Answer:
3
Step-by-step explanation:
5 × 3 -15 = 15 - 15 = 0
Let a, b, c, d, e, f be integers selected from the set {1, 2, . . . , 100}, uniformly and at random with
replacement. Set
M = a + 2b + 4c + 8d + 16e + 32f.
What is the expected value of the remainder when M is divided by 64?
So the expected value of the remainder when M is divided by 64 is approximately 0.2080.
To find the expected value of the remainder when M is divided by 64, we can find the probability that M is congruent to each possible remainder modulo 64 and then sum these probabilities multiplied by the corresponding remainders.
For a positive integer n, let P(n) denote the probability that a positive integer chosen from the set {1, 2, . . . , 100} is congruent to n modulo 64. Then
P(0) = P(64) = P(128) = ... = 1/100
P(1) = P(65) = P(129) = ... = 1/100
P(63) = P(127) = P(191) = ... = 1/100
Since the integers a, b, c, d, e, and f are chosen independently and uniformly at random from the set {1, 2, . . . , 100}, the probability that M is congruent to n modulo 64 is P(n)^6.
Therefore, the expected value of the remainder when M is divided by 64 is
E = 0 * P(0)^6 + 1 * P(1)^6 + 2 * P(2)^6 + ... + 63 * P(63)^6
= (0^6 + 1^6 + 2^6 + ... + 63^6) * P(0)^6
= (0 + 1 + 2 + ... + 63) * P(0)^6
= 2080 * (1/100)^6
= 0.2080
So the expected value of the remainder when M is divided by 64 is approximately 0.2080.
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For a positive integer n, let P(n) denote the probability that a positive integer chosen from the set {1, 2, . . . , 100} is congruent to n modulo 64. Then
P(0) = P(64) = P(128) = ... = 1/100
P(1) = P(65) = P(129) = ... = 1/100
P(63) = P(127) = P(191) = ... = 1/100
Since the integers a, b, c, d, e, and f are chosen independently and uniformly at random from the set {1, 2, . . . , 100}, the probability that M is congruent to n modulo 64 is P(n)^6.
Therefore, the expected value of the remainder when M is divided by 64 is
E = 0 * P(0)^6 + 1 * P(1)^6 + 2 * P(2)^6 + ... + 63 * P(63)^6
= (0^6 + 1^6 + 2^6 + ... + 63^6) * P(0)^6
= (0 + 1 + 2 + ... + 63) * P(0)^6
= 2080 * (1/100)^6
= 0.2080
Write a quadratic function h whose only zero is 2.
h(x) =
Answer:
h(x) = (x-2)^2
Step-by-step explanation:
Consider the polynomial g(x) = 4x³ - x² - 24x + 6
a. List all possible rational zeros of the polynomial. (Assume all numbers shown are both + and -).
O 1, 2, 4, 1/2, 1/3, 2/3, 4/3, 1/6
O 1, 2, 3, 4, 6, 1/2, 3/2, 1/3, 2/3, 4/3, 1/4, 3/4, 1/6
O 1, 2, 3, 4, 6, 1/2, 3/2, 1/4, 3/4
1, 2, 3, 6, 1/2, 3/2, 1/4, 3/4
b. List all actual zeros of the polynomial (rational, irrational, real, and complex).
Give exact answers, separated by commas as necessary.
Zeros:
a. The rational roots of the polynomial g(x) = 4x³ - x² - 24x + 6 is 1/4.
b. The rational and irrational roots of the polynomial g(x) = 4x³ - x² - 24x + 6 are 1/4 and ± √6.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, A cubic polynomial function g(x) = 4x³ - x² - 24x + 6.
Therefore,
g(x) = 4x(x² - 6) - 1(x² - 6).
g(x) = (4x - 1)(x² - 6).
g(x) = (4x - 1)(x + √6)(x - √6).
Hence, x = 1/4, ± √6.
So, The roots of the polynomial are 1/4 and ± √6.
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Can someone help me with this? I’m confused
Answer:
Option 4
Step-by-step explanation:
The domain of this function is the possible values of n that are suitable for this function. Since n represents a number of vehicles, the domain of n should be a whole number (since you cannot have a negative number of vehicles or half of a vehicle).
hope this helps :)
Seventeen less than the product of 3 and a number is -50. what is the answer?
The number from the expression is 22. 3
What is an algebraic expression?An algebraic expression can be defined as a mathematical expression that consists of variables, terms, constants, coefficients, and factors.
