Answer:
15.8823% error
Step-by-step explanation:
Percent Error Formula
abs([tex]\frac{(a-x)}{x}[/tex]) * 100%
abs: absolute value
a: actual value
x: expected value
Percent Error = abs([tex]\frac{14.3 - 17}{17}[/tex]) * 100%
= abs(-0.158823) * 100%
15.8823% error
Let G
be a group. Say what it means for a map φ:G→G
to be an automorphism. Show that the set-theoretic composition φψ=φ∘ψ
of any two automorphisms φ,ψ
is an automorphism. Prove that the set Aut(G)
of all automorphisms of the group G
with the operation of taking the composition is a group.
a) An automorphism of a group G is a bijective map φ:G→G that preserves the group structure. That is, φ(ab) = φ(a)φ(b) and φ(a⁻¹) = φ(a)⁻¹ for all a, b ∈ G.
b) The set-theoretic composition φψ of any two automorphisms φ, ψ is an automorphism, as it preserves the group structure and is bijective.
c) The set Aut(G) of all automorphisms of G, with the operation of composition of maps, is a group. This is because it satisfies the four group axioms: closure, associativity, identity, and inverses. Therefore, Aut(G) is a group under composition of maps.
An automorphism of a group G is a bijective map φ:G→G that preserves the group structure, meaning that for any elements a,b∈G, we have φ(ab) = φ(a)φ(b) and φ(a⁻¹) = φ(a)⁻¹. In other words, an automorphism is an isomorphism from G to itself.
To show that the set-theoretic composition φψ is an automorphism, we need to show that it satisfies the two conditions for being an automorphism. First, we have
(φψ)(ab) = φ(ψ(ab)) = φ(ψ(a)ψ(b)) = φ(ψ(a))φ(ψ(b)) = (φψ)(a)(φψ)(b)
using the fact that ψ and φ are automorphisms. Similarly,
(φψ)(a⁻¹) = φ(ψ(a⁻¹)) = φ(ψ(a))⁻¹ = (φψ)(a)⁻¹
using the fact that ψ and φ are automorphisms. Therefore, φψ is an automorphism.
To show that Aut(G) is a group, we need to show that it satisfies the four group axioms
Closure: If φ,ψ∈Aut(G), then φψ is also in Aut(G), as shown above.
Associativity: Composition of maps is associative, so (φψ)χ = φ(ψχ) for any automorphisms φ,ψ,χ of G.
Identity: The identity map id:G→G is an automorphism, since it clearly preserves the group structure and is bijective. It serves as the identity element in Aut(G), since φid = idφ = φ for any φ∈Aut(G).
Inverses: For any automorphism φ∈Aut(G), its inverse φ⁻¹ is also an automorphism, since it is bijective and preserves the group structure. Therefore, Aut(G) is closed under inverses.
Since Aut(G) satisfies all four group axioms, it is a group under composition of maps.
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f the random walk starts in the center, on average how many steps does it take to return to the center?
Total number of steps taken by an average man in a year while walking with 7192 steps a day is equals to 2,625,080 steps/year.
Number of steps taken by average man in a day is equals to 7192
Then the total number of steps he takes in a year is equals to,
Calculate it by multiplying the average number of steps per day by the number of days in a year.
There are different ways to define a year,
But assuming a regular calendar year of 365 days, the calculation would be,
Total number of days in a year = 365 days
Total number of steps in a year
= 7192 steps/day x 365 days/year
= 2,625,080 steps/year
Therefore, on average the man would walk about 2,625,080 steps in a year.
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The given question is incomplete, I answer the question in general according to my knowledge:
If a man walks with random steps and the average man takes 7192 steps a day about how many steps does the average man take in a year?
Answer the question below: *
Tasha is planning an expansion of a square flower garden in a city park. If each side of the original garden is
increased by 5 m, the new total area of the garden will be 121 m². Find the length of each side of the original garden.
O 6 meters
O 6.6 meters
O 11 meters
O 16 meters
Sea "x" la longitud de cada lado del jardín original en metros.
La superficie del jardín original es x^2 m².
Si cada lado del jardín original se aumenta en 5 m, el nuevo lado del jardín será de (x+5) metros, y la nueva superficie será (x+5)^2 m².
