Write a recursive sequence that represents the sequence defined by the following explicit formula:

Write A Recursive Sequence That Represents The Sequence Defined By The Following Explicit Formula:

Answers

Answer 1

The recursive sequence that represents the sequence defined by the following explicit formula is given as follows:

[tex]a_1 = -32[/tex][tex]a_{n + 1} = -\frac{1}{4}a_n[/tex]

What is a geometric sequence?

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The first term and the common ratio for this problem is given as follows:

[tex]a_1 = -32, q = -\frac{1}{4}[/tex]

The common ratio means that each term is the previous term multiplied by -1/4, hence the recursive formula is given as follows:

[tex]a_{n + 1} = -\frac{1}{4}a_n[/tex]

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Related Questions

what is the area of the square if it’s 15 by 15

Answers

Answer:

225 is the answer

15 times 15

Step-by-step explanation:

write a quadratic function that passes through points (5,0) (9,0) (7,-20)

Answers

The quadratic function that passes through points is P(x) = 5(x - 5)(x - 9)

Writing the quadratic function that passes through points

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

Zeros at (5,0) (9,0) Point (7,-20)

The quadratic function, P(x), in factored form  is represented as

P(x) = a * product of (x - zeros)

So, we have

P(x) = a(x - 5)(x - 9)

Using the point (7, -20), we have

a(7 - 5)(7 - 9) = -20

So, we have

a = 5

Recall that

P(x) = a(x - 5)(x - 9)

So, we have

P(x) = 5(x - 5)(x - 9)

Hence, the function is P(x) = 5(x - 5)(x - 9)

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-12 divided by 3 5/9

Answers

your answer is 3.375

what is the solution to the equation 0.5x - 1.25 = 3.5?

Answers

Answer:

Step-by-step explanation:

Add '-1.25' to each side of the equation.

1.25 + -1.25 + -0.5x = 0.75 + -1.25 + 3.5n

Combine like terms: 1.25 + -1.25 = 0.00

0.00 + -0.5x = 0.75 + -1.25 + 3.5n

-0.5x = 0.75 + -1.25 + 3.5n

Combine like terms: 0.75 + -1.25 = -0.5

-0.5x = -0.5 + 3.5n

Divide each side by '-0.5'.

x = 1 + -7n

Simplifying

x = 1 + -7n

The students at Kayla's school are forming teams of three students for a quiz bowl competition. Kayla is assuming that each member of a team is equally likely to be male or female. She uses a coin toss (heads = female, tails = male) to simulate this probability. Here is Kayla's data from 50 trials of 3 coin tosses:



thh tth tth tht thh htt hth hht hth tth tth hht hth tht tht tth tth thh thh htt tht thh tth hht hth thh tht tth hht thh hhh tth tth hth htt tht thh hhh htt thh htt ttt tht ttt thh hht hth htt hht hth



According to this data, what is the experimental probability that a team will consist of two girls and a boy?

0.33
0.375
0.23
0.46

Answers

The required, experimental probability that a team will consist of two girls and a boy is 0.33. Option A is correct.

To find the experimental probability that a team will consist of two girls and a boy, we need to count the number of times that Kayla got a team with two girls and one boy and divide that by the total number of trials.

So, out of 50 trials, there were 17 trials where the team had two girls and one boy. Therefore, the experimental probability is:

17/50 = 0.34

Therefore, it is 0.34, which is closest to option (A) 0.33.

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The sales data for July and August of a frozen yogurt shop are approximately normal.

The mean daily sales for July was $270 with a standard deviation of $30. On the 15th of July, the shop sold $315 of yogurt.

The mean daily sales for August was $250 with a standard deviation of $25. On the 15th of August, the shop sold $300 of yogurt.

Which month had a higher z-score for sales on the 15th, and what is the value of that z-score?

a.)
August, with a z-score of 1.67.
b.)
July, with a z-score of 1.5.
c.)
July, with a z-score of 1.8.
d.)
August, with a z-score of 2.

Answers

Answer: D

Step-by-step explanation:

To determine which month had a higher z-score for sales on the 15th, we need to calculate the z-scores for each month's sales.

