an office space is for rent downtown. The rate is $16 per square foot per month. The space measures 22 ft x 18 ft. How much will cost to rent this space for a year.

A. $56,800
B. $6336
C. $76,032
D. $39,600

If the cost of advertising was $100,000 and the reach or circulation was 10,000,000 people, then the CPM is $10.

Cost per thousand (CPM), which is also called cost per mille, is a marketing word used to denote the price of 1,000 advertisement prints on one web page. If a publisher of a website charges $2.00 CPM, that means an advertiser must pay $2.00 for every 1,000 prints of its ad.

The CPM is calculated by dividing the cost of the advertisement by the number of people reached and then multiplying by 1000.

Given that the cost of advertising was $100,000 and the reach was 10,000,000 people, the CPM can be calculated as follows:

CPM = ($100,000 / 10,000,000) × 1000 = $10.

So, the CPM is $10.

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Answer:g

Step-by-step explanation:

Answer:

Undifined

Step-by-step explanation:

To maximize revenue in a monopoly market with a demand function of p = 195 - 0.40x and a revenue function of R = px, the price that will maximize revenue is $97.50.

The revenue function is given by R = px, where p is the price per unit and x is the number of units sold. In a monopoly market, the demand function represents the relationship between price and quantity demanded.

To find the price that maximizes revenue, we need to determine the price that corresponds to the maximum point of the revenue function. The revenue function can be rewritten as R = (195 - 0.40x)x.

To find the maximum point, we can take the derivative of the revenue function with respect to x and set it equal to zero. Differentiating R with respect to x, we get dR/dx = 195 - 0.80x. Setting this derivative equal to zero, we have 195 - 0.80x = 0.

Solving for x, we find x = 243.75. Substituting this value back into the demand function p = 195 - 0.40x, we can calculate the price that maximizes revenue: p = 195 - 0.40(243.75) = $97.50.

Therefore, the price that will maximize revenue in this monopoly market is $97.50.

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The function, p(x) = cos²x/ sin 2x  has a limit that is undefined (does not exist) as x approaches 0.

The correct option therefore option b;

b. As x approaches 0, the limit of p(x) does not exist

Here, we have,

We have,

The given function is presented as follows;

p(x) = cos²x/ sin 2x

Required;

The limit of the function as x approaches (zero) 0

we have,

The limit of a function at a given point within the domain of the function is the value of the function as the function's argument approaches a.

Therefore, the limit of the given function at the point x = 0 is given by the function's value as the argument of the function, x approaches 0.

cos²(0) = 1

sin(2×0) = sin(0) = 0

Therefore;

p(x) = cos²0/ sin 2(0) = infinity

Therefore, the limit of the function does not exist as x approaches 0

The correct option is therefore, option b

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Answer:The answer 60.7371385562.

Step-by-step explanation:

The square root of 3,689 is approximately 60.74.

\(\sqrt{3689} = 60.74\) (approx)

The equation of the osculating plane is 24x + 12√10(y-π) - 3z - 6π√10 = 0.

Given curve,  x=5sin(3t), y=t, z=5cos(3t); (0, π,-5).

To find the normal plane equation, the unit normal vector of the curve at the point must first be found. The unit tangent and unit binormal vectors are both derived from the unit tangent vector.

To calculate the tangent vector, the following steps are taken:

Equation of the curve is given as,

x=5sin(3t),

y=t,

z=5cos(3t).

Differentiating above equation with respect to t, we get;

dx/dt = 15 cos(3t)

dy/dt = 1

dz/dt = -15 sin(3t)

The unit tangent vector T is given by,

T = 1/√(dx/dt² + dy/dt² + dz/dt²) (dx/dt i + dy/dt j + dz/dt k)

Substituting the given values, we get

T = (3√10/10) i + (1/√10) j - (3/√10) k

Since we have to find the normal vector, we will differentiate the unit tangent vector,T, to get the unit normal vector N.

Let's differentiate T to obtain N:

dn/dt = 1/√(dx/dt² + dy/dt² + dz/dt²) [d²x/dt² i + d²y/dt² j + d²z/dt² k] + {(-1/2)(2t)(2t')/√(dx/dt² + dy/dt² + dz/dt²)³} [dx/dt i + dy/dt j + dz/dt k]

On substituting, we get,

N = (-9/√10) i + (3√10/10) j + (9/√10) k

Therefore, the normal plane equation is given by,(-9/√10)(x) + (3√10/10)(y-π) + (9/√10)(z+5) = 0.

