Each week, a train travels the same route 47 times. About
how many times does the train travel the route in 43 weeks?
A 1,500 times
B 200 times
C 150 times
D 2,000 times

The break-even point is 1100 products sold. This means that if the store can sell 1100 products, it will be able to cover its costs and make a profit.

What is average ?

The average is a measure of central tendency that is calculated by adding a set of values together and dividing the sum by the number of values. It is also known as the arithmetic mean. It is a way to represent a typical value of a dataset.

The break-even point is the point at which the cost of the products equals the revenue from the sales of the products. To find the break-even point, we need to set the cost function (C(x) = 550 + 3.00x) equal to the revenue function (R(x) = 5.50x) and solve for x.

C(x) = 550 + 3.00x = R(x) = 5.50x

3.00x = 5.50x - 550

0.50x = 550

x = 1100

So the break-even point is 1100 products sold. This means that if the store can sell 1100 products, it will be able to cover its costs and make a profit.

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If the perimeter of a rectangular living room is 38 meters, the length of the living room is 105 meters.

The perimeter of a rectangle is the sum of the lengths of all its sides. Let's denote the length of the living room as "L". The formula for the perimeter of a rectangle is:

Perimeter = 2(length + width)

We know that the width of the living room is 9 meters, and the perimeter is 38 meters. Substituting these values in the formula, we get:

38 = 2(L + 9)

Dividing both sides by 2, we get:

19 = L + 9

Subtracting 9 from both sides, we get:

L = 105

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Step-by-step explanation:

5 more than a number, the sum of a number and 5, the total of a number and 5,

Answer:

Step-by-step explanation:

derivative:zero becouse ever number has daritive is zero

6:

Answer: Correct me if I am wrong, but this is how I think you should solve it.

Step-by-step explanation:

1. Simplify 8×5 to 40.

−2×(40+9)−6×7

2. Simplify 40+9 to 49.

−2×49−6×7

3. Simplify −2×49 to −98.

−98−6×7

4. Simplify 6×7 to 42.

−98−42

5. Simplify

−140

Your all done! Hope this helps.

The solution to the linear programming problem is:

Maximum value of z = 120

x₁ = 0, x₂ = 6

To solve the given linear programming problem using the graphical method, we first need to plot the feasible region determined by the constraints and then identify the optimal solution.

The constraints are:

x₁ + x₂ ≥ 12

x₁ + x₂ ≤ 6

x₁, x₂ ≥ 0

Let's plot these constraints on a graph:

The line x₁ + x₂ = 12:

Plotting this line on the graph, we find that it passes through the points (12, 0) and (0, 12). Shade the region above this line.

The line x₁ + x₂ = 6:

Plotting this line on the graph, we find that it passes through the points (6, 0) and (0, 6). Shade the region below this line.

The x-axis (x₁ ≥ 0) and y-axis (x₂ ≥ 0):

Shade the region in the first quadrant of the graph.

The feasible region is the overlapping shaded region determined by all the constraints.

Next, we need to find the corner points of the feasible region by finding the intersection points of the lines. In this case, the corner points are (6, 0), (4, 2), (0, 6), and (0, 0).

Now, we evaluate the objective function z = 15x₁ + 20x₂ at each corner point:

For (6, 0): z = 15(6) + 20(0) = 90

For (4, 2): z = 15(4) + 20(2) = 100

For (0, 6): z = 15(0) + 20(6) = 120

For (0, 0): z = 15(0) + 20(0) = 0

From the evaluations, we can see that the maximum value of z is 120, which occurs at the corner point (0, 6).

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Answer:

6h+14k

Step-by-step explanation:

Multiply 2by 3h which gives 6h then multiply 7k by 2 which gives 14k.

Since 6h and 14k are not like terms u cannot add so your answer will be 6h + 14k.

Answer:

9h² + 42hk + 49k²

Step-by-step explanation:

Given

(3h + 7k)²

= (3h + 7k)(3h + 7k)

Each term in the second factor is multiplied by each term in the first factor, that is

3h(3h + 7k) + 7k(3h + 7k) ← distribute both parenthesis

= 9h² + 21hk + 21hk + 49k² ← collect like terms

= 9h² + 42hk + 49k²

Step-by-step explanation:

Option A is the right answer.

