What is the 32nd term of the arithmetic sequence where a1 = −33 and a9 = −121? −396 −385 −374 −363

Final answer:

To calculate i^3, we use the powers of i, where i = √-1. We find that i² = -1, and thus i³ = i² × i = -1 × i = -i.

Explanation:

The value of i to the power of 3, denoted as i3, can be determined by understanding the fundamental properties of the imaginary unit i, where i is defined as i = √-1. To find i3, we start by considering the powers of i:

i1 = i,

i2 = -1,

i3 = i2 × i = -1 × i = -i,

i4 = (i2)2 = (-1)2 = 1.

Therefore, the value of i3 is -i.

Answer:

Given the system of equations:

[tex]y = 6x+6[/tex]         .....[1]

[tex]y = -x^2+5x+6[/tex]      .....[2]

Equate these two equations we have;

[tex]-x^2+5x+6 = 6x+6[/tex]

Subtract 6 from both sides we have;

[tex]-x^2+5x= 6x[/tex]

Subtract 6x from both sides we have;

[tex]-x^2-x= 0[/tex]

⇒[tex]-x(x+1) = 0[/tex]

By zero product property we have;

⇒x = 0 and x+1= 0

⇒x = 0 and x=-1

Substitute these values in [1] we have;

For x = 0

y = 6(0)+6 = 6

for x = -1

y =6(-1)+6 = -6+6=  0

Therefore, the solutions of the given systems are, (0, 6) and (-1, 0)

Answer:

The standard form of the given number is [tex]8.73\times 10^{16}[/tex].

Step-by-step explanation:

Standard form of a number is a easy ways to write very small numbers and very large numbers.

In the standard form the number is written as the number lies between 1 to 10 and multiple of power of 10.

The given number is

[tex]8.73e16[/tex]

It can be written as

[tex]8.73e16=87300000000000000[/tex]

[tex]8.73e16=8.73\times 10^{16}[/tex]

Therefore the standard form of the given number is [tex]8.73\times 10^{16}[/tex].

Hello!

Answer:

B. -3/4

*The answer must have a fraction.*

Step-by-step explanation:

Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]

[tex]\frac{6-3=3}{(-2)-2=-4}=\frac{3}{-4}=-\frac{3}{4}[/tex]

Slope is -3/4

Answer is -3/4

Hope this helps!

Thanks!

-Charlie

Have a great day!

:)

:D

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

Number of times a die rolled = 500

Number of times an odd number occurs =325

so, the experimental probability would be

[tex]\dfrac{325}{500}\\\\=0.65[/tex]

And we know that

Number of outcomes in a die = 3

Number of total outcomes = 6

So, The theoretical probability would be

[tex]\dfrac{3}{6}=\dfrac{1}{2}=0.5[/tex]

So, The experimental probability is larger than the theoretical probability.

Hence, Second option is correct.

There are two cases here:

Case 1: First card chosen is a queen

Case 2: First card chosen is not a queen.

Adding both the cases, we get 1722117221 = 452452 = 113113

In a simpler case: Think about it this way: Shuffle a deck of cards randomly. The probability of drawing a queen as your second card is the same as the probability that the second card in the deck is a queen, which is clearly 4/52.

Answer:

61 sales.

Step-by-step explanation:

Let x represent present sales.

We have been given that you need to increase your sales by 35% this month. You are currently at 45 sales.

To find the number of sales to meet the goal, we will find 35% of 45 and add to 45 as:

[tex]\text{The number of sales to meet the goal}=45+\frac{35}{100}*45[/tex]

[tex]\text{The number of sales to meet the goal}=45+0.35*45[/tex]

[tex]\text{The number of sales to meet the goal}=45+15.75[/tex]

[tex]\text{The number of sales to meet the goal}=60.75[/tex]

[tex]\text{The number of sales to meet the goal}\approx 61[/tex]

Therefore, you need to make 61 sales to meet you goal.

Final answer:

Explaining how to find the reflection of a point across the y-axis and then the x-axis that is option C is correct.

Explanation:

To find the reflection of point R(-2, 9) first across the y-axis and then across the x-axis, we apply the transformations for each axis separately. When reflecting across the y-axis, the x-coordinate changes sign, making it (-2, -9). Then, reflecting across the x-axis changes the sign of the y-coordinate, resulting in the final reflection at point (2, -9).

Answer:

A) 5

B) 200

C) 25.5

D) 14/3

E) 77 1/2

Step-by-step explanation:

We have been given a function [tex]f(x)=10.25x[/tex], where, [tex]f(x)[/tex] represents the amount of money earned after x hours.

We are asked to choose the elements of the domain of the function.

Since the x represents time in hours, so negative numbers wouldn't be domain of the given function. as times cannot be negative.

Therefore, options A, B, C ,D and E are correct choices.

Answer:

The first 5 is the right answer

Step-by-step explanation:

The expression that represents the length of one side of the square is (x+2)

In mathematics, a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface.

Given,

Area of the square = [tex]x^{2} +4x+4[/tex]

Area of the square = l × l

were l is the length

Then,

[tex]x^{2} +4x+4=(x+2)(x+2)[/tex]

Hence, The expression that represents the length of one side of the square is (x+2)

Learn more about polynomial and area here

https://brainly.com/question/22576901

#SPJ2

Answer:

All of the above

Step-by-step explanation:

A 15 kg box has more inertia than a 10 kg box. --TRUE

Inertia is a property of matter related to its mass. The more mass an object has, the greater its inertia. S o the statement is correct since 15 kg is greater in mass than 10 kg therefore it has more inertia.

Forces occur in equal and opposite force pairs.  -- TRUE  

This statement is correct and is known as Newton's third law. Which tells us that for every force of action there is  a reaction force that is equal in magnitude but opposite in direction.

Objects in motion will keep moving at the same velocity unless acted upon by an outside force.  -- TRUE  

This is Newton's first law of motion, it tells us that an object will retain its state of rest or movement as long as there is no resulting force  or external force acting on it.

Answer: 10 times

Step-by-step explanation:

Option: C is the correct answer.

     C) It is not a function because each package number has two different prices.

Function--

Function is a mapping from a set A to set B such that each element of set A is mapped to a unique number.

i.e. every element has a single image.

Here a package number has two different rates or prices.

(Since let set A is package number and set B is a price of the package. )

As element of set A has more than one image.

         Hence, it is not a function.

Final answer:

The scale factor for the scale drawing of a car with a scale of 1 inch : 3 feet is 1:36, or the fraction 1/36.

Explanation:

The student has a scale drawing of a car with a scale of 1 inch : 3 feet. To find the scale factor for this drawing, you need to convert feet into inches since the scale is given in inches to feet. There are 12 inches in a foot, so 3 feet is the same as 36 inches. Therefore, the scale for the car drawing is 1 inch on the drawing for every 36 inches of the actual car.

The scale factor is the ratio of the dimension in the drawing to the actual dimension of the object. In this case, the scale factor is 1:36, which can be written as the fraction 1/36. This means that every inch on the scale drawing represents 36 inches on the actual car.

Answer:

Step-by-step explanation:

Definition of an outlier:

A value that "lies outside" (is much smaller or larger than) most of the other values in a set of data.

Here in the scatter plot we can see that

(3,9) deviates from other values very much.

Outlier An extreme value in a set of data which is much higher or lower than the other numbers.  Outliers are to be removed to get accurate results since they have the power to affect the mean value of the data but have little effect on the median or mode of a given set of data.

That is why when outliers are present mean or mode is the better mode to measure central tendency.

Answer:

y = 3/4x - 4

Step-by-step explanation:

Solving for y: