Describe and explain the difference between explicit formulas for arithmetic
sequences and explicit formulas for geometric sequences.
Answer:
Arithmetic sequence: \(a_{n}=a_{1}+(n-1)d\)
Geometric sequence: \(a_{n}=a_{1}(r)^{n-1}\)
Step-by-step explanation:
The arithmetic sequence: is the sequence whos terms increased or decreased by a constant amount.
Examples:
4, 7, 10, 13, 16, ........................ (increased by 3)25, 20, 15, 10, ......................... (Decreased by 5)The explicit formula for the nth term of the arithmetic sequence is:
\(a_{n}=a_{1}+(n-1)d\) \(a_{1}\) is the first termd is the constant difference between each two consecutive termsn is the position of the number in the sequence
The geometric sequence: is the sequence whos consecutive terms have a constant ratio
Examples:
1, 2, 4, 8, 16, ........................ (Multiplying by 2)625, 125, 25, 5, ......................... (Dividing by 5)The explicit formula for the nth term of the geometric sequence is:
\(a_{n}=a_{1}(r)^{n-1}\) \(a_{1}\) is the first termr is the constant ratio between each two consecutive termsn is the position of the number in the sequence* Arithmetic sequence →→→→→→ Geometric sequence
Has a constant difference →→→→→→ Has a constant ratio
\(a_{n}=a_{1}+(n-1)d\) →→→→→→ \(a_{n}=a_{1}(r)^{n-1}\)
\(d=a_{n}-a_{n-1}\) →→→→→→ \(r=\frac{a_{n}}{a_{n-1} }\)
Compare the budgets of Hong Kong, United States of America, and
Korea based on your definition of a budget, in terms of contents,
formats, advantages, and disadvantages, etc.
The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.
A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:
Hong Kong Budget:United States Budget:
Contents: The US budget comprises revenue, expenditures, and deficit or surplus. It includes an analysis of taxes, social security, and Medicare.Format: The US budget is presented in a complex and lengthy format, including tables, graphs, and other financial documents.Advantages: The budget provides detailed information on tax expenditures and encourages public participation in the budget process.Disadvantages: The budget can be challenging to understand due to its complexity, and it may not provide an accurate depiction of federal spending.Korean Budget:
Contents: The Korean budget comprises revenue, expenditures, and surplus or deficit. It includes detailed information on taxes, social security, and public welfare.Format: The Korean budget is presented in a clear and concise format, including tables and charts to aid understanding.Advantages: The budget is easy to understand, and it promotes transparency and accountability. It also provides detailed information on social welfare expenditures.Disadvantages: The budget may not provide an accurate depiction of government spending, and it may not include information on hidden expenditures.Learn more about Budget:
https://brainly.com/question/26894404
#SPJ11
Let A={0,1,2,3} and B={1,2,4,8}. Put in a correct symbol between the quantities, (There may be more than one correct choice. a. B b. A B c. AB={0,1,2,3,4,8),
The correct symbol to use between the quantities A and B is the union symbol (∪). Therefore, the correct choice is:
c. AB = {0, 1, 2, 3, 4, 8}
The union of two sets, denoted by the symbol (∪), represents the combination of all elements from both sets without repetition. In this case, A = {0, 1, 2, 3} and B = {1, 2, 4, 8}. When we take the union of these two sets, we combine all the elements from A and B, resulting in the set AB = {0, 1, 2, 3, 4, 8}. Therefore, the correct choice is c, AB = {0, 1, 2, 3, 4, 8}.
To understand the concept of set union, it is essential to consider the individual elements in sets A and B. Set A contains the elements {0, 1, 2, 3}, and set B contains the elements {1, 2, 4, 8}. When we take the union of these sets, we combine all the elements without duplication.
In this case, set AB would include all the elements from both sets: {0, 1, 2, 3} from set A, and {1, 2, 4, 8} from set B. However, since 1 and 2 appear in both sets, we only include them once in the union. Thus, the final union set AB is {0, 1, 2, 3, 4, 8}.
It's important to note that the order of elements in a set doesn't matter, and duplicate elements are removed when taking the union. The union operation allows us to combine multiple sets into a single set, containing all the unique elements from each set.
Learn more about set union here:
brainly.com/question/30748800
#SPJ11
i need help on these
Answer:
The answer is A and then B
Step-by-step explanation:
6 numbers that have a median of 8 a mean of 9 and a range of 13?
Answer:
5,6,8,8,9,18
Step-by-step explanation:
...................
11) Which statement best shows active listening?
Question 11 options:
The listener focuses on the speaker, remains undistracted, and may ask clarifying questions.
The listener remains active in other activities while listening to increase productivity.
The listener writes down everything the speaker says to help with understanding.
The listener focuses on the speaker and interrupts as many times as needed to ask questions.
