The first 4 terms in a sequence are 8,5,2,-1 What is the recursive equation?

Answer:

below

Step-by-step explanation:

2 * 27    + 2*22    + 2*22  + 2 * 98 = 338 in

Real numbers include both rational and irrational numbers. All rational and irrational numbers, such as the integers (-2, 0, 1), fractions (1/2, 2.5), and the number 3, are considered real numbers.

Given f(x)=|x|, g(x)=[x]

[tex]& \text { fog }(x)=|[x]| \\[/tex]

[tex]- \\2[/tex][tex]\end{array}\right]=-1+} \\[/tex]

Simplifying,

[tex]{gof}(\mathrm{x})=[|\mathrm{x}|] \\[/tex]

[tex]{fog}\left(-\frac{}{\mathbb{R}}\right)={ }_{\mid}-{ }_{\mathbb{R}}\right]_{\mid}=|-1|=1 \\[/tex]

To ;learn more about real numbers, refer to:

https://brainly.com/question/17201233

#SPJ1

When revolved over the {x} axis will occupy more volume as compared to when revolved over the {y} axis.

Given is that one bag of pebbles covers 5 ft² and costs $8.99​​.

Refer to the image attached. The reflection over the {x} axis will occupy more volume as compared to the reflection over the {y} axis. The figure generated in both the cases would be a cuboidal prism structure.

Therefore, when revolved over the {x} axis will occupy more volume as compared to when revolved over the {y} axis.

To solve more questions on algebraic expressions, visit the link below-

brainly.com/question/1041084

#SPJ1

Answer:

The linear equation giving the demand x in terms of the rent p can be written as x = 40 - 0.042p, where x is the number of occupied units and p is the monthly rent.

To find the required sample size for a resturant owner wishes to estimate the proportion of people who eat atleast three a week, we can use the formula for the margin of error of a proportion estimate. Therefore, the required sample size is 663.

Margin of error = z * [tex]\sqrt{(p * (1 - p) / n)}[/tex]

where z is the z-score corresponding to the desired level of confidence (for 90% confidence, z = 1.645), p is the population proportion (0.4 in this case), and n is the sample size.

We want the length of the confidence interval to be below 0.03, so the margin of error should be less than 0.03 / 2 = 0.015.

Substituting the values and solving for n, we get:

[tex]0.015=1.645 * \sqrt{(0.4 * (1 - 0.4) / n)}[/tex]

[tex]n = (1.645 / 0.015)^2 * 0.4 * (1 - 0.4)[/tex]

[tex]n = 661.84[/tex]

Therefore, the required sample size is 662. To be safe, we can round up to the next whole number, so the required sample size is 663.

You can learn more about sample size at

https://brainly.com/question/29227552

#SPJ4

The equivalent expression that uses the Greatest common Factor (GCF) of each term in the expression are 16 (2x+1 ), 32 ( x + 0.5 ) ,16 ( 2x+1 )  and 16 (2x+1)

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expressions,

2 ( 16x+ 8 )

= 2 * 8 ( 2x+ 1 )

= 16 ( 2x+1 )

16 (2x+1 )

= 16 * 2 ( x + 1/2 )

=32 ( x + 0.5 )

4(8x+4)

= 4 * 4 ( 2x+ 1 )

= 16 ( 2x+1 )

8 (4x+2)

= 8 * 2 ( 2x+1 )

= 16 (2x+1)

Therefore, The equivalent expression that uses the Greatest common Factor (GCF) of each term in the expression are 16 (2x+1 ), 32 ( x + 0.5 ) ,16 ( 2x+1 )  and 16 (2x+1)

To learn more about Algebraic expression from given link.

https://brainly.com/question/953809

#SPJ1

Answer:

Below

Step-by-step explanation:

2005 is 7 years after 1998   x= 7

S = 1.7 (7) x 5.5 = 65.45   (billion)

Answer:

C

Step-by-step explanation:

The standard form of a circle is

(x-a)^2 + (y-b)^2 = r^2

Where (a, b) is the centre and r is the radius

Answer:

84 tables are available

Step-by-step explanation:

30% = 30 ÷ 100

120 x (30 ÷ 100) = 36

36 tables are reserved hence

120-36 = 84

84 tables are available

The final price for the members after the discount is $395.52.

What is meant by discount price?