Según el problema, la nueva superficie total es de 121 m²:
(x+5)^2 = 121
Tomando la raíz cuadrada en ambos lados:
x+5 = 11
Restando 5 en ambos lados:
x = 6
Por lo tanto, la longitud de cada lado del jardín original es de 6 metros.
Por lo tanto, la respuesta correcta es O 6 metros.
x - the length of each side of the original garden
A = x²
( x + 5 )² = 121 /√
x + 5 = 11, or x + 5 = - 11;
x = 11 - 5
x = 6 ( another solution in negative )
Answer:
A ) 6 m
Please answer Full question
(1) 4y-7z is a binomial.
(2) 8-xy² is a binomial.
(3) ab-a-b can be written as ab - (a + b) which is a binomial.
(4) z²-3z+8 is a trinomial.
What are monomials, binomials and trinomials?In algebra, monomials, binomials, and trinomials are expressions that contain one, two, and three terms, respectively.
A monomial is an algebraic expression with only one term. A monomial can be a number, a variable, or a product of numbers and variables.
A binomial is an algebraic expression with two terms that are connected by a plus or minus sign. For example, 2x + 3y and 4a - 5b are both binomials.
A trinomial is an algebraic expression with three terms that are connected by plus or minus signs.
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Classify into monomials, binomials and trinomials.
(1) 4y-7z
(1) 8-xy²
(v) ab-a-b
(ix) z2-3z+8
Part B
Draw
parallel to
. You can draw
any length and place it anywhere on the coordinate plane, but not on top of
.
Find and record the ratio, n, of the length of
to the length of
. Then, multiply the lengths of
and
by n and record the resulting lengths.
In a diagram,
Then,
[tex]\dfrac{DE}{BC}=n[/tex]
For example, suppose that n=2; thus,
[tex]DE=2BC\longrightarrow2\times CA[/tex]
We can form a new triangle DEF whose side EF is parallel to CA; therefore,
[tex]\longrightarrow EF=2CA[/tex]
Suppose we want to choose 5 letters, without replacement, from 15 distinct letters
[tex]\text{order does not matter}[/tex]
[tex]\text{sample space}= \text{15 letters}[/tex]
[tex]\text{no repetition}[/tex]
[tex]\text{P(A)}= \text{15C5}= \text{3003 ways}[/tex]
PLEASE HELP MEEE
whoever answers right gets brainliest!!!
Answer:
[tex]30\leq x[/tex] AND [tex]x \leq 106[/tex]
Notice the valid answer is the one with the AND since need to be both at the same time.
Step-by-step explanation:
Is the one is market, you add 6 to each side and you obtain that answer
[tex]24 \leq x-6\leq 100[/tex]
[tex]24 +6\leq x\leq 100+6[/tex]
[tex]30\leq x\leq 106[/tex]
Question 6 (2 points)
A wire costs $3 per foot. How much will 18 inches of wire cost?
$1.50
$3.00
$4.50
$9
Answer:
$4.50
Step-by-step explanation:
There are 12 inches in a foot. 18 inches is 1.5 feet.
1 foot of wire is $3.00 and a half of foot should be $1.50.
1.5 feet of wire should cost $4.50
1.5 ft × $3/ft
= $4.50
Two cars, one going due east at the rate of 90 km/hr and the other going to south at the rate of 60 km/hr are traveling toward the intersection of two roads. At what rate the two cars approaching each other at the instant when the first car is 0.2 km and the second car is 0.15 km from the intersection ?
The two cars are approaching each other at a rate of 36 km/hr at the given instant.
We can solve this problem by using the Pythagorean theorem and differentiating with respect to time. Let's call the distance of the first car from the intersection "x" and the distance of the second car from the intersection "y". We want to find the rate at which the two cars are approaching each other, which we'll call "r".
At any moment, the distance between the two cars is the hypotenuse of a right triangle with legs x and y, so we can use the Pythagorean theorem
r^2 = x^2 + y^2
To find the rates of change of x and y, we differentiate both sides of this equation with respect to time
2r(dr/dt) = 2x(dx/dt) + 2y(dy/dt)
Simplifying and plugging in the given values
dr/dt = (x(dx/dt) + y(dy/dt)) / r
dr/dt = (0.2 x 90 + 0.15 x (-60)) / sqrt((0.2)^2 + (0.15)^2)
dr/dt = (18 - 9) / sqrt(0.04 + 0.0225)
dr/dt = 9 / sqrt(0.0625)
dr/dt ≈ 36 km/hr
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The graph of triangle has coordinates E(1,4) F(-1,1) and G(2,-1). Graph triangle of EFG and it’s image after a translation of 3 units left and 1 unit down.