For July:

z-score = (x - μ) / σ

where x is the sales on the 15th, μ is the mean daily sales for July, and σ is the standard deviation of daily sales for July.

Plugging in the values, we get:

z-score for July = (315 - 270) / 30 = 1.5

For August:

z-score = (x - μ) / σ

where x is the sales on the 15th, μ is the mean daily sales for August, and σ is the standard deviation of daily sales for August.

Plugging in the values, we get:

z-score for August = (300 - 250) / 25 = 2

Since the z-score for August is higher than the z-score for July, August had a higher z-score for sales on the 15th.

The value of the z-score for August's sales on the 15th was 2.

7
Select the correct answer from the drop-down menu.
Which term best fits the sentence?
After you make a decision, the next step in the decision-making process is to
whether you made the right choice.
Reset
Next
This step will help you det

Answers

Answer:

Step-by-step explanation: bot

The directional derivative of f= x^2 y z^3 along x = e^-t , y = 1 + 2 sint , z = t -cost at t =0

Answers

The directional derivative of f = x²yz³ along vector i + 2j + 2k at x = [tex]e^{-t}[/tex] , y = 1 + 2 sin t , z = t -cost at t =0 is 2/3.

Given that the functions are,

x = [tex]e^{-t}[/tex]

y = 1 + 2 sin t

z = t - cos t

At t = 0 the point will be,

x = e⁰ = 1

y = 1 + 2 sin 0 = 1

z = 0 - cos 0 = -1

So the point is (1, 1, -1).

The vector is,

a = i + 2j + 2k

unit vector of a = (i + 2j + 2k)/√(1² + 2² + 2²) = (i + 2j + 2k)/3

Given the function is, f = x²yz³

Grad. f = 2xyz³.i + x²z³.j + 3x²yz².k

directional derivative is given by

= (Grad. f)*(unit vector of a) at (1, 1, -1)

= (2xyz³.i + x²z³.j + 3x²yz².k)*(i + 2j + 2k)/3 at (1, 1, -1)

= (2xyz³ + 2x²z³ + 6x²yz²)/3 at (1, 1, -1)

= (-2 - 2 +6)/3

= 2/3

Hence required directional derivative is 2/3.

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The question is incomplete. The complete question will be -

"The directional derivative of f= x^2 y z^3 along vector i + 2j + 2k at x = e^-t , y = 1 + 2 sin t , z = t -cost at t =0"

The sun of the 2 digits of a certain number is 5. If 9 is added to the original number, the new number will have the original digits reversed. Find the number

Answers

Answer:

23

Step-by-step explanation:

Assume the digits are

1, 4 or 2,3

The number can be 14, 41, 23, 32

Test each one:

14 + 9 = 23 does not work

41 + 9 = 50 does not work

23 + 9 = 32 works

32 + 9 = 41 does not work

complete the table AB=1?, BC=3?

Answers

Answer:

angle B = 60 degree

AB = 2 cm

BC = 2 cm

Step-by-step explanation:

an equilateral triangle is a triangle with the following properties:

1. all sides equal

2. all angels equal to 60 degree

As a result:

angle B = 60 degree

AB = 2 cm

BC = 2 cm

According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table:
Month
Average Maximum Monthly Temperature
Jan
48.1
Feb
50.9
Mar
62.4
Apr
67.0
May
76.5
Jun
83.9
Jul
86.8
Aug
88.1
Sep
79.2
Oct
69.9
Nov
59.5
Dec
49.6

Let x represent the months and y represent the average maximum monthly temperature.
Plot the data on a scatterplot. Choose the plot that best represents the data.
a.
On a coordinate plane, points are at (1, 48.1), (2, 50.9), (3, 62.4), (4, 67), (5, 76.5), (6, 83.9), (7, 86.8), (8, 88.1), (9, 79.2), (10, 69.9), (11, 59.5), (12, 49.6).
b.
On a coordinate plane, points are around (5, 85), (6, 90), (7, 80), (8, 70), (9, 60), (10, 50), (48, 1), (50, 3), (62, 4), (66, 4), (76, 5), (82, 8).
c.
On a coordinate plane, points are around (0, 49), (1, 52), (2, 62), (3, 68), (4, 78), (5, 85), (50, 12), (60, 10), (70, 10), (80, 9), (88, 8), (87, 9), (89, 9).
d.
On a coordinate plane, points are around (0, 48), (2, 52), (13, 50).



Please select the best answer from the choices provided

Answers

a) On a coordinate plane, points are at (1, 48.1), (2, 50.9), (3, 62.4), (4, 67), (5, 76.5), (6, 83.9), (7, 86.8), (8, 88.1), (9, 79.2), (10, 69.9), (11, 59.5), (12, 49.6)  best represents the data.

This is because the data represents a set of paired values, with the months as the independent variable (x) and the average maximum monthly temperature as the dependent variable (y). A scatter plot is the appropriate graph for displaying this type of data.

Option a shows the correct placement of the data points on a scatter plot, with the x-axis representing the months and the y-axis representing the average maximum monthly temperature. The points are clearly organized in a sequence from January to December, with an upward trend in temperature from the winter months to the summer months, followed by a gradual decrease in temperature in the fall and winter months.

Option b has the correct range of temperatures, but the points are not arranged in a logical sequence and are scattered randomly across the graph. Option c also has a similar issue with random placement of points and does not reflect the actual values in the data set. Option d only has three points and does not represent the complete data set.

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Find a quadratic equation which has solutions x=7 and x=-9. Write the quadratic form in the simplest standard form x^2+bx+c=0

Answers

Answer: x^2+2x-63

Step-by-step explanation:

Quadratic Equation = x^2-(Sum of Solution)x+(Product of Solution)

                                =x^2-(7-9)+(7*(-9))

                                =x^2+2x-63

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Laura is 3 ft tall how tall is Laura in inches

Answers

36 inches


Multiply 3 by 12 because there are 12 inches in a single foot.

3 x 12 = 36
1ft=12inches
So your gonna multiply 3 by 12 to get your total amount in inches
3ft*12inch=36inches

can someone please help me what is 11 1/8 + 2 3/4??? please

Answers

Answer: 13 7/8

Step-by-step explanation:

11 + 1/8 + 3/4 + 2 = 13 7/8

Suppose you invest $5,000 in an account earning 4.71% APR compounded
monthly. How much money will be in the account after 15 years?

Answers

$9,664.47

After 15 years the account will have $9,664.47

Find the 8th term of the geometric sequence 10, 50, 250,...

Answers

The 8th term of the sequence is 781, 250.

We have geometric sequence 10, 50, 250,...

First term= 10

Common ratio = 50/10 = 5

So, the 8th term of sequence is

= 10 x [tex]r^{8-1[/tex]

= 10 x [tex]r^7[/tex]

= 10 x [tex](5)^7[/tex]

= 10 x 5 x 5 x 5 x 5 x5 x 5 x 5

= 10 x 78125

= 781, 250

Thus, the 8th term of the sequence is 781, 250.

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Select all numbers that are irrational.

Answers

Answer:

The irrational numbers are:

368.5468432...

14.19274128...

√.156

Box 1&3 are the answer

Area/ Perimeter question. Any help? i have an assignment to complete.

Answers

Answer:

13 + 8 + 13 + (1/2)(8π) = 34 + 4π feet

= 46.57 feet

2. An equation for a line is = 6/5 . What will the new equation of this line be after it is rotated 90° counterclockwise around the origin

Answers

If new equation of this line be after it is rotated 90° counterclockwise around the origin, the equation of the new line after rotation is y = (-5/6)x

To find the new equation of a line after it is rotated 90° counterclockwise around the origin, we need to use the following formula:

(x', y') = (-y, x)

where (x, y) are the coordinates of a point on the original line, and (x', y') are the coordinates of the corresponding point on the new line after rotation.

We can start by finding the slope of the original line, which is given by:

y = (6x/5)

Rearranging this equation, we get:

x = (5/6)y

This tells us that the slope of the original line is 5/6.

To find the equation of the new line after rotation, we need to apply the formula above to two points on the original line. Let's choose two easy points to work with, such as (0,0) and (5,6).

