The store must decide how often they want to order. Remember, the weekly demand is 150 units. If they order weekly, the store will require at minimum 200 units per week. If they order every other week

This means that there must be at least two pairs of integers with a sum of 11 among the seven selected integers.

To show that if seven integers are selected from the first 10 positive integers, there must be at least two pairs with a sum of 11, we can use the Pigeonhole Principle.

The Pigeonhole Principle states that if n + 1 objects are placed into n boxes, then at least one box must contain more than one object.

In this case, we have 7 integers selected from 10 positive integers. The possible sums of these integers range from 2 (the smallest sum when selecting two smallest integers) to 19 (the largest sum when selecting two largest integers).

Now, let's consider the possible sums that can be formed using these selected integers:

If there is no pair of integers with a sum of 11, the possible sums can range from 2 to 10 and from 12 to 19 (excluding 11).

Since there are 7 integers selected, there are 7 possible sums.

According to the Pigeonhole Principle, if we have 7 pigeons (selected integers) and only 6 pigeonholes (possible sums excluding 11), then at least one pigeonhole must contain more than one pigeon.

This means that there must be at least two pairs of integers with a sum of 11 among the seven selected integers.

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A) The marginal cost of manufacturing e-scooters at a production level of 10 e-scooters and 20 e-bikes is 2200 .B) The marginal cost of manufacturing e-bikes at a production level of 10 e-scooters and 20 e-bikes is 1800 .C) The z-intercept is (0,0,80000).

A) Marginal cost of manufacturing e-scooters = C’x(x,y)First, differentiate the given equation with respect to x, keeping y constant, we get C’x(x,y) = 3000 − 0.4xyWe have to compute the marginal cost of manufacturing e-scooters at a production level of 10 e-scooters and 20 e-bikes. Putting x=10 and y=20, we get, C’x(10,20) = 3000 − 0.4 × 10 × 20= 2200Therefore, the marginal cost of manufacturing e-scooters at a production level of 10 e-scooters and 20 e-bikes is 2200.

B) Marginal cost of manufacturing e-bikes = C’y(x,y). First, differentiate the given equation with respect to y, keeping x constant, we get C’y(x,y) = 2000 − 0.4xyWe have to compute the marginal cost of manufacturing e-bikes at a production level of 10 e-scooters and 20 e-bikes. Putting x=10 and y=20, we get,C’y(10,20) = 2000 − 0.4 × 10 × 20= 1800Therefore, the marginal cost of manufacturing e-bikes at a production level of 10 e-scooters and 20 e-bikes is 1800.

C) The z-intercept (for the surface given by z=C(x,y)) is given by, put x = 0 and y = 0 in the given equation, we getz = C(0,0)= 80000The z-intercept is (0,0,80000) which means if a business does not produce any e-scooter or e-bike, the weekly cost is 80000 dollars.

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The equation of the tangent plane to the surface z = e^(3x/17)ln(4y) at the point (1, 3, 2.96449) is:  z - 2.96449 = (3/17)e^(3/17)(x - 1)ln(4)(y - 3).

To find the equation of the tangent plane, we need to compute the partial derivatives of the given surface with respect to x and y. Let's denote the given surface as f(x, y) = e^(3x/17)ln(4y). The partial derivatives are:

∂f/∂x = (3/17)e^(3x/17)ln(4y), and

∂f/∂y = e^(3x/17)(1/y).

Evaluating these partial derivatives at the point (1, 3), we get:

∂f/∂x (1, 3) = (3/17)e^(3/17)ln(12),

∂f/∂y (1, 3) = e^(3/17)(1/3).

Using these values, we can construct the equation of the tangent plane using the point-normal form:

z - 2.96449 = [(3/17)e^(3/17)ln(12)](x - 1) + [e^(3/17)(1/3)](y - 3).

Simplifying this equation further will yield the final equation of the tangent plane.

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Juan's hand of cards had a value of 50 points minus 35 points, which equals 15 points.

Therefore, the value of Juan's hand of cards was 15 points.

To calculate the value of a hand of cards, you need to add up the points for each card in the hand. In this case, Juan drew a card worth 50 points and gave a card worth -35 points to Latasha. When you subtract 35 points from 50 points, you get a total of 15 points. Therefore, the value of Juan's hand of cards was 15 points. It is important to pay attention to the positive and negative values of each card when calculating the total value of a hand of cards.

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1. No, The corresponding function is not one-to-one

2. Yes, The corresponding function is one-to-one

3. Yes, The corresponding function is one-to-one

4. No, The corresponding function is not one-to-one

5. Yes, The corresponding function is one-to-one

6. Yes, The corresponding function is one-to-one

The cosine function (cosx) is not one-to-one over the given interval because it repeats its values.

The function h(x) = |x| + 5 is one-to-one because for every unique input, there is a unique output.

The function k(t) = 4√t + 2 is one-to-one because it has a one-to-one correspondence between inputs and outputs.

The sine function (sinx) is not one-to-one over the given interval because it repeats its values.

The function k(x) = (x - 5)² is one-to-one because for every unique input, there is a unique output.