To find the osculating plane equation, the coordinates of the point of tangency (P) and the principal normal vector, N, are required.

The equation of the osculating plane is then written as follows:

xT + yN = c,

where c is a constant value that is calculated by substituting the coordinates of P into the equation.Let us calculate the value of P and N,

To find the value of P, we substitute t=π in the given curve,

Thus,

x(π) = 5sin(3π) = 0,y(π) = π,z(π) = 5cos(3π) = -5

Therefore, the point of tangency P is (0, π, -5).

From the above derivation, we know that the unit normal vector N is(-9/√10) i + (3√10/10) j + (9/√10) k

Therefore, the unit principal normal vector is given by,

B = T x N= [(3√10/10) i + (1/√10) j - (3/√10) k] x [- (9/√10) i + (3√10/10) j + (9/√10) k]

= [(3√10/10) (9/√10) + (3/√10) (3/√10)] i + [(9/√10) (1/√10) - (3√10/10) (- 3/√10)] j + [(1/√10) (- 3/√10) - (3√10/10) (3√10/10)] k

= (24/√10) i + (12√10/10) j - (3/√10) k

The osculating plane equation is given by,

xT + yB = c

Now substituting x=0, y=π and z=-5 in above equation, we get

c = π(12√10/10) = (6π√10/5)

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Answer:

\(\displaystyle f'(x) = \frac{4}{x^2}\)

General Formulas and Concepts:

Calculus

Limits

Differentiation

The definition of a derivative is the slope of the tangent line:                             \(\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}\)

Step-by-step explanation:

Step 1: Define

Identify.

\(\displaystyle f(x) = -\frac{4}{x}\)

Step 2: Differentiate

∴ the derivative of the given function will be equal to 4 divided by x².

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

79/40 = 1.975

162.5% = 1.625

1.975-1.625 = 0.35

Step-by-step explanation:

a. (0,0), (5,0), (3.75, 3.75), (3.5,4.5), (0,8);

b. x = 3.5, y = 4.5, OFV = 59.5;

c. s1 = 0, s2 = 2, s3 = 0.

a. The extreme points of the feasible region are the vertices of the polygon formed by the intersection of the constraint lines. In this case, the extreme points are (0,0), (5,0), (3.75, 3.75), (3.5,4.5), and (0,8).

b. To find the optimal solution and the objective function value, we evaluate the objective function at each extreme point and choose the point that maximizes the objective function. In this case, the point (3.5, 4.5) maximizes the objective function with a value of 59.5. Therefore, the optimal solution is x = 3.5 and y = 4.5, and the objective function value is 59.5.

c. The slack variables represent the surplus or slack in each constraint. We calculate the slack variables by subtracting the actual value of the left-hand side of each constraint from the right-hand side. In this case, the values of the slack variables are s1 = 0 (indicating no slack in the first constraint), s2 = 2 (indicating a surplus of 2 in the second constraint), and s3 = 0 (indicating no slack in the third constraint).

Therefore, the correct option is:

a. (0,0), (5,0), (3.75, 3.75), (3.5,4.5), (0,8);

b. x = 3.5, y = 4.5, OFV = 59.5;

c. s1 = 0, s2 = 2, s3 = 0.

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Part A: The point (2, 80) represents that when the number of hours is 2, the number of miles of water in the tank is 80.

Part B: y = 40x

The theory used in this question is the concept of proportional relationships.

A proportional relationship between two variables is one in which one variable is a constant multiple of the other.

In this case, the number of miles of water in the tank is a constant multiple of the number of hours.

The equation y = mx is used to describe a proportional relation, where m is the constant of proportionality.

The equation for the proportional relationship between hours, x, and number of miles, y, of water in a tank can be written in the form of y = mx. To find the value of m, we can use the point (2, 80) from the graph. We know that when x = 2, y = 80. We can use this information to solve for m.

m = y/x

m = 80/2

m = 40

Therefore, the equation for the proportional relationship is y = 40x.

