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What is the value of the expression 18 + (6 - 3) 32 - 9?

To find the surface area and volume of a pentagonal pyramid with an apothem of 3√2 and a height of 3, we need to use several formulas.

The apothem of a regular pentagon is the distance from the center of the pentagon to the midpoint of one of its sides. The area of a regular pentagon with side length s and apothem a is given by the formula:

A = (5/2) × s × a

The volume of a pyramid is given by the formula:

V = (1/3) × A × h

where A is the base area of the pyramid and h is the height of the pyramid.

To find the surface area of the pentagonal pyramid, we need to find the area of each face and add them together. Each face of the pentagonal pyramid is a triangle with one side as the base of the pyramid and the other two sides as the slant height of the pyramid. The slant height can be found using the Pythagorean theorem:

l = √(h^2 + a^2)

where h is the height of the pyramid and a is the apothem of the base.

Substituting the given values, we get:

l = √(3^2 + (3√2)^2)

l = √(9 + 18)

l = √27

l = 3√3

The base of the pyramid is a regular pentagon, so we can find its area using the formula:

A = (5/2) × s × a

where s is the length of one side of the pentagon.

The apothem of the pentagon is given as 3√2, so we can find the length of one side using the apothem and the formula for the apothem of a regular pentagon:

a = s / (2√(5-2√5))

3√2 = s / (2√(5-2√5))

s = 6√(5-2√5)

Therefore, the base area of the pyramid is:

A = (5/2) × s × a

A = (5/2) × 6√(5-2√5) × 3√2

A ≈ 31.18

To find the surface area of the pyramid, we need to find the area of each of the five triangular faces. Each face has the same base area A and the same slant height l, so we can use the formula for the area of a triangle:

A = (1/2) × b × h

where b is the length of the base and h is the height of the triangle (which is the slant height of the pyramid).

Substituting the given values, we get:

A = (1/2) × A × l

A = (1/2) × 31.18 × 3√3

A ≈ 26.83

Since there are five triangular faces, the total surface area of the pentagonal pyramid is:

S = 5 × A

S ≈ 134.13

To find the volume of the pyramid, we can use the formula:

V = (1/3) × A × h

Substituting the given values, we get:

V = (1/3) × 31.18 × 3

V ≈ 31.18

Therefore, the surface area of the pentagonal pyramid is approximately 134.13 square units, and the volume of the pyramid is approximately 31.18 cubic units.

In the binomial expansion of (1−4x) P, |x|< 1/4, the coefficient of x² is equal to the coefficient of x4 and the coefficient of x³ is positive. The value of p is greater than 2.

The binomial expansion of (1-4x)^P is given by:

(1-4x)^P = 1 + P(-4x) + C(P,2)(-4x)^2 + C(P,3)(-4x)^3 + ...

We know that the coefficient of x^2 is equal to the coefficient of x^4, so we can set the terms equal to each other:

C(P,2)(-4)^2 = C(P,4)(-4)^4

We also know that the coefficient of x^3 is positive, so we can set the term greater than 0:

C(P,3)(-4)^3 > 0

Solving for P in the first equation, we get:

P(P-1)(-4)^2 = P(P-1)(16) = P(P-1)(4)(4) = P(P-1)(C(2,1))(C(3,1))

Solving for P in the second equation, we get:

P(P-1)(P-2)(-4)^3 > 0

P(P-1)(P-2)(64) > 0

From these equations we can see that P is greater than 2.

Therefore the value of P is greater than 2.

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Answer:

Revolution traveled by me = 30π ft.

Revolution traveled by my friend = 20π ft.

Difference between revolutions = 10π ft.

Step-by-step explanation:

In one revolution, I travel 2π(15) = 30π ft., and my friend travels 2π(10) = 20π ft., so my revolution is 30π - 20π, or 10π, ft. longer than my friend's revolution.

