a 7th grader: 14/40.

Probability of selecting an 8th grader: 17/40.

To find the probability of not selecting a 7th grader, we need to consider the complementary event, which is selecting either a 6th grader or an 8th grader.

Calculate the probability of not selecting a 7th grader:

Probability = 1 - Probability of selecting a 7th grader.

Probability = 1 - 14/40.

Probability = 26/40.

Simplify the fraction, if necessary:

The probability can be reduced by dividing both the numerator and denominator by their greatest common divisor, which is 2 in this case.

Probability = 13/20.

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Mr Mathebula says that more than 60% of the learners achieved above 25 out of 50.  To verify Mr. Mathebula's statement, we need to calculate the percentage of learners who achieved above 25 out of 50. In this case, 60.1% is not greater than 60%, so Mr. Mathebula's statement would be incorrect.

To verify Mr. Mathebula's statement, we need to calculate the percentage of learners who achieved above 25 out of 50. Let's assume there are a total of 'n' learners in the class.

First, we need to determine the number of learners who scored above 25. Let's denote this as 'x'. Since the statement mentions that more than 60% of the learners achieved above 25, we can assume 'x' to be any number greater than 0.6n.

Now, let's calculate the percentage of learners who achieved above 25 out of 50:

Percentage = (x / n) * 100

Since we want to verify whether Mr. Mathebula's statement is correct, we need to determine if the calculated percentage is greater than 60%.

If we assume that 'x' is the lowest possible value of 0.6n + 1 (to satisfy the "more than 60%" condition), the percentage becomes:

Percentage = ((0.6n + 1) / n) * 100

Simplifying this expression:

Percentage = (0.6 + 1/n) * 100

Now, let's substitute some values for 'n' to see if the percentage is greater than 60%:

If we consider 'n' to be 100, the percentage becomes:

Percentage = (0.6 + 1/100) * 100 = 60.6%

Since 60.6% is greater than 60%, Mr. Mathebula's statement holds true for this scenario.

However, if we consider 'n' to be 1000, the percentage becomes:

Percentage = (0.6 + 1/1000) * 100 = 60.1%

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To describe how long Rosa's rocket flew, we can use the given information that Rosa's rocket flew 2.5 seconds longer than 1.5 times the number of seconds Gina's rocket flew.

Let's denote the number of seconds Gina's rocket flew as x. According to the information given, Rosa's rocket flew 1.5 times the number of seconds Gina's rocket flew, which is 1.5x. Additionally, Rosa's rocket flew 2.5 seconds longer than that.

Therefore, the expression that describes how long Rosa's rocket flew is:

1.5x + 2.5

So Rosa's rocket flew for 1.5x + 2.5 seconds.

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The height where the pumpkin lands on the hill is approximately 13 meters.

The height where the pumpkin lands on the hill, we need to determine the point where the height of the hill (y) equals the height of the pumpkin (h(x)).

1. Equate the two height functions: Setting the equations y = 0.8x and h(x) = -0.3x^2 + 3.8x equal to each other allows us to find the x-value where the heights are equal.

  0.8x = -0.3x^2 + 3.8x

2. Simplify the equation: Rearrange the equation to form a quadratic equation.

  0 = -0.3x^2 + 3x - 3.8x

  0 = -0.3x^2 - 0.8x

3. Solve for x: To find the x-value where the heights are equal, solve the quadratic equation. The solutions will give the points where the pumpkin lands on the hill.

  Using a quadratic solver or factoring, we find that x = 0 and x ≈ 13.33.

4. Determine the height: Substituting the x-value into either the hill equation or the pumpkin equation gives us the height.

  Using the hill equation, y = 0.8(13.33) ≈ 10.67.

Therefore, the height where the pumpkin lands on the hill is approximately 13 meters (rounded to the nearest whole number).

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The expression m/CDJ is equal to (4x)(3x - 8). To simplify the expression m/CDJ, we need to substitute the value of CDJ with its equivalent expression. Based on the given information, CDJ is equal to (3x - 8).

To further simplify the expression, we multiply the numerator m by the factor in the denominator, which is (4x). This gives us (4x)m/(3x - 8).  Therefore, m/CDJ can be rewritten as m/(3x - 8). So, the simplified expression for m/CDJ is (4x)(3x - 8). The result is a product of the two factors, 4x and (3x - 8), and it represents the value of m/CDJ.

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Answer:

The imperial gallon (also known as the UK gallon) is used in Commonwealth countries and some Caribbean states. It is equal to 4.54609 liters or 277.42 cubic inches.

so the answer is 4.54609 liters

Step-by-step explanation:

The value of the car 5 years after it is purchased will be approximately $18,844.45. To calculate the value of the car after 5 years, we need to apply the annual depreciation rate of 7.25% to the initial purchase price of $28,000.

