Which number is a rational number?
A. \sqrt(15)

B. 2.6457513110...

C. 17.156


D. \root(3)(85)

180 Red folders, 192 Blue folders, and 372 total folders.

Step-by-step explanation:

I'm not sure if I'm doing this correctly but it seems fitting to me, so basically, I multiplied 5x36 to get 180, then multiplied 6x32 to get 192. Next, I added 180+192 to get 372 total folders.

The given expression is (8+6i) - (8-6i). The terms with "8" cancel each other out, leaving us with 6i + 6i Combining like terms, we get 12i. The difference between (8+6i) and (8-6i) is 12i.

The given expression is (8+6i) - (8-6i).

To find the difference, we subtract the second complex number from the first.
(8+6i) - (8-6i) can be simplified as follows:
8 + 6i - 8 + 6i
The terms with "8" cancel each other out, leaving us with:
6i + 6i
Combining like terms, we get:
12i
Therefore, the difference between (8+6i) and (8-6i) is 12i.

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Yes, the probability assignments given to the four outcomes of an experiment are valid. Probabilities are calculated subjectively, and the decision maker assigned probabilities to the four outcomes of the experiment, which is perfectly acceptable.

Probability is a numerical measure of the likelihood of an event occurring, ranging from 0 to 1.

An event that is certain to happen has a probability of 1, while an event that is impossible has a probability of 0. The probability of any other event lies somewhere between 0 and 1.

Probability assignments, which are subjectively determined probabilities, are valid as long as they meet the following criteria:

In this case, the probability assignments are valid because they meet both of the above criteria. The probabilities assigned are between 0 and 1, and when the probabilities are added together, the sum is 1.

Therefore, the given probability assignments are valid.

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Answer:

x=-6

Step-by-step explanation:

-5x+1=31

-5x=30

x=-6

Answer:

C

Step-by-step explanation:

5-5-5-5-5-5+5+5+5+5+5+5+5+5+5+5 = 35

The Laplace domain equation X(s) is found to be X(s) = (s + 2)/(s^2 + 5s + 6). The time domain equation x(t) can be obtained by applying the inverse Laplace transform to X(s), resulting in x(t) = e^(-t) - e^(-2t).

Given the Laplace domain equation X(s), we need to substitute the given parameters and find its expression in terms of s. The equation provided is X(s) = (s + 2)/(s^2 + 5s + 6).

To obtain the time domain equation x(t), we need to apply the inverse Laplace transform to X(s). The inverse Laplace transform of X(s) will give us x(t) in terms of t.

Applying the inverse Laplace transform to X(s) involves finding the inverse transform of each term separately. The inverse Laplace transform of (s + 2) is simply 1, representing the unit step function. The inverse Laplace transform of (s^2 + 5s + 6) is e^(-t) - e^(-2t), which can be obtained through partial fraction decomposition.

Therefore, the time domain equation x(t) is given by x(t) = e^(-t) - e^(-2t), where t represents time.

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Answer: 7 and 8

Step-by-step explanation:

7 squared is 49 and 8 squared is 64. 60 is in between those numbers so that is the answer! Pls mark brain linear of this helped!

Answer:

-3/2 = -1.5

Step-by-step explanation:

u can use wolfram alpha for stuff like that

A parametric representation using spherical-like coordinates for the upper half of the ellipsoid 4(x₁)² + 9y² + 36z² is given by:

x = 2r cosθ sinφ

y = 3r sinθ sinφ

z = 6r cosφ, where 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π/2.

We want to find a parametric representation for the upper half of the ellipsoid 4(x₁)² + 9y² + 36z² = 36. To do this, we can use spherical-like coordinates, which are similar to spherical coordinates but with an additional parameter to account for the asymmetry of the ellipsoid.

We start by assuming that the ellipsoid is centered at the origin, so we can write it as:

(x₁/3)² + y²/4 + z²/1 = 1

We can then express x, y, and z in terms of the parameters r, θ, and φ:

x = r cosθ sinφ

y = r sinθ sinφ

z = r cosφ

We can use these equations to find r, θ, and φ in terms of x, y, and z, and substitute into the equation of the ellipsoid to obtain:

[(x₁/3)² + (y/2)² + z²]/1 = 1

Simplifying, we get:

r² = 36/(4 cos²θ sin²φ + 9 sin²θ sin²φ + 36 cos²φ)

We can then use the equations for x, y, and z in terms of r, θ, and φ to obtain the desired parametric representation:

x = 2r cosθ sinφ

y = 3r sinθ sinφ

z = 6r cosφ

We restrict φ to the range 0 ≤ φ ≤ π/2 to obtain only the upper half of the ellipsoid. The range of θ is 0 ≤ θ ≤ 2π, which allows us to cover the entire surface of the ellipsoid.

