1.0
Im in need for help..

The formula for the sequence is an = [tex]2^n[/tex], where n is a positive integer. This formula is proven correct using mathematical induction.

To find a formula for the sequence defined by a1 = 1 and ak = 2ak-1, we can use mathematical induction to establish a pattern and then derive the formula. Here's how we can solve it step by step:

Step 1: Base case:

For k = 1, we have a1 = 1.

Step 2: Assume the formula holds for some positive integer n, where n ≥ 1.

Assume that an = [tex]2^{n-1[/tex] for some positive integer n.

Step 3: Use the assumption to prove the formula for the next term.

Now, let's prove that an+1 = [tex]2^n[/tex] holds.

Using the recursive formula ak = 2ak-1, we have:

an+1 = 2an

Substituting the assumed formula an = [tex]2^{n-1[/tex], we get:

an+1 = 2([tex]2^{n-1[/tex])

To simplify, we have:

an+1 = [tex]2^n[/tex]

Step 4: Conclusion:

Based on the assumption and the proof for the next term, we can conclude that the formula an = [tex]2^n[/tex] holds for all positive integers n ≥ 1.

Therefore, the formula for the sequence defined by a1 = 1 and ak = 2ak-1 is an = [tex]2^n[/tex].

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Answer:

Kala's first step.

Step-by-step explanation:

Solving linear equations.

But Kala did not do that. Instead, she skipped the first stages and moved on ahead, making her equation invalid.

Answer:

Step-by-step explanation:

Complete question

A) Sebastian's account will have about $28.67 less than Yolanda's account. B) Sebastian's account will have about $9.78 less than Yolanda's account. C) Yolanda's account will have about $28.67 less than Sebastian's account. D) Yolanda's account will have about $9.78 less than Sebastian's account.

For Sebastian

Amount = [tex]P (1 + \frac{r}{n})^{nt}[/tex]

Substituting the given values we get

A =

[tex]790 (1 + \frac{6.8}{100*1})^{3*1} \\962.367[/tex]

For Yolanda

Amount  [tex]= P(1+rt)[/tex]

[tex]A = 815 (1 + \frac{7.2}{100}*3)\\A = 991.04[/tex]

Yolanda's account will have about $28.67 less than Sebastian's account

Option C is correct

Answer:

6 apples

Step-by-step explanation:

3 apples cost $1.00

so for $2.00, 2x3÷1=6

hope it helps. plz mark me as brainliest.

Answer:

6 apples

Step-by-step explanation:

if three apples are 1 dollar then every time you add a dollar you would get three more apples

so it would look somthing like

1$ = 3 apples

2$= 6 apples

3$= 9 apples  

4$= 12 apples

so on

The angular frequency of the sinusoidal function that approximates the temperature profile when t is large is 7π.

The general solution to the heat equation with boundary conditions is u(x,t) = A sin(kx) e^(-kt) + B cos(kx) e^(-kt), where k is the wavenumber and t is time. The wavenumber is related to the angular frequency by k = 2π/a, where a is the length of the rod. In this case, k = 7π/a. Therefore, the angular frequency is 7π.

The amplitude of the sinusoidal function will decay to 0 as t approaches infinity. This is because the exponential term e^(-kt) will decrease as t increases.

The initial condition u(x,0) = 10 + sin 3x + 20 sin 5x + 2 sin 7x can be matched to the general solution by setting A = 10, B = 0, k = 3, and k = 5.

The boundary conditions u(0,t) = u(a,t) = 0 can be satisfied by setting A sin(3a) e^(-kta) + B cos(3a) e^(-kta) = 0 and A sin(5a) e^(-kta) + B cos(5a) e^(-kta) = 0. These equations can be solved to find A = 0 and B = 0.

The solution u(x,t) = 0 is a sinusoidal function of x whose amplitude is decaying to 0. The angular frequency of this function is k = 2π/a = 7π.

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28.571429% that is 2

hope this helped

Answer:

50% Is the answer

Answer:

the 1 one

Step-by-step explanation:

Answer:

113.4=x(18)

x=6.3

Step-by-step explanation:

It says the product of a number, x, and 18 is 113.4. Since it says product there will be multiplication. The word "is" tells us that x and 18 equals 113.4. Is x= 6.3, 6.3 times 18 equals 113.4. This is a true equation.