Using the formula, we can find the new coordinates of these points after rotation:

(0', 0') = (-0, 0) = (0,0)

(5', 6') = (-6, 5)

Now we can find the slope of the new line using these two points:

slope = (6' - 0') / (5' - 0') = 5/-6 = -5/6

In summary, to find the new equation of a line after rotating 90° counterclockwise around the origin, we can use the formula (x', y') = (-y, x) to find the new coordinates of two points on the original line, and then use these points to find the slope of the new line. In this case, the new equation of the line is y = (-5/6)x.

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A total of $8000 is invested: part at 6% and the remainder at 10%
. How much is invested at each rate if the annual interest is $760

Answers

The requried, $1000 is invested at 6%, and $7000 is invested at 10%

Let x be the amount invested at 6%, and y be the amount invested at 10%. We know that x + y = $8000 since the total amount invested is $8000.

We also know that the annual interest earned on the 6% investment is 0.06x, and the annual interest earned on the 10% investment is 0.1y. The total annual interest earned is given as $760.

So we have the system of equations:

x + y = 8000 (1)

0.06x + 0.1y = 760 (2)

We can use either substitution or elimination to solve for x and y. Here, we'll use elimination. Multiplying equation 1 by 0.06, we get:

0.06x + 0.06y = 480 (3)

0.1y - 0.06y = 0.04y = 280

y = $7000.

Substituting y = $7000 into equation 1, we get:

x + $7000 = $8000

So x = $1000.

Therefore, $1000 is invested at 6%, and $7000 is invested at 10%.

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Pls help and show how you got the answer :) I really appreciate it

Answers

In 2006, the population will reach 109 million.

The correct answer is an option (d)

Here function [tex]f(x)=100(1.0153)^x[/tex] represents the population (in millions) x years after 2000

We need to find the year x when the population will reach 109 million.

i.e., for f(x) = 109, we need to find the value of x.

Consider function f(x),

[tex]f(x)=100(1.0153)^x[/tex]

Substitute f(x) = 109

⇒ [tex]109=100(1.0153)^x[/tex]

⇒ [tex](1.0153)^x=1.09[/tex]

Taking logarithm on both the sides.

⇒ x ln(1.0153) = ln(1.09)

⇒ x = ln(1.09) / ln(1.0153)

⇒ x = 5.675

⇒ x ≈ 6

So, the required year would be,

2000 + 6 = 2006

Therefore, the correct answer is an option (d)

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Nicole made 10 dozen cupcakes. She made 20% with chocolate icing, 30% with vanilla icing, and 50% with powdered sugar. How many of each kind of cupcake did she make?

Answers

Answer:

2 Dozen Chocolate, 3 Dozen Vanilla, 5 Dozen Sugar.

Explanation:

0.5 x 10 = 5.

0.3 x 10 = 3.

0.2 x 10 = 2.

Write an equation then find the value of y when x =16. Show all work.

Answers

Answer:

Answer is A

Step-by-step explanation:

A) y = -1/2x represents a proportional relationship because the equation can be written in the form y = kx, where k is a constant. In this case, k = -1/2, which means that y is proportional to x with a constant of proportionality of -1/2.

B) y = 2x - 4 does not represent a proportional relationship because the equation cannot be written in the form y = kx. If we try to write it in this form, we get y/x = 2 - 4/x, which means that y/x is not constant. Therefore, y is not proportional to x with a constant of proportionality.

Homework help?!?!?!

Answers

Answer:

1. The slope of the line is 3. The line goes up 3, over 1, and since slope is rise/run, the slope is 3.

2. The slope of the line is 4. The line goes up 4, over 1, and since slope is rise/run, the slope is 4.

3. The slope of the line is 2. The line goes up 2, over 1, and since slope is rise/run, the slope is 2.

4. The slope of the line is -4. The line goes down 4, over 1, and since slope is rise/run, the slope is -4.

The gradients of line equations are listed below:

m = 3m = 4m = 2m = - 3

How to determine the gradient of a line

In this question we have four cases of line equations shown on Cartesian plane, whose gradients must be found. The gradient of each line can be computed by means of secant line formula and two points:

m = Δy / Δx

Where:

Δx - Change in independent variable.Δy - Change in dependent variable.