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The inequality expression given as 2 - |6 + 12x| > -28 has a solution of -3 < x < 2

From the question, the inequality is given as

2-|6+12x|>-28

Rewrite properly as

2 - |6 + 12x| > -28

Subtract 2 from both sides

- |6 + 12x| > -30

Divide both sides by -1

|6 + 12x| < 30

Remove the absolute bracket

So, we have the following representation

-30 < 6 + 12x < 30

Add -6 to all sides of the inequality

So, we have

-36 < 12x < 24

Multiply through by 1/12

So, we have

-3 < x < 2

Hence, the solution to the expression is -3 < x < 2

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The translation transformation of the parent function in the graph, indicates that the equation for each of the specified graphs, using the form y = f(x - h) + k, are;

a. y = f(x) + 3

b. y = f(x - 3)

c. y = f(x - 1) + 2

A transformation of a function is a function that takes a specified function or graph and modifies them into another function or graph.

The points on the graph of the specified function f(x) in the diagram are; (0, 0), (1.5, 1), (-1.5, -1)

The graph is the graph of a periodic function, with an amplitude of (1 - (-1))/2 = 1, and a period of about 4.5

Therefore, we get;

a. The graph in part a consists of the parent function shifted up three units. The transformation that can be represented by the vertical shift of a function f(x) is; f(x) + a or f(x) - a

Therefore, the translation of the graph of the parent function is; f(x) + 3

b. The graph of the parent function in the graph in part b is shifted to the right two units, and the vertical translation is zero units, down or up.

The translation of the graph of a function by h units to the right or left can be indicated by an subtraction or addition of h units to the value of the input variable, therefore, the translation of the function in the graph of b is; y = f(x - 3) + 0 = f(x - 3)

c. The translation of the graph in part c are;

A vertical translation 2 units upwards

A horizontal translation 1 unit to the right

The equation representing the graph in part c is therefore; y = f(x - 1) + 2

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Given:

A table is given

Required:

To calculate mean of the data

Explanation:

We know the formula to calculate mean

Required answer:

75

(a) The range of c₁ (the objective coefficient of x₁) for which this BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ (the right-hand side of the second constraint) for which this BFS remains optimal is 3 ≤ b₂ < 4.

(c) The dual price of the second constraint is 0.

(a) The optimality condition for a linear programming problem requires that the objective coefficient of a non-basic variable (here, x₁) should not increase beyond the dual price of the corresponding constraint. In this case, the dual price of the second constraint is 0, indicating that increasing the coefficient of x₁ will not affect the optimality of the basic feasible solution. Therefore, the range of c₁ for which the BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ for which the BFS remains optimal is determined by the allowable range of the corresponding dual variable. In this case, the dual price of the second constraint is 0, implying that the dual variable associated with that constraint can vary within any range. As long as 3 ≤ b₂ < 4, the dual variable remains within its allowable range, and thus, the BFS remains optimal.

(c) The dual price of a constraint represents the rate of change in the objective function value per unit change in the right-hand side of the constraint, while keeping all other variables fixed. In this case, the dual price of the second constraint is 0, indicating that the objective function value does not change with variations in the right-hand side of that constraint.

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If the $69 cost of electric-toothbrush includes 50% "price-markup", then the cost for the store to purchase it was (d) $46.

Let the cost for the store to purchase the electric toothbrush be = "C".

We know that the "final-price" of the toothbrush, includes the 50% markup, which is = $69,

The price with the 50% markup is calculated by adding 50% of the original cost to the original cost.

So, we have :

⇒ Final price = Original cost + 50% of original cost,

Substituting the value of "final-price" as $69,

We get,

⇒ $69 = C + 0.5C,

⇒ $69 = 1.5C,

⇒ C = $46;

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

An electric toothbrush costs $69, including a 50% price markup. What was the cost for the store to purchase the electric toothbrush?

(a) $19.00

(b) $23.00

(c) $34.50

(d) $46.00

The absolute maximum value is f(0,±2) = 4 and the absolute minimum value is f(1,0) = -1.

The given function is  F(x,y) = \(x^{2}\) + \(y^{2}\) - \(2x\)   → 1

D is the closed triangular region with the vertices (0,0), (0,2) and (0,-2).

Differentiate 1 partially with respect to x:

df/dx =  \(x^{2}\) + \(y^{2}\) - \(2x\)

\(f^{'}\)(x) = 2x - 2

Differentiate 1 partially with respect to y:

df/dy = \(x^{2}\) + \(y^{2}\) - \(2x\)

\(f^{'}\)(y)  = 2y

Consider \(f^{'}\)(x) = 0 and \(f^{'}\)(y) = 0 to find the critical points.