To find the 90% confidence interval for the true proportion of adults in the town with health insurance, we can use the formula:

[tex]\[\text{{Confidence Interval}} = \left( \hat{p} - Z \cdot \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}, \hat{p} + Z \cdot \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \right)\][/tex]

where:

- [tex]\(\hat{p}\)[/tex] is the sample proportion (69/88 in this case)

- [tex]\(Z\)[/tex] is the Z-score corresponding to the desired confidence level (90% corresponds to [tex]\(Z = 1.645\)[/tex] for a two-tailed test)

- \(n\) is the sample size (88 in this case)

Substituting the values into the formula, we have:

[tex]\[\text{{Confidence Interval}} = \left( \frac{69}{88} - 1.645 \cdot \sqrt{\frac{\frac{69}{88} \cdot \left(1-\frac{69}{88}\right)}{88}}, \frac{69}{88} + 1.645 \cdot \sqrt{\frac{\frac{69}{88} \cdot \left(1-\frac{69}{88}\right)}{88}} \right)\][/tex]

Evaluating the expression, we find the confidence interval to be approximately (0.742, 0.892).

The confidence interval is approximately (0.742, 0.892).

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Yes, based on the information, it should be noted that social recommendations can increase ad effectiveness.

The study you mentioned found that viewers who arrived at an advertising video through social media recommendations were more likely to correctly recall the brand being advertised than viewers who arrived by browsing. This is because social recommendations come from people we trust, and we are more likely to be influenced by their opinions.

First, social recommendations are more personalized. They are based on the interests of the person who is making the recommendation, so they are more likely to be relevant to the person who is receiving the recommendation. Second, social recommendations are more credible. We trust the opinions of our friends and family, so we are more likely to believe their recommendations. Third, social recommendations are more timely. They are shared in real time, so they are more likely to be relevant to the current moment.

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The expected value of X(t), E{X(t)}, is 0, indicating that on average, the process X(t) fluctuates around the zero mean. The autocovariance function R(t₁, t₂) is given by R(t₁, t₂) = e^(-ω₀|t₁-t₂|), which signifies that the covariance between X(t₁) and X(t₂) decays exponentially with the difference in time values |t₁-t₂|.

To find E{X(t)}, we need to calculate the expected value of the given process X(t) = Acos(ω₀t) + Bsin(ω₀t), where A and B are independent random variables with mean 0.

E{X(t)} = E{Acos(ω₀t) + Bsin(ω₀t)}

Since E{A} = E{B} = 0, the expected value of each term is 0.

E{X(t)} = E{Acos(ω₀t)} + E{Bsin(ω₀t)}

          = 0 + 0

          = 0

Therefore, E{X(t)} = 0.

To find R(t₁, t₂), the autocovariance function of X(t), we need to calculate the covariance between X(t₁) and X(t₂).

R(t₁, t₂) = Cov[X(t₁), X(t₂)]

Since A and B are independent random variables with σ²_A = σ²_B = 1, the covariance term becomes:

R(t₁, t₂) = Cov[Acos(ω₀t₁) + Bsin(ω₀t₁), Acos(ω₀t₂) + Bsin(ω₀t₂)]

Using trigonometric identities, we can simplify this expression:

R(t₁, t₂) = Cov[Acos(ω₀t₁), Acos(ω₀t₂)] + Cov[Bsin(ω₀t₁), Bsin(ω₀t₂)] + Cov[Acos(ω₀t₁), Bsin(ω₀t₂)] + Cov[Bsin(ω₀t₁), Acos(ω₀t₂)]

Since A and B are independent, the covariance terms involving them are 0:

R(t₁, t₂) = Cov[Acos(ω₀t₁), Acos(ω₀t₂)] + Cov[Bsin(ω₀t₁), Bsin(ω₀t₂)]

Using trigonometric identities again, we can simplify further:

R(t₁, t₂) = cos(ω₀t₁)cos(ω₀t₂)Cov[A,A] + sin(ω₀t₁)sin(ω₀t₂)Cov[B,B]

Since Cov[A,A] = Var[A] = σ²_A = 1 and Cov[B,B] = Var[B] = σ²_B = 1, the expression becomes:

R(t₁, t₂) = cos(ω₀t₁)cos(ω₀t₂) + sin(ω₀t₁)sin(ω₀t₂)

          = cos(ω₀(t₁ - t₂))

Therefore, R(t₁, t₂) = e^(-ω₀|t₁-t₂|).

