suppose s is a recursively defined set, defined by - the number 1 is in s - if n is in s, then so is 3n 2 - if n is in s, then so is 5n - 1 - if n is in s, then so is n 7. suppose you want to prove using structural induction that all members of s have a certain property. what do you have to prove in the base step? group of answer choices that the number 1 has the property, and the numbers 5, 4 and 8. that the numbers 5, 4 and 8 have the property. that the number 1 has this property. that the numbers 5, 4 and 8 are in the set s.

Answer:

Step-by-step explanation:

The distances they jumped were

x,y,z

y=x+2

z=x+2+2=x+4

x+y+z=12.69

x+x+2+x+4=12.69

3x+6=12.69

3x=6.69

x=2.23

So Jack jumped 2.23m, Alex jumped 4.23m, and Amir jumped 6.23m.

Answer:

7. 5

8. 33. 3333 or 100/ 3

9. 18/7

10. 30 /7

Answer:

1/4

Step-by-step explanation:

The three common elements of an optimization problem are b. decisions, constraints, and an objective.

Decisions refer to the choices or actions that can be taken in order to achieve a specific goal. Constraints are the limitations or restrictions that must be considered when making decisions. An objective is the goal that needs to be achieved, and it can be either maximizing or minimizing a specific quantity. In an optimization problem, the task is to find the optimal decision variables that satisfy the given constraints and achieve the objective.

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Answer:

11) -11

12) -12

13) 7

14) -60

15) -56

16) -378

17) -126

18) -4

19) -3

20) -12

Answer:

see below

Step-by-step explanation:

1.  75

2.  -14

3.  91

4.  67

5.  24

6.  112

7.  91

8.  44

9.  15

10.  -11

11.  -11

12.  -12

13.  7

14.  -60

15.  -56

16.  -378

17.  -126

18.  -4

19.  -3

20.  -12

The height to which the hollow sphere rolls up the incline is the same as the height to which the hollow cylinder rolls up, which is 1.0 m in this case.

To determine the height to which the hollow sphere rolls up the incline, we can use the principle of conservation of energy. The initial kinetic energy of both the hollow cylinder and hollow sphere is the same since they have the same mass and initial velocity. This kinetic energy is converted into potential energy as they roll up the incline. The potential energy gained by an object of mass m and height h is given by the formula:

PE = mgh

Since both the hollow cylinder and hollow sphere have the same mass, we can compare their potential energies. Let's assume the potential energy gained by the hollow cylinder is PE_cylinder and the potential energy gained by the hollow sphere is PE_sphere.

PE_cylinder = mgh_cylinder  ... (1)

PE_sphere = mgh_sphere  ... (2)

Since the initial velocity and mass are the same for both objects, we can equate their potential energies:

PE_cylinder = PE_sphere

mgh_cylinder = mgh_sphere

h_cylinder = h_sphere

Therefore, the height to which the hollow sphere rolls up the incline is the same as the height to which the hollow cylinder rolls up, which is 1.0 m in this case.

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so we know that the factors of (x-6) and (x+2) will yield a remainder of -14, thus by the remainder theorem we can say that the values of x = 6 and x = -2 will yield -14, that is for our function f(6) = f(-2) = -14, so let's plug those two values and see what we get for our "k" and "f"

\(\boxed{x=6}\hspace{5em}f(6)=-x^3+fx^2+kx-62\\\\\\ -14=-(6)^3+f(6)^2+k(6)-62\implies -14=36f+6k-278 \\\\\\ 264=36f+6k\implies 264=6(6f+k)\implies \cfrac{264}{6}=6f+k \\\\\\ 44=6f+k\implies 44-6f=k \\\\[-0.35em] ~\dotfill\\\\ \boxed{x=-2}\hspace{5em} f(-2)=-x^3+fx^2+kx-62\\\\\\ -14=-(-2)^3+f(2)^2-k(2)-62\implies -14=8+4f-2k-62 \\\\\\ -14=4f-2k-54\implies 40=4f-2k\implies 40=2(2f-k)\)