In a relation, where the input is the number of people and the output is the number of sweaters the anser to the question is  relation a function is C. No, because the same number of people might have a different number of sweaters.

A mathematical function is , rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Hence, from the question, we can see that the number of the people do not equate the number of sweaters. Therefore, option C is correct.

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Answer:

it will be c

Step-by-step explanation:

Answer:

solving the inequality \(-31>x-48\) we get: \(\mathbf{x<17}\)

Step-by-step explanation:

We need to solve the inequality \(-31>x-48\)

Solving the inequality and finding value of x:

\(-31>x-48\)

First we will be switching sides i.e. left hand side will become right hand side and right hand side will become left hand side.  In doing so, the inequality sign i.e. > will be reversed and changed with <

\(x-48<-31\)

Now, for finding value of x, we will be adding 48 on both sides

\(x-48+48<-31+48\\x<17\)

The value of x is less than 17 i.e. \(\mathbf{x<17}\)

So, solving the inequality \(-31>x-48\) we get: \(\mathbf{x<17}\)

The solution to the given LP problem using the simplex method is: x1 = 2, x2 = 0, z = 8

To solve the LP problem using the simplex method, we need to convert the problem into standard form, which involves introducing slack and surplus variables. The problem can be rewritten as follows:

Minimize z = 4x1 - x2

Subject to:

2x1 + x2 + x3 = 8

x2 + x4 = 5

-x1 + 2x2 - x5 = 4

x1, x2, x3, x4, x5 ≥ 0

The initial tableau for the simplex method is as follows:

markdown

Copy code

    | x1 | x2 | x3 | x4 | x5 | RHS |

Cj | 4 | -1 | 0 | 0 | 0 | |

zj | 0 | 0 | 0 | 0 | 0 | 0 |

CB | 0 | 0 | 0 | 0 | 0 | |

cj-zj | -4 | 1 | 0 | 0 | 0 | |

BV | x1 | x2 | x3 | x4 | x5 | |

We apply the simplex method to find the optimal solution. After performing the iterations and calculations, we find that the optimal solution is:

x1 = 2

x2 = 0

z = 8

The tableau after the final iteration is as follows:

markdown

Copy code

    | x1 | x2 | x3 | x4 | x5 | RHS |

Cj | 4 | -1 | 0 | 0 | 0 | |

zj | 8 | 0 | 0 | 0 | 0 | 8 |

CB | x1 | x2 | x4 | x3 | x5 | |

cj-zj | 0 | 0 | 0 | 0 | 0 | |

BV | x1 | x2 | x4 | x3 | x5 | |

By applying the simplex method to the given LP problem, we find that the optimal solution is x1 = 2, x2 = 0, and the objective function value is z = 8. This solution satisfies all the constraints and minimizes the objective function.

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The magnitude of the cross product between vectors a and b is 14.93 units squared. The dot product between vectors a and b is 36.73 units. The dot product between the sum of vectors a and b and vector b is 50.27 units.

(a) To find the magnitude of the cross product between vectors a and b, we can use the formula ∣a × b∣ = ∣a∣ ∣b∣ sin(θ), where θ is the angle between the two vectors. Since vectors a and b are given in the component form, we can calculate the cross-product as follows:

a × b = (5.7 * 5.5 - 3.4 * 2.9) k^ = 14.93 k^, where k^ is the unit vector along the z-axis.

Therefore, ∣a × b∣ = 14.93 units squared.

(b) The dot product between vectors a and b is given by a ⋅ b = (5.7 * 2.9) + (3.4 * 5.5) = 36.73 units.

(c) To find the dot product between the sum of vectors a and b and vector b, we first calculate the sum of vectors a and b:

a + b = (5.7 + 2.9) i^ + (3.4 + 5.5) j^ = 8.6 i^ + 8.9 j^

Then, we take the dot product between the sum of vectors a and b and vector b:

(a + b) ⋅ b = (8.6 * 2.9) + (8.9 * 5.5) = 50.27 units.

(d) The component of vector a along the direction of vector b can be found by taking the dot product of vectors a and b and dividing it by the magnitude of vector b:

Component of a along b = (a ⋅ b) / ∣b∣ = 36.73 / √\(((2.9)^2 + (5.5)^2)\) = 2.44 units.

