Simplify $\frac{\sqrt{40\cdot9}}{\sqrt{49}}$.

Answer:

  76 ft²

Step-by-step explanation:

You want the area of a trapezoid with bases 6 ft and 13 ft, and height 8 ft.

The area formula for a trapezoid is ...

  A = 1/2(b1 +b2)h

  A = 1/2(6 ft +13 ft)(8 ft) = 76 ft²

The area of the figure is 76 square feet.

__

Additional comment

The length of the longer base on the right is the sum of 6 ft and 7 ft. It is 13 ft.

The area of the figure is 76 square feet.

the area of a trapezoid is: 76 ft².

Here, we have,

from the given figure, we get,

The length of the longer base on the right is the sum of 6 ft and 7 ft. It is 13 ft.

We have to find the area of a trapezoid with bases 6 ft and 13 ft, and height 8 ft.

Trapezoid

The area formula for a trapezoid is

 A = 1/2(b₁ +b₂)h

 A = 1/2(6 ft +13 ft)(8 ft)

     = 76 ft²

so, we get,

The area of the figure is 76 square feet.

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The required with the help of trig ratios we have,
1. x = 30.69
2. x =23.21
4. angle T = 61.42°
5. angle T = 28.5°

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
1.

Apply the sine rule,
Sin21 = perpendicular/hypotenus
sin21 = 11 / x
x = 11/sin21
x = 30.69

Similarly,
2. x =23.21
4. angle T = 61.42°
5. angle T = 28.5°

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The moment generating function of the lifetime is (1/(1-2t)).

The lifetime X of a microchip has a density function given by F(x) = { 0.5e^(-x/2) for x>0, 0 else.

a) The mean lifetime of this microchip is given by the integral of xF(x) from 0 to infinity. This can be calculated as follows:

Mean = ∫_0^∞ xF(x) dx = ∫_0^∞ x(0.5e^(-x/2)) dx = -xe^(-x/2)|_0^∞ + 2∫_0^∞ e^(-x/2) dx = 2[-2e^(-x/2)|_0^∞] = 4

So the mean lifetime of this microchip is 4 years.

b) The standard deviation of the lifetime of this microchip is given by the square root of the variance. The variance is the integral of (x-mean)^2 F(x) from 0 to infinity. This can be calculated as follows:

Variance = ∫_0^∞ (x-4)^2(0.5e^(-x/2)) dx = ∫_0^∞ (x^2 - 8x + 16)(0.5e^(-x/2)) dx = 8 - 16 + 16 = 8

So the standard deviation of the lifetime of this microchip is √8 = 2.828 years.

c) The probability that this microchip will work for more than 3 years is given by the integral of F(x) from 3 to infinity. This can be calculated as follows:

P(X > 3) = ∫_3^∞ F(x) dx = ∫_3^∞ (0.5e^(-x/2)) dx = -e^(-x/2)|_3^∞ = e^(-3/2) = 0.223

So the probability that this microchip will work for more than 3 years is 0.223.

d) The probability that this microchip will work for more than 5 years knowing that it has been working for more than 2 years is given by the conditional probability P(X > 5 | X > 2). This can be calculated as follows:

P(X > 5 | X > 2) = P(X > 5 and X > 2)/P(X > 2) = P(X > 5)/P(X > 2) = (∫_5^∞ F(x) dx)/(∫_2^∞ F(x) dx) = (e^(-5/2))/(e^(-2/2)) = e^(-3/2) = 0.223

So the probability that this microchip will work for more than 5 years knowing that it has been working for more than 2 years is 0.223.

e) The moment generating function of the lifetime is given by the integral of e^(tx)F(x) from 0 to infinity. This can be calculated as follows:

MGF(t) = ∫_0^∞ e^(tx)F(x) dx = ∫_0^∞ e^(tx)(0.5e^(-x/2)) dx = 0.5∫_0^∞ e^((2t-1)x/2) dx = 0.5[(2/(2t-1))e^((2t-1)x/2)|_0^∞] = (1/(1-2t))

So the moment generating function of the lifetime is (1/(1-2t)).

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The graph of the system of inequalities is a circle with center (0,0) and radius of 100 units for the regular version and 2000/21.95 units for the deluxe version.

Inequality in math is a mathematical statement that states two expressions are not equal. It can be written using symbols such as <, >, or ≠. Inequality statements are used to compare values or expressions and to describe ranges of values that satisfy certain conditions.