\(\cfrac{40}{2}=2f-k \implies 20=2f-k\implies \stackrel{\textit{substituting from the equation above}}{20=2f-(44-6f)} \\\\\\ 20=2f-44+6f\implies 64=2f+6f\implies 64=8f\implies \cfrac{64}{8}=f \\\\\\ \boxed{8=f}\hspace{5em}\stackrel{\textit{since we know that}}{44-6f=k}\implies 44-6(8)=k\implies \boxed{-4=k}\)

Answer:

15, 16,31

Step-by-step explanation:

The rule is that each time you add by 7, like in the first 2.  4+7=11 and 7+7=14

Answer:

r<9

Step-by-step explanation:

r/3 + 5 < 8

Subtract 5 from each side

r/3 + 5-5 < 8-5

r/3 < 3

Multiply each side by 3

r/3 *3 <3*3

r<9

Answer:

Below

Step-by-step explanation:

a)  DIRECT variation    y = k  x

                                    10 = k (4)

                                      10/4 = k = 2.5

                y = 2.5 x

b)    y = 2.5 x

       y = 2.5 (10) = 25

45:60 is equivalent to 15:20

45/15: 60/15

3:4

15/5: 20/5

3: 4

Hence 45 to 60 is equivalent to 15 to 20.

Answer:

hope this is correct

Answer:

AC ≈ 2.87

Step-by-step explanation:

Using the sine ratio in the right triangle

sin35° = \(\frac{opposite}{hypotenuse}\) = \(\frac{AC}{AB}\) = \(\frac{AC}{5}\)

Multiply both sides by 5

5 × sin35° = AC , thus

AC ≈ 2.87 ( to the nearest hundredth )

number greater than R and less than S is 0,45

Answer:

0.45

Step-by-step explanation:

R = .34

S = .66

.30 is less than R and less than S

.70 is greater than R and greater than S

.75 is greater than R and greater than S

.45 is the only one that is greater than R and less than S

Hope this helped <3 brainliest please :)

Answer What does 1.5 mean on a number?

If a half = 0.5 and one =1, than one and a half is 1+0.5=1.5. So, 1.5 = one and a half.

Step-by-step explanation:

The factorised form of the expression given 4x² +4x +1 according to the task content is; (2x+1) (2x+1).

It follows from the task content that the given expression is; 4x² +4x +1.

Hence, it follows from factorisation convention that the expression above can be rewritten as;

4x² +2x +2x +1

= 2x(2x+1) +1(2x+1)

= (2x+1) (2x+1)

Hence, the required factorisation renders the factors as (2x+1) and (2x+1).

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Applying law of sine and law of cosine, the unknown values x and y are 16.2 units and 37.1 degrees respectively.

To determine the value of x and y in the given triangle, we can use law of sine or law of cosine depending on the variables available and what we need to determine.

Applying law of cosine;

x² = 15² + 10² - 2(15)(10)cos78

x² = 225 + 100 - 300cos78

x² = 225 + 100 - 62.4

x² = 262.6

x = √262.6

x = 16.2 units

From this, we can apply law of sine to determine y;

x / sin X = y / sin Y

Substituting the values into the formula above;

16.2 / sin78 = 10 / sin y

Cross multiply both sides and solve for y;

16.2siny = 10sin78

sin y = 10sin78 / 16.2

sin y = 0.6038

y = sin⁻¹ (0.6038)

y = 37.14°

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The Five P's technique is a problem-solving approach that involves identifying and addressing key elements to effectively solve a problem. It consists of five steps: Problem, Purpose, Plan, Process, and Product. In this explanation, I will use the example of improving customer satisfaction in a restaurant to illustrate each step of the Five P's technique.

Problem: Begin by clearly defining the problem. For instance, the problem could be that customer satisfaction ratings have been consistently low in the restaurant.

Purpose: Determine the purpose or objective of solving the problem. In this case, the purpose could be to improve customer satisfaction and increase positive reviews.

Plan: Develop a plan to address the problem. For example, the plan could involve training the staff on customer service, enhancing the menu options.

Process: Execute the plan by implementing the identified strategies. This may include conducting staff training sessions, revamping the menu, and setting up a feedback mechanism for customers to share their experiences.