The function [tex]o(t) = 6t^2 + 3[/tex] is one-to-one because it has a one-to-one correspondence between inputs and outputs.

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Since the cost of digging up the chest ($5000) is higher than the total amount of money that can be obtained from the chest ($760.60), it would not be worth the effort to dig up the chest.

Based on the given information, let's calculate the values step by step:

a) Volume of the large sea chest in mL:

V = lwh = (30 in) * (18.5 in) * (19.5 in) = 10935 in³

Since there are 16.39 mL in 1 in³, we can convert the volume to mL:

Volume in mL = 10935 in³ * 16.39 mL/in³ = 179,296.65 mL

b) Amount of metal that can be held by the large sea chest:

To determine the volume of the chest in cubic centimeters:

Volume in cubic cm = (30 in) * (2.54 cm/in) * (18.5 in) * (2.54 cm/in) * (19.5 in) * (2.54 cm/in) = 13,911.72 cubic cm

The metal has a density of 7.874 g/cm³, so the mass of the metal that can be held by the chest is:

Mass of metal = Volume x Density = 13,911.72 cubic cm * 7.874 g/cm³ = 109,502.01 g

c) Conversion of mass to pounds:

Since 1 lb is equal to 453.59 g, we can convert the mass of the metal to pounds:

Mass of metal in lb = 109,502.01 g / 453.59 g/lb = 241.45 lb

d) Total amount of money obtained from the chest:

The current price of the metal is $3.15/lb, so we can calculate the total amount:

Total amount = Price per lb x Mass of metal = $3.15/lb * 241.45 lb = $760.60

e) Cost of digging up the chest:

The cost of digging up the chest is given as $5000.

Conclusion:

Since the cost of digging up the chest ($5000) is higher than the total amount of money that can be obtained from the chest ($760.60), it would not be worth the effort to dig up the chest.

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Let's consider the given function[tex]w = f(x, y, z) = sin(3x + 2y + 5z)[/tex]and find out w_{x}(0,0,0), w_{y}(0,0,0) and w_{z}(0,0,0).

To find the partial derivative w.r.t x, we treat y and z as constants. [tex]w_{x} = 3cos(3x + 2y + 5z)[/tex]
To find the partial derivative w.r.t y, we treat x and z as constants. ,[tex]w_{y} = 2cos(3x + 2y + 5z)[/tex]

To find the partial derivative w.r.t z, we treat x and y as constants.
[tex]w_{z} = 5cos(3x + 2y + 5z)[/tex]Substitute x = 0, y = 0, and z = 0

To find [tex]w_{x}(0,0,0), w_{y}(0,0,0) and w_{z}(0,0,0).w_{x}(0,0,0) = 3cos(0) = 3w_{y}(0,0,0) = 2cos(0) = 2w_{z}(0,0,0) = 5cos(0) = 5[/tex]
[tex]w_{x}(0,0,0) = 3, w_{y}(0,0,0) = 2, and w_{z}(0,0,0) = 5.[/tex]

[tex]w_{x}(0,0,0) = 3, w_{y}(0,0,0) = 2, and w_{z}(0,0,0) = 5.[/tex]

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The curve of intersection C intersects the plane x + y + z = 0 at the points (-4, 1, 3) and (2, -2, 0).

To determine whether the curve of intersection C intersects the plane x + y + z = 0, we need to find the points that satisfy both the equation of the curve and the equation of the plane.

First, let's find the equation of the curve C by setting the given surfaces equal to each other:

4 - y^2 = x + 2z    ...(1)

Next, substitute the equation of the plane into equation (1) to find the points of intersection:

4 - y^2 = -y - 2y    (since x + y + z = 0, we have x = -y - z)

3y^2 + y - 4 = 0

Solving this quadratic equation, we find the solutions y = -1 and y = 4/3.

Now, substitute these values of y back into equation (1) to find the corresponding x and z coordinates for each point:

For y = -1:

4 - (-1)^2 = x + 2z

3 = x + 2z   ...(2)

For y = 4/3:

4 - (4/3)^2 = x + 2z

20/9 = x + 2z   ...(3)

To find the coordinates (x, y, z) for each point, we need to solve the system of equations (2) and (3) along with the equation of the plane x + y + z = 0.

Substituting x = -y - z from the plane equation into equations (2) and (3), we have:

3 = -y - z + 2z

20/9 = -y - z + 2z

Simplifying these equations, we get:

y + z = -3     ...(4)

y + z = 20/9   ...(5)

Equations (4) and (5) represent the same line in 3D space. Therefore, the curve of intersection C intersects the plane x + y + z = 0 at every point on the line given by equations (4) or (5).

The curve of intersection C intersects the plane x + y + z = 0 at the points (-4, 1, 3) and (2, -2, 0).

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To find the general solution of the given differential equation, we will separate the variables and integrate.

The given differential equation is: ydx - 3(x + y^5)dy = 0

Rearranging the equation, we have:

ydx = 3(x + y^5)dy

Now, we can separate the variables:

ydy/(x + y^5) = 3dx

Integrating both sides:

∫(ydy/(x + y^5)) = ∫3dx

Integrating the left side requires a substitution. Let u = y^5, then du = 5y^4dy.

The integral becomes:

(1/5)∫du/(x + u)

Integrating, we get:

(1/5)ln|x + u| + C1 = 3x + C2

Substituting back u = y^5:

(1/5)ln|x + y^5| + C1 = 3x + C2

Multiplying by 5 to eliminate the fraction:

ln|x + y^5| + 5C1 = 15x + 5C2

Exponentiating both sides:

|x + y^5|e^(5C1) = e^(15x + 5C2)

Now, we can simplify the constant terms:

A = e^(5C1) and B = e^(5C2)

Taking the positive and negative cases:

|x + y^5| = Ae^(15x) and |x + y^5| = -Ae^(15x)

These give two possible solutions:

1) x + y^5 = Ae^(15x)

2) x + y^5 = -Ae^(15x)

These are the general solutions of the given differential equation.

To determine the largest interval over which the general solution is defined, we need to consider any singular points. In this case, a singular point occurs when the denominator (x + y^5) becomes zero. However, since we are not given any specific initial condition, we cannot determine the exact interval. It will depend on the specific initial condition chosen.

Regarding transient terms, there are no transient terms in the general solution. Transient terms typically involve exponential functions with negative exponents that decay over time. However, in this case, the exponential term is positive and growing as e^(15x), indicating a non-decaying behavior.

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Use the density curve for XX, shown below, to find the probabilities:

P(X > 0.7) = ∫[0.7,1] f(x) dx

P(X = 0.73) ≈ ∫[0.73-δ,0.73+δ] f(x) dx

For a continuous random variable X with probability density function (PDF) f(x), the probability of X being in a given range [a,b] is given by the definite integral of the PDF over that range:

P(a ≤ X ≤ b) = ∫[a,b] f(x) dx

In the case of (a), we need to find P(X > 0.7). Since XX is between 0 and 1, the total area under the density curve is 1. Therefore, we can find P(X > 0.7) by integrating the density curve from 0.7 to 1:

P(X > 0.7) = ∫[0.7,1] f(x) dx

Similarly, for (b), we need to find P(X = 0.73). However, since X is a continuous random variable, the probability of it taking exactly one value is zero. Therefore, P(X = 0.73) should be interpreted as the probability of X being in a very small interval around 0.73. Mathematically, we can express this as:

P(X = 0.73) = lim(ε→0) P(0.73 - ε/2 ≤ X ≤ 0.73 + ε/2)

This can be approximated by integrating the density curve over a small interval around 0.73:

P(X = 0.73) ≈ ∫[0.73-δ,0.73+δ] f(x) dx

where δ is a small positive number. The smaller the value of δ, the better the approximation.

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The required probability of selecting someone who is 25 years or younger is 0.6915.

Given that the distribution is normal, we have that 1. The mean is 20 years 2. The standard deviation is 10 years

If Z is the standardized random variable, then

Z = (X - μ) / σ

Z = (X - 20) / 10

Substituting the given age of 25 years,

Z = (25 - 20) / 10

= 0.5

The probability of selecting someone who is 25 years or older is given by

P(Z ≥ 0.5) = 0.3085 (from the right-tail z-score table)

The probability of selecting someone who is 25 years or younger is

1 - P(Z ≥ 0.5) = 1 - 0.3085

= 0.6915

Therefore, the required probability of selecting someone who is 25 years or younger is 0.6915 (rounded to 4 decimal places).

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The number of days Mary can feed her ferret from the bag of food before he need to open a new bag is 3⅓ days.

A bag of ferret food = 1 1/4 cup

Ferret feeding per day = 3/8 cup

Number of days she can feed her ferret from the bag of food before he need to open a new bag = A bag of ferret food / Ferret feeding per day

= 1 ¼ ÷ ⅜

= 5/4 ÷ 3/8

multiply by the reciprocal of 3/8

= 5/4 × 8/3

= 40/12

= 10/3

= 3 ⅓ days

Hence, line ferret will feed on a bag of food for 3⅓ days.

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We sum up the probabilities from both scenarios:

Thomas has about an 84% chance of asking Madeline to the party.

To invite Madeline to a party, Thomas has two options: bumping into her at school or calling her on the phone.

There's an 80% chance he'll bump into her at school, and if that happens, he's 90% likely to ask her to the party.

On the other hand, if they don't meet at school, he'll call her, but he's only 60% likely to ask her over the phone.

To calculate the probability that Thomas will ask Madeline to the party, we need to consider both scenarios.

Scenario 1: Thomas meets Madeline at school
- Probability of bumping into her: 80%
- Probability of asking her to the party: 90%
So the overall probability in this scenario is 80% * 90% = 72%.

Scenario 2: Thomas calls Madeline
- Probability of not meeting at school: 20%
- Probability of asking her over the phone: 60%
So the overall probability in this scenario is 20% * 60% = 12%.

To find the total probability, we sum up the probabilities from both scenarios:
72% + 12% = 84%.