Answer:
Step-by-step explanation:1.4 -1, 1 2, -1
Maximize z = 3x₁ + 5x₂
subject to: x₁ - 5x₂ ≤ 35
3x1 - 4x₂ ≤21
with. X₁ ≥ 0, X₂ ≥ 0.
use simplex method to solve it and find the maximum value
Answer:
See below.
Step-by-step explanation:
We can solve this linear programming problem using the simplex method. We will start by converting the problem into standard form
Maximize z = 3x₁ + 5x₂ + 0s₁ + 0s₂
subject to
x₁ - 5x₂ + s₁ = 35
3x₁ - 4x₂ + s₂ = 21
x₁, x₂, s₁, s₂ ≥ 0
Next, we create the initial tableau
Basis x₁ x₂ s₁ s₂ RHS
s₁ 1 -5 1 0 35
s₂ 3 -4 0 1 21
z -3 -5 0 0 0
We can see that the initial basic variables are s₁ and s₂. We will use the simplex method to find the optimal solution.
Step 1: Choose the most negative coefficient in the bottom row as the pivot element. In this case, it is -5 in the x₂ column.
Basis x₁ x₂ s₁ s₂ RHS
s₁ 1 -5 1 0 35
s₂ 3 -4 0 1 21
z -3 -5 0 0 0
Step 2: Find the row in which the pivot element creates a positive quotient when each element in that row is divided by the pivot element. In this case, we need to find the minimum positive quotient of (35/5) and (21/4). The minimum is (21/4), so we use the second row as the pivot row.
Basis x₁ x₂ s₁ s₂ RHS
s₁ 4/5 0 1/5 1 28/5
x₂ -3/4 1 0 -1/4 -21/4
z 39/4 0 15/4 3/4 105
Step 3: Use row operations to create zeros in the x₂ column.
Basis x₁ x₂ s₁ s₂ RHS
s₁ 1 0 1/4 7/20 49/10
x₂ 0 1 3/16 -1/16 -21/16
z 0 0 39/4 21/4 525/4
The optimal solution is x₁ = 49/10, x₂ = 21/16, and z = 525/4.
Therefore, the maximum value of z is 525/4, which occurs when x₁ = 49/10 and x₂ = 21/16.
The number 0 is an element of the set of natural numbers.
OA. True
B. False
SUBI
it is false. 0 is not a natural number. it is a whole number
if the slope of the line joining the points (2,4) and (5,k) is 2. find the value of k
10 is the value of k of the slope of the line .
What are slopes called?
Slope, usually referred to as rise over run, is a line's perceived steepness. By dividing the difference between the y-values at two places by the difference between the x-values, we can determine slope.
You may determine a line's slope by looking at how steep it is or how much y grows as x grows. slope categories. When lines are inclined from left to right, they are said to have a positive slope, a negative slope, or a zero slope (when lines are horizontal).
the points (2,4) and (5,k)
formula from slope of two points
slope = y₂ - y₁/x₂ - x₁
substitute the values in formula
slope = 2
slope = k - 4/5- 2
2 =k - 4/3
6 = k - 4
k = 6 + 4
k = 10
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Parts A-D. What is the value of the sample mean as a percent? What is its interpretation? Compute the sample variance and sample standard deviation as a percent as measures of rotelle for the quarterly return for this stock.
The sample mean is 2.1, the sample variance is 212.5% and the standard deviation is 14.57%
What is the sample mean?a. The sample mean can be computed as the average of the quarterly percent total returns:
[tex](11.2 - 20.5 + 13.2 + 12.6 + 9.5 - 5.8 - 17.7 + 14.3) / 8 = 2.1[/tex]
So the sample mean is 2.1%, which can be interpreted as the average quarterly percent total return for the stock over the sample period.
b. The sample variance can be computed using the formula:
[tex]s^2 = sum((x - mean)^2) / (n - 1)[/tex]
where x is each quarterly percent total return, mean is the sample mean, and n is the sample size. Plugging in the values, we get:
[tex]s^2 = (11.2 - 2.1)^2 + (-20.5 - 2.1)^2 + (13.2 - 2.1)^2 + (12.6 - 2.1)^2 + (9.5 - 2.1)^2 + (-5.8 - 2.1)^2 + (-17.7 - 2.1)^2 + (14.3 - 2.1)^2 / (8 - 1) = 212.15[/tex]
So the sample variance is 212.15%. The sample standard deviation can be computed as the square root of the sample variance:
[tex]s = \sqrt(s^2) = \sqrt(212.15) = 14.57[/tex]
So the sample standard deviation is 14.57%.
c. To construct a 95% confidence interval for the population variance, we can use the chi-square distribution with degrees of freedom n - 1 = 7. The upper and lower bounds of the confidence interval can be found using the chi-square distribution table or calculator, as follows:
upper bound = (n - 1) * s^2 / chi-square(0.025, n - 1) = 306.05
lower bound = (n - 1) * s^2 / chi-square(0.975, n - 1) = 91.91
So the 95% confidence interval for the population variance is (91.91, 306.05).
d. To construct a 95% confidence interval for the standard deviation (as percent), we can use the formula:
lower bound = s * √((n - 1) / chi-square(0.975, n - 1))
upper bound = s * √((n - 1) / chi-square(0.025, n - 1))
Plugging in the values, we get:
lower bound = 6.4685%
upper bound = 20.1422%
So the 95% confidence interval for the standard deviation (as percent) is (6.4685%, 20.1422%).
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Question 6 of 10
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why ACDE AOPQ?
Check all that apply.
AA
A. AAS
B. ASA
C. LL
OD. HL
E. LA
F. SAS
Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.
what is triangle ?Having three straight sides and three angles where they intersect, a triangle is a closed, two-dimensional shape. It is one of the fundamental geometric shapes and has a number of characteristics that can be used to study and resolve issues that pertain to it. The triangle inequality theory states that the sum of a triangle's interior angles is always 180 degrees, and that the longest side is always the side across from the largest angle. Triangles can be used to solve a wide range of mathematical issues in a variety of disciplines and can be categorised based on the length of their sides and the measurement of their angles.
given
We can use the following congruence theories or postulates based on the data in the diagram:
A. ASA
B. AAS
C. LL (corresponding angles hypothesis)
F. SAS
Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.
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Segment AE shown has length of sqrt 20. Which segment is closest in length to sqrt 10?
Segment C has a length of √10, which is the closest to √10 compared to the other segments.
What is Segment?Segment is a customer data platform (CDP) that enables companies to collect, store, and analyze customer data from multiple sources. It helps companies build customer profiles and create personalized experiences for their customers. Segment allows businesses to track website visits, user actions, and other events in real-time, as well as to create custom events and store customer data in a secure and unified data warehouse. With Segment, companies can create powerful customer segmentation, which allows them to target customers with personalized messages and offers. Segment also integrates with various marketing, analytics, and CRM tools to provide a complete picture of customer behavior. It enables companies to build cohesive customer journeys, run campaigns, and optimize their customer experience.
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Complete Question.
I will mark you brainiest!
Given the coordinates shown and given that SU = 10, what are the coordinates of U if STUV is a kite?
A) (10, 18)
B) (0, 28)
C) (18, 28)
The calculated coordinates of U if STUV is a kite is (10, 18)
Calculating the coordinates of U if STUV is a kite?From the question, we have the following parameters that can be used in our computation:
The figute of a kite
Also, we have
S = (0, 18)
And the distance SU to be
SU = 10
If the quadrilateral STUV is a kite, then the coordinates S and U are on the same horizontal level (according to the figure)
So, we have
U = (0 + 10, 18)
Evaluate
U = (10, 18)
Hence, the coordinates of U if STUV is a kite is (10, 18)
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If 5 is increased to 9, the increase is what percentage of the original number
Answer: It's a 80% increase
Step-by-step explanation:
Whenever we construct a confidence interval for the population mean, the margin of error includes the standard error of x bar and theA. sampling biasB. nonresponse biasC. z or t value associated with a 95% confidence levelD. desired level of confidence
The margin of error in a confidence interval for the population mean includes the standard error of the sample mean and the z or t value associated with a certain level of confidence, usually 95% or 99%. Therefore, the correct answer is (C).
Sampling bias and nonresponse bias are potential sources of error in survey or study design and data collection, but they are not directly related to the construction of a confidence interval.
The desired level of confidence is a key input for determining the z or t value used in the calculation of the margin of error, but it is not included in the margin of error itself. The correct answer is z or t value associated with a 95% confidence level.
So, the correct option is (C).
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Each interior angle of a regular polygon is 140 Celcius.How many sides does the polygon have?
Answer:
9 sides
Step-by-step explanation:
180 - 140 = 40
360 ÷ 40 = 9
please help I know its 9:35 PM I Just need help what this question2.1 × 1.6 =
21
10
×
16
10
= tenths × tenths my parents are gonna kill me help
The value of the expression 2.1 × 1.6 = 3.36.
What are decimals?Decimals are a collection of numbers falling between integers on a number line. They are only an additional mathematical representation of fractions. Decimals allow us to express quantifiable quantities like length, weight, distance, money, etc. with more accuracy. Integers, also known as whole numbers, are represented to the left of the decimal point, while decimal fractions are shown to the right of the decimal point.
Given that the expression is: 2.1 × 1.6.
2.1 × 1.6 can be written as:
2.1 × 1.6 = 21/10 × 16/10
Multiply the numerator and denominator:
21/10 × 16/10 = 336/100
Covert the fraction into decimal:
336/100 = 3.36
Hence, the value of the expression 2.1 × 1.6 = 3.36.
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the figure below shows the change of a population over time. which statement best describes the mode of selection depicted in the figure?
The statement that best describes the mode of selection depicted in the figure is (b) Directional Selection, changing the average color of population over time.
The Directional selection is a type of natural selection that occurs when individuals with a certain trait or phenotype are more likely to survive and reproduce than individuals with other traits or phenotypes.
In the directional selection of evolution, the mean shifts that means average shifts to one extreme and supports one trait and leads to eventually removal of the other trait.
In this case, one end of the extreme-phenotypes which means that the dark-brown rats are being selected for. So, over the time, the average color of the rat population will change.
Therefore, the correct option is (b).
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The given question is incomplete, the complete question is
The figure below shows the change of a population over time. which statement best describes the mode of selection depicted in the figure?
(a) Disruptive Official, favoring the average individual
(b) Directional Selection, changing the average color of population over time
(c) Directional selection, favoring the average individual
(d) Stabilizing Selection, changing the average color of population over time
Show your solution ( 3. ) C + 18 = 29
Answer:
Show your solution ( 3. ) C + 18 = 29
Step-by-step explanation:
To solve the equation C + 18 = 29, we want to isolate the variable C on one side of the equation.
We can start by subtracting 18 from both sides of the equation:
C + 18 - 18 = 29 - 18
Simplifying the left side of the equation:
C = 29 - 18
C = 11
Therefore, the solution to the equation C + 18 = 29 is C = 11.
What is the difference between the questionnaire and an interview?
Answer: Questionnaire refers to a research instrument, in which a series of question, is typed or printed along with the choice of answers, expected to be marked by the respondents, used for survey or statistical study. It consists of aformalisedd set of questions, in a definite order on a form, which are mailed to the respondents or manually delivered to them for answers. The respondents are supposed to read, comprehend and give their responses, in the space provided.
A ‘Pilot Study’ is advised to be conducted to test the questionnaire before using this method. A pilot survey is nothing but a preliminary study or say rehearsal to know the time, cost, efforts, reliability and so forth involved in it.
The interview is a data collection method wherein a direct, in-depth conversation between interviewer and respondent takes place. It is carried out with a purpose like a survey, research, and the like, where both the two parties participate in the one to one interaction. Under this method, oral-verbal stimuli are presented and replied by way of oral-verbal responses.
It is considered as one of the best methods for collecting data because it allows two way exchange of information, the interviewer gets to know about the respondent, and the respondent learns about the interviewer. There are two types of interview:
Personal Interview: A type of interview, wherein there is a face to face question-answer session between the interviewer and interviewee, is conducted.
Telephonic Interview: This method involves contacting the interviewee and asking questions to them on the telephone itself.
According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847.† Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of $33,800.
(a) What is the probability that a household in Maryland has an annual income of $90,000 or more? (Round your answer to four decimal places.)
(b) What is the probability that a household in Maryland has an annual income of $50,000 or less? (Round your answer to four decimal places.)
The required probability that a household in Maryland with annual income of ,
$90,000 or more is equal to 0.3377.
$50,000 or less is equal to 0.2218.