Answer: It translates into 0≤x≤7

Let x=real numbers

The probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

The given data is

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

(a) calculate mean value of x:

μ = E(x)

  = ∑(xi.P(xi))

 = 4.13

(b)  calculate variance of x:

σ² = ∑(xi - E(x))².P(xi)

   = 1.81331

(c)  calculate standard deviation of x:

σ = √σ²

σ = √1.831

σ = 1.3539

The likelihood that the quantity of systems sold will be within one standard deviation of the its mean:

P(μ  - σ < x < μ  + σ ) = P(4.13 - 13539 < x < 4.13 + 1.3539)

                                = P(2.7761 < x < 5.4839)

                                = P(x = 3) + P(x = 4) + P(x = 5)

                                = 0.13 + 0.30 + 0.31

                                = 0.74

Thus, the probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

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The complete question is-

Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in one month is given by the following table.

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

What is the probability that the number of systems sold is within 1 standard deviation of its mean value?

Answer: It is in quadrant II

Answer:

B could be 2, 4, 6, 8, 10

Step-by-step explanation:

Any even number because 7 is an odd number and an odd+even will equal always equal an odd. The same goes for the odd+odd= even etc

Answer: 225°

Step-by-step explanation:

To convert radians to degrees, multiply by 180/π (1 rad = 180° )

(5π/4) * (180/π/) = 225°

Answer:

\({ \rm{y = - 3x + 5}}\)

Gradient = -3

• Parallel lines have the same gradient, therefore gradient, m is -3

\({ \rm{y = mx + c}}\)

• At point (0, -4)

\({ \rm{ - 4 = ( - 3 \times 0) + c}} \\ \\ { \rm{c = - 4}}\)

y intercept is -4

\({ \boxed{ \boxed{ \mathfrak{answer : }}{ \rm{\: \: y = - 3x - 4}}}}\)

Answer:

above answer is correct

mrk that braniliest

Answer:

First at

5/4 +(√3)/2s

then at

5/4 -(√3)/2

Step-by-step explanation:

h(t) = -16t^2 + 40t + 47 = 60

so all we need to do it find the solution of the equation

so 16t^2 - 40t + 13 = 0

and as we know

root = (-b+-√(b^2-4ac))/2a

so

root = 5/4 +-(√3)/2

The area of the surface generated by revolving the curve x = 5t, y = 5t, 0 ≤ t ≤ 5 about the x-axis is 673.1π square units. When revolving the same curve about the y-axis, the surface area is 1346.3π square units. The point (-7√2, -7√2) is plotted on the coordinate plane. For this point, two sets of polar coordinates are (10√2, -45°) and (10√2, 315°).

To find the surface area generated by revolving the curve x = 5t, y = 5t, 0 ≤ t ≤ 5 about the x-axis, we can use the formula for the surface area of revolution: A = ∫2πy√(1 + (dy/dx)²) dx.

In this case, dy/dx = 1, so the integral simplifies to ∫2πy dx.

Substituting the given curve equations, we have ∫2π(5t) dx = 10π∫t dx = 10π∫dt = 10π[t] from 0 to 5 = 50π.

Evaluating this gives 50π ≈ 157.1 square units.

Multiplying by 4 to account for all quadrants, we get the final surface area of 200π ≈ 673.1π square units when revolving about the x-axis.

When revolving the same curve about the y-axis, the formula for surface area becomes A = ∫2πx√(1 + (dx/dy)²) dy. Here, dx/dy = 1, so the integral simplifies to ∫2πx dy.

Substituting the curve equations, we have ∫2π(5t) dy = 10π∫t dy = 10π∫dt = 10π[t] from 0 to 5 = 50π.

Evaluating this gives 50π ≈ 157.1 square units.

Multiplying by 4, we get the final surface area of 200π ≈ 673.1π square units when revolving about the y-axis.

The point (-7√2, -7√2) is plotted on the coordinate plane. The x-coordinate represents the radial distance (r) and the y-coordinate represents the angle (θ) in polar coordinates.

Using the distance formula, we find r = √((-7√2)² + (-7√2)²) = 10√2. The angle θ can be determined using the inverse tangent function: θ = atan(-7√2 / -7√2) = atan(1) = -45°.

Since this point lies in the fourth quadrant, the angle can also be expressed as 315°. Thus, the two sets of polar coordinates for the point (-7√2, -7√2) are (10√2, -45°) and (10√2, 315°).

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The rate of heat transfer in the heat exchanger is 100.25 kW, and the exit temperatures of the water and oil streams are 48.1°C and 73.4°C, respectively. The effectiveness of the heat exchanger is 0.743.