These expressions are also seen to be made up of mathematical or arithmetic operation, such as;
SubtractionAdditionMultiplicationDivisionBracketParentheses, etcSome examples of algebraic expressions;
2x + 6
3x + 8
From the information given;
Let the number be x
Then'
3x - 17 = - 50
collect like terms
3x = 67
Make 'x' the subject
x = 22. 3
Hence, the value is 22. 3
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30 POINTS. The county rummage sale arranges 250 tables in three groups. The group on the left has 75 tables. The group on the right has 80 tables. Write an equation to find the number of tables in the middle group. Then sovle your equation.
Answer: There are 95 tables in the middle group
Step-by-step explanation:
There are a total number of 250 tables.
There are three groups.
We know how many tables the left and right groups have
let x be the number of tables in the middle
75+80+x=250
155+x=250
x=95
In a class of students, the following data table summarizes how many students have
cat or a dog. What is the probability that a student chosen randomly from the class
does not have a cat or a dog?
Has a dog
Does not have a dog
Has a cat Does not have a cat
7
4
6
12
Answer:
8/33
p(d'c')
not having a cat=12/18
not a dog =4/11
12/18×4/11=8/33
Ans=8/33
27/22 as a decimal rounded to the nearest hundreth
The expression as a rounded decimal is 1.23
How to evaluate the expression as a rounded decimalFrom the question, we have the following parameters that can be used in our computation:
27/22
To start with, we evaluate the expression using a calculator
So, we have the following representation
27/22 = 1.22727272727
Next, we approximate to the nearest hundredth
So, we have the following representation
27/22 = 1.23
Hence, the approximated expression is 1.23
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A simple random sample of n subjects is selected in such a way that every possible sample of the same size n has the same chance of being chosen. (A simple random sample is often called a random sample, but strictly speaking, a random sample has the weaker requirement that all members of the population have the same chance of being selected.) Determine whether each of the following is a simple random sample and a random sample. Complete parts a through c. .. a. In Major League Baseball, there are 30 teams, each with an active roster of 25 players. The names of the teams are printed on 30 separate index cards, the cards are shuffled, and one card is drawn. The sample consists of the 25 players on the active roster of the selected team. This sample a simple random sample. It v a random sample. b. For the same Major League Baseball population described in part (a), the 750 names of the players are printed on 750 separate index cards, and the cards are shuffled. Twenty-five different cards are selected from the top. The sample consists of the 25 selected players. This sample V a simple random sample. It v a random sample c. For the same Major League Baseball population described in part (a), a sample is constructed by selecting the 25 youngest players. This sample a simple random sample. It a random sample.
This sample a simple random sample. It v a random sample.
What is simple random sample?A selection of participants from a population is randomly chosen by the researcher using simple random sampling, a sort of probability sampling. The probability of getting chosen is the same for every person in the population.A simple random sample is a subset of people picked at random from a larger group, all with the same probability. It is the process of choosing a sample at random.Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are the four main types of random (probability) sampling.This sample a simple random sample. It v a random sample.To learn more about simple random sample refer to:
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9 more than the quantity of 6 less than a number n is 18
Answer: n = 15
Step-by-step explanation:
9 + n - 6 = 18
3 + n = 18
n = 15
brett needs 2/3 cups of yogurt for one smoothie. He wants to know how many smoothies he can make with 2 4/6 cups of yogurt. which division expression can be used to represent the situation
Answer:
4
Step-by-step explanation:
2 4/6 = 16/6Based on the given conditions, formulate:
16/6 ÷ 2/3
Divide a fraction by multiplying its reciprocal:
16/6 × 3/2
(16 × 3) ÷ (6 × 2)
48/12 = 4
Thus, Brett can make 4 smoothies with 2 4/6 cups of yogurt.
Find an equivalent fraction of 36/48
having denominator 6.
An equivalent fraction of 36/48 having denominator 6 could be 6/6 only.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
we are given a fraction as 36/48.
We can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.
We have to only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers.
In this case we have a clue which is 48,
6 x 8 = 48
Then we would want to take the 6 and times it by the denominator which is 6
So 6 x 6 = 36
An equivalent fraction of 36/48 is 6/6.
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The serving size for the granola that Ted likes to eat for breakfast is 3/4 cup. How many servings are there in a box that holds 13 cups?
A 41-year old woman has $398,100.00 in an IRA account. Due to medical concerns of a family member, she decided to make no additional contributions to the account but expect it to grow at 8% compounded every 4 months. How much does she expect to have in the account when she retires at age 65?
She expects to have $2710591.78 when she retires at age 65 with the principal amount is 398100, the interest rate is 8%, time period is 24 and number of times interest applied is 3 by the concept of compound interest.