\(f^{'}\)(x) ⇒ 2x -2 =0

x = 1

\(f^{'}\)(y) ⇒ 2y

y = 0

Thus, the critical point is (x,y) = (1,0).

Calculate the values of f(x,y) at (0,0), (0,2), (0,-2) and (1,0).

At (x,y) = (0,0)

f(0,0) ⇒ 0 + 0 - 0 = 0

At (x,y) = (0,2)

f(0,2) ⇒ 0 + 4 - 0 = 4

At (x,y) = (0,-2)

f(0,-2) ⇒ 0 + 4 - 0 = 4

At (x,y) = (1,0)

f(1,0) ⇒ 1 + 0 - 2 = -1

Therefore, the absolute maximum is f(0,±2) = 4 and the absolute minimum is f(1,0) = -1.

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Answer:

£252

Step-by-step explanation:

The ratio of their profit is 9 ; 5 = 9x : 5x ( x is a multiplier )

Bill gets £72 more than Mischa , then

9x = 5x + 72 ( subtract 5x from both sides )

4x = 72 ( divide both sides by 4 )

x = 18

Total received = 9x + 5x = 14x = 14(18) = £252

Answer:

No Solution

Step-by-step explanation:

None

Answer:

he can rolled upto 70 times when he roled in 35 time

Answer:

12^2 + 4x

Step-by-step explanation:

We need to solve the area of these two rectangles separately.

Equation: 4x(3x+1) --> 12x + 4

Area: 12x^2 + 4x

Hope this helps.

Answer:

0.9/3=0.3 First one

Step-by-step explanation:

0.9/3=0.3

The boxes are being divided into 3 equal parts and each section has 0.30 squares

Answer:

The answer is A: 0.9÷3=0.3

Step-by-step explanation:

The boxes are equally divided into thirds

Answer: 1/2

11/16 - 3/16 = 1/2

Answer:

Sum of the first 70 terms is 12,775

Step-by-step explanation:

For the 9th term, the formula is;

a + 8d = 50

For the 12th

a + 11d = 65

Subtract this from the equation above;

3d = 15

d = 15/3 = 5

To get a, we have a + 8(5) = 50

a = 10

The 70th term

will be

a + 69d

= 10 + 69(5)

= 355

Sum of the first 70

= n/2(a + L)

= 70/2( 10 + 355)

= 35 * 365 = 12,775

8x-5[8]=16

8x=16+40

8x=56

x=7

The 90% confidence interval obtained from examining 653 customers in one fast food chain's drive-through has a lower bound of 178.2 seconds and an upper bound of 181.6 seconds. This means that based on the sample data collected from the 653 customers, we can be 90% confident that the true average drive-through service time for this fast food chain falls within the range of 178.2 seconds to 181.6 seconds.

In other words, if we were to repeatedly sample 653 customers from the same fast food chain's drive-through and calculate confidence intervals, approximately 90% of those intervals would contain the true average service time of the entire population of customers.

The range between the lower and upper bounds of the confidence interval provides an estimate of the precision or uncertainty associated with our sample mean.

The narrower the interval, the more precise our estimate of the true population mean becomes. In this case, the interval is relatively narrow, indicating a relatively precise estimate of the average drive-through service time for this fast food chain based on the sample data.

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The statement provided is actually the opposite of the correct definitions.

In database terminology, a field refers to a single piece of information that is stored in a database table. A field can contain a variety of data types such as text, numbers, dates, and so on. For example, in a database table of customer information, there might be fields for the customer's name, address, phone number, and email.

A record, on the other hand, is a complete set of information about an entity in a database. A record consists of a collection of fields that are all related to each other. For example, in the customer information table mentioned above, a single record might represent a specific customer, and would contain all the fields related to that customer (name, address, phone number, email, etc.).

So to summarize, a field is a single piece of information within a record, while a record is a collection of related fields that together represent a complete set of information about an entity in a database.

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For a wheelchair ramp with a length of 82 inches has a horizontal distance of 80 inches is mathematically given as

v = 18inches

Generally, the equation for vertical distance is mathematically given as

r^2 = h^2 + v^2

(82)^2 = (80)^2 +v^2

6724 = 6400 + v^2

v^2 = 6724-6400

v^2 = 324

v = \(\sqrt{324}\)

v = 18inches

In conclusion, the ramp's vertical distance is

v = 18inches

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