To solve this problem using the NTU method, we first calculate the heat capacity rates for both the water and oil streams. The heat capacity rate is the product of mass flow rate and specific heat capacity.

For the water stream, it is 0.1 kg/s * 4180 J/kg °C = 418 J/s °C, and for the oil stream, it is 0.2 kg/s * 2200 J/kg °C = 440 J/s °C.

Next, we determine the overall heat transfer coefficient, U, by dividing the total heat transfer coefficient, 340 W/m² °C, by the inner surface area of the tubes. The inner surface area can be calculated using the formula for the surface area of a tube:

π * tube diameter * tube length * number of passes = π * 0.018 m * 3 m * 12 = 2.03 m².

Then, we calculate the NTU (Number of Transfer Units) using the formula: NTU = U * A / C_min, where A is the surface area of the exchanger and C_min is the smaller heat capacity rate between the two streams (in this case, 418 J/s °C for water).

After that, we find the effectiveness (ε) from the NTU using the equation:

ε = 1 - exp(-NTU * (1 - C_min / C_max)), where C_max is the larger heat capacity rate between the two streams (in this case, 440 J/s °C for oil).

Finally, we can calculate the rate of heat transfer using the formula:

Q = ε * C_min * (T_in - T_out), where T_in and T_out are the inlet and outlet temperatures of the hot oil.

The rate of heat transfer in the exchanger is 100.25 kW, and the exit temperatures of the water and oil streams are 48.1°C and 73.4°C, respectively. The effectiveness of the heat exchanger is 0.743.

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In the competitive equilibrium of this two-consumer economy with two goods, the prices are (p1 *, p2 *) = (1, 1). This means that both goods are priced at 1 unit each.

Illustrate the economy in an Edgeworth box. The Edgeworth box represents the set of feasible allocations of goods between the two consumers, A and B. The axes represent the quantities of goods 1 and 2, and the box shows the possible combinations of goods that can be produced and consumed in the economy.

To derive the competitive equilibrium, we need to find an allocation of goods that maximizes the utility of each consumer, given their budget constraints and the prices of the goods.

Consumer A's utility function is uA(x1A, x2A) = (x1A)^3 + x2A, and consumer B's utility function is uB(x1B, x2B) = (x1B)^(1/3) + (x2B)^(1/2).

Consumer A's budget constraint is p1*x1A + p2*x2A = p1*x1A + x2A = 0*1 + 1*1 = 1, since the initial endowment of A is (0, 1) and the prices are (p1*, p2*) = (1, 1). Similarly, consumer B's budget constraint is p1*x1B + p2*x2B = 2*1 + 1*1 = 3, given the endowment of B is (2, 1).

Solve for the optimal allocation of goods for each consumer. Consumer A's utility is maximized at the point where the indifference curve uA(x1A, x2A) = constant is tangent to the budget constraint. Similarly, consumer B's utility is maximized where the indifference curve uB(x1B, x2B) = constant is tangent to the budget constraint.

At the competitive equilibrium, the allocation of goods is determined by the tangency of the indifference curves with the budget constraints. The competitive equilibrium allocation is the point where both consumers are maximizing their utility given the prices and budget constraints.

Given the prices (p1*, p2*) = (1, 1), the competitive equilibrium allocation is determined by the tangency of the indifference curves with the budget constraints. The specific allocation of goods depends on the specific shapes and positions of the indifference curves and budget constraints, which are not provided in the question.

In summary, in the competitive equilibrium of this two-consumer economy, with prices (p1*, p2*) = (1, 1), the specific allocation of goods depends on the shapes and positions of the indifference curves and budget constraints, which are not provided in the question.

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The number of rows in the log stack is 2. To find the number of rows in this log stack, we need to find the number of times we can subtract 3 from 48 until we reach 24.

48 - 3 = 45

45 - 3 = 42

42 - 3 = 39

We keep subtracting 3 until we reach 24. When we reach 24, we have found the second row, so the number of rows in the stack is 2.

