(a) Find three positive numbers whose product is 27 and whose sum is minimal. (Enter your answers as a comma-separated list.)
(b) Find three positive numbers whose sum is 27 and whose product is maximal.

We will use the growth rate formula shown below:

Where

F is the future amount

P is the initial amount

r is the rate of growth

n is the number of years

Given,

P = 300

F = 500 [after 4 years]

n = 4

We will have to find r. Substituting, we get:

The growth rate is r = 0.14 [rounded]

In percent, it is:

0.14 * 100 = 14%

The spherical coordinates for each are a)  (√171, \(\pi\)/3, 0.962) and (√32, -\(\pi\)/2, 2.177).

To convert from rectangular coordinates (x, y, z) to spherical coordinates (ρ, θ, Φ), we use the following formulas:

ρ = √(x² + y² + z²)

θ = arctan(y/x)

Φ = arccos(z/ρ)

(a) For the point (3, 3√3, 6√3), we have:

ρ = √(3² + (3√3)² + (6√3)²) = √(63 + 108) = √171

θ = arctan(3√3/3) = \(\pi\)/3

Ф = arccos(6√3/√171) ≈ 0.962

So the spherical coordinates are (ρ, θ, Ф) ≈ (√171, \(\pi\)/3, 0.962).

(b) For the point (0, -4, -4), we have:

ρ = √(0² + (-4)² + (-4)²) = √32

θ = arctan(-4/0) = -\(\pi\)/2 (Note that x = 0 and y = -4, so we are in the third quadrant where arctan is negative infinity or -\(\pi\)/2.)

Ф = arccos(-4/√32) ≈ 2.177

So the spherical coordinates are (ρ, θ, Ф) ≈ (√32, -\(\pi\)/2, 2.177).

The spherical coordinates for each are a)  (√171, \(\pi\)/3, 0.962) and (√32, -\(\pi\)/2, 2.177).

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Answer:

There are 18 bananas

Step-by-step explanation:

6 x 3 = 18

18 bananas.

Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

La fórmula para calcular la longitud de una circunferencia es:

Longitud = π * Diámetro

En este caso, si el diámetro es de 32 cm, podemos calcular la longitud de la siguiente manera:

Longitud = π * 32 cm

El valor de π (pi) es una constante que representa la relación entre la circunferencia de un círculo y su diámetro. Usualmente, se aproxima a 3.14159.

Por lo tanto, la longitud de la circunferencia sería:

Longitud ≈ 3.14159 * 32 cm

Calculando el resultado:

Longitud ≈ 100.53096 cm

Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

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The given rational expression is improper because the degree of the numerator is greater than or equal to the degree of the denominator.

A rational expression is considered proper when the degree of the numerator is less than the degree of the denominator. In this case, the numerator of the expression is a polynomial of degree 2 (7x² + 8x - 2), and the denominator is a polynomial of degree 2 (x² - 25).

Since the degree of the numerator is equal to the degree of the denominator, the given rational expression is improper.

To rewrite the improper expression as the sum of a polynomial and a proper rational expression, we can perform polynomial division. Dividing the numerator (7x² + 8x - 2) by the denominator (x² - 25), we can obtain a polynomial quotient and a proper rational expression. However, without specifying the desired form of the rewritten expression, I am unable to provide the exact answer.

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Answer:

answer is 55° ..........

Answer:

The building itself is 1,250 feet and 102 stories high.

Uhm what class is this for

Arithmetic operations are inappropriate for the nominal scale, but they are applicable to both the ratio and interval scales. C is correct answer

Arithmetic operations are inappropriate for the nominal scale (option d).

The nominal scale is the lowest level of measurement, where data is categorized into distinct categories or labels without any inherent order or numerical value. Examples of nominal scale data include gender, nationality, or categories like colors.

Arithmetic operations, such as addition, subtraction, multiplication, or division, are not meaningful or applicable to nominal scale data. Nominal data only provide information about the frequency or presence of categories, and the categories themselves do not possess quantitative values that can be manipulated mathematically.

For instance, consider a nominal variable like "color" with categories of "red," "blue," and "green." It does not make sense to add or divide the colors or perform any arithmetic operations on them. The categories are merely labels and do not represent numerical values or quantities.

On the other hand, arithmetic operations are appropriate for both the ratio scale (option a) and the interval scale (option b).

The interval scale represents data where the differences between values are meaningful, but there is no true zero point. Examples of interval scale data include temperature measured in Celsius or Fahrenheit. Arithmetic operations such as addition and subtraction can be applied to interval scale data to calculate differences or changes.

The ratio scale represents data that have a true zero point, and arithmetic operations can be meaningfully performed. Examples of ratio scale data include height, weight, or time. Arithmetic operations such as addition, subtraction, multiplication, and division can be used on ratio scale data to calculate ratios, proportions, or differences.

In summary, arithmetic operations are inappropriate for the nominal scale, but they are applicable to both the ratio and interval scales.

C is correct answer

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The probability of finding a sample mean (Y¯) of 1.5 ounces or more when the liquor tax has no impact on consumption (µ = 0). To determine this probability, we would use the Central Limit Theorem and the z-score formula.

Since the population mean (µ) is 0, we'll need to know the population standard deviation (σ) and the sample size (n) to proceed. Without these values, it's impossible to provide an exact probability. However, I can explain the general process.

First, you would calculate the standard error (SE) using the formula SE = σ / √n. Next, you would find the z-score, which is the difference between the sample mean (Y¯) and the population mean (µ) divided by the standard error: z = (Y¯ - µ) / SE.

Once you have the z-score, you can look it up in a standard normal distribution table or use a calculator to find the probability associated with it. In this case, you're looking for the probability of finding a sample mean of 1.5 ounces or more, which corresponds to the area to the right of the z-score in the distribution.

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Answer: Credit cards

Step-by-step explanation:

(you can search it up as well)

Answer:9 hours

Step-by-step explanation:

when rounding to the nearest tenth, you use the number behind the decimal to determine which way you go. if it's below five(.1, .2, .3, .4) then you go down, if its above five(.6, .7, .8, .9) you would up. in this case, it's above fine, so we round up, which would make the total hours Andreas spent on the project 9 hours.

l = a x w

Hes trying to find lenth so the equal we be getting a and w's attention

The number of shirts that the debate club need to sell on order to break even would be = 17 T-shirts.

The total amount of money that the company producing the T-shirts will charge the club = $250

The total charge contains the following:

The amount to sell each T-Shirt. = $15 each.

The number of T-shirts that can be sold = 250/15 = 16.6

That is approximately = 17 T-shirts.

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Answer:

Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer

Option A, B and C lines on the drawing would be greater than 12 meters in real life.

A scale drawing is an object that has been enlarged.

By multiplying each length by a scale factor, an expansion alters the size of an object, making it larger or smaller.

A ratio is typically used to describe a drawing's scale.

4cm = 6 meters

so, 1 cm = 6/4 mt = 1.5mt

a) 6cm = 6×1.5 mt = 9mt

b) 10 cm = 10×1.5 mt = 15mt

c) 12 cm = 12×1.5mt = 18mt

d) 16 cm = 16×1.5mt = 24mt

Option A, B and C lines on the drawing would be greater than 12 meters in real life.

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The distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

The time, t = π / 2 sec,

Calculate the distance by using the formula given below,

\(Distance = r\times time\)

So, for distance, a = 1 × π / 2 =  π / 2

for distance, b = 1 × π =  π

for distance, c = 1 × 3 π / 2 =  3 π / 2

Therefore, the distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

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The driving time along this stretch was reduced by 36% for a person who always drives at the speed limit.

To calculate the percent reduction in driving time along the stretch, we need to consider the effects of both the distance decrease and the speed increase.

First, let's assume the original distance of the stretch was D. After the reconstruction, the distance is now 0.8D (since it was decreased by 20%).

Next, let's assume the original speed limit was S. After the reconstruction, the speed limit is now 1.25S (since it was increased by 25%).

To calculate the original driving time along the stretch, we would use the formula: time = distance / speed. So the original driving time would be D/S.

After the reconstruction, the driving time would be (0.8D) / (1.25S) = 0.64D/S.

To calculate the percent reduction in driving time, we can use the formula: (original time - new time) / original time * 100%.

Plugging in the values we calculated, we get:

(original time - new time) / original time * 100% = (D/S - 0.64D/S) / (D/S) * 100% = 36%.

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To find the length of the curve y = ln(cos(x)) from 0 to π/3, we can use the arc length formula for a curve defined by a function y = f(x):

L = ∫[a to b] √(1 + (f'(x))²) dx.

In this case, the function is y = ln(cos(x)). Let's first find the derivative:

y' = d/dx ln(cos(x)).

Using the chain rule, we have:

y' = -tan(x).

Now we can calculate the arc length:

L = ∫[0 to π/3] √(1 + (-tan(x))²) dx.

Simplifying the integrand, we have:

L = ∫[0 to π/3] √(1 + tan²(x)) dx.

Using the trigonometric identity tan²(x) + 1 = sec²(x), we can rewrite the integrand as:

L = ∫[0 to π/3] √(sec²(x)) dx.

Taking the square root of sec²(x), we have:

L = ∫[0 to π/3] sec(x) dx.

Integrating sec(x), we get:

L = ln|sec(x) + tan(x)| [0 to π/3].

Evaluating the integral at the upper and lower limits, we have:

L = ln|sec(π/3) + tan(π/3)| - ln|sec(0) + tan(0)|.

Simplifying further, we have:

L = ln|2 + √3| - ln|1 + 0|.

Since ln|1| = 0, the second term on the right-hand side becomes 0, and we are left with:

L = ln|2 + √3|.

Therefore, the length of the curve y = ln(cos(x)) from 0 to π/3 is ln|2 + √3|.

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After answering the given query, we can state that We know that equation (-12 + 3m) must be negative because cos   0, which means that 3m  12 or m  4. As a result, choice A) m  4 is correct.

The equals sign (=) is used in mathematical equations to denote equality between two assertions. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in mathematics. For instance, the equal sign places a space between the integers in the equation 3x + 5 = 14. The relationship between the two lines on either side of a character can be expressed mathematically. Frequently, the logo and the specific component of software are the same. such as, for example, 2x - 4 = 2.

Between two vectors a and b, the dot product is

A = B given by |a| |b| cos

where  is the angle between the vectors a and b, and |a| and |b| are their relative magnitudes. We are aware that cos   0 because we are aware that the angle between vectors a and b is acute

a · b = (-3)(4) + m(3) = -12 + 3m

The size of the vector an is:

|a| = √((-3)^2 + m^2) = √(9 + m^2)

The strength of the vector b is:

|b| = √(4^2 + 3^2) = 5

We can now determine the cos using the dot product formula:

cos = (a b) / (|a | |b|) = (-12 + 3m) / (5 (9 + m2)

We know that (-12 + 3m) must be negative because cos   0, which means that 3m  12 or m  4.

As a result, choice A) m  4 is correct.

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The correct option is c. 33%.

The job rate of industry’s percent increase from 2003 to 2013 is 33%.

The percentage increase would be the change between the final and initial values given as a percentage. We need the initial value and the enhanced (new) value to calculate the percentage.

In other words, % growth is a measurement of percent change that indicates the amount by which a quantity increases in magnitude, strength, or value.

If the % rise is negative, we might conclude that there is corresponding proportion reduction. Let's look at the percentage growth calculation now.

Now, according to the question;

Total Number of years = 10 years

Total number of new jobs created = 2.65 thousand x 10

                                                         = 26.5 thousand

                                                         = 26,500

Number of jobs in 2013 = 78,900 + 26,500

                                       = 105,400

Percentage increase = (105,400 - 78,900)/78,900 x 100

                                   = 26,500/78,900 x 100

                                   = 0.3359 x 100

                                    = 33.59%

Percentage increase = 33% (approx)

Therefore, the percentage increases in the job between 2003 and 2013 is 33%.

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Answer:

C

Step-by-step explanation:

The given function is f(x) = 2(3x) = 6x.

The domain of the function is all real numbers since there are no restrictions on the input x. Therefore, the correct answer is:

Domain: (-∞, ∞)

To find the range, we can consider the fact that the function is a linear function with a positive slope of 6. This means that the output values increase as the input values increase.

The lowest possible output value occurs when x = 0, which gives f(0) = 0. As x increases, the output values increase without bound. Therefore, the range of the function is:

Range: (0, ∞)

So, the correct answer is:

Domain: (-∞, ∞)

Range: (0, ∞)

Answer:

\(x=-\frac{19}{2}\)

Step-by-step explanation:

hope that was the answer you were looking for :/

Answer:

x = -19/2

Step-by-step explanation:

\(-2x+5=24\)

Then subtract 5 from 24

\(-2x=19\)

Then divide -2 by 19 to get:

\(x = -\frac{19}{2}\)

Hope this helps!

Answer:

56 degrees

Step-by-step explanation:

If you look at the m<KLN you can see that it is an acute angle. So, with this being said you have to know that the measure KLN is going to be less than 90 degrees. So you would subtract 180 and 124 and you would get 56 degrees.

I hope this helps :)

Answer:

0/21 or 0%

Step-by-step explanation:

There are no purple bows and 21 other bows.

Answer:

0/21 or 0%

Step-by-step explanation:

A circle's arc length can be determined from its radius and central angle using the formula Length of an Arc = r, where is in radians.

Length of an Arc = r, where is in radians, is a formula that may be used to calculate the arc length of a circle given its radius and central angle. A circle's length is equal to (r/180)r, where r is the radius and is the angle. The length of the arc on a circle of radius r intercepted by a central angle is S = r.

Multiply the radius (6 in) by the central angle's measurement in radians to determine the length of the arc. Remember that the angle must be expressed in radians in order to employ the calculation s = r.

Assuming that is measured in radians, the formula for the length s of the arc that is intercepted on a circle with radius r by a central angle is: s = r.

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The amplitude of the trigonometric function is the distance from the middle line (or axis) to the highest point on the graph, which is 4 in this case. The period is the distance between two consecutive peaks (or troughs) on the graph, which is 2π in this case.

Therefore, the correct answer is D) 4;2π.
The graph of a trigonometric function: Its amplitude is _ and its period is _. Based on the provided options, the correct answer is D) 4;2π. This means that the amplitude of the trigonometric function is 4, and its period is 2π.

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Answer:

I think D but im bad at 5hat stuff

Step-by-step explanation: