Transversal relations ( find x)

With a price of $1.25, 7,500 goods would be sold and a profit of $3,635 would be made. This price would maximize profit.

Profit in economics is the difference between an economic entity's revenue from outputs and all of its input costs.

It is equivalent to total income less total expenses, which includes both direct and indirect expenses.

Establishing sales methods and capturing your clients' interest requires first analyzing how profitable your goods and services are.

So, since you need to sell a certain number of items to maximize your profit, setting the price at $ 1.50 will enable you to sell 5000 items, and lowering the price by $10 will enable you to sell an additional 1000 items.

Assuming your fixed costs total $ 2000 and the cost of production per item is $ 0.50, you must determine the price to set per item, the number of items sold, and the maximum profit.

(5000 x 1.50) - (5000 x 0.50) - 2000 = 3000

(6000 x 1.40) - (6000 x 0.50) - 2000 = 3400

(7000 x 1.30) - (7000 x 0.50) - 2000 = 3600

(8000 x 1.20) - (8000 x 0.50) - 2000 = 3600

(7500 x 1.25) - (7500 x 0.50) - 2000 = 3625

Therefore, with a price of $1.25, 7,500 goods would be sold and a profit of $3,635 would be made. This price would maximize profit.

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Correct question:
You want to sell a certain number n of items in order to maximize your profit. Market research tells you that if you set the price at $1.50, you will be able to sell 5000 items, and for every 10 cents you lower the price below $1.50 you will be able to sell another 1000 items. Suppose that your fixed costs (“start-up costs”) total $2000, and the per item cost of production (“marginal cost”) is $0.50.

Solve the above engineering problem using calculus.

Hints: Find the price to set per item and the number of items sold in order to maximize profit, and also determine the maximum profit you can get.

To achieve M3, you must present your work using coherent, logical development of principles/concepts in determining the maximum profit and use technical language accurately.

To achieve D1, you must evaluate the validity of your answer using the given data.

The expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x is: x * (1 - 1/8).

An expression in mathematics is a combination of numbers, variables, and operations that represent a value or set of values.

The expression calculates the reduction of x by 1/8 of x by subtracting 1/8 of x from x, which is x * 1/8. By subtracting this from x, the expression calculates x reduced by 1/8 of x. The expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x is:

x * (1 - 1/8).

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The component of a linear programming model that is NOT listed is "Decision variables."

A linear programming model consists of several components that work together to optimize a given objective while considering various constraints. The components of a linear programming model include:

Constraints: These are the limitations or restrictions that define the feasible set of solutions. Constraints restrict the values that decision variables can take.

Objective Function: This function represents the goal or objective of the linear programming problem. It is either minimized or maximized based on specific criteria.

Feasible Region: Also known as the feasible set or feasible solution space, this refers to the collection of all points that satisfy each constraint in the linear programming problem. It represents the set of possible solutions that meet all the given constraints.

However, "Decision variables" is not a component of a linear programming model but rather the unknowns or variables that we want to determine in order to optimize the objective function.

Decision variables are not a component of a linear programming model. The components of a linear programming model include constraints, objective function, and feasible region. The feasible region refers to the collection of all points that satisfy each constraint in the linear programming problem.

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Step-by-step explanation:

(0,-3) and (1,0) this are the point

Answer:

\(x = -8\)

Step-by-step explanation:

\(\begin{cases}2y = 2x + 12\\2-y = 4\end{cases}\)

It would be easier to start with the second equation.

\(2 - y = 4 \text{ // Add y and subtract 4}\\\to 2 - y - 4 = 4 - y - 4\\\to -2 = y\)

From here, we can substitute \(y = -2\) into the first equation, to solve for \(x\).

\(2(-2) = 2x + 12\\\to -4 = 2x + 12 \text{ // Subtract 12 on both sides}\\\to -4 - 12 = 2x + 12 - 12\\\to -16 = 2x \text{ // Divide by 2}\\\to -\frac{16}2 = \frac{2x}2\\\to -8 = x\)

By solving the systems of equations we can say there were 373 children and 235 adults who swam at the public pool that day.

To determine the number of children and adults who swam at the public pool, we can set up a system of equations based on the given information.

Let's assume the number of children is represented by 'C' and the number of adults by 'A'.

From the problem, we have the following information:

1. The total number of people who used the pool is 608:

C + A = 608

2. The total receipts from admission were $1029.50:

1.50C + 2.00A = 1029.50

To solve this system of equations, we can use various methods, such as substitution or elimination.

Using the substitution method, we can solve the first equation for C:

C = 608 - A

Substituting this value into the second equation:

1.50(608 - A) + 2.00A = 1029.50

912 - 1.50A + 2.00A = 1029.50

0.50A = 117.50

A = 235

Substituting the value of A back into the first equation:

C + 235 = 608

C = 373

Therefore, there were 373 children and 235 adults who swam at the public pool that day.

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Answer:

b

Step-by-step explanation:

formula

(y-k)^2 = 4a(x-h) horizontal parabol

a = 7 - 2 =5

(y-k)^2 = 4*5*(x-h)

(y-k)^2 = 20(x-h)

k=3 , h=2

(y-3)^2 = 4a(x-2)

Interest = A - (50 * 456)

To determine how much you will have in the IRA when you retire at age 65, we can use the formula A = P[(1 + r)^t - 1] / r, where A is the future value, P is the monthly deposit, r is the monthly interest rate, and t is the number of months.

a. In this case, the monthly deposit is 50, the monthly interest rate is 5% or 0.05, and the number of months is (65 - 27) * 12 = 456 (from age 27 to 65).

Using the formula, we can calculate:
A = 50[(1 + 0.05)^456 - 1] / 0.05

b. To find the interest, we can subtract the total deposits from the future value:
Interest = A - (P * t)

In this case:
Interest = A - (50 * 456)

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The 9th term of the geometric sequence is 2304.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Example:

2, 4, 8, 16 is a geometric sequence.

We have,

9, -18, 36

First term = 9

Common difference = -18/9 = -2

Now,

The nth term of a geometric sequence.

= a\(r^{n-1}\)

For n = 9,

= 9 \((-2)^{9 - 1}\)

= 9 x \((-2)^8\)

= 9 x 256

= 2304

Thus,

The 9th term is 2304.

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Match the following with the given options:

1. An angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon - Central angle of a regular polygon2. The common center of its inscribed and circumscribed circles - Center of a regular polygon3. The distance from the center of the polygon to a vertex - Radius of a regular polygon4. The perpendicular distance from the center of the polygon to a side - Apothem of a regular polygonA polygon is a two-dimensional object that has three or more straight sides and angles. A regular polygon is a polygon with equal sides and equal angles.

A regular polygon is a shape that has all its sides the same length and all of its angles the same degree. Below are the matched answers for the given options.1. An angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon - Central angle of a regular polygonThe central angle of a regular polygon is defined as the angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon.

The angle measures (360 / n) degrees, where n is the number of sides of the polygon.2. The common center of its inscribed and circumscribed circles - Center of a regular polygonThe center of a regular polygon is the point at which its axes of symmetry intersect. The center is also the common center of the circumscribed and inscribed circles.3. The distance from the center of the polygon to a vertex - Radius of a regular polygonThe radius of a regular polygon is defined as the distance from the center of the polygon to any vertex. It is also the distance from the center of the polygon to the midpoint of a side

.4. The perpendicular distance from the center of the polygon to a side - Apothem of a regular polygonThe apothem of a regular polygon is defined as the perpendicular distance from the center of the polygon to a side. It is also the radius of the inscribed circle.

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It can be inferred that there is a statistically significant result if the confidence interval excludes the value of zero effect.

Confidence Interval;

In statistics, confidence is another word for probability. For instance, if you create a confidence interval with a 95% confidence level, you can be sure that 95 times out of 100 the estimate will fall between the upper and lower values indicated by the confidence interval.