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The benefit-cost ratio (B/C) for Option A is 0.9085, while for Option B it is 0.9553. Since a B/C ratio greater than 1 indicates a favorable investment, Option B is recommended as it has a higher B/C ratio. Option A is recommended based on the B/C analysis.

Explanation:
To calculate the benefit-cost ratio (B/C) for both options, we need to consider the cash flow diagrams (CFDs) and the given data:
Option A:
First cost = $500
Annual revenue = $138.70
Option B:
First cost = $200
Annual revenue = $58.30

Step-by-step calculation:
1. Calculate the net present value (NPV) for each option:
NPV_A = Annual revenue * (1 - (1 + MARR)^(-life span)) / MARR
NPV_A = $138.70 * (1 - (1 + 0.10)^(-5)) / 0.10 = $454.26
NPV_B = $58.30 * (1 - (1 + 0.10)^(-5)) / 0.10 = $191.06
2. Calculate the benefit-cost ratio (B/C) for each option:
B/C_A = NPV_A / First cost_A
B/C_A = $454.26 / $500 = 0.9085
B/C_B = NPV_B / First cost_B
B/C_B = $191.06 / $200 = 0.9553

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Answer:

  2.6

Step-by-step explanation:

A is after the 6th of 10 spaces between 2 and 3. It has the value 2 +6/10 = 2.6.

Step-by-step explanation:

\( f(x) = - 3 {x}^{2} + 9x - 2\)

A) f(-2) + f(1) = -32 + 4 = -28

B) f(-2) - f(1) = -32 - 4 = -36

The bag weight at the 84th percentile of the distribution is 9.17 ounces. This means that 84% of the bags will weigh less than 9.17 ounces, and 16% of the bags will weigh more than 9.17 ounces.

The 84th percentile is the point on the distribution where 84% of the data is below it and 16% of the data is above it. In this case, the 84th percentile is equal to the mean plus 1 standard deviation, or 9.12 + 0.05 = 9.17 ounces.

To calculate the 84th percentile, we can use the following formula:

percentile = mean + z * standard_deviation

where:

percentile is the desired percentile, in this case 84

mean is the average weight of the bags, 9.12 ounces

z is the z-score for the 84th percentile, which is 0.84

standard_deviation is the standard deviation of the weights, 0.05 ounces

Plugging these values into the formula, we get:

percentile = 9.12 + 0.84 * 0.05 = 9.17 ounces

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Answer: 52

Step-by-step explanation: 13 x 4 = 52

The expected mass of the sample in the year of 2021 is given as follows:

9 mg.

An exponential function is defined as follows:

y = a(b)^x.

For which the parameters are given as follows:

The initial mass was of 130 mg, hence the parameter a is given as follows:

a = 130.

In two years, the mass decayed to 80 grams, hence the parameter b can be obtained as follows:

b² = 80/130

b = square root(80/130)

b = 0.78446454055.

This means that the exponential function for the mass of the sample in x years after 2010 is given as follows:

y = 130(0.78446454055)^x.

2021 is 11 years after 2010, hence the expected mass is obtained as follows:

y = 130(0.78446454055)^11

y = 9 mg.

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Answer:

Option D is correct.

No solution

Step-by-step explanation:

2(x+7)=8

Apply 2 into bracket:

2x+14=8

2x=8-14

2x=-6

Divide both sides by 2:

x=-3

hence here is no option for x=-3, so answer is no solution.

A beverage company has decided to manufacture a new juice with mixed flavors, which is prepared from orange and pineapple. The vitamin contents are 5% of vitamin A and 2% of vitamin C in the orange flavor, while pineapple flavor contains 8% of vitamin C.

The company's policies are to add at least 20 L of orange flavor to the new juice and limit the vitamin C content to no more than 5%. The cost of orange flavor is $1000 per liter, while the cost of pineapple flavor is $400 per liter.To satisfy a minimum demand of 100 L of juice, we must determine the optimal amount of each flavor to use.A) A linear programming model is needed for the company to solve this problem (Minimize production cost of the new juice)B) Use a graphic solution for this problem.The objective function of the optimization problem can be given as:min C = 1000x + 400yThe constraints that the company has are,20x + 0y ≥ 100x + y ≤ 5x ≥ 0 and y ≥ 0The feasible region can be identified by graphing the inequality constraints on a graph paper. Using a graphical method, we can find the feasible region, and by finding the intersection points, we can determine the optimal solution.The graph is shown below; The optimal solution is achieved by 20L of orange flavor and 80L of pineapple flavor, as indicated by the intersection point of the lines. The optimal cost of producing 100 L of juice would be; C = 1000(20) + 400(80) = $36,000.C) If the company decides that the juice should have a vitamin C content of no more than 7%, it would alter the problem's constraints. The new constraint would be:x + y ≤ 7Dividing the equation by 100, we obtain;x/100 + y/100 ≤ 0.07The objective function and the additional constraint are combined to create a new linear programming model, which is solved graphically as follows: The feasible region changes as a result of the addition of the new constraint, and the optimal solution is now achieved by 20L of orange flavor and 60L of pineapple flavor. The optimal cost of producing 100 L of juice is $28,000.

In conclusion, the optimal amount of each flavor that should be used to satisfy a minimum demand of 100 L of juice is 20L of orange flavor and 80L of pineapple flavor with a cost of $36,000. If the company decides that the juice should have a vitamin C content of no more than 7%, the optimal amount of each flavor is 20L of orange flavor and 60L of pineapple flavor, with a cost of $28,000.

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Answer:

\(1 \frac{3}{14}\)

Step-by-step explanation:

\(\frac{3}{7} (2\frac{5}{6}) \\= \frac{3}{7} ( \frac{17}{6} )\\= \frac{17}{14} \\=1 \frac{3}{14}\)

Answer: -24x^2+28x

Step-by-step explanation: -4x*6x-(-4x)*7 to -24x^2+28x

The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Let x represent the number of pounds of bananas sold and y represent the grapes sold, hence:

x + y = 52   (1)

Also:

x + 2.25y = 72    (2)

The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72

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Answer:

\(263.755\)

Step-by-step explanation:

\(48.7 \times 61.2 \div 11.3 \\ 2,980.44 \div 11.3 \\ = 263.755752 \)

hope this helps

brainliest appreciated

good luck! have a nice day!

The right answer is 263.755

Look at the attached picture

Hope it will help you

Good luck on your assignment..

Answer: x =24

Step-by-step explanation:

3(2x-5)-4x=33

6x - 15 -4x = 33

2x - 15 = 33

2x = 48

x = 24

Answer:

x = 24

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(2x−5)−4x=33

(3)(2x)+(3)(−5)+−4x=33(Distribute)

6x+−15+−4x=33

(6x+−4x)+(−15)=33(Combine Like Terms)

2x+−15=33

2x−15=33

Step 2: Add 15 to both sides.

2x−15+15=33+15

2x=48

Step 3: Divide both sides by 2.

2x/2 = 48/2

x = 24

There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8

Answer:

I think the answer you're looking for is 86400

Step-by-step explanation:

Answer: The exponential function is typically defined as:

f(x) = e^x

where e is a mathematical constant approximately equal to 2.71828.

To understand how this function is derived, we need to start with the concept of compound interest. Suppose we have an investment that earns an annual interest rate of r, and let P be the initial principal investment. After one year, the investment will be worth P(1 + r). If we leave the investment for another year, the value will be P(1 + r)^2, and after n years, the value will be P(1 + r)^n.

Now, suppose we want to know what happens to the value of the investment as the time period becomes infinitely small (i.e., in the limit as n approaches infinity). We can do this by considering the limit of the expression (1 + r/n)^n as n approaches infinity. This limit is known as the exponential constant e.

Using calculus, we can prove that the limit of (1 + 1/n)^n as n approaches infinity is equal to e. We can then use this result to define the exponential function as e^x, where x is any real number.

Using the definition of e^x, we can show that the derivative of the exponential function is itself. That is:

d/dx e^x = e^x

This result is known as the exponential function's own derivative property, and it is one of the reasons why the exponential function is so important in mathematics.

Step-by-step explanation:

Answer| range: {15, 11, 7, -3, -7}

Step-by-step explanation:

Plug in the domain to find the range:

x = 4

2(-4) + y = 7

-8 + y = 7

y = 15

x = -2

2(-2) + y = 7

-4 + y = 7

y = 11

x = 0

2(0) + y = 7

0 + y = 7

y = 7

x = 5

2(5) + y = 7

10 + y = 7

y = -3

x = 7

2(7) + y = 7

14 + y = 7

y = -7

Answer:

4

Step-by-step explanation:

if you divide 2,560 by 640 you get 4.

hope this helps you.

The answer is 3 using bodmas

it would be beneficial to analyze other variables such as gender and opinion on the topic for a more comprehensive understanding of the local political opinion.

If the standard deviation of the ages is zero, then all individuals in the sample must have the same age of 25 years old. This means that the sample is not diverse and may not be representative of the entire neighborhood's opinion on the political topic. Therefore, conclusions drawn from this sample may not accurately reflect the opinions of the entire population. It is important to ensure that the sample is diverse and representative to make valid conclusions about a sensitive political topic.
Based on the data you collected, which includes age, gender, and opinion on the local sensitive political topic, you calculated the average age to be 25 years old and the standard deviation of the ages to be zero years old. This means that all individuals in your neighborhood are exactly 25 years old. Since there is no variation in age, it would be beneficial to analyze other variables such as gender and opinion on the topic for a more comprehensive understanding of the local political opinion.

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