The salesperson must sell at least 100 units of either the regular or deluxe version and their total sales must be at least $2000 in order to receive the bonus.

The company offers a bonus to salespeople who can meet certain sales goals. This encourages salespeople to be more motivated to sell the product and to increase their overall sales. It also helps the company increase their profits by providing incentives for salespeople to increase their sales. By offering the bonus, the company is able to attract more salespeople who are willing to work hard and reach their sales goals in order to receive the bonus. This allows the company to increase their market share and their profits.

The bonus also helps to retain existing salespeople who might otherwise be tempted to leave the company. By offering the bonus, the company is able to reward loyal salespeople who have consistently performed well and have contributed to the company's success. This helps the company to maintain a stable and productive sales team, which is beneficial for the company's long-term success.

Overall, offering a bonus to salespeople who meet certain sales goals is a beneficial strategy for the company. It encourages salespeople to be more motivated and increase their sales, while also helping the company to attract and retain quality salespeople. This helps the company to grow and increase their profits in the long run.

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Health club A costs $18 more than health club B charges.

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x - 2 depicts a linear function because it is a straight line in the coordinate plane.

Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.

An example of a non-linear function is a quadratic function.

Given, The equation y = 35x + 40 represents health club B charges.

And the equation for health club A is, 35x + 58.

Now, To obtain how much more health club A charges we have to take the difference which is,

= (35x + 58) - (35x + 40).

= 35x - 35x + 58 - 40.

= $18 more.

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Answer:

B. y=7x

Step-by-step explanation:

A direct proportion is where the ratio is constant. The ratio will stay the same. Therefore, y = 7x, this ratio will stay constant making it a direct proportion.

Hope this helps : )

The base, which is equal to 1.3, is one of the values in the equation g(x)=18(1.3)x.

The monthly growth rate of the insect population is represented by this number. Since 1.3 is 1 + 30% represented as a decimal, the population is specifically growing by 30% each month. When the growth rate is compounded each month, this indicates that the insect population is expanding quickly over time.

If we enter x=3 into the function, for instance, we obtain g(3)=18(1.3)3=18(2.197)=39.546. This indicates that the anticipated bug population after three months is 39,546. Pest control is frequently required to preserve ecosystem balance since this exponential growth might, if unchecked, result in a very huge insect population.

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The polynomial without fractions is 2x^4 + x^3 + 7x^2 + 4x - 4.

To make the polynomial contain only whole numbers, we need to find the least common denominator (LCD) of the fractions and multiply each term by the LCD.

The LCD of the fractions 1/2 and 7/2 is 2.

So, we multiply each term by 2 to get rid of the fractions:

2(x^4) + 2(1/2 x^3) + 2(7/2 x^2) + 2(2x) + 2(-2)

Simplifying the terms gives us:

2x^4 + x^3 + 7x^2 + 4x - 4

Therefore, the polynomial without fractions is 2x^4 + x^3 + 7x^2 + 4x - 4.

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The standard form for the quadratic equation written in vertex form y = 2(x - 2)² + 5 is y = 2x² - 8x + 13.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

To change the equation y = 2(x - 2)² + 5 from vertex form to standard form, we need to expand the squared term and simplify the expression.

Here are the steps -

Start with the vertex form: y = 2(x - 2)² + 5.

Expand the squared term using the formula (a - b)² = a² - 2ab + b².

In this case, a = x and b = 2, so we have -

y = 2(x - 2)(x - 2) + 5

y = 2(x² - 4x + 4) + 5

Multiply the coefficient 2 by each term inside the parentheses -

y = 2x² - 8x + 8 + 5

Combine the constant terms -

y = 2x² - 8x + 13

This is the standard form of the quadratic equation.

In standard form, the quadratic equation is written as y = ax² + bx + c, where a, b, and c are constants.

In this case, a = 2, b = -8, and c = 13.

Therefore, the standard form is y = 2x² - 8x + 13.

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The situations that best represent the scenario shown in the graph of the quadratic functions, y = x² and y = x² + 3 include the following:

B. "From x = -2 to x = 0, the average rate of change for both functions is negative."

C. "For the quadratic function, y = x² + 3, the coordinate (2, 7) is a solution to the equation of the function."

D. "The quadratic function, y = x², has an x-intercept at the origin."

In Mathematics, the x-intercept of the graph of any function simply refers to the point at which the graph of a function crosses or touches the x-coordinate (x-axis) and the y-value or value of "y" is equal to zero (0).

In this context, we can logically deduce that the x-intercepts of the graph of the given equation y = x² is at the origin:

x = (0, 0)

For the the coordinate (2, 7), we would evaluate the quadratic function, y = x² + 3 as follows;

7 = 2² + 3

7 = 4 + 3

7 = 7 (True).

By critically observing the graph of both functions, we can logically deduce that their average rate of change is negative from x = -2 to x = 0.

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Answer:

Step-by-step explanation:

Answer:Price of the table yesterday is x.

Price of the table today is $513.

$513 is 76% of yesterday's price x. 76% can be also written down as 76 divided by 100 (percentage) or 76/100 = 0.76.

Formula we can set up now is: x= 513 / 0.76 (To get the price of yersterday's table we need to divide the price of today's table with percentage in decimal form).

x= 675

The price of yesterday's table was $675 since 76% of that price (675 times 0.76) equals 513 dollars.

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

Step-by-step explanation: There are 4 primes. So the probability for the first draw is 4/9. Since the card is not replaced, the second probability is 3/8. 3/8 * 4/9 is 12/72, which simplifies into 1/6.

a)

i)  The function is not harmonic.

ii). The function is harmonic.

b) v is also harmonic in D

a) A function is harmonic if it satisfies the Laplace equation:

∂²u/∂x² + ∂²u/∂y² = 0

i) For the function u = x² + 2x - 4², we can take the partial derivatives with respect to x and y:

∂u/∂x = 2x + 2

∂u/∂y = 0

∂²u/∂x² = 2

∂²u/∂y² = 0

Plugging these into the Laplace equation, we get:

2 + 0 = 0

This is not true, so the function is not harmonic.

ii) For the function u = 2e* cos(y), we can take the partial derivatives with respect to x and y:

∂u/∂x = 0

∂u/∂y = -2e* sin(y)

∂²u/∂x² = 0

∂²u/∂y² = -2e* cos(y)

Plugging these into the Laplace equation, we get:

0 + (-2e* cos(y)) = 0

-2e* cos(y) = 0

This is true for all values of y, so the function is harmonic.

The harmonic conjugate of a function u(x,y) is a function v(x,y) such that f(z) = u(x,y) + i*v(x,y) is analytic. To find the harmonic conjugate of u = 2e* cos(y), we can use the Cauchy-Riemann equations:

∂u/∂x = ∂v/∂y

∂u/∂y = -∂v/∂x

Plugging in the partial derivatives of u, we get:

0 = ∂v/∂y

-2e* sin(y) = -∂v/∂x

Integrating both equations with respect to x and y, we get:

v = C₁

v = 2e* cos(y) + C₂

Setting these equal to each other and solving for v, we get:

v = 2e* cos(y) + C

So the harmonic conjugate of u = 2e* cos(y) is v = 2e* cos(y) + C, where C is a constant.

b) If u is the harmonic conjugate of v in a domain D, then f(z) = u(x,y) + i*v(x,y) is analytic in D. This means that f(z) satisfies the Cauchy-Riemann equations:

∂u/∂x = ∂v/∂y

∂u/∂y = -∂v/∂x

If we take the partial derivatives of these equations with respect to x and y, we get:

∂²u/∂x² = ∂²v/∂x∂y

∂²u/∂x∂y = -∂²v/∂x²

∂²u/∂y∂x = -∂²v/∂y²

∂²u/∂y² = ∂²v/∂y∂x

Adding the first and last equations, we get:

∂²u/∂x² + ∂²u/∂y² = ∂²v/∂x∂y + ∂²v/∂y∂x

Since the mixed partial derivatives are equal, this simplifies to:

∂²u/∂x² + ∂²u/∂y² = 0

So u is harmonic in D. Similarly, we can add the second and third equations to get:

∂²v/∂x² + ∂²v/∂y² = 0

So v is also harmonic in D. Therefore, if u is the harmonic conjugate of v in a domain D, then both u and v are harmonic in D.

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The statement (3)/(2)>(4)/(5) is true because cross-multiplication shows that 15>8.

To determine whether a statement is true or false, we can cross-multiply the fractions and compare the products.

