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

your answer is 3.375

$9,664.47

After 15 years the account will have $9,664.47

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

d = -5sin(0.24t).

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

y = Asin(Bx) + C.

The parameters are given as follows:

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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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.

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

Answer: 13 7/8

Step-by-step explanation:

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

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

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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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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Answer:

Step-by-step explanation: bot

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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Answer:

225 is the answer

15 times 15

Step-by-step explanation:

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"

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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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.

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

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

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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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:

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:

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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Answer:

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

= 46.57 feet

Answer:

The irrational numbers are:

368.5468432...

14.19274128...

√.156

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.

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

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.

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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Answer:46

Step-by-step explanation:

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

134+x=180

x=180-134

x=46

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.

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

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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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.