Discounts are price reductions that store owners offer on items or services that are otherwise priced as marked. This portion of the rebate is typically provided to boost sales or get rid of excess inventory. The price of an item as stated by the manufacturer or seller, without any price reduction, is known as the List price or Marked Price. After any discounts or price reductions from the list price, the selling price is the final price at which an item is actually sold.

Given,

  The cost price of the computer = $370.80

 The selling price at first = $618

a) The markdown percentage = 20%

The selling price after this markdown = 618 - (618 * 20/100)

                                                              = 618 - 123.6 = $494.4

b) Additional discount for the members of the store's loyalty club = 20%

  The final selling price for the members = 494.4 - (494.4 * 20/100)

                                                                    = 494.4 - 98.88 = $395.52

Therefore the final price for the members after the discount is $395.52.

To learn more about discounts, follow the link.

https://brainly.com/question/1548141

#SPJ1

The value of P(t) is [tex]\frac{dP}{dt} = k \cdot \sqrt{P}[/tex]  and there will be approximately 220 fish in the lake after 1.6 years.

(a) This is a separable differential equation and can be solved using the separation of variables. We have:

[tex]\frac{dP}{dt}[/tex] = k * [tex]\sqrt{P}[/tex]

[tex]\frac{dP}{\sqrt{P}}[/tex] = k * dt

Integrating on both sides:

2 * [tex]\sqrt{P}[/tex] = k * t + C1

where C1 is a constant of integration. Solving for P, we have:

P(t) = [tex](k * t + C1)^2[/tex] / 4

Using the initial condition P(0) = C, we can solve for C1:

C = [tex](C1)^2[/tex] / 4

C1 = 2 * [tex]\sqrt{C}[/tex]

Therefore, we have:

[tex]\frac{dP}{dt} = k \cdot \sqrt{P}[/tex]

(b) There will be approximately 220 fish in the lake after 1.6 years.

Using the values given, we have:

C = 102

t = 7 months = 7/12 years = 0.5833 years

P(7 months) = 155

We can use this information to solve for k:

[tex]155 =[/tex] [tex]\frac{(k * 0.5833 + 2 *\sqrt{102})^2}{4}[/tex]

[tex]k = \frac{(4 * 155 - 4 * 2^2 *\sqrt{102})}{0.5833^2}[/tex]

Now that we have k, we can find P(1.6 years):

[tex]P(t) = \frac{\left( k \cdot t + 2 \cdot \sqrt{C} \right)^2}{4}[/tex]

By solving, the final value of k is approximately = 10.04

Substituting the value of k, we get:

P(1.6 years) = [tex]\frac{\left( 10.04 \cdot 1.6 + 2 \cdot \sqrt{102} \right)^2}{4}[/tex]

By evaluating the expression, we get:

P(1.6 years) = 220.72

So, there will be approximately 220 fish in the lake after 1.6 years.

To learn more about differential equations:

https://brainly.com/question/1164377

#SPJ4

The appropriate response in each dropdown are

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

Function = g(x)

Also, we have:

The function g is continuous at a=2

This means that the limit at x approaches +2 is to infinity

Read more about functions a

https://brainly.com/question/28532394

#SPJ1

Rounded to the nearest integer, this is 140165 lb.

The height of the water above the gate is 25 ft - 5 ft = 20 ft.

The width of the water perpendicular to the gate is half the width of the dam, or 60 ft / 2 = 30 ft.

The area of the equilateral triangle is (8 ft)^2 * √(3) / 4 = 8 * 8 * √(3) / 4 = 16 * √(3) ft^2.

The volume of the water pressing against the gate is the product of the height, width, and area:

20 ft * 30 ft * 16 * √(3) ft^2 = 2400 ft^3 * √(3).

Finally, the hydrostatic force is the product of the volume, the density of water, and g (acceleration due to gravity):

2400 ft^3 * √(3) * 62.4 lb/ft^3 * 9.8 m/s^2 = approximately 140164.96lb

Therefore, Rounded to the nearest integer is 140165 lb.

Learn more about equilateral triangle https: brainly.com/question/30285619

#SPJ1

Given matrix [tex]\left[\begin{array}{cccc}1&7&3&-4\\0&1&-1&3\\0&0&0&2\\0&0&1&1\end{array}\right][/tex], so the solution set is empty.

Correct option: c

Mathematicians analyze matrices as a subject of study in a field called matrix theory. It started out as a branch of linear algebra but quickly expanded to cover topics in graph theory, algebra, combinatorics, and statistics. When it's necessary to summarise an infinite or limited collection of objects grouped in rows and columns, matrices are utilised. The initial set of a matrix's attributes are those of its constituent entities. Solving linear equations is made easier by it. Matrices are incredibly priceless items that are used in a variety of contexts. In addition to mathematical applications, matrices are employed in a wide range of scientific disciplines.

Given that,

[tex]\left[\begin{array}{cccc}1&7&3&-4\\0&1&-1&3\\0&0&0&2\\0&0&1&1\end{array}\right][/tex]

now exchange R₄ ↔ R₃

[tex]\left[\begin{array}{cccc}1&7&3&-4\\0&1&-1&3\\0&0&1&1\\0&0&0&2\end{array}\right][/tex]

Therefore, rank of main matrix = 3

rank of Augmented matrix = 4

So, rank of main matrix < rank of Augmented matrix

Thus, there is no solution.

Also we can say, the solution set is empty.

correct option: c

To know more about matrix refer to:

https://brainly.com/question/28060752

#SPJ1

If a polygon has four congruent angles then it can be a square and rectangle. Therefore the converse is not always true because square also have this property

The 4 basic property of a rectangle are;

1. A rectangle is a quadrilateral.

2. The opposite sides are parallel and equal to each other.

3. Each interior angle is equal to 90 degrees.

The sum of all the interior angles is equal to 360 degrees.

4.The diagonals bisect each other.

Both the diagonals have the same length.

Some of these properties are also for square. The difference between a square and a rectangle is that the sides of are all equal but only the opposite sides of a rectangle are equal. Both angles in square and rectangle are congruent, they are all 90°.

Therefore the converse of the statement "If a polygon has four congruenet

angles, then it is a rectangle." is not always true because both rectangle and square as these properties

learn more about the property of rectangle from

https://brainly.com/question/12190011

#SPJ1

The linear function h is given by h(x) = -2x + 20. To find this, we need to solve a system of two equations and two unknowns, x and b.

A linear function is a mathematical equation that describes a straight line. It is defined by an equation of the form y = mx + b, where x and y are variables, and m and b are constants that determine the slope and y-intercept of the line, respectively. Linear functions are used to describe relationships between two variables, such as in graphing, statistical analysis, and economics. Linear functions can also be used to model complex systems, such as the stock market or the behavior of other physical systems.

The linear function h is given by h(x) = -2x + 20. To find this, we need to solve a system of two equations and two unknowns, x and b. The two equations are:

h(4) = -14

h(-4) = 26

We can solve for x and b by subtracting the two equations from each other:

h(4) - h(-4) = -14 - 26

-2(4 + (-4)) = -40

-2(0) = -40

Now we can solve for b by substituting 4 into the equation and solving for b:

h(4) = -2(4) + b

-14 = -8 + b

b = 6

Therefore, the linear function h is given by h(x) = -2x + 6.

To find h(9), we can substitute 9 into the equation and solve for h(9):

h(9) = -2(9) + 6

h(9) = -18 + 6

h(9) = -12

To learn more about function

https://brainly.com/question/17043948

#SPJ1

The derivative of the logarithm function y = ln |e^z| with respect to z is equal to 1/z, assuming each branch of the logarithm function is analytic.

The Chain Rule formula computes the derivative of the combination of two or more functions.

For composite functions, the chain rule in differentiation is defined. If f and g are functions, the chain rule expresses the derivative of their combination.

d/dx [f(g(x))] = f'(g(x)) g'(x)

The chain rule states that if y = f(u) and u = g(x), then the derivative of y with respect to x is given by:

dy/dx = df/du * du/dx

Let f(z) = ln |z| and let g(z) = e^z.

Then, for the composition y = f(g(z)),

we have:

u = g(z) = e^z

f(u) = ln |e^z| = ln |u|

du/dz = e^z

df/du = 1/u = 1/e^z

Now, we can use the chain rule to find the derivative of y with respect to z:

dy/dz = df/du * du/dz

= (1/e^z) * e^z

= 1/z

For more questions on Chain rule

https://brainly.com/question/30329626

#SPJ4

The factor g(x) grows over the interval from 14 to 16 is approximately 1.41

To determine the factor by which g(x) grows over the interval from 14 to 16, we need to find the ratio of the values of g(x) at x = 16 and x = 14, then take its exponential.