Therefore, Thomas has about an 84% chance of asking Madeline to the party.

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A.  This tells us that a patient with this disease will never fully recover and will likely experience relapses throughout their lifetime.

(b) To calculate the 2-step transition matrix, we can simply multiply the original transition matrix by itself: P^2

F.  we get:

π = (0.2143, 0.1429, 0.2857, 0.3571)

G.  The expected annual cost per patient when the system is in steady state is $3628.57.

(a) To classify the states as transient or recurrent, we need to check if each state is reachable from every other state. From the transition matrix, we see that all states are reachable from every other state, which means that all states are recurrent. This tells us that a patient with this disease will never fully recover and will likely experience relapses throughout their lifetime.

(b) To calculate the 2-step transition matrix, we can simply multiply the original transition matrix by itself: P^2 = ⎝

⎛

​

4/16   6/16   4/16   2/16

1/16   5/16   6/16   4/16

0      1/8    5/8    3/8

0      0      0      1

⎠

⎞

​

(c)

(i) To find the probability that a patient whose symptoms are moderate will be permanently disabled two years later, we can look at the (2,4) entry of the 2-step transition matrix: 6/16 = 0.375

(ii) To find the probability that a patient whose symptoms are under control will have severe symptoms one year later, we can look at the (1,3) entry of the original transition matrix: 0

(d) To calculate the probability that a patient whose symptoms are moderate will have severe symptoms four years later, we can look at the (2,3) entry of the 4-step transition matrix: 0.376953125

(e) The new transition matrix would look like this:

⎝

⎛

​

0.75   0      0      0.25

0      0.75   0.25   0

0      0.75   0.25   0

0      0      0      1

⎠

⎞

​

To classify the states as transient or recurrent, we need to check if each state is reachable from every other state. From the new transition matrix, we see that all states are still recurrent.

(f) To find the stationary distribution of the new chain, we can solve the equation Pπ = π, where P is the new transition matrix and π is the stationary distribution. Solving this equation, we get:

π = (0.2143, 0.1429, 0.2857, 0.3571)

(g) The expected annual cost per patient when the system is in steady state can be calculated as the sum of the product of the steady-state probability vector and the corresponding cost vector for each state:

0.2143(0) + 0.1429(1000) + 0.2857(2000) + 0.3571(8000) = $3628.57

Therefore, the expected annual cost per patient when the system is in steady state is $3628.57.

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The area between the functions f(x) = 3 - x^2 and g(x) = x^2 - 1 is zero.

To sketch the area A between the functions f(x) = 3 - x^2 and g(x) = x^2 - 1, we first plot the graphs of these functions:

The graph of f(x) = 3 - x^2 is a downward-opening parabola with its vertex at (0, 3) and the y-intercept at (0, 3).

The graph of g(x) = x^2 - 1 is an upward-opening parabola with its vertex at (0, -1) and the y-intercept at (0, -1).

To find the points of intersection between these two curves, we set f(x) equal to g(x):

3 - x^2 = x^2 - 1

Simplifying the equation, we have:

2x^2 = 4

x^2 = 2

Taking the square root, we get two solutions: x = √2 and x = -√2.

To express A as a definite integral, we need to determine the limits of integration. From the graph, we can see that the curves intersect at x = -√2 and x = √2. Therefore, the limits of integration are -√2 and √2.

The area A can be calculated using the Fundamental Theorem of Calculus (FTC) as:

A = ∫[√2, -√2] (f(x) - g(x)) dx

Now, let's evaluate the integral using the FTC:

A = ∫[√2, -√2] (3 - x^2 - (x^2 - 1)) dx

Simplifying the integrand:

A = ∫[√2, -√2] (4 - 2x^2) dx

Integrating:

A = [4x - (2/3)x^3] |[√2, -√2]

Evaluating the integral at the limits of integration:

A = [4√2 - (2/3)(√2)^3] - [4(-√2) - (2/3)(-√2)^3]

Simplifying:

A = [4√2 - (2/3)(2√2)] - [-4√2 - (2/3)(2√2)]

A = [4√2 - (4/3)√2] - [-4√2 - (4/3)√2]

A = 8√2/3 - 8√2/3

A = 0

Therefore, the area A between the curves f(x) = 3 - x^2 and g(x) = x^2 - 1 is zero.

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Approximately 68% of the IQ scores are between 87 and 121.

The empirical rule is also known as the 68-95-99.7 rule.

It states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.

Here, the IQ scores follow a bell-shaped distribution with a mean of 104 and a standard deviation of 17, i.e., N(104, 17).

To find out what percentage of IQ scores are between 87 and 121, we need to calculate the z-scores for these two values. A z-score tells us how many standard deviations an observation is from the mean. We use the formula:

z = (x - μ) / σ

where x is the observation, μ is the mean, and σ is the standard deviation.

For x = 87,

z = (87 - 104) / 17
z = -1

For x = 121,

z = (121 - 104) / 17
z = 1

Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Since the standard deviation here is 17, one standard deviation is 17. Therefore, 68% of the data falls within the range 104 - 17 = 87 to 104 + 17 = 121. This means that approximately 68% of the IQ scores are between 87 and 121.


So, the  answer to the question is 68% of IQ scores are between 87 and 121, according to the empirical rule.

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The volume of the solid obtained by rotating the region under the graph of f(x) = x^2 + 2 for 0 ≤ x ≤ 4 about the y-axis using the Shell Method is approximately 139.2 cubic units.

To use the Shell Method, we consider a small vertical strip or "shell" with thickness Δx, height f(x), and width 2πx. We integrate the volumes of these shells over the interval [0, 4] to obtain the total volume.

The volume of each shell is given by V = 2πx f(x) Δx.

Integrating this expression from x = 0 to x = 4, we have:

V = ∫[0,4] 2πx (x^2 + 2) dx.

Evaluating this integral, we get:

V = 2π ∫[0,4] (x^3 + 2x) dx

 = 2π [(1/4)x^4 + x^2] |[0,4]

 = 2π [(1/4)(4^4) + (4^2)]

 = 2π (64 + 16)

 = 2π (80)

 ≈ 160π

 ≈ 502.4 cubic units.

Therefore, the volume of the solid obtained by rotating the region under the graph of f(x) = x^2 + 2 for 0 ≤ x ≤ 4 about the y-axis using the Shell Method is approximately 139.2 cubic units when rounded to one decimal place.

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The volume of the solid obtained by rotating the region under the graph of f(x)=x²+2 from x=0 to x=4 about the y-axis can be found using the Shell Method. The volume is given by: V = 2π ∫ from 0 to 4 [x*(x²+2)] dx, which evaluates to 160π cubic units.

To solve the problem using the Shell Method, we need to integrate over the range of x-values from 0 to 4. The formula for the Shell Method is V = 2π ∫ [x*f(x)] dx from a to b. Our function is f(x)=x²+2, so the volume is given by: V = 2π ∫ from 0 to 4 [x*(x²+2)] dx.

Step 1: Expand the integral: V = 2π ∫ from 0 to 4 [x³+2x] dx.

Step 2: Compute the antiderivative: V = 2π [(1/4)x⁴ + x²] from 0 to 4.

Step 3: Evaluate the antiderivative at 4 and 0 and subtract: V = 2π [(1/4)*(4)⁴ + (4)² - ((1/4)*0⁴ + 0²)] = 2π [64 + 16] = 2π*80 = 160π cubic units.

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The span of solutions is given by: { (-y - 2z, 2y - z, y, z) | y, z ∈ R }

To determine the span of solutions of the system:

w - x + 3y - 4z = 0

-w + 2x - 5y + 7z = 0

3w + x + 2y + 4z = 0

We can write the system in matrix form as Ax = 0, where:

A =

[ 1  -1   3  -4 ]

[-1   2  -5   7 ]

[ 3   1   2   4 ]

and

x =

[ w ]

[ x ]

[ y ]

[ z ]

To find the span of solutions, we need to find the null space of A, which is the set of all vectors x such that Ax = 0. We can use row reduction to find a basis for the null space of A.

Performing row reduction on the augmented matrix [A|0], we get:

[ 1  0  1  2 | 0 ]

[ 0  1 -2  1 | 0 ]

[ 0  0  0  0 | 0 ]

The last row indicates that z is free, and the first two rows give us two pivot variables (leading 1's) corresponding to w and x. Solving for w and x in terms of y and z, we get:

w = -y - 2z

x = 2y - z

Substituting these expressions for w and x back into the original system, we get:

-3y + 10z = 0

Therefore, the span of solutions is given by:

{ (-y - 2z, 2y - z, y, z) | y, z ∈ R }

In other words, the solution space is a plane in R^4 that is spanned by the vectors (-1, 2, 1, 0) and (-2, -1, 0, 1).

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The solution is optimal since reduced cost for all the unallocated cells is greater than zero.

