Which expression could be used to find any term in the following pattern?

1,8, 27, 64, ...

Select one:

a. 3x
b. 4x
C. x^2
d. x^3

pls answer :)

Answer:

20 pages

Step-by-step explanation:

15/3 = 5 so Ryan takes 5 pages of notes every hour

5 x 4 = 20 so Ryan takes 20 pages of notes in 4 hours

Answer:

20

Step-by-step explanation:

15 divided by 3 is 5 so that means they did 5 pages each hour 5 times 4 equals 20

The functions f, g, h and k are \(f(x)=15\cdot 3^{x}\), \(g(x) = 26\cdot 0.5^{x}\), \(h(x) = 7\cdot 8^{x}\) and \(k(x) = 280\cdot 0.143^{x}\), respectively.

A function is monotonous when is either increasing or decreasing for all value of \(x\). A power function is a case of a monotonous function, whose model is defined below:

\(y = y_{o}\cdot r^{x}\) (1)

Where:

Now we proceed to define each function:

\(f(x)=15\cdot 3^{x}\) (2)

\(g(x) = 26\cdot 0.5^{x}\) (3)

\(h(x) = 7\cdot 8^{x}\) (4)

\(k(x) = 280\cdot 0.143^{x}\) (5)

The functions f, g, h and k are \(f(x)=15\cdot 3^{x}\), \(g(x) = 26\cdot 0.5^{x}\), \(h(x) = 7\cdot 8^{x}\) and \(k(x) = 280\cdot 0.143^{x}\), respectively. \(\blacksquare\)

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Answer:

2(n+18)

18(2+n)

2•(18•n)

I hope this helps

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Step-by-step explanation:

Radius : 6 ft

Diameter: 12 ft

Area:

\(\pi {r}^{2} = \pi {6}^{2} = \\ = 113.097336 = 113.1. {ft}^{2} \)

circumference :

\(2\pi \times r = 2\pi \times 6 = \\ = 37.6991118 = 37.7 \: ft\)

Step-by-step explanation:

Hey there!!

While finding the coordinates of any point, you remember to use formula first and then equate it.

So, let's begin to work accordingly.

Here, X (3,4) is a coordinate. And Y (-1,9) is a midpoint.

Let another endpoint of line be Z(x,y).

We have,

\(midpoint \: of \: xz = (\frac{x1 + x2}{2} ,\frac{y1 + y2}{2} \))

Now,

\(( - 1,9) = (\frac{3 + x}{2} ,\frac{4 + y}{2} \))

As they are equal, equating with their corresponding elements we get,

\( - 1 = \frac{3 + x}{2} \)

or, -2 = 3+x

Therefore, x= -5.

Now, again;

Equating with their corresponding elements we get,

\(9 = \frac{4 + y}{2} \)

or, 18 = 4+y

Therefore, y = 14.

Therefore, the coordinates of Z are (-5,14).

Hope it helps...

Answer:Z(-5,14)

Step-by-step explanation:Here, X (3,4) is a coordinate. And Y (-1,9) is a midpoint.

Let another endpoint of line be z(x,y)

We have,

Midpoint of XZ=((x1+x2)/2,(y1+y2)/2)

that is, (-1,9)=((3+x)/2,(4+y)/2)

Equating with their corresponding elements we get,

-1=((3+x)/2

-2=3+x

∴x=-5

Now,

Equation with their corresponding elements, We get,

9=((4+y)/2)

18=4+y

∴y=14

∴The coordinates of z are (-5,14).

Answer:

4, -2

Step-by-step explanation:

Hello, please consider the following.

\(\begin{aligned}4x^2-8x-32=0 &\text{ ***We divide by 4.***}\\\\x^2-2x-8=0 &\text{ ***We complete the square. ***}\\\\(x-1)^2-1-8=(x-1)^2-9=0 &\text{ ***We move the constant to the right.***}\\\\(x-1)^2=9=3^2 &\text{ ***We take the root.***}\\\\x-1=\pm3 &\text{ ***We add 1.***}\\\\x=1+3=\boxed{4} \ & or \ x=1-3=\boxed{-2}\end{aligned}\)

Thanks

Answer: i think its 134

Step-by-step explanation:

The members of the given set in this problem are given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

The union and intersection sets of multiple sets are defined as follows:

The intersection of the sets Y and Z for this problem is given as follows:

Y ∩ Z = {0, 6, 23, 26}

(which are the elements that belong to both of the sets).