The expected value of X(t), E{X(t)}, is 0, indicating that on average, the process X(t) fluctuates around the zero mean. The autocovariance function R(t₁, t₂) is given by R(t₁, t₂) = e^(-ω₀|t₁-t₂|), which signifies that the covariance between X(t₁) and X(t₂) decays exponentially with the difference in time values |t₁-t₂|.

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Answer:

6

Step-by-step explanation:

because  i had the same question and the departments where 6

Answer:

Hey! I can teach you this.

The range is the distance between the highest and lowest numbers.

In this case, the lowest number is 3, and the highest is 54, making the range 54 - 3, which is 51.

Because 3 is 51 away from 54. I hope this helps you!

Step-by-step explanation:

If x=10

2(10)²(10-5)

200 × 5

=1000

10x=10(10)

=100

Answer:

12/5

Step-by-step explanation:

Pythagorean theorem=> adjacent side=5

tanx=oppx/adjx

tanx=12/5

Answer:

i think 2

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The small triangle is half the size of the entire triangle. 27/2 = 13.5

Answer:

negative

positive

negative

zero

positive

Step-by-step explanation:

Situation 1: A football team's first play resulted in a loss of 15 yards.

negative

Situation 2: A store marks up the price of a calculator $5.20.

positive

Situation 3: Nina withdrew $50 from her bank account.

negative

Situation 4: A porpoise is swimming at sea level.

zero

Situation 5: Kylie scored 2 goals in yesterday's soccer game.​

positive

To determine which functions are solutions of the given differential equation y'' + y = 3 sin(x), we need to check if plugging each function into the differential equation satisfies the equation. We will examine each option and identify the functions that satisfy the equation.

The differential equation y'' + y = 3 sin(x) represents a second-order linear homogeneous differential equation with a particular non-homogeneous term.
(a) Plugging y = 3 sin(x) into the differential equation gives 0 + 3 sin(x) ≠ 3 sin(x). Therefore, y = 3 sin(x) is not a solution.
(b) Plugging y = (3/2)x sin(x) into the differential equation gives (3/2) sin(x) + (3/2)x sin(x) = (3/2)(1 + x) sin(x), which is not equal to 3 sin(x). Therefore, y = (3/2)x sin(x) is not a solution.
c) Plugging y = 3x sin(x) - 4x cos(x) into the differential equation gives 6 cos(x) - 4 sin(x) + 3x sin(x) - 3x cos(x) = 3 sin(x), which satisfies the equation. Therefore, y = 3x sin(x) - 4x cos(x) is a solution.
(d) Plugging y = 3 cos(x) into  the differential equation gives -3 sin(x) + 3 cos(x) = 3 sin(x), which is not equal to 3 sin(x). Therefore, y = 3 cos(x) is not a solution.
(e) Plugging y = (-3/2)x cos(x) into the differential equation gives (3/2) sin(x) - (3/2)x cos(x) = (-3/2)(x cos(x) - sin(x)), which is not equal to 3 sin(x). Therefore, y = (-3/2)x cos(x) is not a solution.
Based on the analysis, the only function that is a solution to the given differential equation is y = 3x sin(x) - 4x cos(x) (option c).

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Answer:

1.8 inches

Step-by-step explanation:

Create a proportion where x is the distance on the map

[tex]\frac{1}{55}[/tex] = [tex]\frac{x}{99\\}[/tex]

Cross multiply and solve for x

55x = 99

x = 1.8

So, the distance on the map is 1.8 inches

Answer:

1.8 inches

Step-by-step explanation:

Scales on a map always represent the direct proportion.