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The probability that Yaniq gets a total of less than 7: 2/9

The probability that Yaniq gets a total of more than 9: 2/9

The completed table has the total as:

5, 7,9, 6, 810,7, 9, 11

b. The probability that Yaniq gets a total of more than 9:

E: (10, 11)

P(E) = 2/9

Given that the total outcomes is 9

c. The probability that Yaniq gets a total of less than 7:

F; (5,6)

P(F)= 2/9

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Answer:

a. sin 300 = -∛3/2, cos 300 = 1/2

b. sin -225 = √2/2, cos -225 = √2/2

c. sin 5π/6 = 1/2, cos 5π/6 = -3√2

d. sin -4π/3 = √3/2, cos -4π/3 = -1/2

Step-by-step explanation:

See unit circle

In summary, when a sample falls outside the control limits on an X-bar control chart, it signals a potential problem, and further investigation and corrective actions should be taken to identify and resolve the issue.

In an X-bar control chart, the upper control limit (UCL) and lower control limit (LCL) are set to monitor the process and detect any significant variations.

Given:

UCL = 0.65 inch

LCL = 0.35 inch

The next six samples are:

Sample 1: 0.60 inch

Sample 2: 0.37 inch

Sample 3: 0.45 inch

Sample 4: 0.48 inch

Sample 5: 0.53 inch

Sample 6: 0.62 inch

To determine what should be done, we need to check whether any of the samples fall outside the control limits.

Sample 1: 0.60 inch

Within control limits

Sample 2: 0.37 inch

Below the lower control limit (LCL)

Since Sample 2 falls below the lower control limit, it indicates a significant deviation from the expected process. This suggests that there might be an issue with the process or measurement.

Based on this result, the appropriate action would be to investigate the cause of the variation and take corrective measures to address the issue. It may involve analyzing the process, checking for any equipment malfunction, or reevaluating the measurement procedure.

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Answer:

....the answer is 682.5

Answer:

The answer is 702. Hope it helped! :D

Step-by-step explanation:

Answer:

b = -2

Step-by-step explanation:

Hello!

Solve the equation:

We can plug it back in to the original equation to see if it works:

The solution works.

We have to determine the exact values of the sine, cosine, and tangent of the angle 11π/12 using the identity pi/4 + 2pi/3. The angles that we'll be working with are 11π/12, pi/4, and 2π/3.

To solve the given problem, we first need to determine the values of sine, cosine, and tangent of pi/4 and 2π/3, which will help us in determining the exact values of these trigonometric functions for 11π/12. The angle 11π/12 can be expressed as pi/4 + 2π/3. Using the identity of pi/4 and 2π/3 we can easily determine the value of sin, cos, and tan of 11π/12.To find the value of sine of 11π/12, we first have to determine the sine values of pi/4 and 2π/3. The sine of pi/4 is √2/2, while the sine of 2π/3 is √3/2.

We can use these values to determine the sine of 11π/12. Similarly, we can use the cosine and tangent of pi/4 and 2π/3 to determine the cosine and tangent of 11π/12.Finally, the exact values of the sine, cosine, and tangent of 11π/12 are:Sin (11π/12) = (√6 - √2)/4 Cos (11π/12) ⇒ (√6 - √2)/4 Tan (11π/12) ⇒ 1

Therefore, we can conclude that the exact values of the sine, cosine, and tangent of the angle 11π/12 are (√6 - √2)/4, (√6 - √2)/4, and 1, respectively.

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The ability for Nike to manufacture its own shoes and then build stores for distribution is an example of Forward Integration.

What is forward integration ?

In order to lower manufacturing costs and increase efficiency, a sort of vertical integration known as "forward integration" moves up the supply chain.

An operational competency is what?

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The value of the piecewise function for f(3) is 4

From the question, we have the following parameters that can be used in our computation:

f(x) = 2x if x < 1

f(x) = 1/2x + 5/2 if x >= 1

The function f(3) implies that we make use of the function

f(x) = 1/2x + 5/2

This is because it is valid for x >= 1

substitute the known values in the above equation, so, we have the following representation

f(3) = 1/2 * 3 + 5/2

Evaluate

f(3) = 4

Hence, the piecewise function for f(3) is 4

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Answer:

There are twelve combinations, two sides of one coin to one side of a dice

Step-by-step explanation:

meaning the dice face each have at least two sides of a coin so 6 times 2 is twelve

Answer:

C.) 4:9

Step-by-step explanation:

\(10*16=160\\24*15=360\\160:360=4:9\)

Answer:

C

Step-by-step explanation:

Given ratio of sides = a : b , then

ratio of areas = a² : b²

Here

ratio of sides = 16 : 24 = 2 : 3 , then

ratio of area = 2² : 3² = 4 : 9 → C

Answer:

4

Step-by-step explanation:

Step 1: Write equation

5x - 2(2x - 1) = 2(3x - 4)

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

5(2) - 2(2(2) - 1) = 2(3(2) - 4)

10 - 2(4 - 1) = 2(6 - 4)

10 - 2(3) = 2(2)

10 - 6 = 4

4 = 4

Here we see that x = 2 is indeed a solution

Step 4: Find 2x

2(2) = 4

Answer:

It is 4

Step-by-step explanation:

Answer:

$20

Step-by-step explanation:

They will require 4.4 days to complete the remaining work together.

What is work?

Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.

Ann alone take time  = 10 days to translate a document.

Work done in 1 day by Ann = 1 / 10

In 2 days = 2 / 10

Work left = 8 / 10

Now, Ben alone take = 12 days to translate a document.

Work done in 1 day by Ben = 1 / 12

After adding, we get

Combined work of both Ann and Ben in 1 day = 1 / 10 + 1 / 12 = 11 / 60

Time taken to complete the rest of the work = 8 / 10 ÷ 11 / 60

= 48 / 11 = 4.4 days.

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Using  Central Limit Theorem (CLT) an approximate distribution of y is  0.2578, 0.1902 ,0.9963 , 0.9765.

To use the Central Limit Theorem (CLT), we need to find the mean and variance of the distribution of the sample mean Y.

The mean of the distribution of X is given by:

E[X] = ∫x f(x) dx = ∫x 3x^2 dx (from 0 to 1) = 3/4

The variance of the distribution of X is given by:

Var(X) = ∫(x - E[X])^2 f(x) dx = ∫(x - 3/4)^2 3x^2 dx (from 0 to 1) = 1/20

By the CLT, the sample mean Y is approximately normally distributed with mean μ = E[X] = 3/4 and variance σ^2 = Var(X)/n, where n is the sample size.

For each of the given values of n and σ^2, we can compute the standard deviation σ as σ = sqrt(σ^2/n), and then use the standard normal distribution to find the probability that Y falls in the given interval.

For example, for (n, σ^2) = (64, 0.021), we have:

σ = sqrt(0.021/64) = 0.077

Z1 = (0.7 - μ)/σ = (0.7 - 0.75)/0.077 ≈ -0.649

Z2 = (0.75 - μ)/σ = (0.75 - 0.75)/0.077 = 0

P(0.7 < Y < 0.75) = P(Z1 < Z < Z2) = P(-0.649 < Z < 0) = 0.2578 (from standard normal distribution table)

Similarly, for the other cases, we have:

(n, σ^2) = (64, 0.021)

P(0.7 < Y < 0.75) = 0.2578

(n, σ^2) = (64, 0.00033)

P(0.75 < Y < 0.8) = P(Z < 0.904) - P(Z < 0.309) ≈ 0.1902 (from standard normal distribution table)

(n, σ^2) = (256, 0.021)

P(0.7 < Y < 0.75) = P(Z < 2.597) - P(Z < -0.649) ≈ 0.9963 (from standard normal distribution table)

(n, σ^2) = (256, 0.00033)

P(0.75 < Y < 0.8) = P(Z < 2.128) - P(Z < 0.542) ≈ 0.9765 (from standard normal distribution table)

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The relationship between the mean and MAD is used. Then the mean absolute deviation (MAD) is 0.

It is the average distance between each data point and the mean.

Dr. Oguz counted the number of cubs in 10 tiger cub litters and then arranged the numbers from smallest to largest.

The numbers of cubs in each litter were 1, 1, 2, 2, 3, 3, 3, 4, 5, and 6.

The mean of these measurements is 3.

The mean absolute deviation (MAD) is given by

\(\rm MAD = \dfrac{\Sigma |x -\mu| }{N}\)

N be the number of observation

μ be the mean

\(\rm MAD = \dfrac{2+2+1+1+0+0+0-1-2-3}{10}\\\\MAD = \dfrac{6-6}{0}\\\\MAD = 0\)

The mean absolute deviation (MAD) is 0.

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