Let's evaluate g(x) at x=14 and x=16:

g(14) = 4^14 - 4 = 16384

g(16) = 4^16 - 4 = 65536

The factor by which g(x) grows over the interval from 14 to 16 is:

(g(16) / g(14))^(1/(16-14)) = (65536 / 16384)^(1/2) = 2^(1/2) = 1.41

So, g(x) grows by a factor of approximately 1.41 over the interval from 14 to 16.

Learn more about interval of a function on:

https://brainly.com/question/1503051

#SPJ1

Arithmetic operations provide meaningful results for variables that c. are quantitative.

For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-" Multiplication (Identifying the result; "" Finding the quotient in division (")

The commutative laws of addition and multiplication, such as a + b = b + a and ab = ba, the associative laws of addition and multiplication, such as a + (b + c) = (a + b) + c and a(bc) = (ab)c, as well as the distributive law, which links addition and...

Therefore, option C is correct.

Learn more about variables at:

https://brainly.com/question/25223322

#SPJ1

Answer:

4x² + 5x - 6  = 0

Step-by-step explanation:

Quadratic equation:

             [tex]\boxed{x^2-(sum \ of \ roots)x+product \ of \ roots=0}[/tex]

    [tex]Sum \ of \ roots = -2 + \dfrac{3}{4}[/tex]

                           [tex]= \dfrac{-2*4}{1*4}+\dfrac{3}{4}\\\\=\dfrac{-8}{4}+\dfrac{3}{4}\\\\=\dfrac{-5}{4}\\\\[/tex]

[tex]\sf product \ of \ roots =-2 *\dfrac{3}{4}[/tex]

                         [tex]=\dfrac{-6}{4}[/tex]

Quadratic equation:

      [tex]x^2 - \left(\dfrac{-5}{4}\right)x+\left(\dfrac{-6}{4}\right)=0[/tex]

Multiply the entire equation by 4,

        4x² - (-5)x + (-6) = 0

         4x² + 5x - 6  = 0

The maximum acceleration attained on the interval [0,3] by the particle whose velocity is given by: v(t) = t3 – 3t2 + 12t + 4 is 21

The correct answer is an option (a)

The velocity function is given by,

v(t) = t³ – 3t² + 12t + 4

We differentiate above function to get the acceleration function which will be

a(t) = v'(t)

a(t) = 3t² - 6t + 12 + 0

a(t) = 3t² - 6t + 12

Consider the interval [0,3]

We find the value of acccleration function at the end of the intervals.

For t = 0,

a(0) = 3(0)² - 6(0) + 12

a(0) = 0 - 0 + 12

a(0) = 12

And for t = 3,

a(3) = 3(3)² - 6(3) + 12

a(3) = 27 - 18 + 12

a(3) = 21

This means, the function a(t) is increasing and the maximum value of function a(t) would be at t = 3.

Therefore, the maximum acceleration attained on the interval [0,3] is 21

Learn more about the function here:

https://brainly.com/question/28193995

#SPJ4

The correct matching is given below.

A. (x, y)= (-y, x) represents the reflection.

B. (x, y) = (x + 9,y - 2) represents the translation.

C. (x, y) = (x - 9,y + 2) represents the translation.

D. (x, y) = (-x, y) represents the reflection.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The translation does not change the shape and size of the geometry. But changes the location.

The reflection does not change the shape and size of the geometry. But flipped the image.

A. (x, y) = (-y, x), this represents the reflection over the line y = -x.

B. (x, y) = (x + 9,y - 2), this represents the translation.

C. (x, y) = (x - 9,y + 2), this represents the translation.

D. (x, y) = (-x, y), this represents the reflection over the y-axis.

More about the transformation of a point link is given below.

https://brainly.com/question/27224339

#SPJ1

Answer: (x' , y') = (x - 9, y + 2)

Step-by-step explanation:

I took the test

After adding the given angles 10 + 24 + 26, which comes to 60°, we know that is is an acute angle.

A protractor can be used to measure acute angles, which are those that are smaller than 90°.

A form of angle known as an obtuse angle is one that is always greater than 90° but less than 180°.

An acute angle is one that is smaller than 90 degrees in length.

The correct angle is larger than this angle (which is equal to 90 degrees).