In this case, (3)*(5)>(2)*(4), which simplifies to 15>8. Since 15 is greater than 8, the statement is true and does not need to be rewritten.

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Answer:

55%

Step-by-step explanation:

When you have a question that asks you about a percentage and it gives you a fraction, most of the time you just have to divide the numbers. In this case you will do 11/20=0.55 and you will change the decimal to a percentage. Which will be 55%.

The domains of each function and each composite function are as follows:

domain of f: (-∞, ∞)
domain of g: (-∞, ∞)
domain of f ∘ g: (-∞, ∞)
domain of g ∘ f: (-∞, ∞)

To find the composite functions f ∘ g and g ∘ f, we need to substitute the function g(x) into f(x) for f ∘ g, and the function f(x) into g(x) for g ∘ f.

(a) f ∘ g = f(g(x)) = f(x3 + 1) = 3(x3 + 1) − 8 = 3x3 + 3 − 8 = 3x3 − 5

(b) g ∘ f = g(f(x)) = g(3x − 8) = (3x − 8)3 + 1 = 27x3 − 72x2 + 64x − 511

The domain of a function is the set of all values of x for which the function is defined.

The domain of f is all real numbers, since there are no restrictions on the values of x. So the domain of f is (-∞, ∞).

The domain of g is also all real numbers, since there are no restrictions on the values of x. So the domain of g is (-∞, ∞).

The domain of f ∘ g is the same as the domain of g, since the values of x are first substituted into g(x) before being substituted into f(x). So the domain of f ∘ g is (-∞, ∞).

The domain of g ∘ f is the same as the domain of f, since the values of x are first substituted into f(x) before being substituted into g(x). So the domain of g ∘ f is (-∞, ∞).

Therefore, the domains of each function and each composite function are as follows:

domain of f: (-∞, ∞)
domain of g: (-∞, ∞)
domain of f ∘ g: (-∞, ∞)
domain of g ∘ f: (-∞, ∞)

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Since the two hexagons are similar, their corresponding sides are in the same ratio as the scale factor.

Let x be the length of a side of the smaller hexagon, then the corresponding length of a side of the larger hexagon can be expressed as (3/7)x.

The area of a hexagon can be calculated using the formula: A = (3√3/2)s², where s is the length of a side.

Since the area of the smaller hexagon is 18 m², we can solve for x as follows:

18 = (3√3/2)x²

x² = 12/√3

x = 2√3

Now we can calculate the area of the larger hexagon:

Area of the larger hexagon = (3√3/2)(3/7x)² = (3√3/2)(3/7(2√3))² = 54/49 m²

Finally, we can calculate the volume of the larger hexagon, assuming it is a regular hexagonal prism:

Volume of the larger hexagon = Area of hexagon x Height

The height of the hexagonal prism is the same as the length of the side of the larger hexagon, which is (3/7)x:

Volume of the larger hexagon = (54/49) x (3/7)x = 54/343 x² ≈ 0.212 x²

Substituting the value of x, we get:

Volume of the larger hexagon ≈ 0.212 x (2√3)² = 1.272 m³

Therefore, the volume of the larger hexagon is approximately 1.272 m³.

Well, I'm not sure if it's correct but I got 42.

I got this by doing something along the lines of:

1) 18/x = 3/7

2) Cross multiply

3) 3x = 126

4) Divide both sides by 3

5) x = 42

A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.

A graph of the system of inequalities is shown on the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:

2x + 3y = 192.

Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;

x + y = 72

For the constraints, we have the following system of linear inequalities:

x ≥ 0.

y ≥ 0.

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The fraction of candies left behind is 3/7.

To find the fraction of candies left behind, we need to divide the total number of candies by the number of candies in each pack and find the remainder. This remainder will be the numerator of the fraction and the number of candies in each pack will be the denominator.

Step 1: Divide the total number of candies by the number of candies in each pack: 3242 ÷ 7 = 463 with a remainder of 3

Step 2: The remainder, 3, is the numerator of the fraction and the number of candies in each pack, 7, is the denominator. So the fraction of candies left behind is 3/7.

The fraction of candies left behind is 3/7.

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Answer: I believe its A.

Step-by-step explanation:

We have proven that in given triangle ∠BACB is congruent to ∠DECD, as required.

Similarity of triangles refers to the property of having the same shape but not necessarily the same size. Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.