What is compound interest?Interest that is paid on the principal and interest at regular periods is known as compound interest. The interest is calculated for the new principal at regular intervals after the interest that has already accumulated has been combined with the existing principal amount. The initial principal plus the interest that has accrued thus far are added together to form the new principal.
Interest on the principal + periodic compound = compound interest.
According to the question the principal amount is 398100, the interest rate is 8%, time period is 24 and number of times interest applied is 3.
Here the interest is compounded every 4 months
So, the formula of compound interest is as follows:
A=p (1+ [tex]\frac{r}{n}[/tex]) ∧ (n× t)
Where P is the principal balance, r is the interest rate, n is the number of times interest is compounded per year and t is the number of years.
Here the interest is compounded every 4 months hence the value of n is 12/4 which is equal too 3.
Insert the values of p, n, t, r in above equation,
A=398100(1+[tex]\frac{8}{300}[/tex]) ∧ (3×24)
A=398100× (1.027) ∧ (72)
A=398100×6.809
A=2710591.78
She expects to have amount $2710591.78 when she retires at age 65.
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The display summarizes grades on a World History exam.
A vertical box plot is titled world history exams, with a minimum of 54, a maximum of 94, a lower quartile of 70, a median of 83, and an upper quartile of 88.
Which of the following describes the data set?
The data is univariate and categorical.
The data is univariate and numerical.
The data is bivariate and categorical.
The data is bivariate and numerical.
The option that best describes the data is The data is band numerical
What is univariate data?This kind of data just has one variable. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis.
In this case the one variable is World History scores exam
What are numerical data?Data that is expressed as numbers rather than in any linguistic or descriptive form is referred to as numerical data.
Numerical data, also known as quantitative data, is gathered in number form and differs from all other sorts of number data because it can be calculated mathematically and statistically.
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metodo gráfico
y-2x=o
y+x=3
por favor ayúdenme doy coronita
HELPPP!!!!! I need help with the ASAP PLEASE HELEP ME
The value of x is 7/3 and the value of y is -11/3 for the given equations.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the equations are 2x - 2y = 12 and -8x -y = -15. The value of x and y will be calculated as,
2x - 2y = 12
-8x - y = -15
Solve the above equation,
2x - 2(-8x + 15) = 12
2x + 16x - 30 = 12
18x = 42
x = 42 / 18
x = 7 / 3
The value of y is calculated as,
-8x - y = -15
y = ( -8 x 7 / 3 ) +15
y = (-56 + 45) /3
y = -11 / 3
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Ester writes 6 x 7 = 42 to find
the number of students seated
at tables. Describe what each
factor represents.
Answer:
6 rows to 7 steal in each rows
CAN SOMEONE HELP WITH THIS QUESTION?✨
The time required to grow $5000 to $8300, if the rate of interest is 7.5 %, is 7 years.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
The principal amount, p = $5000,
The amount, A = $8300
The rate of interest, r = 7.5 %,
Calculate the time as shown below,
[tex]A = p(1 + r / 400)^{4n}[/tex]
8300 = 5000 (1 + 7.5 / 400)⁴ⁿ
8300 / 5000 = (1 + 0.01875)⁴ⁿ
1.66 = (1.0188)⁴ⁿ
1.66 = (1.077)ⁿ
(1.077)⁷ = (1.077)ⁿ
n = 7
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Luis has 60 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 216 square meters. Solve for the dimensions (length and width) of the field. The dimensions are __ meters by __ meters .
The dimensions are 12 meter by 18 meter .
what is perimeter of rectangle ?perimeter of rectangle = 2(length + width)
length and width of the Luis plot by L and W, respectively.
We know that the perimeter, is 60 meters. So we can write:
2L + 2W = 60
Simplifying this equation, we can divide both sides by 2:
L + W = 30
now , area of the plot is 216 square meters:
L x W = 216
use substitution to solve for one of the variables. Let's solve for L in the first equation:
L = 30 - W
We can substitute this expression for L into the second equation:
(30 - W) x W = 216
[tex]W^2 - 30W + 216 = 0[/tex]
We can solve this quadratic equation using the quadratic formula:
W = [30 ± [tex]\sqrt{30^2 - 4 * 1 * 216}[/tex] / 2
Simplifying:
W = [30 ± 6] / 2
So W = 18 or W = 12.
If W = 18, then L = 30 - 18 = 12.
If W = 12, then L = 30 - 12 = 18.
Therefore, the dimensions are 18 meters by 12 meters or 12 meters by 18 meters.