The statement that best shows active listening is "The listener focuses on the speaker, remains undistracted, and may ask clarifying questions.". So, correct option is A.
Active listening is an important communication skill that involves paying full attention to what the speaker is saying, both verbally and non-verbally. Active listening requires the listener to be fully engaged in the conversation, understand the speaker's perspective, and respond appropriately.
Option A) best shows active listening because it includes key aspects of this skill. Focusing on the speaker and remaining undistracted shows that the listener is fully engaged in the conversation, while asking clarifying questions demonstrates an effort to understand the speaker's message.
On the other hand, Option B) is not an example of active listening as it suggests the listener is not fully engaged in the conversation. Option C) may be helpful for taking notes, but does not necessarily demonstrate active listening, as the listener may miss non-verbal cues or tone of voice.
Option D) can be seen as interrupting the speaker and not allowing them to fully express their thoughts, which can hinder effective communication.
So, correct option is A.
To learn more about active listening click on,
https://brainly.com/question/1917378
#SPJ1
3a x 5b to the power of C Divided by D =2581
IF YOU ANSWER THIS CORRECT YOULL BE REWARDED WITH 100 POINTS THIS QUESTION IS VERY HARD
Answer: 3 x (5b) = 15ab C = 15ab D = 2581 == 2581
Step-by-step explanation: Use the given functions to set up and simplify C.
which one matches the picture description
Answer:
356.82
Step-by-step explanation:
Which term refers to coordination, balance, and orientation in three-dimensional space?
Equilibrium is the term refers to coordination, balance, and balance in three dimensional space.
The equilibrium condition of an object exists when Newton's first law is valid. An object is in equilibrium in a reference coordinate system when all external forces (including moments) acting on it are balanced. This means that the net result of all the external forces and moments acting on this object is zero.
There are three types of equilibrium: stable, unstable, and neutral.
Examples of equilibrium in everyday life:
A book kept on a table at rest. A car moving with a constant velocity. A chemical reaction where the rates of forward reaction and backward reaction are the same.
Learn more about equilibrium here: https://brainly.com/question/13463225
#SPJ4
Which is equal to 1/58^8 ? a.58^-8 b.-1/58^-8 c.58^8 d.1/(58)^-8
a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.
How to evaluate this expression ?To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.
Applying this rule to the expression 1/58^8, we get:
1/58^8 = 1/(58^8) = 58^-8
Therefore, the correct answer is 58^-8.
It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:
1/58^8 = (1/58)^8 = 58^-8
This simplification shows that the correct answer is still 58^-8.
To learn more about evaluating expression refer :
https://brainly.com/question/28337857
#SPJ1
Mr. Green orders some cookies from a local youth group. Using his order form shown below, complete the last column to find the total to be paid. Quantity Description Unit Price Total of Line 1 Krispy Kosmos $2.89 $ 2 Chewy Chocos $3.19 $ 1 Gooey Globs 2.99 $ Total $ 5.2% tax $ Total to be paid $ a. $9.54 b. $12.26 c. $12.90 d. $18.64 Please select the best answer from the choices provided A B C D
From the computation done, it can be denoted that the total price that will be paid will be $12.90.
1 Krispy Kosmos at $2.89 = $2.89
2 Chewy Chocos at $3.19 each = 2 × $3.19 = $6.38
1 Gooey Globs at $2.99 = $2.99
Total = $2.89 + $6.38 + $2.99 = $12.26
We'll then add the sales tax of 5.2%, therefore, the total value will be:
= $12.26 + (5.2% × $12.26)
= $12.26 + $0.638
= $12.90
In conclusion, the correct option is $12.90.
Learn more about prices on:
https://brainly.com/question/1293276
Answer:
C
Step-by-step explanation:
Edg 2022
The first Epistle of John was written about A.D is :
45
60-65
90-95
97
The first Epistle of John was written about AD of between 95 and 110 . So, by this our option should be 97 AD, which is true.
The Fourth of the Catholic Epistles, The First Epistle of John[a] is the first of the Johannine epistles in the New Testament. The authorship of the Johannine writings is disputed among academics. The First Epistle's author is identified as John the Evangelist, who most scholars do not consider to be the same person as John the Apostle. The three Johannine epistles are thought to have been written by the same person by the majority of scholars, however it is unclear if the same person wrote the Gospel of John.
Learn more about Epistle here:
https://brainly.com/question/30006419
#SPJ4
set up an integral for solving dydx=x2 x when y(4)=19
The given equation is dydx=x2x and we have to solve the equation when y(4)=19. To solve this equation, we will use the integral of the given equation.
The integral of the equation is y=x3/3 + C, where C is a constant.
We know that y(4)=19, so we can plug in 4 for x and 19 for y to solve for C.
Therefore, C = 19 - (43/3) = 23/3.
So, the solution to the equation is y=x3/3 + 23/3.