Therefore,

The confidence level is 95% if your significance level is 0.05. The hypothesis test is statistically significant if the P value is lower than your significance (alpha) level. The findings are statistically significant if the confidence interval excludes the null hypothesis value. 0

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Answer:

For the first one the answer is:

<K = 31°

Sorry I don't know the second one.

Answer:35

Step-by-step explanation:

take 180 and subtract those numbers and u get ur answer

Answer:

the answet is x=-2 and y=5

The next whole number after 434 in the base-five system is 440

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

Number = 434

Base = base 5

The general rule is that

In a number base system n, the highest number in the system is n - 1

Using the above as a guide, we have the following:

In a number base system 5, the highest number in the system is 4

So, we have

434 + 1

Evaluate the sum

434 + 1 = 440

Hence, the next whole number after 434 in the base-five system is 440

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Step-by-step explanation:

Decreased by 92% = 8% of original

8% of original value = New value = 13.12

100% of original value = 13.12 * (100/8) = 164.

The original value is 164.

it take for all the water to drain from the tank is 1 hour 11 min 26 sec for a water tank is shaped like a vertical circular cylinder

Using the Bernoulli's laws to use the conserved energy

Solve the speed and the radio of this speed of the tank is open to the air

p₀ + ρgh₀ + ½ρv₀² = p₁ + ρgh₁ + ½ρv₁²

5000Pa + 1000kg/m³ * 9.8m/s² * 0.800m + 0 = 0 + 0 + ½ * 1000kg/m³ *

v²

v² = 25.68  m²/s²

v1 = 5.06 m/s

Because it is open the cylinder tank so P=0 pa so:

0 Pa + 1000kg/m³ * 9.8m/s² * 0.800m + 0 = 0 + 0 + ½ * 1000kg/m³ * v²

v² = 15.68  m²/s²

v2 = 3.96 m/s

The ratio on the air is solve using both velocities so:

R = v1/v2 = 5.06 m/s / 3.96 m/s

R = 1.27

Now to find the time it takes for the tank to drain if the tank is open to the air

dh/dt = -u

dh/dt = -v * A/A'

dh/dt = v*(.02m)²/(2.0m)² = -v / 10000

and we can further substitute for v:

dh/dt = -(1/1e4)*√[(p+9800h)/500]

Solve replacing

-(1000/49)*√(49000h) = t + C

-(1000/49)*√(49000*0.8) = 0 + C

C = - 4040.6

Then when h = 0,

t = 4286 s

t = 1 hr, 11 min, 26 sec  

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Answer:

Yes it is possible

Step-by-step explanation:

Given

\(n = 20\)

\(x= 7\) --- correct

\(y = -4\) --- wrong

\(z = 0\) --- empty answer

Required

Is a total of -11 possible?

To do this, we apply trial by error method.

After so many approaches, I found the following solution

\(x \to 3\) -- Got 3 correctly

\(y \to 8\) --- Failed 8

\(z \to 9\) ---- Didn't answer 9

The above will give a score of -11.

We have:

\(3x+8y+9z\)

\(3x+8y+9z = 3 * 7 + 8 * -4 + 9 * 0\)

\(3x+8y+9z = 21-32 + 0\)

\(3x+8y+9z = -11\)

Hence, a score of -11 is possible

The right answer is: E, according to the Central Limit Theorem for proportionality. The statistic is inaccurate.

In probability theory, the central limit theorem establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.

The Central Limit Theorem establishes that for a proportion p in a sample of size n:

The expected value is μ=р

The standard error is s=\(\sqrt{\frac{p(1-p)}{n} }\)

In this problem, the expected value is different of the expected of μ=р , hence, the statistic is biased, and the correct option is E.

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Answer:

i guess 3 rd option is correct. ........hope it helps u ♥♥♥♥

We need to evaluate the line integral ∫CF.dr for two different paths, r1(t) and r2(t), where F = (x^2 + y^2) dx + 2xy dy.

We will use the fundamental theorem of line integrals to determine if F is conservative.

Since F has continuous first-order partial derivatives, we can check if F is conservative by verifying that ∂F/∂y = ∂M/∂x, where M = x^2 + y^2 and N = 2xy are the components of F. We have:

∂F/∂y = 2xy = ∂M/∂x

Therefore, F is conservative.