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Which equations have the same value of X as 5/6x + 2/3=-9? Select three options
The equations have the same value of x are,
A) 5x + 4 = -54
B) 6(5/6x + 2/3) = -9(6)
C) 5x = -58
What is equation?
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation
3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
Consider the given equation
5/6 x + 2/3 = -9
Subtract 2/3 from both sides,
5/6x + 2/3 - 2/3 = -9 - 2/3
5/6x = -29/3
[tex]x = -\frac{29}{3}*\frac{6}{5}\\ x = -11.6[/tex]
The value of x is -11.6.
Hence, the equations have the same value of x are,
A) 5x + 4 = -54
B) 6(5/6x + 2/3) = -9(6)
C) 5x = -58
After solving above these equations we get the same value of x which is -11.6.
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Complete question:
Which equations have the same value of x as 5/6x + 2/3 = -9? Select three options. 6(5/6x + 2/3) = -9
6(5/6x + 2/3) = -9(6)
5 x + 4 = -54 5 x + 4 = -9
5 x = -13
5 x = negative 58
Jeremiah makes \dfrac{4}{5}
5
4
start fraction, 4, divided by, 5, end fraction of the free throw shots he attempts in basketball. Jeremiah likes to shoot free throws until he misses one. Let FFF be the number of shots it takes Jeremiah to miss his first free throw. Assume that the results of each shot are independent.
Find the mean and standard deviation of FFF.
Round your answers to one decimal place.
\mu_F \approxμ
F
≈mu, start subscript, F, end subscript, approximately equals
shots
\sigma_F \approxσ
F
≈sigma, start subscript, F, end subscript, approximately equals
shots
80% is her free throw shooting percentage.
What is Fraction?Fractions are used to represent smaller pieces (or parts) of a whole. The parts might make up one thing, or more than one thing. Either way, altogether, they make up what's called a whole.
Given that, Jeremiah makes 4/5 of the free throw shots he attempts in basketball. Jeremiah likes to shoot free throws until he misses one. Let F be the number of shots it takes Jeremiah to miss his first free throw.
We can construct a fraction in which the numerator is how many shots she makes, and the denominator is how many shots she took overall.
We now have the following fraction:4/5
To convert this to a percentage, we want the denominator to be 20/20
= 4/5×20/20
= 80/100
= 0.8
Now multiply 0.8 with 100
= 0.8×100=80
Hence, 80% is her free throw shooting percentage.
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In how many ways can the digits in the number 7,400,000 be arranged?
Jim has to choose between two gym membership plans. Plan A: $50 monthly membership fee and $10 per visit. Plan B: $25 one time membership fee and $15 per visit. How many visits must Jim make to make Plan A the cheaper option?
How many visits for them to cost the same?
The same cost of both of the plan of the gym will be in 5 visits. And plan B is better than Plan A as B is cheaper than A.
What is an expression?In mathematics, expression is the combining of variables with the application of operations and prescribed rules. It could take the shape of an equation, some numbers, etc.
We have,
plan A consists of :
Amount for monthly membership fee = $50
Cost per visit = $10
The expression of total fees would be:
50+10x,
where x is the number of times Jim visits the gym.
Plan B consists of :
Amount for monthly one time membership fee = $25
Cost per visit = 15
The expression of total fees would be:
25 + 15x,
where x is the number of times Jim visits the gym.
Here, x denotes the number of visits.
Let us suppose x = 1
Then, fees for plan A would be:
50 + 10 x1 = $60
Fees for plan B would be:
25 + 15 x1 = $40
To find the same cost in x number of visits:
We equate both the expressions.
50+10x = 25 + 15x
15x - 10x = 50 - 25
5x = 25
x = 5
That means, if Jim visits 5 times, the gym, then he would have the similar cost for both of the plans.
Hence, Plan B is better than Plan A as B is cheaper than A. The same cost of both of the gym will be in 5 visits.
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Rick deposits $3 into his bank account. The following week, he deposits 3 times that amount. Each week after that, he deposits 3 times the amount he did the previous week. How much does he deposit in all during the first 3 weeks (THERE ARE 2 PAGES
Rick's deposit in first 3 weeks is $39
What is Rick's weekly deposit ?1. Rick's deposit in the second week = 3 times($3)
= 3(3)
= 9
= [tex]3^{2}[/tex]
The exponential expression for Rick's 2nd week deposit = [tex]3^{2}[/tex]
Where, Base = 3
Exponent = 2
2. Rick's deposit in 1st week = $3
Rick's deposit in 2nd week = 3 (3) = $9
Rick's deposit in 3rd week = 3 (9) = $27
Rick's deposit in first 3 weeks = 3+9+27
= $39
Rick's deposit in all in the first 3 weeks is $39
3. Rick's deposit for 15 weeks = [tex]3^{15}[/tex]
= $1,43,48,907.