Product: Evaluate the outcome of the implemented strategies and assess the results. Monitor customer satisfaction ratings, review feedback from customers, and analyze any changes in positive reviews and customer loyalty. Adjust the strategies as needed to further enhance customer satisfaction.

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Answer:

C. 2 -9

4 -6

6 -3

Step-by-step explanation:

Answer:c

Step-by-step explanation:

Josh bought a new book that cost $13.95 and some bookmarks

Let the cost of the bookmarks be b.

It then followed that the cost of the new book plus the cost of the bookmarks will give the total cost of $20.30

Mathematically,

Hence $13.95+b=$20.30; b=$6.35 is the answer, the third option

Step-by-step explanation:

One cable company charges $50 per month for their basic plan, plus $75 installation. A second company charges $55 per month, but offers free installation. For what number of months is the first plan cheaper than the second plan?

50m + 75 < 55m

subtract 50m from both sides:

50m + 75 -50m < 55m - 50m

75 < 5m

divide both sides by 5:

75/5 < 5m/5

15 < m

or m > 15

so:

The first plan cheaper than the second plan after 16+ months

False. When multiple people access the same access point (AP), the communication to the wired world is not limited to approximately 1 Mbps per user.

The available bandwidth is shared among the users connected to the AP, but the exact speed each user experiences depends on various factors such as the total bandwidth provided by the AP, the number of users actively utilizing the network, and the nature of their online activities.

The speed experienced by each user can fluctuate depending on network congestion and the type of traffic being generated. For example, if all users are engaging in bandwidth-intensive activities like streaming high-definition videos or downloading large files simultaneously, it can impact the overall network performance, resulting in slower speeds for each individual user. However, if the network is underutilized or the users are engaged in less demanding tasks, each user may experience higher speeds closer to the maximum capacity provided by the AP.

Therefore, the statement that communication to the wired world is limited to approximately 1 Mbps per user when ten people access the same AP is false. The actual speed experienced by each user will depend on various factors and can vary significantly.

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The percentage of Alberto's income that is used to pay for his rent and groceries is 40%.

Amount for rent = $896

Amount for groceries = $384

Total amount = $1280

Therefore, the percentage of Alberto's income that is used to pay for his rent and groceries will be:

= 1280/3200 × 100

= 0.4 × 100

= 40%

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Answer

40% of Alberto's income is used to pay rent and goceries.

Step-by-step explanation:

1. Add his rent and goceries....

2. =$1280

3.Divide: 1280/3200

4.=0.4

5. 0.4x100

6. =40%

At point P[-6,257), the function has a maximum value of 257.

To find the maximum point of the given function y = x^3 + 3x^2 - 72x + 95, we need to take the derivative of the function and set it equal to zero.

y' = 3x^2 + 6x - 72

Setting y' equal to zero:

0 = 3x^2 + 6x - 72

Simplifying:

0 = x^2 + 2x - 24

Factoring:

0 = (x + 6)(x - 4)

So, the critical points are x = -6 and x = 4.

To determine if these points are maxima or minima, we need to take the second derivative of the function.

y'' = 6x + 6

At x = -6, y'' is negative (-30), indicating a maximum.

At x = 4, y'' is positive (30), indicating a minimum.

Therefore, the maximum point of the function is at x = -6.

Substituting x = -6 into the original function:

y = (-6)^3 + 3(-6)^2 - 72(-6) + 95

y = 257
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It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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Answer:

The whole cake

Step-by-step explanation:

(1/4)*4=1

Answer:

B, C, E

Step-by-step explanation:

I hope this helps you!

Step-by-step explanation:

Add 1/4 and 1/3.

\(\frac{1 \times 3}{4 \times3} =\frac{3}{12}\)

\(\frac{1 \times 4}{3 \times 4} =\frac{4}{12}\)

\(\frac{4}{12} +\frac{3}{12} =\frac{7}{12}\)

Subtract 7/12 from the whole (1) or (12/12):

\(\frac{12}{12} -\frac{7}{12} =\frac{5}{12}\)

\(\frac{5}{12}\) of the pizza is left.

Answer:

I am going to say it is 1.75kg

Step-by-step explanation:

If u multiply 0.25 by seven the seven is the weeks then you would get 1.75

hope this helps