To set up an integral for solving dy/dx = x^2 when y(4) = 19, we need to use the Fundamental Theorem of Calculus. This theorem states that if F(x) is an antiderivative of f(x), then the integral of f(x) from a to b is F(b) - F(a).
First, we need to find the antiderivative of x^2. The antiderivative of x^2 is (x^3)/3 + C, where C is a constant.
You can read more about antiderivative at https://brainly.com/question/21627352
#SPJ11
If n orange juice is made up of concentrate and water in the ratio 3:8. What fraction of the mixture is concentrate?
Answer:your answer should be 2
Step-by-step explanation:
Please help me the picture is above I’ll mark as the brainliest, please just edit and write on the picture above and send it. Tank you. :)
Answer:
function is a parabola, with a lowest point of -4
Step-by-step explanation:
g(x)=x^-4
g(-3)= -3^2-4 = 9-4 = 5
g(-2)= -2^2-4 = 4-4 = 0
g(-1)= -1^2-4 = 1-4 = -3
g(0)= 0^2-4 = 0-4 = -4
g(1)= 1^2-4 = 1-4 = -3
g(2)= 2^2-4 = 4-4 = 0
g(3)= 3^2-4 = 9-4 = 5
Find the total surface area. rectangular prism 2 A. 132 yd² B. 1,238 yd² C. 896 yd² D. 2,736 yd²
The total surface area is 1308 meters square
How to determine the total surface area?From the question, we have the following dimensions
Length = 19 m
Width = 16 m
Height = 10 m
The total surface area is then calculated as:
Total surface area = 2 * (Length * Width + Width * Height + Length * Height)
Substitute the known values in the above equation
Total surface area = 2 * (19 * 16 + 16 * 10 + 19 * 10)
Evaluate the expression
Total surface area = 1308
Hence, the total surface area is 1308 meters square
The question is incomplete, and the resources cannot be found online.
So, I used the attached figure to answer the question
Read more about total surface area at
https://brainly.com/question/26638955
#SPJ1
Answer:1,238yd squared
Step-by-step explanation:
For the matrix A below, find a nonzero vector in Nul A, a nonzero vector in Col A, and a nonzero vector in Row A = 1350 012-7 A nonzero column vector in Nul Ais A nonzero column vector in Col A is A nonzero column vector in Row Ais
As per row echelon form of the matrix, the column space for the given matrix A is { [1 0], [3 1] }
The term row echelon form of the matrix is defined as a matrix is in echelon form if it has the shape resulting from a Gaussian elimination.
Here we have given the following matrix
\(\begin{bmatrix}1 &3 &5 &0 \\0 & 1 & 2 & -3\end{bmatrix}\)
As we all know that the column space is a space spanned by the columns of the initial matrix that correspond to the pivot columns of the reduced matrix.
As per the definition of row echelon the given matrix is already in the row echelon form.
So, the column space is written as, first two columns
=> \(\begin{bmatrix}1 \\0\end{bmatrix}\begin{bmatrix}3 \\1\end{bmatrix}\\\)
To know more about matrix here.
https://brainly.com/question/28180105
#SPJ4
Liz travels at a constant velocity of 65 miles per hour toward Tucson. Tucson is 275 miles away. How long will it take her to get there?
Answer:
4.23076923077
Step-by-step explanation:
if you need a remainer please comment hope this helps also if you do put this in if you need a shorder anwser put 4.2307
are whole numbers _______ a natural number? always, sometimes, or never.
Answer:
sometime
Step-by-step explanation:
a natural number is a positive number ranging from 1-infinity and a whole number is a full number without fractions or decimals but can also be negative. Hope this helps.
Answer:
whole numbers are sometimes a natural number
Step-by-step explanation:
negative numbers are whole numbers but not natural
What is the expected number of female children in a family with three children?
O 1
O 1.5
O 2
O 2.5
Using the probability, the expected number of female children in a family with three children is 1.5. The option 2 is correct.
In the given question, we have to find the expected number of female children in a family with three children.
The possibility of having girls in family is 0,1,2 or 3.
From the 8 possible sequences, only one of them give the possibility of 0 girls.
So the probability of 0 girls is 1/8.
There are total 3 ways of having 1 girl.
That is: GBB, BGB, and BBG.
Thus, the probability of 1 girl is 3/8.
Similarly checking for having 2 girls with probability 3/8
Having 3 girls with probability 1/8.
The predicted number of girls is calculated as a weighted average of all potential numbers, where a number's weight is determined by its likelihood of occurring.
The anticipated number of girls is therefore
= 1/8⋅0+3/8⋅1+3/8⋅2+1/8⋅3
= 0+3/8+6/8+3/8
=(3+6+3)/8
=12/8
=1.5
Hence, the expected number of female children in a family with three children is 1.5.