Case 1: (x₁, y₁) = (- 1, - 4), (x₂, y₂) = (1, 2)

m = [2 - (- 4)] / [1 - (- 1)]

m = 3

Case 2: (x₁, y₁) = (- 1, - 1), (x₂, y₂) = (0, 3)

m = [3 - (- 1)] / [0 - (- 1)]

m = 4

Case 3: (x₁, y₁) = (- 1, - 1), (x₂, y₂) = (1, 3)

m = [3 - (- 1)] / [1 - (- 1)]

m = 2

Case 4: (x₁, y₁) = (0, 4), (x₂, y₂) = (2, - 2)

m = (- 2 - 4) / (2 - 0)

m = - 3

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Which diagram depicts as a positive angle in standard position?

Answers

Answer:

A.

Step-by-step explanation:

A positive angle has the initial side at the positive x-axis and the terminal side rotated counterclockwise from it.

That is shown in diagram A.

Find the value of x in the figure below 53° ,24° and x°

Answers

Answer:46

Step-by-step explanation:

traingle ABD = 53 + 24 + 47 + x = 180

134+x=180

x=180-134

x=46

A restaurant hired 18 servers for one banquet. They pay a full time server $21.00 per hour and a part time server $15.50 per hour. If the labor cost of the restaurant was $312.00 per hour, how many full time and part time servers were there for the banquet?

Answers

Let's assume that x servers were full-time and y servers were part-time. Then we can write two equations based on the given information:

x + y = 18 (since there were 18 servers in total)

21x + 15.5y = 312 (since the labor cost was $312 per hour)

To solve for x and y, we can use elimination or substitution. Here's one way to use elimination:

Multiply the first equation by 15.5 to get 15.5x + 15.5y = 279.

Subtract the first equation from the second equation to get 5.5x = 33.

Divide both sides by 5.5 to get x = 6.

Now we know that there were 6 full-time servers. We can substitute this value into either of the two equations to solve for y:

6 + y = 18

y = 12

Therefore, there were 6 full-time servers and 12 part-time servers at the banquet.

tia's favorite stargergy for multiplying polynomials is to make a box that fits the two factors

Answers

Using Tia's box method, the multiplication of the polynomials (x + 2)(x² -3x + 5) in the standard form is  x³ - x² - x + 10

Here, we need to multiply the polynomials (x + 2)(x² -3x + 5)

Tia's stargergy for multiplying polynomials is to make a box that fits the two factors.

Using Tia's box method,

          x²          -3x            +5

x         x³           -3x²          +5x

+2     +2x²         -6x           +10

Consider (x + 2)(x² -3x + 5)

= (x . x²) - (x . 3x) + (x . 5) + (2x²) -(2 × 3x) + (2 × 5)

= x³ - 3x² + 5x + 2x² - 6x + 10

= x³ - 3x² + 2x² + 5x - 6x + 10

= x³ - x² - x + 10

This is the required polynomial.

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Find the complete question below.

can someone help me with this

Answers

The sine equation for the object's height is given as follows:

d = -5sin(0.24t).

How to define the sine function?

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

A: amplitude.B: the period is 2π/B.C: vertical shift.

The amplitude for this problem is of 5 inches, hence:

A = 5.

The period is of 1.5 seconds, hence the coefficient B is given as follows:

2π/B = 1.5

B = 1.5/2π

B = 0.24.

The function starts moving down, hence it is negative, so:

d = -5sin(0.24t).

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The curve above is the graph of a sinusoidal function. It goes through the points
and
. Find a sinusoidal function that matches the given graph. If needed, you can enter
=3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits.

Answers

The sinusoidal function that matches the specified graph, expressed using π ≈ 3.1416 is; y ≈ 4·sin(0.628·(x + 3))

What is a sinusoidal function?

A sinusoidal function is a periodic function that is based on either the sine or the cosine function.

