make x the subject. 4x-5=t(x+m)

The volume of the wedge is π/8 cubic meters.

To find the volume of the wedge, follow these steps:
1. First, find the radius of the tree by dividing the diameter by 2.

Since the diameter is 2 meters, the radius (r) is 1 meter.
2. The angle of inclination of the second cutting plane is given as 45 degrees.

Since a full circle is 360 degrees, find the fraction of the circle that the wedge represents by dividing 45 by 360.

This gives us 45/360 = 1/8.
3. The volume of a cylinder can be calculated using the formula V = π\(r^2h,\)

where r is the radius and h is the height.

In this case, the height of the wedge (h) is equal to the radius (r), which is 1 meter.

So, the volume of the whole cylinder (tree) would be V = π\((1^2)(1)\)

= π cubic meters.
4. Now, multiply the volume of the whole cylinder by the fraction representing the wedge (1/8) to find the volume of the wedge: (1/8) × π = π/8 cubic meters.

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Answer:

x = 29

Step-by-step explanation:

(x + 3) + (x - 1) + (x + 1) = 90

3x + 3 = 90

3x = 87

x = 29

Answer:

x = 29

Step-by-step explanation:

(x+3)+(x-1)+(x+1) = 90

90 = 3x +3

3x = 87

x = 29

Answer:

49 days

Step-by-step explanation:

answer forty nine days

Answer:

c= (1/4,2)

Step-by-step explanation:

i did the test and it came out correct i promise !

The required intersection point of the two given lines is y = 2 and x = 1/4.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Given the equation of the lines
5y=8x + 8 - - - - (1)

7y = -8x + 16 - - - - (2)

Adding equations 1 and 2
12y = 24
y = 2

now, from equation 1
5(2) = -8x + 8
x = 1/4

Thus, the required intersection point of the two given lines is y = 2 and x = 1/4.

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Answer:

choice 2

Step-by-step explanation:

the best choice for the baby pool is choice 2 because they need a pool that hold less than 15 cubic feet water and choice 2 when i calculate the volume of the given number : 4ft*3ft*1=12 cubic feet which is less than 15 cubic feet.

the other choices show that the volume  of choice 1 : 5ft*5ft*1=25 cubic feet which is greater than what they ask for.

choice 3 : 4ft*4ft*2ft=16 cubic feet greater than 15 cubic feet

9514 1404 393

Answer:

  D.  7

Step-by-step explanation:

The equation is ...

  x = a(y +1)² -3

For the point (x, y) = (4, 0), we have ...

  4 = a(0 -1)² -3

  7 = a . . . . . . . . . . . . add 3, simplify

The leading coefficient is 7.

The current in the inductor at 7.05 s is approximately 17.63 A.          

The relationship between voltage and current in an inductor is given by V = L(di/dt), where V is the voltage, L is the inductance, and di/dt is the rate of change of current with time. We can rearrange this equation to get di/dt = V/L.

Given the voltage across the inductor as \((3t + 25.4)^{1/2}\), we can find the current as: di/dt = V/L = \((3t + 25.4)^{1/2}\) \(/ 10.6\)  Integrating this expression with respect to t, we get:  i(t) =  / 10.6 + C  where C is the constant of integration.

We can find the value of C using the initial condition that the current is 8.25 A at t = 0:  \(i(0) = (20/9) * (3(0) + 25.4)^{(3/2)} / 10.6 + C = 8.25\) Solving for C, we get C = 8.25 - 0.7956 = 7.4544.

Therefore, the expression for the current through the inductor is: \(i(t) = (20/9) * (3t + 25.4)^{(3/2)} / 10.6 + 7.4544\) At t = 7.05 s, the current through the inductor is:\(i(7.05) = (20/9) * (3(7.05) + 25.4)^{(3/2)} / 10.6 + 7.4544\) = 17.63 A (approx).

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Answer: 6 of the specials were salmon filets.

Step-by-step explanation: 10% of 60 is 6.

10/100 x 60.

Answer:

Step-by-step explanation: D: he portrays april much more negatively.

T. S. Eliot in "The Waste Land" differ in his interpretation of the subject matter from Geoffrey Chaucer in The Canterbury Tales as He portrays April much more negatively. Thus, option D is correct.

The Waste Land emphasizes the moral, cultural, and social deterioration of contemporary society brought on by the commercializing of life and the availability of everything for purchase. Even in the area of love, there is an issue of gain and loss. People no longer have moral principles or beliefs.

Eliot describes a world of desolate panoramas, despair, and spiritual emptiness in his writings, giving readers a somber impression of the earth and those who live there. He also argues that those who live in this world are destined to suffer since they are powerless to change their circumstances.