To prove: ∠BACB = ∠DECD

We know that, BD ∥ AE and C is the midpoint of AE.

Therefore, triangle ACE and triangle BCD are similar by the Converse of the Corresponding Angles Postulate. Hence, we have:

∠CAB = ∠CBD .... (1) (corresponding angles)

∠CAE = ∠CDB .... (2) (corresponding angles)

Also, we know that in triangle ACE, angles 3 and 4 are alternate interior angles formed by a transversal. Therefore, angles 3 and 4 are congruent. Similarly, in triangle BCD, angles 1 and 2 are congruent.

Therefore, we can write:

∠ACB = ∠BCD .... (3) (angles of similar triangles)

Adding equations (1) and (3), we get:

∠BACB = ∠DECD

Hence, we have proven that ∠BACB is congruent to ∠DECD, as required.

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The simplified result of is (6m^(2) + 13m - 15) / (m^(2) + 9m + 18).

Step 1: Flip the second fraction:

(mn)/(m^(2)+9m+18) ÷ (m)/(6m^(2)+13m-15) = (mn)/(m^(2)+9m+18) × (6m^(2)+13m-15)/(m)

Step 2: Change the division sign to multiplication:

(mn)/(m^(2)+9m+18) × (6m^(2)+13m-15)/(m)

Step 3: Multiply the numerators and denominators:

= (mn)(6m^(2)+13m-15) / (m^(2)+9m+18)(m)

Step 4: Simplify the result:

= (6m^(3)n + 13m^(2)n - 15mn) / (m^(3) + 9m^(2) + 18m)

= (mn)(6m^(2) + 13m - 15) / (m)(m^(2) + 9m + 18)

= (6m^(2) + 13m - 15) / (m^(2) + 9m + 18)

So the simplified result is (6m^(2) + 13m - 15) / (m^(2) + 9m + 18).

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The expected value of the game in which you have a (1/20) chance of winning  is $1.50.  The probability of a student scoring between 75 and 89 is 0.5536. The probability of a student scoring above 85 is 0.4562.

1. To find the expected value of the game, we need to multiply the probability of each outcome by the value of that outcome and then add them together.

E(X) = (1/20)($300 + $15) + (19/20)(-$15)

E(X) = $315/20 - $285/20

E(X) = $30/20

E(X) = $1.50

So the expected value of the game is $1.50.

2. To find the probability of a student scoring between 75 and 89, we need to use the z-score formula:

z = (x - μ)/σ

For x = 75, z = (75 - 84)/9 = -1

For x = 89, z = (89 - 84)/9 = 0.56

Using a z-table, we can find the probability of a student scoring between these two z-scores:

P(-1 < z < 0.56) = P(z < 0.56) - P(z < -1)

P(-1 < z < 0.56) = 0.7123 - 0.1587

P(-1 < z < 0.56) = 0.5536

So the probability of a student scoring between 75 and 89 is 0.5536.

3. To find the probability of a student scoring above 85, we need to use the z-score formula:

z = (x - μ)/σ

For x = 85, z = (85 - 84)/9 = 0.11

Using a z-table, we can find the probability of a student scoring above this z-score:

P(z > 0.11) = 1 - P(z < 0.11)

P(z > 0.11) = 1 - 0.5438

P(z > 0.11) = 0.4562

So the probability of a student scoring above 85 is 0.4562.

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1) The sale price on the painting is $1,235.

2) The regular price of the mechanic's tool set is $340.

3) The regular price of the battery is $111.84.

1) To find the sale price on a painting that has a regular price of $1,900 and is on sale for 35% off the regular price, we can use the formula: sale price = regular price - (regular price * discount rate).
In this case, the sale price would be $1,900 - ($1,900 * 0.35) = $1,900 - $665 = $1,235.
So the sale price of the painting is $1,235.

2) To find the regular price of a mechanic's tool set that is on sale for $204 after a markdown of 40% off the regular price, we can use the formula: regular price = sale price / (1 - discount rate).
In this case, the regular price would be $204 / (1 - 0.40) = $204 / 0.60 = $340.
So the regular price of the mechanic's tool set is $340.

3) To find the regular price of a battery that has a discount price of $85 and is on sale for 24% off the regular price, we can use the formula: regular price = sale price / (1 - discount rate).
In this case, the regular price would be $85 / (1 - 0.24) = $85 / 0.76 = $111.84.
So the regular price of the battery is $111.84.