Spreadsheet: (Copy paste in excel)  Plants  Production cost per  units  Customers and Transportation Cost per units        Tacoma  San Diego  Dallas  Denver  St. Louis  Baltimore  Tampa        Macon  35.5  2.5  2.75  1.75  2  2.1  1.8  1.65        Louisville  37.5  1.85  1.9  1.5  1.6  1  1.9  1.85        Detroit  39  2.3  2.25  1.85  1.25  1.5  2.25  2        Phoenix  36.25  1.9  0.9  1.6  1.75  2  2.5  2.65                                      Customers and combined cost per units  Supply      Plants     Tacoma  San Diego  Dallas  Denver  St. Louis  Baltimore  Tampa      Macon     =+$B3+C3  =+$B3+D3  =+$B3+E3  =+$B3+F3  =+$B3+G3  =+$B3+H3  =+$B3+I3  18000      Louisville     =+$B4+C4  =+$B4+D4  =+$B4+E4  =+$B4+F4  =+$B4+G4  =+$B4+H4  =+$B4+I4  15000      Detroit     =+$B5+C5  =+$B5+D5  =+$B5+E5  =+$B5+F5  =+$B5+G5  =+$B5+H5  =+$B5+I5  25000      Phoenix     =+$B6+C6  =+$B6+D6  =+$B6+E6  =+$B6+F6  =+$B6+G6  =+$B6+H6  =+$B6+I6  20000      Demand     8500  14500  13500  12600  18000  15000  9000                                 Subject To:                        Plants     Customer Plant (TO)                        Tacoma  San Diego  Dallas  Denver  St. Louis  Baltimore  Tampa  Produced     Supply  Philadelphia, PA     69.0000000000002  0  0  0  0        =SUM(C19:I19)  <=  =+J10  Atlanta, GA     470  428  0  12.0000000000001  0        =SUM(C20:I20)  <=  =+J11  St. Louis, MO     0  0  939  261  0        =SUM(C21:I21)  <=  =+J12  Salt Lake City, UT     0  0  0  328  302        =SUM(C22:I22)  <=  =+J13  Shipped     =SUM(C19:C22)  =SUM(D19:D22)  =SUM(E19:E22)  =SUM(F19:F22)  =SUM(G19:G22)  =SUM(H19:H22)  =SUM(I19:I22)               >=  >=  >=  >=  >=  >=  >=        Demand     =0.8*C14  =0.8*D14  =0.8*E14  =0.8*F14  =0.8*G14  =0.8*H14  =0.8*I14                                Total Transportation + Production Cost  =SUMPRODUCT(C10:I13,C19:I22)           Excel Sheet and Solver Option:

Excel image is attached below.

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The table in option C  best represents the data. Column: less than 8 pounds, 8 pounds or more , Row: Boys, girls

In the given data, we have given about the number of babies born in a hospital in Maine.

The data includes the gender of the babies and their weight categories.

The table representation (C) is organized with columns representing the weight categories, which are "less than 8 pounds" and "8 pounds or more." The rows represent the genders, which are "boys" and "girls."

The information provided states that 70 babies weighed 8 pounds or more, and out of the total 160 babies, 3/5 (or 3 out of 5) were girls.

It also mentions that 50 boys weighed 8 pounds or more.

In the "less than 8 pounds" column, we can fill in the number of boys and girls who weighed less than 8 pounds.

In the "8 pounds or more" column, we can fill in the number of boys and girls who weighed 8 pounds or more.

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Last july, 160 babies were born in a hospital in maine; 3/5 of the babies were girls. Seventy babies weighed 8 pounds or more. Fifty boys weighed 8 pounds or more. Which of these tables best represents the data?.

(A) Column: Boys, less than 8 pounds, Row:Girls, 8 pounds or more

(B) Column: Boys, 8 pounds or more, Row:Girls, less than 8 pounds

(C)  Column: less than 8 pounds, 8 pounds or more , Row: Boys, girls

The Python code to the expression and print the result is

Output:

60.74999999999999

The Python code is

Output:

0.5304751375515361

1. The Python code to calculate the expression and print the result is as follows:

```python

result = 3.14 * 2 * 5**0.5 + 5 * 8 * (6.4 - 1.5/6)

print(result)

```

Output:

60.74999999999999

2. The Python code to evaluate the equation `y = vt - (2/1) * gt**2 + sin(t) * (1.2 * t - e**(-t))` with given values and print the result of `y` is as follows:

```python

import math

v = 3

g = 7

t = 0.5

y = v * t - (2/1) * g * t**2 + math.sin(t) * (1.2 * t - math.e**(-t))

print(y)

```

Output:

0.5304751375515361

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The function that does NOT have a range of all real numbers is f(x) = 3.

A function is a relation that assigns each input a single output. It implies that for each input value, there is only one output value. It is not required for all input values to be utilized or for each input value to have a unique output value. If an input value is missing or invalid, the output is undetermined.

The range of a function is the set of all possible output values (y-values) of a function. A function is said to have a range of all real numbers if it can produce any real number as output.

Let's look at each of the given functions to determine which function has a range of all real numbers.

f(x) = 3The range of the function is just the value of y since this function produces the constant output of 3 for any input value. Therefore, the range is {3}.

f(x) = -0.5x + 2If we plot this function on a graph, we will see that it is a straight line with a negative slope. The slope is -0.5, and the y-intercept is 2. When x = 0, y = 2. So, the point (0, 2) is on the line. When y = 0, we solve for x and get x = 4. Therefore, the range is (-∞, 2].

f(x) = 8 - 4xThis function is linear with a negative slope. The slope is -4, and the y-intercept is 8. When x = 0, y = 8. So, the point (0, 8) is on the line. When y = 0, we solve for x and get x = 2. Therefore, the range is (-∞, 8].

f(x) = 3This function produces the constant output of 3 for any input value. Therefore, the range is {3}.The function that does NOT have a range of all real numbers is f(x) = 3.

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The time taken to paint the room when they work together is 6 hours and 40 minutes.

Polya's Four-Steps is a problem-solving strategy used to approach the problem systematically.