Therefore, option D is the correct option.

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Answer:

F & B

Step-by-step explanation:

Answer:

C, D, E

Step-by-step explanation:

Remote angles theorem; when one side of a triangle is extended, the angle formed must equal the sum of the two angles in the triangle, that it isn't adjacent to.

C. (m<4) > (m<1), this has to be true because of remote angles theorem.

(m<4) must be greater than (m<1) because it is equal to (m<1) + (m<2)

D. (m<4) > (m<2), apply the same logic here, as was applied to the first problem.

E. (m<1) + (m<2) = (m<4), this is essentially remote angles theorem.

The solution to the recurrence relation an = 2(an/2) + d with an = 1 is simply an = 1.

To solve the given recurrence relations, we can use a technique called substitution. Let's solve each relation separately.

Recurrence relation: an = (an/2) + d

To solve this relation, we need to express the term an in terms of smaller terms until we reach the base case. Let's substitute an/2 in place of an:

an = (an/2) + d

= [(an/4) + d] + d

= (an/4) + 2d

Continuing this process, we can express an in terms of smaller terms:

an = (an/8) + 3d

= (an/16) + 4d

In general, we can write:

an = (an/2^k) + kd

Now, let's find the value of k when an = 1 (initial condition):

1 = \((1/2^{k})\)+ kd

Rearranging the equation:

1 - kd = \(1/2^{k}\)

Multiplying both sides by \(2^{k}\):

\(2^{k} - k2^{k} d = 1\)

This equation cannot be solved analytically in general. However, we can approximate the value of k using numerical methods or by using software tools such as Wolfram Alpha or numerical solvers in programming languages.

Once we have the value of k, we can substitute it back into the general formula to find the nth term, an, for any given n.

Recurrence relation: an = 2(an/2) + d

Using the same substitution technique as above, we can express an in terms of smaller terms:

an = 2(an/2) + d

= 2[2(an/4) + d] + d

= 4(an/4) + 3d

Continuing this process, we have:

an = 2^k (an/2^k) + kd

Again, to find the value of k when an = 1:

\(1 = 2^{k} (1/2^{k}) + kd\)

1 = 1 + kd

Since kd = 0 for k = 0 (initial condition), we have k = 0.

Therefore, the solution to the recurrence relation an = 2(an/2) + d with an = 1 is simply an = 1.

Please note that if the value of d is non-zero, the recurrence relation may have different solutions or properties.

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Answer:

i would say its C but im not 100% sure

Step-by-step explanation:

step 1

Find the center of the circle

we have that

the center of the circle is the midpoint between the endpoints

sp

step 2

Find the radius of the circle

we have that

the distance between endpoints is equal to the diameter of circle

so

D=15-1=14 units -------> (difference of the y-coordinates)

Remember that the radius is half the diameter

r=D/2

r=14/2=7 units

step 3

Find the equation of the circle

(x-h)^2+(y-k)^2=r^2

where

*h,k) is the center

r is the radius

substitute

(x-9)^2+(y-8)^2=7^2

(x-9)^2+(y-8)^2=49

The sample proportion of teddy bears among the shopkeeper's sample of 67 stuffed animals is approximately 0.34, while the population proportion, estimated based on the sample, is also approximately 0.34

To calculate the sample proportion, we divide the number of teddy bears in the sample (23) by the total number of stuffed animals in the sample (67). This gives us a sample proportion of approximately 0.34.

For the population proportion, since the sample is representative of the entire store, we can use the sample proportion as an estimate. Therefore, the population proportion of teddy bears among all the stuffed animals in the store is also approximately 0.34.

The sample proportion is specific to the shopkeeper's sample of 67 stuffed animals and represents the observed proportion within that sample. On the other hand, the population proportion is an estimate of the true proportion of teddy bears among all the stuffed animals in the store, based on the sample data. Since the sample is randomly chosen, it is expected to provide a reasonable estimate of the population proportion. In this case, the sample proportion and population proportion are both approximately 0.34, indicating that around 34% of the stuffed animals in the store are teddy bears.

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The first term, a1, in the geometric series is -3.

What is Geometric Series?

A geometric series is a series for which the ratio of two consecutive terms is a constant function of the summation index. The more general case of a ratio and a rational sum-index function produces a series called a hypergeometric series. For the simplest case of a ratio equal to a constant, the terms have the form

To find the first term, a1, in a geometric series given the sum, Sn = 93, the common ratio, r = 2, and the number of terms, n = 5, we can use the formula for the sum of a geometric series:

Sn = a1 * (1 - r^n) / (1 - r)

Plugging in the given values, we have:

93 = a1 * (1 - 2^5) / (1 - 2)

Simplifying the expression:

93 = a1 * (1 - 32) / (-1)

93 = a1 * (-31)

Now we can solve for a1 by dividing both sides of the equation by -31:

a1 = 93 / -31

a1 = -3

Therefore, the first term, a1, in the geometric series is -3.

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Answer:

132 over 5 is the correct answer

Answer:

\(x \leqslant - 4\)

Step-by-step explanation:

\( - 3(x + 4) - 2 \geqslant 2x + 6\)

\( - 3x - 12 \geqslant 2x + 6\)

\( - 3x14 \geqslant 2x + 6\)

\( - 3x - 2x \geqslant 6 + 14\)

\( - 5x \geqslant 20\)

\( \frac{ - 5x}{ - 5} \leqslant \frac{20}{ - 5} \)

\(x \leqslant - 4\)

WHEN DIVIDING OR MULTIPLYING BY A NEGATIVE NUMBER, YOU MUST CHANGE THE SIGNS:

\( \leqslant \\ \geqslant \\ > \\ < \)

Complete question is;

Tiothy evaluated the expression using x = 3 and y = –4. The expression is (xy^(-2))/(3x²y^(−4))

1. (1/3)x^(−1)(y²) 2. ((1/3)^(3−1))(−4²) 3. (1/3)(1/3)(−4)² 4. (1/3)(1/3)(−16) 5. −16/9 Analyze Timothy's steps. Is he correct? If not, why not?

A) Yes, he is correct.

B) No, he needed to add the exponents when he simplified the powers of the same base.

C) No, he needed to multiply 3 and –1 instead of creating a positive exponent in a fraction.

D) No, his value of (negative 4) squared should be positive because an even exponent indicates a positive value.

Answer:

D) No, his value of (negative 4) squared should be positive because an even exponent indicates a positive value.

Step-by-step explanation:

The expression is;

(xy^(-2))/(3x²y^(−4))

Simplifying this using law of indices gives;

⅓(x^(1 - 2)) × (y^(-2 -(-4))

This gives;

= (⅓x^(-1)) × y²

= ⅓ × (1/x) × y²

We are told that x = 3 and y = –4, thus;

= ⅓ × ⅓ × (-4)²

Square of a negative number is positive, thus (-4)² = 16

Thus;

⅓ × ⅓ × (-4)² = 16/9

Looking at the answer Timothy got, it's clear he made a mistake of not getting a positive number when he squared -4.

Thus,option D is the correct answer.

Answer:

D

Step-by-step explanation:

i got it correct

Answer:

2482

Step-by-step explanation:

Because this sequence starts with -13 and adds 5 each time, the 500th term will be 5(499)-13=2482. Hope this helps!

Answer:

2482

Step-by-step explanation:

(i) Large Table Required are 3 and Small Table required are 8

(ii) Price of Student Ticket is $5.5 and Adult Ticket is $7.5

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

(i)

Seats in Large Table = 12

Cost of Large Table = $50

Seats in Small Table = 8

Cost of Small Table = $25

Let, Number of Large Tables = x

Number of Small Tables = y

According to the Question:

12x + 8y = 100

50x + 25y = 350

x = 3, y = 8 (refer graph 1)

(ii)

Cost of Student Ticket = x

Cost of Adult Ticket  = y

According to the Question:

16x + 3y = 110.5

12x + 4y = 96

x = $5.5, y = $7.5 (refer graph 2)

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The values of g obtained at each corner point and identify the minimum value. The corresponding corner point will give us the minimum value of g, x + 3y = 33

To solve the linear programming problem, we need to find the values of x and y that minimize the objective function g = 30x + 80y, while satisfying the given constraints.
The constraints are:
1. 11x+15y ≥ 255
2. x+3y ≥ 33
3. x ≥ 0
4. y ≥ 0
To find the minimum value of g, we can use a graphical method or the simplex method.

Let's use the graphical method in this case.
First, let's plot the feasible region determined by the given constraints.

This region is the area in the coordinate plane that satisfies all the constraints.
After plotting the constraints, we can shade the region that satisfies all the constraints.

The feasible region is the shaded area.
Next, we need to determine the corner points of the feasible region.

These corner points are the vertices of the shaded area.
Once we have the corner points, we substitute each corner point's coordinates into the objective function

g = 30x + 80y and calculate the corresponding value of g.
We then compare the values of g for each corner point to find the minimum value.