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Javier has 90 more uncommon cards than rare cards.

To find out how many more uncommon cards Javier has than rare cards, we need to multiply the number of packs he has by the number of each type of card in a pack, and then subtract the number of rare cards from the number of uncommon cards. We can do this with the following equation:

Uncommon cards - Rare cards = Difference

First, we'll multiply the number of packs by the number of each type of card:

45 packs × 3 uncommon cards = 135 uncommon cards
45 packs × 1 rare card = 45 rare cards

Now we'll subtract the number of rare cards from the number of uncommon cards to find the difference:

135 uncommon cards - 45 rare cards = 90

So, the number of uncommon cards is 90 more than the rare cards.

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Answer:

We do not have enough information to find the exact value of f(2.5) without additional assumptions about the nature of the exponential function. However, we can make an estimate using the given data and the properties of exponential functions.

First, we can write the general form of an exponential function as:

f(x) = a * b^x

where a is the initial value or y-intercept, and b is the base or growth factor. We can use the two given data points to set up a system of equations and solve for a and b:

f(-1) = a * b^(-1) = 18

f(5) = a * b^5 = 75

Dividing the second equation by the first equation, we get:

f(5) / f(-1) = (a * b^5) / (a * b^(-1)) = b^6 = 75 / 18 = 25 / 6

Taking the sixth root of both sides, we get:

b = (25 / 6)^(1/6) ≈ 1.472

Substituting this value of b into the first equation, we get:

a = f(-1) / b^(-1) = 18 / 1.472 ≈ 12.223

Therefore, we have the exponential function:

f(x) ≈ 12.223 * 1.472^x

Using this function, we can estimate the value of f(2.5) as:

f(2.5) ≈ 12.223 * 1.472^(2.5) ≈ 34.311

Note that this is only an estimate, and the exact value of f(2.5) may be different depending on the specific nature of the exponential function.

Answer: The function to express the total amount of money Martin will make as a function of the number of calls he makes is:

Total Money = (Number of hours worked x Base pay per hour) + (Bonus pay per hour x Number of bonus calls)

Where:

Number of hours worked = 4

Base pay per hour = $75 / 4 = $18.75 (since he works for 4 hours every day and receives $75)

Bonus pay per hour = ($5.50 x (Number of bonus calls)) / 4 (since he works for 4 hours every day and receives a bonus of $5.50 per call over 35 in one hour, which is equivalent to $5.50 / 4 per call)

Number of bonus calls = (Total calls - (Number of hours worked x Baseline calls per hour))

Using this formula, we can calculate how much money Martin will make for the day if he makes a total of 45 calls every hour:

Number of bonus calls = (45 - (4 x 35)) = 5

Bonus pay per hour = ($5.50 x 5) / 4 = $6.875

Total Money = (4 x $18.75) + (4 x $6.875) = $75 + $27.50 = $102.50

Therefore, if Martin makes a total of 45 calls every hour, he will make $102.50 for the day.

Step-by-step explanation:

The 9th term of the geometric sequence 3, -15, 75, ... is 1171875.

The given sequence is 3, -15, 75, ... We can see that each term is obtained by multiplying the previous term by -5. Therefore, the common ratio is -5.

We can use the formula for the nth term of a geometric sequence to find the 9th term. The formula is given by:

aₙ = a₁ x rⁿ⁻¹

where,

aₙ = nth term of the sequence

a₁ = first term of the sequence

r = common ratio of the sequence

n = index of the term we want to find

Using the given sequence, we have:

a₁ = 3 (first term)

r = -5 (common ratio)

To find the 9th term, we substitute n=9 into the formula:

a₉ = a₁ x r⁹⁻¹

a₉ = 3 x (-5)⁸

a₉ = 3 x 390625

a₉ = 1171875

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The main of the given function f(x) is all real numbers except x=-4.

To find the main, we need to find the roots of the function. That is, we need to find out the values of x for which the value of f(x) is equal to 0.


Solving for the roots, we get the following equation:
8x2-9x+1=0


Solving this equation using the quadratic formula yields:
x = (-9 ± √73)/16


Therefore, the roots of the equation are:
x = 0.41 and -4.41


Since the only root which belongs to all real numbers is x = -4, it is the main of the given function.

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