The union of the above set with the set X is given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

(elements that belong to at least one of the sets).

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Answer:

when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³

Step-by-step explanation:

Let the initial length of the sides of the cube = x unit

when the length of the cube = x ;  volume of the cube = length × breadth × height = x × x × x = x³ (unit)³

when the length increased by 1 unit,

new length = (x + 1) unit

New volume = (x + 1) × (x + 1) × (x + 1)

multiplying the first two brackets

New volume = (x² + 2x + 1 ) (x + 1)

espanding the brackets

New volume = x³ + 2x² + x + x² + 2x + 1

New volume = x³ + 3x² + 3x + 1 (unit)³

Change in volume:

(New volume) - (old volume)

(x³ + 3x² + 3x + 1) - (x³)

x³ + 3x² + 3x + 1 - x³

collecting like terms:

(x³ - x³) + 3x² + 3x + 1

0 + 3x² + 3x + 1

change in volume = 3x² + 3x + 1

Therefore, when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³

Linear regression is a system of plotted points which shows a relationship between two given variables. The required linear equation is: y = 4x.

A graph is a plotted coordinate on a Cartesian plane which shows the relationship between two variables. A system of plotted points in relations to variables that shows a linear relationship is termed linear regression.

In a linear regression, the plotted points can be described by an equation:

y = bx + c

where: y is the dependent variable

            x is the independent variable

            b is the slope of the graph

            c is the intercept

Therefore, considering the given question;

the slope of the graph = \(\frac{change in y}{change in x}\)

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

                = \(\frac{8}{2}\)

slope of the graph = 4

While there is no intercept, thus intercept is zero.

Therefore, the required equation that shows the relationship between liters of water and number of minutes is:

                       y = 4x

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The Solution:

Representing the given triangle as below:

We are asked to find the perimeter of the above triangle.

The perimeter of a triangle is the sum of all the lengths around the triangle.

So, The perimeter is

Therefore,

Answer:

The answer is 11,337,408

Step-by-step explanation:

6^2 = 36, 3^2 = 9, 3^3 = 27, and 6^4 = 1296.

when you multiply them all together, you get 11,337,408.

Answer:

6 cm

Step-by-step explanation:

Volume of the given cylinder is calculated using the formula
V = π r ² l

r = radius of the cylinder = diameter/2

Here r = 4/2 = 2 cm

V = 150 cm³

and we are asked to calculate l

Plugging in known values
150 = π · 2³ · l

switch side:
π · 2³ · l = 150

π · 8 · l = 150

l = 150/8π

= 5.96831 cm

To the nearest centimeter we would round this up to 6 cm (Answer)

The incorrect statement is:

B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.

In the given statement, there is an error in the inequality. The correct statement should be:

The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.

When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:

- 5x < 15x^2 and 15x^2 < 3

Simplifying the first inequality:

- 5x < 15x^2

Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:

- 5 < 15x

Simplifying the second inequality:

15x^2 < 3

Dividing by 15, we get:

x^2 < 1/5

Taking the square root (assuming x ≥ 0), we have two cases:

x < 1/√5 and -x < 1/√5

Combining these inequalities, we get:

- 5 < 15x and x < 1/√5 and -x < 1/√5

Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.

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Answer:

The probability of not picking a pink jelly bean: 11/15    

Step-by-step explanation:

As we know that the maximum value of the probability of an event would always be 1.

Given that the probability of picking a pink jelly bean out of a bag is 4/15.

Thus, the probability of not picking a pink jelly bean can be calculated by subtracting 4/15 from the maximum probability '1'.

i.e.

Probability of not picking a pink jelly bean = max probability - 4/15

                                                                       = 1 - 4/15

                                                                      = 11/15

Therefore, the probability of not picking a pink jelly bean: 11/15                                                                    

The conditions are not met, then alternative methods, such as a two-sample t-interval or non-parametric methods, may be more appropriate.The use of a two-sample z-interval for a difference in population proportions is appropriate when the following conditions are met:

The samples are independent of each other.

The samples are both random and representative of their respective populations.The sample sizes are large enough such that the number of successes and failures in each sample are both greater than or equal to 10.The populations from which the samples are drawn are both large relative to the sample sizes.

If these conditions are met, then the sampling distribution of the difference in sample proportions can be approximated by a normal distribution, and a two-sample z-interval can be used to estimate the difference in population proportions with a certain level of confidence. If the conditions are not met, then alternative methods, such as a two-sample t-interval or non-parametric methods, may be more appropriate.

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Question :-Which of the following indicates that the use of a two-sample z-interval for a difference in population proportions is appropriate?

Two populations of interest exist.

The variable of interest is categorical.

The intent is to estimate a difference in sample proportions.

Part A ;

For Bus:

mean = 17.5

median = 15

mode= 15 and 16

Range= 17

For walking:

mean = 20.5

median = 20.5

mode= 20 and 21

Range= 3

For Bus

To calculate the mean:

= 16+14+15+14+31+15/6

= 105/6

= 17.5

To calculate the median;

= 14,14,15,15,16,31

= 15+15/2 = 15

To calculate the range:

= 31-14 = 17

For walking;

To calculate the mean:

= 19+20+20+21+21+22/6

= 123/6

= 20.5 mins

To calculate the median

= 20+21/2

= 20.5

To calculate the mode:

=20 and 21

To calculate the range:

= 22-19

= 3

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Answer:

radius

Step-by-step explanation:

With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.

One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.

So, in the given situation:

TR and WY are as follows:
TR/WU

24/2

2/1

Similarly,

TS/WV

2/1

7/x

7/3.5

Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

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Answer:  2,175 divided by 12 will give you 181.25.

The Definition of the Derivative correctly stated by

In mathematics, a derivative is the rate at which a function changes in relation to a variable. Calculus and differential equations issues must be solved using derivatives.

As, we know by definition of derivative

= \(\lim_{h \to 0}\) f(x+h)- f(x) / h

Also, the Derivative also shows the Slope of the secant line.

and, derivative is widely used to the rate of change then it also shows

Instantaneous rate of change.

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3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

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Answer:

v = 339,3 in/sec

Step-by-step explanation:

The wheels are moving at a rate of 6 rps (revolutions per second), and the length of the wheel is (L) is

L = 2*π*r        where r is a radius of the wheel

L = 2*π*9   (in)

L = 56,55 ( in)

L will be the traveled length by car in each turn of the wheel

Since the wheel has a rate of 6 turns by second, then we need to multiply de numbers of turns by second  times, the traveled length in 1 turn, in order to get the speed of the car

Then:

v ( speed of the car ) is:

v = 6 * 56,55 ( in/sec)

v = 339,3 in/sec

Angular speed tails that how fast a object resolves.the car is moving with the velocity of 339.43 inches/second.

To find the angular speed of the wheel, we need to know about the angular speed.

Angular speed is the rate of change of angle with respect to time of an object. Angular speed tails that how fast a object resolves.

It can be given as,

\(\omega=\dfrac{v}{r}\)

Here,  is the \(v\) linear velocity and \(r\) is the radius.

Given information-

The radius of the wheels of the car is 9 inch.

The revolutions per second of the each wheel is 6 rpm.

As the wheel rotates at 6 revolutions per seconds. The one rev/sec equals to the \(2\pi\) rad.

Thus the angular velocity is,

\(w=2\pi N\)

\(\omega=2\pi \times 6\\\omega=12\pi\)

Put the values in the above formula,

\(\omega=\dfrac{v}{r}\\12\pi=\dfrac{v}{9}\\\)

Solve for \(v\)

\(v=9\times12\pi\\v=9\times12 \times\dfrac{22}{7} \\v=339.43\)

Hence the car is moving with 339.43 inches/second.

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Answer:  d. mutually exclusive

Step-by-step explanation:

Mutually exclusive events are those events that cannot happen at the same time. If one event happens, the other has a zero chance of happening at the same time.

Event A and Event B here are Mutually Exclusive because you cannot turn left and right at the same time. If you listen to your brother and turn left, you cannot also listen to your sister and turn right at the same time.

Answer:

D={1, 8,0}

R={-9, 8,1,9}

Step-by-step explanation:

Here,

we, know, domain(D) =set of all first elements

thus, D={1,8,0}

again, range(R) =set of all second elements

thus R={-9,8,1,9}

Answer:

13ft a second it's just a an average it the feet divided by the time by 2