Compare the distances as fractions:

Inches on the map

________________  =  [tex]\frac{1}{55} = \frac{x}{99}[/tex]

Miles on the ground

[tex]x = \frac{1x99}{55}[/tex]

[tex]x = \frac{99}{55}[/tex]

[tex]x = \frac{9}{5} = 1\frac{4}{5}[/tex]

x = 1.8 inches

Answer:

3 bagel recipe and 2 doughnut recipes are needed

Step-by-step explanation:

Given the expression

3d + 5b = 21 .. 1

d + b = 5 .... 2

We can use the expression to look for the amount of doughnut recipe and bagel recipe needed by solving the equations simultaneously

Multiply equation 1 by 1 and 2 by 3 to have;

3d + 5b = 21 .. 3

3d + 3b = 15 .... 4

Subtract 3 from 4

5b - 3b = 21 - 15

2b = 6

b = 6/2

b = 3

Substitute b = 3 into equation 2;

From 2,

d = b = 5

d + 3 = 5

d = 5 - 3

d = 2

Hence 3 bagel recipe and 2 doughnut recipes are needed

Step-by-step explanation:

Answer:

When light strikes an object, its rays can be either absorbed or reflected. A solid black object absorbs almost all light, while a shiny smooth surface, such as a mirror, reflects almost all light back. When reflected off a flat mirror, light bounces off at an angle equal to the angle it struck the object.

Step-by-step explanation:

A hose will be needed vertical walls to run along the entire outer edge of the floor and up around the door of the greenhouse 88 feet .

To calculate the length of the hose needed to run along the entire outer edge of the floor and up around the door of the greenhouse, we need to consider the perimeter of the floor and the additional distance around the door.

The perimeter of the floor is the sum of the lengths of all four sides of the rectangle. Since the greenhouse is 20 ft long and 16 ft wide, the perimeter of the floor is:

Perimeter of floor = 2(length + width) = 2(20 ft + 16 ft) = 2(36 ft) = 72 ft

In addition to the floor perimeter, to account for the distance around the door. The door is 8 ft wide, so the additional distance around the door is:

Distance around door = 2(width of door) = 2(8 ft) = 16 ft

calculate the total length of the hose needed by adding the perimeter of the floor and the distance around the door:

Total length of hose = Perimeter of floor + Distance around door = 72 ft + 16 ft = 88 ft

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a) The determination of the equivalent units of production for materials and conversion costs is as follows:

                                                       Units       Materials       Conversion

Completed and transferred out  12,500        12,500            12,500

Ending work in process                2,850         2,850                1,710

Total equivalent units                  15,350       15,350              14,210

b) The calculation of the unit costs is as follows:

                                      Direct Materials     Conversion Costs

Production costs                $42,980                 $34,104

Total equivalent units           15,350                    14,210

Unit costs                              $2.80                      $2.40

c) The preparation of the cost reconciliation schedule is as follows:

                                         Direct Materials  Conversion Costs  Total Costs

Beginning work in process      $0                        $0                     $0

Cost to be accounted for       $42,980                 $34,104          $77,084

Total production costs           $42,980                 $34,104          $77,084

Costs accounted for units:

Completed / transferred out $35,000               $30,000         $65,000

Ending work in process          $7,980                   $4,104          $12,084

Total costs accounted for    $42,980                 $34,104         $77,084

Equivalent units are the multiplication of the number of physical (or actual) units on hand by the percentage of completion of the units.

1. Completed and transferred out 12,500 units.

2. Beginning work in process = $0

Ending work in process = 2,850 units 60% complete

Production Costs

Direct materials costs = $42,980 100% complete in terms of materials at July 31.

Direct labour = $15,700

Manufacturing overhead = $18,404

Total conversion costs = $34,104 ($15,700 + $18,404)

Equivalent units of production:

                                                       Units       Materials       Conversion

Completed and transferred out  12,500        12,500            12,500

Ending work in process                2,850         2,850 (100%)    1,710 (60%)

Total equivalent units                  15,350       15,350              14,210

Unit costs:

                                      Direct Materials     Conversion Costs

Production costs                $42,980                 $34,104

Total equivalent units           15,350                    14,210

Unit costs                              $2.80                      $2.40

                                 ($42,980 ÷ 15,350)    ($34,104 ÷ 14,210)

Cost Reconciliation Schedule:

                                         Direct Materials  Conversion Costs  Total Costs

Beginning work in process      $0                        $0                     $0

Cost to be accounted for       $42,980                 $34,104          $77,084

Total production costs           $42,980                 $34,104          $77,084

Costs accounted for units:

Completed / transferred out $35,000               $30,000         $65,000

                                 (12,500 x $2.80)              (12,500 x $2.40)

Ending work in process          $7,980                   $4,104          $12,084

                                   (2,850 x $2.80)              (1,710 x $2.40)    

Total costs accounted for    $42,980                 $34,104         $77,084

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Answer:

276 in^2

Step-by-step explanation:

2((6*6)/2) + 2(6*12) + (8*12) = 276 in^2

Answer:

No

Step-by-step explanation:

Say n was equal to 2

7(2) + 6 =20

13(2) = 26

The formula for C(x) is `C(x) = 4.75x + 500,000`.

The total cost of producing 100,000 items is $5,250,000.

The marginal cost of the items to be produced in this plant is $4.75.

Given, Company analysts have determined that a linear function is a reasonable estimation for the total cost C(x) in dollars of producing x items. They estimate the cost of producing 10,000 items as $547,500 and the cost of producing 50,000 items as $737,500.

(a) Find a formula for C(x)

For the given data, let C(x) be the cost of producing x items, we have the two points (10,000, 547,500) and (50,000, 737,500).

We have to find the slope of the line passing through these points.

slope of the line `

m = (y2 - y1) / (x2 - x1)`m = (737,500 - 547,500) / (50,000 - 10,000)m = 190,000 / 40,000m = 4.75

Formula for C(x) can be found by using the slope-intercept form of the equation of a line.

C(x) = mx + b

We know, m = 4.75

Using the point (10,000, 547,500), we get

547,500 = 4.75 (10,000) + b.b = 547,500 - 47,500

b = 500,000

Therefore, the formula for C(x) is `

C(x) = 4.75x + 500,000`

So, the formula for C(x) is `C(x) = 4.75x + 500,000`.

(b) Find the total cost of producing 100,000 items.

Total cost of producing 100,000 items is C(100,000).

C(x) = 4.75x + 500,000

C(100,000) = 4.75 (100,000) + 500,000= 4,750,000 + 500,000= 5,250,000

Therefore, the total cost of producing 100,000 items is $5,250,000.

(c) Find the marginal cost of the items to be produced in this plant.

Marginal cost is the cost incurred for producing one additional item. It can be found by taking the first derivative of the cost function with respect to x.

C(x) = 4.75x + 500,000 `

=>` `dC(x)/dx = 4.75`

The marginal cost of the items to be produced in this plant is $4.75.

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Answer:

I give bases example the triangle pyramid

relation R on set A = {23, 51, 36, 75, 35, 11, 102, 9, 10, 29}, aRb means a ≡ b (mod 3), which indicates that a and b have the same remainder when divided by 3.

In the given relation R on set A = {23, 51, 36, 75, 35, 11, 102, 9, 10, 29}, aRb means a ≡ b (mod 3), which indicates that a and b have the same remainder when divided by 3.

To represent this relation R in digraph notation, we can draw a directed graph where each element of set A is represented as a node, and there is a directed edge from node a to node b if aRb holds true.

Let's go through each element of set A and determine the directed edges based on the given relation R:

1. For 23, its remainder when divided by 3 is 2. Therefore, there will be an edge from 23 to itself.

2. For 51, its remainder when divided by 3 is 0. There will be an edge from 51 to itself.

3. For 36, its remainder when divided by 3 is 0. There will be an edge from 36 to itself.

4. For 75, its remainder when divided by 3 is 0. There will be an edge from 75 to itself.

5. For 35, its remainder when divided by 3 is 2. There will be an edge from 35 to itself.

6. For 11, its remainder when divided by 3 is 2. There will be an edge from 11 to itself.

7. For 102, its remainder when divided by 3 is 0. There will be an edge from 102 to itself.

8. For 9, its remainder when divided by 3 is 0. There will be an edge from 9 to itself.

9. For 10, its remainder when divided by 3 is 1. There will be an edge from 10 to itself.

10. For 29, its remainder when divided by 3 is 2. There will be an edge from 29 to itself.

In this digraph, each node represents an element from set A, and the directed edges indicate the relation R (a ≡ b mod 3).

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