For instance, acute angles include 30°, 45°, 60°, 75°, 33°, 55°, 85°, etc.

So, we have the angles:
10°, 24° and 26°.

Add all 3 angles as follows:

10 + 24 + 26 = 60°

And we know that all angles smaller than 90° are acute angles.

Therefore, after adding the given angles 10 + 24 + 26, which comes to 60°, we know that is is an acute angle.

Know more about acute angles here:

https://brainly.com/question/6979153

#SPJ1

The value of x is 3 and value of y is 2 in 4x + 5y = 22 and 2x + 3y = 12

Two or more expressions with an Equal sign is called as Equation.

The given system of equations are  4x + 5y = 22 and 2x + 3y = 12

Multiply equation 2 with 2

4x+6y=24

Subtract the above equation from equation 1

4x + 5y -4x-6y= 22-24

-y=-2

y=2

Now plug in y value in equation  2x + 3y = 12

2x+6=12

2x=6

Divide both sides by 2

x=3

Hence, the value of x is 3 and value of y is 2 in 4x + 5y = 22 and 2x + 3y = 12

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The total charge on the shell is 678.24 nC, The electric field at the following radial distances from the long axis of the cylinder is (b) 1.524 x 10¹⁶ N/C, (c) 1.75 x 10¹⁵ N/C, (d) 1.63 x 10¹⁵ N/C, and (e) 6.097 x 10¹⁴ N/C.

(a) The total charge of the shell can be found by multiplying the surface charge density by the surface area of the cylinder:

Q = σ × 2π × r × L

where

σ = 9.00 nC/m² (surface charge density)

r = 0.06 m (radius)

L = 200 m (length)

Q = 9.00 nC/m² × 2 × π × 0.06 m × 200 m

Q = 678.24 nC

(b) To find the electric field at a radial distance of 2cm from the long axis of the cylinder, we use the formula:

E = k × Q / r²

where

k = 8.99 x 10⁹ Nm^2/C² (Coulomb's constant)

Q = 678.24 nC (total charge)

r = 0.02 m (radial distance)

E = 8.99 x 10⁹ Nm^2/C² × 678.24 nC/(0.02 m)²

E = 1.524 x 10¹⁶ N/C

(c) To find the electric field at a radial distance of 5.9cm from the long axis of the cylinder, we use the formula:

E = k × Q / r²

where

k = 8.99 x 10⁹ Nm²/C² (Coulomb's constant)

Q = 678.24 nC (total charge)

r = 0.059 m (radial distance)

E = 8.99 x 10⁹ Nm²/C² × 678.24 nC/(0.059 m)²

E = 1.75 x 10¹⁵ N/C

(d) To find the electric field at a radial distance of 6.1cm from the long axis of the cylinder, we use the formula:

E = k × Q / r⁷

where

k = 8.99 x 10⁹ Nm²/C² (Coulomb's constant)

Q = 678.24 nC (total charge)

r = 0.061 m (radial distance)

E = 8.99 x 10⁹ Nm²/C² × 678.24 nC / (0.061 m)²

E = 1.63 x 10¹⁵ N/C

(e) To find the electric field at a radial distance of 10cm from the long axis of the cylinder, we use the formula:

E = k × Q / r²

where

k = 8.99 x 10⁹ Nm²/C² (Coulomb's constant)

Q = 678.24 nC (total charge)

r = 0.10 m (radial distance)

E = 8.99 x 10⁹ Nm²/C² × 678.24 nC / (0.10 m)²

E = 6.097 x 10¹⁴ N/C

To know more about electric field, here

https://brainly.com/question/8971780

#SPJ4

Answer:

Utilities: $315 (7% of $4500)

Labor: $1350 (30% of $4500)

Supplies: $1125 (25% of $4500)

Rent: $1575 (35% of $4500)

Advertising: $135 (3% of $4500)

Answer:

Exercise 37:

In this exercise, the question is to find the x-coordinate of the point of inflection of the graph of the function f(x).

The point of inflection of the graph of the function f(x) is at the x-coordinate of 1.

Answer:

Letter (C)

Step-by-step explanation:

The chart shows the Growth of dollars 1,000 in years on the x-axis and on the y-axis is the account balance. The account balance was 1000 dollars on year 1 and at the end of 18 years, it was 58,000 dollars. This type of data is best modeled by an exponential function because it shows a continuous increase in the account balance over time.