The general form of a sinusoidal function is; y = A·cos(B·(x - C)) + D

The peak and the trough of the graph of the function indicates that the amplitude, A = (4 - (-4))/2 = 4

The vertical shift, D = (4 + (-4))/2 = 0

The period, P = 2·π/B

A cycle is completed in -0.5 - (-10.5) = 10 units of the x-value interval

P = 10 = 2·π/B

Therefore; B = π/5

When x = -8, y = 0, therefore;

0 = 4·sin((π/5)·((-8) - C)) + 0

4·sin((π/5)·((-8) - C)) = 0

sin((π/5)·((-8) - C)) = 0

(π/5)·((-8) - C) = 0

((-8) - C)  = 0

C = -8

When x = 2, y = 0, therefore;

0 = 4·sin((π/5)·(2 - C)) + 0

4·sin((π/5)·(2 - C)) = 0

sin((π/5)·(2 - C)) = 0

(π/5)·(2 - C) = 0

(2 - C)  = 0

C = 2

Similarly; When x = -3, y = 0, therefore; C = -3

y = 4·sin((π/5)·(x + 3))

The value C = -3, corresponds to the horizontal shift of the graph of the sine function, which is shifted 3 units to the left

The sinusoidal function, where π ≈ 3.1416 is therefore;

y ≈ 4·sin((0.628)·(x + 3))

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What net force must act on the bowl of fruit to make it accelerate to the right at a rate of 4. 4 m/s2 (q019) elongate hills of glacial till that are molded by glaciers that flow over them are called group of answer choices loess. kettle holes. drumlins. eskers. 87) An irreversible engine operating between the temperatures of 550 K and 300 K extracts 1.20 kJ of heat from the hot reservoir and produces 0.450 kJ of work. How much entropy is created in the process?A) 0.32 J/KB) 0.68 J/KC) 0.44 J/KD) 0.73 J/KE) 0 J/K A new arrow labeled "lengthens" could be added between __________."target DNA" "DNA strands""primers" "DNA strands""target DNA" "primers""Taq polymerase" "primers" a cultural production system includes a . group of answer choices all of the above communication subsystem managerial subsystem creative subsystem write a function called almostaddition that takes two int arguments. the first argument should not require an argument label. the function should add the two arguments together, subtract 2, then print the result. call the function and observe the printout. What is the pH of a 0.10 M CuCl2 solution?For [Cu(OH2)4]2+, Ka = 1.0 108a. 4.40b. 4.49c. 4.58d. 4.63e. 4.68 Rrenin hydrolyzes angiotensinogen, which is released from the ___________ to form angiotensin i. multiple choice liver kidneys lungs spleen questionwhich statement best describes the noble gases?responsesthey have an outer electron shell that needs only 1 electron.they have an outer electron shell that needs only 1 electron.they are highly reactive.they are highly reactive.they have a full outer electron shell.they have a full outer electron shell.they combine easily with other elements. If Rudy has a 25% tax rate and a 6% after-tax rate of return, a $30,000 tax deduction in four years will save how much tax in today's dollars?A) $30,000.B) $7,500.C) $23,760.D) $5,940.E) None of the choices are correct. you are using my business to promote your restaurant online and attract new customers. what feature can you use to encourage new people to try you out? dynamic ads customer reviews in-search call button insights When a user opens a ______, the e-mail program calls up a web page that displays in the e-mail window. business e-mail rich e-mail simple text e-mail what can a patient in tripod position indicate? Identify the indicator that has two endpoints.alizarin yellow Rcrystal violetphenol redalizarinphenolphthalein the electric charge of magnesium is 222. the electric charge of potassium is 111. write an inequality that correctly compares the charges. There is a spinner with 8 equal areas, numbered 1 through 8. If the spinner is spun one time, what is the probability that the result is a multiple of 2 and a multiple of 3? a bar magnet has a north and south magnetic pole. which of the following equations indicate that when the bar magnet is broken in half, magnetic monopoles are not created? At what speed must a 150 kg football player be moving to have the smae momentum as a 15 g bullet traveling at 300 m/s? in the laboratory you dissolve 19.1 g of manganese(ii) acetate in a volumetric flask and add water to a total volume of 125 ml. what is the molarity of the solution? m. what is the concentration of the manganese(ii) cation? m. what is the concentration of the acetate anion? m. an employer who is providing helicopter pilots under contract to the saudi arabian government to fly muslim pilgrims to mecca could refuse to hire non-muslims or require all pilots to convert to islam. question 5 options: true false