To learn more about probability link is here
brainly.com/question/11234923
#SPJ1
Explain how making a table helps to compare two or more sets of data that have been presented in different ways.
Answer:
By easing the ranking and colerration of the data
Answer: a table is an organized way of displaying data
all data in a table has the same format
you can see how output of a data set changes by looking at a column
you can compare outputs of different functions that have the same input by looking at rows
Step-by-step explanation: edge 2022
The sum of two numbers is 42. The larger number is 6 more than the smaller number. What are the numbers?
Answer:
the smaller number is 18 and the larger number is 24
Identify two angles that are marked congruent to each other on the diagram below.
The angle ONK is congruent to angle NKO
How to identify two angles that are marked congruent to each other on the diagram?In a diagram, congruent angles are identified by the same mark
This means that angles that have the same marks are congruent
From the diagram, we have:
Angles ONK and NKO have the same single mark
Hence, the angle ONK is congruent to angle NKO
Read more about congruent angles at:
https://brainly.com/question/1675117
#SPJ1
The probability of an unfavorable outcome plus the probability of a favorable outcome equals 1.
O True
O False
Your answer is False
A sphere has a diameter of 16 m. What is the volume of the sphere?
What is the Volume?
what is the quotient of 2/5 divided by 3/7
A. 15/14
B. 14/15
C. 35/6
D. 6/36
Answer:
\( = { \tt{ \frac{2}{5} \div \frac{3}{7} }} \\ \\ = { \tt{ \frac{2}{5} \times \frac{7}{3} }} \\ \\ = { \underline{ \tt{ \: \: \frac{14}{15} \: \: }}}\)
Answer: B
2/5 ÷ 3/7
= 2/5 × 7/3
= 2 × 7/5 × 3
= 14/15
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 3/7 is 7/3) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, the fraction result cannot be further simplified by canceling.
Find the ratio of the areas of two circles with radii 4 and 12
Answer:
1:9
Step-by-step explanation:
~Refer to the attachment for the solution.
The given frequency distribution table shows the marks obtained by 32 students in a test.
Marks No. of Students
0-10 2
10-20 10
20-30 9
30-40 4
40-50 7
a. What is the class size?
b. What is the upper limit of the class interval 40-50?
c. What is the lower limit of the class interval 20-30?
d. What is the frequency of the class interval 10-20?
The class size is 10.
The upper limit of the class interval 40 - 50 is 50/
The lower limit of the class interval 20 - 30 is 20.
The frequency of class interval 10 - 20 is 10.
What is the frequency distribution?A class interval is a group of values that are put together for computation in a frequency distribution. An example of a class interval is 20 - 30. The class size is the difference between the upper limit and the lower limit of a class interval. The class size is the same for all the data set.
Class size = upper limit - lower limit
50 - 40 = 10
The upper limit is the biggest number in a class. The lower limit is the smallest number in a class. For example in the class 20 - 30, the upper limit is 30 and the lower limit is 20. The frequency of a distribution is the number of times that data within a class appears in the data set. For example, the class 40 -- 50 appears 7 times in the data set.
To learn more about class interval, please check: https://brainly.com/question/28021783
#SPJ1
The half life of a radioactive kind of americium is 432 years. If you start with 814,816 grams of it, how much will be left after 2,160 years?
25463 grams radioactive kind of americium will be left after 2160 years.
We know that Half Life Formula will be,
\(N=I(\frac{1}{2})^{\frac{t}{T}}\)
where N is the quantity left after time 't'; 'T' is the half life of the substance and 'I' is the initial quantity of the substance.
Given that the initial quantity of the substance (I) = 814816 grams
Half life of the radioactive kind of americium is (T) = 432 years
The time elapsed (t) = 2160 years
Now we have to find the quantity left that is the value of N for the given values.
N = \(814816\times(\frac{1}{2})^{\frac{2160}{432}}=814816\times(\frac{1}{2})^5\) = 814816/32 = 25463 grams.
Hence 25463 grams radioactive kind of americium will be left after 2160 years.
To know about half life formula here
https://brainly.com/question/25750315
#SPJ1
What are the three types of algorithms?
The three types of algorithms are Brute Force algorithm, Greedy algorithm and Recursive algorithm.
What is Brute Force algorithm?As a very general approach to problem solving and an algorithmic paradigm, brute-force search or exhaustive search entails iteratively listing all potential candidates for the solution and determining if each one satisfies the problem's statement.
In order to find the divisors of a natural number n, a brute-force algorithm would count all integers from 1 to n & determine whether each one divides n without leaving a remainder.
A brute-force method might look at all possible configurations of 8 pieces on the 64-square chessboard and determine whether each queen piece may engage in mutually exclusive attacks for each configuration for the eight queens puzzle.
Learn more about Brute Force algorithm
https://brainly.com/question/20115984
#SPJ4