By the fundamental theorem of line integrals, the line integral of a conservative field depends only on the endpoints of the path, and not on the path itself.

Therefore, we can choose any path that connects the same two endpoints and calculate the line integral along that path.

(a) Using r1(t) = t^5i + t^2j, 0 ≤ t ≤ 2:

We have:

dr/dt = 5t^4i + 2tj

Substituting into F, we get:

F = (t^10 + t^4) dt + 2t^3 dt

Therefore, the line integral along r1(t) is:

∫CF.dr = ∫0^2 F(r1(t)).(dr/dt) dt
= ∫0^2 [(t^10 + t^4) dt + 2t^3 dt] . (5t^4i + 2tj)
= ∫0^2 (5t^15 + 7t^5) dt
= (5/16) (2^16 - 1) + (7/6) (2^6 - 1)

(b) Using r2(t) = 5cos(t)i + 2sin(t)j, 0 ≤ t ≤ π/2:

We have:

dr/dt = -5sin(t)i + 2cos(t)j

Substituting into F, we get:

F = (25cos^2(t) + 4sin^2(t)) dt - 20sin(t)cos(t) dt

Therefore, the line integral along r2(t) is:

∫CF.dr = ∫0^(π/2) F(r2(t)).(dr/dt) dt
= ∫0^(π/2) [(25cos^2(t) + 4sin^2(t)) dt - 20sin(t)cos(t) dt] . (-5sin(t)i + 2cos(t)j)
= ∫0^(π/2) (20cos^2(t) - 45sin^2(t)) dt
= 20(π/4) - 45(1/4)

Hence, the value of the line integral for both paths r1(t) and r2(t) is:

(5/16) (2^16 - 1) + (7/6) (2^6 - 1) = 1247.875

Note that the line integral is the same for both paths, as expected for a conservative field.

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Answer:

5

Step-by-step explanation:

Answer

The average for the next test would be 60

Step-by-step explanation:

50+50+50+50+100= 300

then divide by 5 students

300/5 = 60

Answer: 4% tax

Step-by-step explanation:

41.50- 39.90= 1.60 tax

1.60/ 39.90

SOLUTION

From the question, you currently make 15% flat commission on all sales.

Since you make an average of $3,980 in sales weekly, then Gross income becomes

Hence the answer is $597 weekly

Answer:

144

Step-by-step explanation:

Multiply each option together 9X4X4=144

Given w = cos(12x)sin(2y), where x = 4t and y = t⁴, using chain-rule we can differentiate w with respect to t and x to obtain dt/dw = -sin(12x)sin(2y) / (48t³cos(12x)).

To find dt/dw using the chain rule, we differentiate w with respect to t and x separately. Let's start by expressing w in terms of x and y:

w = cos(12x)sin(2y)

Now, we substitute the given values of x and y:

x = 4t

y = t⁴

To find dt/dw, we need to differentiate w with respect to t and x.

First, let's differentiate w with respect to t. Since x = 4t, we apply the chain rule:

dw/dt = dw/dx * dx/dt

dw/dx = -sin(12x)sin(2y) (differentiating cos(12x) with respect to x)

dx/dt = 4 (given x = 4t)

Therefore, dw/dt = -sin(12x)sin(2y) * 4.

Next, we express dt/dw by taking the reciprocal:

dt/dw = 1 / (dw/dt)

= 1 / (-4sin(12x)sin(2y))

Simplifying further:

dt/dw = -1 / (4sin(12x)sin(2y))

= -sin(12x)sin(2y) / (48t³cos(12x))

Hence, dt/dw is given by -sin(12x)sin(2y) / (48t³cos(12x)), where x = 4t and y = t⁴.

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Answer:

Circumference ~ 233.7

Step-by-step explanation:

Use the distance formula to find the radius of the circle with the two coordinates given. The radius of this circle is about 37.2. Plug 37.2 into the formula 2(pi)r to find the Circumference. The answer is 233.7 rounded to the nearest tenth.