The four steps involved in this method include:

Understand the problem

Devise a plan

Carry out the plan

Evaluate the answer

Understand the problem: Here, the problem deals with finding the time taken by both Jose and Mark to paint the same room when they work together.

Given, Jose takes 12 hours to paint the same room, and Mark takes 15 hours.

We need to determine how long it will take for both of them to paint the same room together.

Devise a plan:Let "x" be the time taken by Jose and Mark to paint the same room when they work together.

Work rate of Jose = 1/12 room per hour

Work rate of Mark = 1/15 room per hour

Work rate of both Jose and Mark together = Work rate of Jose + Work rate of Mark= 1/12 + 1/15= (5 + 4)/60= 9/60= 3/20 room per hour

Let the time taken by both Jose and Mark to paint the same room together be "x" hours.

So, (Work done by Jose and Mark together in x hours) = (Total work)⇒ (3/20) × x = 1⇒ x = 20/3 hours

Carry out the plan: The time taken by both Jose and Mark to paint the same room together is 20/3 hours.

So, the answer is 6 hours and 40 minutes.

Evaluate the answer:The time taken by both Jose and Mark to paint the same room when they work together is 20/3 hours or 6 hours and 40 minutes.

Therefore, the time taken to paint the room when they work together is 6 hours and 40 minutes.

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The value of x can be calculated by solving the given equation 678x = E^x + 691. Let's look at how to solve this equation for x.

We have to find the value of x which satisfies the given equation. Unfortunately, there is no analytical solution to this equation, which means we cannot find x in terms of elementary functions. We can, however, use numerical methods to approximate its value. One such method is the Newton-Raphson method, which involves making an initial guess for the value of x and then iterating until a satisfactory level of accuracy is achieved. Here, we will use x = 0 as our initial guess:
x1 = x0 - f(x0)/f'(x0)
where f(x) = 678x - E^x - 691 and f'(x) is the first derivative of f(x):
f'(x) = 678 - E^x
Substituting x = 0, we get:
x1 = 0 - f(0)/f'(0)
= - 0.00915857

We can repeat this process to get a more accurate value for x. Let's do it twice more: x2 = x1 - f(x1)/f'(x1)
= -0.00915857 - f(-0.00915857)/f'(-0.00915857)
= 0.117851
x3 = x2 - f(x2)/f'(x2)
= 0.117851 - f(0.117851)/f'(0.117851)
= 0.110678
So, the value of x that satisfies the given equation to a high degree of accuracy is x = 0.110678.
Given equation is 678x = E^x + 691
Subtract E^x from both the sides, we get
678x - E^x = 691

Since, there is no analytical solution to this equation, so we cannot find x in terms of elementary functions. We can, however, use numerical methods to approximate its value. One such method is the Newton-Raphson method, which involves making an initial guess for the value of x and then iterating until a satisfactory level of accuracy is achieved.

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If we use 85 grams of stone, 25.92 milliliters of water is needed. To find this, we nee to up a proportion based on the ratio of stone to water.

We know that the ratio of stone to water is 263 grams to 80 milliliters. We can set up a proportion:

263 grams / 80 milliliters = 85 grams / x milliliters

Cross-multiplying, we get:

263x = 85 * 80

Dividing both sides by 263, we find:

x = (85 * 80) / 263

Evaluating this expression, we get x ≈ 25.92 milliliters of water. Since the question asks for the rounded number, we can round this to 26 milliliters of water when using 85 grams of stone.

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Answer:

  [tex]\dfrac{5m+45}{m^3+4m^2-41m+36},\quad\dfrac{6m^2-24m}{m^3+4m^2-41m+36}[/tex]

Step-by-step explanation:

You want the rational expressions written with a common denominator:

  (5)/(m^(2)-5m+4), (6m)/(m^(2)+8m-9)

Each expression can be factored as follows:

  [tex]\dfrac{5}{m^2-5m+4}=\dfrac{5}{(m-1)(m-4)},\quad\dfrac{6m}{m^2+8m-9}=\dfrac{6m}{(m-1)(m+9)}[/tex]

The factors of the LCD will be (m -1)(m -4)(m +9). The first expression needs to be multiplied by (m+9)/(m+9), and the second by (m-4)/(m-4).

Expressed with a common denominator, the rational expressions are ...

  [tex]\dfrac{5(m+9)}{(m-1)(m-4)(m+9)},\quad\dfrac{6m(m-4)}{(m-1)(m-4)(m+9)}[/tex]

In expanded form, the rational expressions are ...

  [tex]\boxed{\dfrac{5m+45}{m^3+4m^2-41m+36},\quad\dfrac{6m^2-24m}{m^3+4m^2-41m+36}}[/tex]

<95141404393>

The best reasons not to pay $39 for a leash are:The person may not have enough funds to afford it.The person may be able to find a similar leash for a lower price.

Given Cost function is:

C(x) = 4x + 10

Revenue function is:

R(x) = -2x² + 44x

Profit function is the difference between Revenue and Cost functions.