This problem is asking for the number of rows in a stack of logs, where the number of logs decreases by three for each row. To solve this problem, we can use a simple mathematical equation. We can start with the number of logs on the bottom row, which is 48, and subtract 3 logs for each subsequent row. To find the total number of rows, we need to determine when the number of logs in a row becomes zero. This can be done by dividing the number of logs on the bottom row by 3, and rounding up to the nearest whole number. In this case, 48 divided by 3 is 16, so we would round up to 17. This means there are 17 rows in total, with the first row having 48 logs, the second row having 45 logs, and so on, until the last row with 24 logs.

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We can say that it's an arithmetic sequence since it has a common rate of change or common difference of 4.

Arithmetic sequences are represented by the following formula:

Recursive formula:

an= nth term

a1= 1st term

n= number of terms

d= common difference

Answer:

Will does.

Step-by-step explanation:

Will earns $260 for working 13 hrs. multiply that by 2.  260 x 2 is 520. 13 x 2 is 26. Will earns $520 for working 26 hours. Joey earns $450 for working 36 hours. Will has a better rate of pay because he earns more than joey does, and he earns more while working less hours than joey. joey earns less money than will and he also works more hours.

The range of the given linear function is option 2, which is all real numbers.

A linear function has a constant rate of change, which means that its graph is a straight line. The equation y = 272+ 9 is in the slope-intercept form,
where the slope is 9 and the y-intercept is 272.

Since the slope is positive, the line will have a positive slope, which means that the y-values will increase as x-values increase. Since there is no restriction on the domain of the function (I > -10), the line will continue to increase indefinitely in both directions. Therefore, the range of the function is all real numbers.

Option 1 (-261) is incorrect because the y-intercept of the function is 272, which is greater than -261.
Option 3 (-261 < y < 261) and option 4 (y > -261) are also incorrect because the function continues to increase indefinitely in both directions, so it will have values greater than 261 and less than -261.

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Answer:

The answer is 2593.678

Step-by-step explanation:

Answer:

6 3/10

Step-by-step explanation:

3 1/2 = 7/2

1 4/5 = 9/5

7/2 x 9/5 = 7x9/2x5 = 63/10 = 6 3/10

Answer:

52.5

Step-by-step explanation:

because you do 15 x 3.5

this gets 52.5

Answer:

52.5

Step-by-step explanation:

because you do 15 x 3.5

this gets 52.5

Step-by-step explanation:

Math textbook with double-digit number of pages split into sections. each section with exactly 12 pages long, with the exception of the epilogue, which is 11 pages long and a trivia fact is presented on the bottom of the 5th page, has total of 35 pages.

Let's assume the number of sections in the math textbook is represented by the variable "n". Each section is 12 pages long, except for the epilogue, which is 11 pages long. Therefore, the total number of pages in the textbook can be calculated as:

Total pages = (12 * n) + 11

Now, let's consider the trivia facts presented on the bottom of every 5th page. If a trivia fact appears on the second-to-last page, it means that the total number of pages in the textbook is a multiple of 5 minus 1.

So, we need to find a value for "n" that satisfies the equation:

(12 * n) + 11 = 5k - 1

Where "k" is an integer representing the number of sets of 5 pages. Rearranging the equation, we get:

12n = 5k - 12

Now, we can start substituting different values of "k" to find a solution that satisfies the equation and gives a double-digit number of pages.

Let's try "k" equals 3. Substituting into the equation:

12n = (5 * 3) - 12

12n = 15 - 12

12n = 3

However, this doesn't give us a double-digit number of pages. Let's try a larger value of "k".

Let's try "k" equals 8:

12n = (5 * 8) - 12

12n = 40 - 12

12n = 28

n = 28 / 12

n = 2.33

Since "n" should be an integer representing the number of sections, we can see that "n" equals 2 satisfies the equation.

Therefore, the textbook has a total of:

Total pages = (12 * 2) + 11

Total pages = 24 + 11

Total pages = 35

So, the textbook has 35 pages.

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The quadratic function's domain for a given function is -2<x>2.

What is the Domain of a quadratic function?

Function given \(x=-2(y-2)^2+2\)

The vertices are represented by the vertex form, y = an (x-h)^2+ k, and (h,k).

h=-2

k=+2

It is clear that this parabola has a minimum value of y = -2 and a maximum value of y=+2.

The quadratic function's domain for a given function is -2<x>2.

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The solutions for the equation \(y=-4(x-2)^2+6\) are as follows \(x = 2 + \sqrt{(6 - Y) / 4}\) or \(x = 2 - \sqrt{(6 - Y) / 4}\).