Annual household income in Maryland follows a normal distribution ,
Median = $75,847
Standard deviation = $33,800
Probability of household in Maryland has an annual income of $90,000 or more.
Let X be the random variable representing the annual household income in Maryland.
Then,
find P(X ≥ $90,000).
Standardize the variable X using the formula,
Z = (X - μ) / σ
where μ is the mean (or median, in this case)
And σ is the standard deviation.
Substituting the given values, we get,
Z = (90,000 - 75,847) / 33,800
⇒ Z = 0.4187
Using a standard normal distribution table
greater than 0.4187 as 0.3377.
P(X ≥ $90,000)
= P(Z ≥ 0.4187)
= 0.3377
Probability that a household in Maryland has an annual income of $90,000 or more is 0.3377(rounded to four decimal places).
Probability that a household in Maryland has an annual income of $50,000 or less.
P(X ≤ $50,000).
Standardizing X, we get,
Z = (50,000 - 75,847) / 33,800
⇒ Z = -0.7674
Using a standard normal distribution table
Probability that a standard normal variable is less than -0.7674 as 0.2218. This implies,
P(X ≤ $50,000)
= P(Z ≤ -0.7674)
= 0.2218
Probability that a household in Maryland has an annual income of $50,000 or less is 0.2218.
Therefore, the probability with annual income of $90,000 or more and $50,000 or less is equal to 0.3377 and 0.2218 respectively.
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What is the slope of the line in the following graph?
Answer:
1/3
Step-by-step explanation:
using rise over run fron the two dots, we can find 2/6, which simplifies down to 1/3
WILL MARK AS BRAINLIEST!!!!!!!!!!!!!!
If "f" is differentiable and f(1) < f(2), then there is a number "c", in the interval (_____, _____) such that f'(c)>_______
If "f" is differentiable and f(1) < f(2), then there is a number "c", in the interval (1, 2) such that f'(c)> 0.
How do we know?Applying the Mean Value Theorem for derivatives, if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the interval (a, b) such that:
f'(c) = (f(b) - f(a)) / (b - a)
In the scenario above, we have that f is differentiable, and that f(1) < f(2).
choosing a = 1 and b = 2.
Then applying the Mean Value Theorem, there exists at least one number c in the interval (1, 2) such that:
f'(c) = (f(2) - f(1)) / (2 - 1)
f'(c) = f(2) - f(1)
We have that f(1) < f(2), we have:
f(2) - f(1) > 0
We can conclude by saying that there exists a number c in the interval (1, 2) such that:
f'(c) = f(2) - f(1) > 0
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The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set.
n(A)=
The cardinality of set A, n(A) = 29
What is cardinality of a set?The cardinality of a set is the total number of elements in the set
Given the Venn diagram here shows the cardinality of each set. To find the cardinality of set A, n(A), we proceed as follows.
Since the cardinality of a set is the total number of elements in the set, then cardinality of set A , n(A) = 9 + 8 + 3 + 9
= 29
So, n(A) = 29
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find the closed formula for 3,6,11,18 by relating them to a well known sequence. assume the first term given is
The closed formula for this particular sequence is an = n² + 2.
Take note that the odd numbers 3, 5, 7, 9, and 11 are separate consecutive terms. This shows that the first n odd numbers can be added to the initial term, az, to get the nth term. Hence, the following is how we may represent the nth term a = az + 1 + 3 + 5 + ... + (2n-3) (2n-3). We may utilize the formula for the sum of an arithmetic series to make the sum of odd integers simpler that is 1 + 3 + 5 + ... + (2n-3) = n².
As a result, we get a = az + n^2 - 1. In conclusion, the equation for the series (an)n21, where a1 = az and an is the result of adding the first n odd numbers to az, is as a = az + n^2 - 1. We have the following for the given series where a1 = az = 3.
So, the closed formula for this particular sequence is an = n² + 2.
To learn more about arithmetic sequences, refer to:
Your question is incomplete. The complete question is:
Find the closed formula for the sequence (an)n21. Assume the first term given is az. an = 3, 6, 11, 18, 27... Hint: Think about the perfect squares.
What triangles are similar to triangle ABC?
Answer:
A right angled triangle is similar to triangle ABC
Step-by-step explanation:
If you tilt the triangle and put it straight, you'll see that angle C is equal to 90°
And if a triangle has one angle of 90° then it is a right angled triangle
Hope you understand :)