We know, no. of weeks in a year = 52
Rick's deposit for 52 weeks ( 1 year ) = 52 times of 3
[tex]=3^{52}\\= 6.4610819e+24[/tex]
Since this is a huge number , Rick cannot keep up this savings plan for a year.
What is an exponential expression?Only a short version of a power can be expressed using an exponential expression. How frequently the base is employed as a factor is shown by the exponent. Any real or complex exponent is acceptable under the notion of exponentiation. For a large number of other algebraic structures, including matrices, exponentiation by integer exponents can also be defined.Compound interest, population expansion, chemical reaction kinetics, wave behaviour, and public-key cryptography are just a few examples of the many domains where exponentiation is widely utilized. It is also used extensively in fields including economics, biology, chemistry, physics, and computer science.To learn more about exponential expression, refer:
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G(x) = 4x - 5, find g(3)
Step-by-step explanation:
this is a college question ? and you don't know how to do that ?
think back to elementary and middle school. and you had to use that all the way through high school as a very, VERY basic skill.
Focus !
g(3) just means that x = 3, and we need to replace every occurrence of x by 3. and then we calculate the result.
g(3) = 4×3 - 5 = 12 - 5 = 7
that's all to it.
Kate and Miley are selling girl scout cookies Kate sold 27 boxes in 45 minutes Miley sold 12 boxes in 30 minutes at the same rates how many total boxes will the girls have sold in one hour?
Kate and Miley sold 60 boxes of cookies in one hour.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b.
Given that,
Cookies sold by Kate in 45 minutes = 27 boxes.
Also,
Cookies sold by Miley in 30 minutes = 12 boxes.
To find the total boxes of cookies sold by girls in one hour,
Use ratio method,
Cookies sold by Kate in 3/4 hours = 27 boxes,
Cookies sold by Kate in 1 hour = 27 x (4/3) = 36
Cookies sold by Miley in 1/2 hours = 12 boxes,
Cookies sold by Miley in 1 hour = 12 x 2 = 24 boxes
Total cookies sold by Kate in Miley in one hour = 36 + 24 = 60
There are 60 boxes of cookies sold by the girls in one hour.
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piecewise function.
Express the function graphed on the axes below as a
Please help me
The piecewise function is:
f(x) = x + 1 if x < 2
f(x) = -7x + 42 if x > 5
How to express the function graphed?On the graph we can see a piecewise function (piecewise means that it has different equations defined for different intervals in the domain).
On the left side, we can see a linear equation that comes from negative infinity and ends at x = 2 with an open circle (so the domain does not contain that value).
That line passes through (-1, 0) and (0, 1), then the slope is:
a = (1 - 0)/(0 -(-1)) = 1
And the y-intercept is y = 1, then the equation of the line is:
y = x + 1
The other line starts at x = 5 (again, open circle) and keeps going, it passes through the points (5, 7) and (6, 0)
The slope is:
a = (0 - 7)/(6 -5) = -7
Then the line is something like:
y = -7*x + b
To find b, we use the point (6, 0)
0 = -7*6 + b
7*6 = 42 = b
Then this line is:
y = -7x + 42
Concluding, the piecewise function is:
f(x) = x + 1 if x < 2
f(x) = -7x + 42 if x > 5
The complete question is : Help please!! Express the function graphed on the axes below as a piecewise function.
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PLEASE HELP god bless you /Barak Allah fic A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined. Given that the number of men is now 60% of the total members, how many of the 50 new members were women?
The required number of new boys in a sports team is 62.
As mentioned in the question, A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
Given that the number of men is now 60% of the total members, how many of the 50 new members were women is to be determined,
Percentage of women, in the team = 100 - 60 = 40%
40% of total members are women = 35 + 50
Total members = 85 / 40%
Total member = 212
Number of new member that are boys = 212 - 85 - 65 = 62 boys
Thus, the required number of new boys in a sports team is 62.
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Please help please and thank you
The list of pairs of triangles are ∠A≅∠N, ∠B≅∠O, ∠C≅∠P for the given similar triangles.
What is meant by triangle?Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.
In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces.
Given triangles are,
ΔABC and ΔNOP
And also given that they are similar triangles.
The pairs of the congruent angles are:
∠A≅∠N
∠B≅∠O
∠C≅∠P
Therefore, the list of pairs of triangles are ∠A≅∠N, ∠B≅∠O, ∠C≅∠P for the given similar triangles.
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