The given equation is in standard form for a quadratic equation, where the coefficient of \(x^2\) is negative. This means the graph of the equation is a downward-opening parabola, and the vertex of the parabola is (2, 6).

To solve the equation, we can first isolate the variable Y on one side:

\(Y - 6 = -4(x - 2)^2\)

Then we can divide both sides by -4:

\((Y - 6) / -4 = (x - 2)^2\)

Next, we can take the square root of both sides:

\(\sqrt{[(Y - 6) / -4] }= x - 2\)

\(\pm \sqrt{(Y - 6) / -4}= x - 2\)

So the solutions are:

\(x = 2 + \sqrt{(6 - Y) / 4}\) or \(x = 2 - \sqrt{(6 - Y) / 4}\)

These equations give the x-coordinates of the points on the graph of the equation for a given value of Y.

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Answer:

4 in approx

Step-by-step explanation:

Step one:

given data

circle with 25 inch circumference

c= 25in

Required:

the radius of the circle

Step two:

the expression for the circumference of a circle is

C= 2πr

making r the subject of the formula we have

r= c/2π

r= 25/2*3.142

r= 25/6.284

r=3.97

r=4 in approx

Answer:4.62x10^13

Step-by-step explanation:

The limiting value of the sequence will be the same even if a different value is assigned to x0.

The limiting value of the sequence is determined by the recursive equation xn = √(1996x\(n^{-1}\)). As n grows infinitely large, the value of xn will approach the same limiting value regardless of the initial value assigned to x0. This is because the recursive equation will continue to generate values that are closer and closer to the limiting value, regardless of the starting point.

Therefore in recursive equations, the limiting value of the sequence will be the same even if a different value is assigned to x0.

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the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.

Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.

The ODEs for the transition probabilities can be written as follows:

dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)

dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)

dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)

dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)

dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)

dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)

where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.

Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.

To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.

The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:

total_rate = q₁₂ + q₁₃

Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:

P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate

In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.

Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

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The volume of the solid is approximately 307.8 cubic units.

To find the volume of the solid obtained by rotating the region bounded by

\(y=x^2+1\) and \($y=9-x^2$\)

about y=-1, we can use the method of cylindrical shells.

Region and axis of rotation

The region we want to rotate is bounded by the parabola \($y=x^2+1$\) and the inverted parabola \($y=9-x^2$\). We can find the points of intersection by setting the two equations equal to each other:

\(x^2+1=9-x^2$\\$2x^2=8$$x^2=4$$x=\pm 2$\)

So the region we want to rotate is:

To use the method of cylindrical shells, we need to think of the region as being made up of an infinite number of thin vertical strips, each with width dx. We will rotate each strip about the line y=-1, creating a cylindrical shell with radius x and height dy.

The volume of each cylindrical shell is given by the formula:

\(dV=2\pi x (y+1) dy\)

We need to integrate this formula from y=1 (the bottom of the region) to y=9 (the top of the region) to get the total volume:

\(V=\int_{1}^{9} 2\pi x (y+1) dy\)

To express x in terms of y, we can solve the equation of the parabola for x:

\($x=\pm\sqrt{y-1}$\)

We'll use the positive square root, since we only need to integrate over the right half of the region:

\(\\$V=\int_{1}^{9} 2\pi (\sqrt{y-1})(y+1) dy$$V=2\pi \int_{1}^{9} (\sqrt{y-1})(y+1) dy$\)

We can simplify this by expanding the expression inside the integral:

\(\ V=2\pi \int_{1}^{9} (\sqrt{y}-\sqrt{y-1}) (y+1) dy$$V=2\pi \int_{1}^{9} (\sqrt{y}y+\sqrt{y}-\sqrt{y-1}y-\sqrt{y-1}) dy$$V=2\pi \left[\frac{2}{3}(y-1)^{3/2}+\frac{2}{3}(y-1)^{1/2}-\frac{2}{5}y(y-1)^{1/2}-\frac{2}{3}y^{3/2}\right]_{1}^{9}$$V=2\pi\left[\frac{464\sqrt{2}}{15}-\frac{38}{3}\right]$\)

V = 307.8 cubic units.

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