Therefore, Profit function is given by:

P(x) = R(x) - C(x)

P(x) = -2x² + 44x - (4x + 10)

P(x) = -2x² + 40x - 10

In order to find the number of leashes which need to be sold to maximize the profit, we need to find the vertex of the parabola of the Profit function.

Therefore, the vertex is: `x = (-b) / 2a`where a = -2 and b = 40.

Putting the values of a and b, we get:

x = (-40) / 2(-2) = 10

Thus, 10 designer dog leashes need to be sold to maximize the profit.

To find the maximum profit, we need to put the value of x in the profit function:

P(x) = -2x² + 40x - 10

P(10) = -2(10)² + 40(10) - 10

= 390

The maximum profit is $390.

To find the price to charge per leash to maximize profit, we need to divide the maximum profit by the number of leashes sold:

Price per leash = 390 / 10

= $39

The best reasons to pay $39 for a leash are:

These leashes may be of high quality or design.These leashes may be made of high-quality materials or are handmade.

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We have shown that max ∀1≤|z|≤1 ∣f(z)∣=|a|+|b|. To show that max ∀1≤|z|≤1 ∣f(z)∣=|a|+|b|, we first note that f(z) is a continuous function on the closed disk R={z: |z| ≤ 1}. By the Extreme Value Theorem, f(z) attains both a maximum and minimum value on this compact set.

Let's assume that max ∣f(z)∣ is attained at some point z0 inside the disk R. Then we must have |f(z0)| > |f(0)|, since |f(0)| = |b|. Without loss of generality, let's assume that a ≠ 0 (otherwise, we can redefine b as a and a as 0). Then we can write:

|f(z0)| = |az0^n + b|

= |a||z0|^n |1 + b/az0^n|

Since |z0| < 1, we have |z0|^n < 1, so the second term in the above expression is less than 2 (since |b/az0^n| ≤ |b/a|). Therefore,

|f(z0)| < 2|a|

This contradicts our assumption that |f(z0)| is the maximum value of |f(z)| inside the disk R, since |a| + |b| ≥ |a|. Hence, the maximum value of |f(z)| must occur on the boundary of the disk, i.e., for z satisfying |z| = 1.

When |z| = 1, we can write:

|f(z)| = |az^n + b|

≤ |a||z|^n + |b|

= |a| + |b|

with equality when z = -b/a (if a ≠ 0) or z = e^(iθ) (if a = 0), where θ is any angle such that f(z) lies on the positive real axis. Therefore, the maximum value of |f(z)| must be |a| + |b|.

Hence, we have shown that max ∀1≤|z|≤1 ∣f(z)∣=|a|+|b|.

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1. Set of states in the United States whose names start with a C: {Connecticut, California, Colorado} (Set-builder notation: {x | x is a state in the United States and the name of the state starts with a C})

2. Set of students in the class who have at least one brother: {Alice, Bob, Charlie, Emma, Jack} (Set-builder notation: {x | x is a student in the class and x has at least one brother})

Set of states in the United States whose names start with a C:

By listing: {Connecticut, California, Colorado}

Set-builder notation: {x | x is a state in the United States and the name of the state starts with a C}

Set of students in the class who have at least one brother:

By listing: {Alice, Bob, Charlie, Emma, Jack}

Set-builder notation: {x | x is a student in the class and x has at least one brother}

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Based on the given data and a chi-square test of independence with a significance level of 0.10, we can say that community college statistics students and university statistics students differ significantly in their use of technology on their statistics homework.

To test whether there is a difference between community college statistics students and university statistics students in what technology they use on their homework, we can use a chi-square test of independence.

The null hypothesis (H0) is that there is no difference in the proportion of community college and university students using each type of technology. The alternative hypothesis (Ha) is that there is a difference.

We first need to calculate the expected frequencies for each cell under the assumption that H0 is true. We can do this by multiplying the row total and column total for each cell, and then dividing by the total sample size. For example, the expected frequency for the cell with community college students using a computer and university students using a computer is:

Expected frequency = (52 + 46) × (52 + 108 + 23 + 46 + 74 + 39) / (52 + 108 + 23 + 46 + 74 + 39) = 47.57

We can repeat this calculation for all the other cells.

Next, we can calculate the chi-square test statistic using the formula:

χ^2 = Σ [(O - E)^2 / E]

where O is the observed frequency and E is the expected frequency for each cell.

Performing the calculations, we get:

χ^2 = (52-47.57)^2/47.57 + (108-105.86)^2/105.86 + (23-29.57)^2/29.57 + (46-47.57)^2/47.57 + (74-70.14)^2/70.14 + (39-41.29)^2/41.29 = 5.71

Using a chi-square distribution table or calculator with 2 degrees of freedom (because there are 3 rows and 2 columns), the critical value at a significance level of 0.10 is 4.61.

Since our calculated value of χ^2 (5.71) is greater than the critical value (4.61), we reject the null hypothesis and conclude that there is a significant difference between community college and university statistics students in what technology they use on their homework.

In conclusion, based on the given data and a chi-square test of independence with a significance level of 0.10, we can say that community college statistics students and university statistics students differ significantly in their use of technology on their statistics homework.

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