This minimum value will give us the optimal solution for the linear programming problem.
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Answer:

\(n=0.001\)

Step-by-step explanation:

\((2\times10)+(5\times1)+(3\times n)=25.003\\\\\implies 20 + 5 + 3n = 25.003\\\\\implies 3n+25=25.003\\\\\implies 3n+25-25=25.003-25\\\\\implies 3n = 0.003\\\\\implies n=0.001\)

The model predicts that the population is decreasing continuously at a rate of 0.022 per year. The predicted population of the inner-city area in 2 years will be approximately 287,086 people.

The population of a certain inner-city area is estimated to be declining according to the model P(t)=300,000e−0.022t where t is the number of years from the present.

What does this model predict the population will be in 2 years? Round to the nearest person.The given function is P(t) = 300,000e^(-0.022t), where t is the number of years from the present.

The model predicts the population in t years to be P(t). Now we can find the predicted population in 2 years by replacing t with 2.P(2) = 300,000e^(-0.022*2)= 300,000e^(-0.044) ≈ 287,086 (rounded to the nearest person)Therefore, the predicted population of the inner-city area in 2 years will be approximately 287,086 people.Main Answer:Thus, the answer to the problem is 287,086 people.

The model predicts that the population will be 287,086 people after 2 years.

The population of a certain inner-city area is estimated to be declining according to the model P(t)=300,000e−0.022t where t is the number of years from the present.

This is an example of exponential decay, where the population is decreasing exponentially with time. The function P(t) gives the population of the area at time t.

The model predicts that the population is decreasing continuously at a rate of 0.022 per year. The rate of decrease is given by the negative sign in the exponent. The value of P(t) decreases as t increases.

The problem asks us to find the predicted population after 2 years. This can be done by finding P(2). Substituting t = 2 in the given function gives P(2) = 300,000e^(-0.022*2).

This simplifies to P(2) = 300,000e^(-0.044) ≈ 287,086 (rounded to the nearest person). Therefore, the predicted population of the inner-city area in 2 years will be approximately 287,086 people.

The population of a certain inner-city area is estimated to be declining according to the model P(t)=300,000e−0.022t where t is the number of years from the present. The model predicts that the population is decreasing continuously at a rate of 0.022 per year. The predicted population of the inner-city area in 2 years will be approximately 287,086 people.

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To price the derivative using the two-period binomial model, we need to calculate the expected payoff of the derivative using the risk-neutral probabilities.

The possible outcomes for the two-period binomial model are H and T,  there are four possible states of the world: HH, HT, TH, and TT.

To calculate the expected payoff we need to calculate the probability of each state occurring. The probability of HH occurring is pp=0.60.6=0.36, the probability of HT and TH occurring is pq+qp=0.60.4+0.40.6=0.48, and the probability of TT occurring is qq=0.40.4=0.16.

Next, we can calculate the expected payoff in HH and TT states, the derivative pays off 1, and in the HT and TH states, the derivative pays off 0. The expected payoff of the derivative in the HH and TT states is 10.36=0.36, and the expected payoff in the HT and TH states is 00.48=0.

We need to discount the expected payoffs back to time 0 using the risk-neutral probabilities.

The probability of that state occurring multiplied by the discount factor, which is 1/(1+r), where r is the risk-free interest rate.

Since this is a risk-neutral model, the risk-free interest rate is equal to 1. Therefore, the risk-neutral probability of each state occurring is

HH: 0.36/(1+1) = 0.18

HT/TH: 0.48/(1+1) = 0.24

TT: 0.16/(1+1) = 0.08

Finally, we can calculate the price of the derivative

Price = 0.181 + 0.240 + 0.240 + 0.081 = 0.26

Therefore, the price of the derivative is 0.26.

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The stone's acceleration is constant at -10 m/s^2. It will reach its maximum height after 4 seconds, at which point it is 240 meters above the ground. The stone's velocity upon impact is -10 m/s.

The equation of motion of the stone is s(t) = -5t² + 30t+200, where s is the directed distance from the ground in meters and t is in seconds. The acceleration of the stone is the derivative of the velocity, which is the derivative of the position.

The derivative of the position is -10t + 30, so the acceleration is -10. The stone will reach its maximum height when the velocity is 0. The velocity is 0 when t = 4, so the stone will reach its maximum height after 4 seconds.

The height of the building is the position of the stone when t = 0, which is 200 meters. The maximum height the stone will reach is the position of the stone when t = 4, which is 240 meters. The velocity of the stone upon impact is the velocity of the stone when t = 8, which is -10 m/s.

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