Each year, the car's value decreases by 7.25% of its current value. To find the value after 5 years, we can use the formula for compound interest, where the initial value is $28,000, the annual interest rate is -7.25%, and the time period is 5 years. Using this formula, we can calculate the value of the car after 5 years to be approximately $18,844.45.

The car's value depreciates by 7.25% each year, which means that the car loses 7.25% of its value annually. This depreciation rate is applied to the current value of the car each year. In this case, the initial purchase price is $28,000. After the first year, the car's value will be 92.75% of $28,000, which is $25,930. After the second year, the car's value will be 92.75% of $25,930, and so on for each subsequent year. After 5 years, the car's value will be approximately $18,844.45, which is the result of applying the annual depreciation rate for each year.

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If the student's score was recorded as 49%, the solution to the mistake would be to correct the score to its accurate value.

To correct the mistake, the teacher needs to determine the actual score of the student. If the recorded score is 49%, it means the student received 49% of the total possible marks. The teacher should review the student's work and re-evaluate their performance to obtain the correct score. Once the correct score is determined, it should be recorded accurately in the student's records. This ensures that the student's academic progress is assessed and reported correctly.

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To solve the given function: f(x) = x², g(x) = 5x, and h(x) = x + 4 for [f ◦ (h ◦ g)](2), we have to calculate for the following steps:

To find [h ◦ g](x), we substitute g(x) into h(x) as follows:

h(g(x)) = g(x) + 4

Substitute g(x) with 5x, we get:

h(g(x)) = 5x + 4

Therefore, [h ◦ g](x) = 5x + 4

To find [f ◦ (h ◦ g)](x), we substitute [h ◦ g](x) into f(x) as follows:

f(h(g(x))) = [h(g(x))]²

Substitute [h ◦ g](x) with 5x + 4, we get:

f(h(g(x))) = [5x + 4]²= (5x + 4)(5x + 4)= 25x² + 40x + 16

Therefore, [f ◦ (h ◦ g)](x) = 25x² + 40x + 16

The final step is to find [f ◦ (h ◦ g)](2). Substitute x = 2, we get:

[f ◦ (h ◦ g)](2)= 25(2)² + 40(2) + 16= 100 + 80 + 16= 196

Hence, we have found that [f ◦ (h ◦ g)](2) = 196.

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The table provided displays the results of Anthony's survey on whether students at his school play a sport, categorized by gender. The question at hand is whether being a girl and playing sports are independent events.

In order to determine if being a girl and playing sports are independent events, we need to understand the concept of independence in probability. Two events are considered independent if the occurrence of one event does not affect the probability of the other event happening.

Looking at the table, we can analyze the data for girls and boys separately. If the proportion of girls playing sports is consistent regardless of the total number of girls surveyed, then being a girl and playing sports can be considered independent events. However, if the proportion of girls playing sports varies depending on the total number of girls surveyed, then being a girl and playing sports are not independent events.

To determine the independence, we would need additional information about the total number of girls surveyed and the proportion of girls playing sports across different sample sizes. Without that information, we cannot definitively conclude whether being a girl and playing sports are independent events based solely on the provided table.

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Ms. Solis' 2008 Honda CR-V depreciates at an average rate of approximately 15.7% per year based on the given information.

To determine the depreciation rate of Ms. Solis' car, we can use the equation for exponential decay, y = [tex]a(1 - r)^t[/tex], where y represents the current value of the car, a is the initial value, r is the depreciation rate, and t is the time in years. We are given that the initial value (a) of the car was $27,500 and the current value (y) in 2022 is $4,480.    

Substituting these values into the equation, we can solve for the depreciation rate (r). Rearranging the equation, we have: r =[tex]1 - (y/a)^(1/t)[/tex]. Plugging in the given values, we find r = [tex]1 - (4,480/27,500)^(1/14)[/tex], where 14 represents the number of years from 2008 to 2022.  

Evaluating the expression, we find that r ≈ 0.157, or approximately 15.7%. Therefore, Ms. Solis' Honda CR-V depreciates at an average rate of around 15.7% per year. This means that, on average, the value of her car decreases by 15.7% each year since its purchase in 2008.

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The next number in the sequence 6, 1, 8, 4, 2, 7 is 3.

To determine the pattern and find the next number in the sequence, we need to observe the given numbers and look for any consistent rule or pattern. Let's examine the given sequence:

6, 1, 8, 4, 2, 7

Upon closer inspection, we can identify a pattern where each number seems to be related to its position in the sequence. Specifically, the first number (6) corresponds to the 1st position, the second number (1) corresponds to the 2nd position, the third number (8) corresponds to the 3rd position, and so on.

By applying this pattern, we can determine that the next number should correspond to the 6th position. Since the sequence follows a repeating pattern with a length of 6, we can cycle back to the beginning. Therefore, the number in the 6th position is 3.

Hence, the next number in the sequence is 3.

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