(1) By 1716 different ways can the offices be filled if each person can hold at most one office.
(2) By 132 number of ways Caden can be the chairperson.
(3) By 1320 of the 1716 total ways the offices can be filled,
(1) If each person can hold at most one office, there are 13 people to choose from for the first office, 12 people remaining to choose from for the second office, and 11 people remaining to choose from for the third office.
Therefore, the number of different ways the offices can be filled is:
13 * 12 * 11 = 1716 ways
(2) If Caden is the chairperson, there are 12 people to choose from for the second office and 11 people remaining to choose from for the third office.
Therefore, the number of ways Caden can be the chairperson is:
12 * 11 = 132 ways
(3) If Caden is an officer, there are 12 people to choose from for the first office, 11 people remaining to choose from for the second office, and 10 people remaining to choose from for the third office.
Therefore, the number of ways Caden can be an officer is:
12 * 11 * 10 = 1320 ways
So, in 1320 of the 1716 total ways the offices can be filled, Caden is one of the elected officers.
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An element with a mass of 870 grams decays by 6.1% per minute. To the nearest minute, how long will it be until there are 270 grams of the element remaining?
I have a regular polygon:
The sum of the interior angles is 1080 degrees. The length of each side is 5". The area is 160 square inches. What is the length of the apothem?
Do not label your answer.
Answer:
To find the apothem of a regular polygon, we can use the formula:
A = (ns^2)/(4tan(180°/n))
Where A is the area, n is the number of sides, s is the length of each side, and tan(180°/n) is the tangent of half of the central angle.
First, we need to find the number of sides of the polygon. To do this, we can use the formula for the sum of the interior angles of a polygon:
(n - 2)180° = 1080°
Solving for n:
n = 6
So the polygon has 6 sides.
Next, we can plug in the values we have into the formula for the apothem:
A = (6s^2)/(4tan(180°/6)) = 160
Expanding the right side:
A = (6s^2)/(4tan(30°)) = 160
Using the tangent identity:
A = (6s^2)/(4(√3/3)) = 160
Multiplying both sides by 4(√3/3) to isolate s^2:
4(√3/3)A = 6s^2
Expanding the left side:
4(√3)A/3 = 6s^2
Dividing both sides by 6:
2(√3)A/3 = s^2
Taking the square root of both sides:
s = √(2(√3)A/3)
Plugging in the value for A:
s = √(2(√3) * 160/3)
Calculating:
s = √(106.667) = 3.25
So the length of each side is 3.25 inches.
Finally, we can find the apothem using the formula:
a = s/2tan(180°/n)
Expanding the right side:
a = 3.25/2tan(30°)
Using the tangent identity:
a = 3.25/2(√3/3)
Dividing both sides by √3/3:
a = 3.25√3
Calculating:
a = 5.5
So the length of the apothem is 5.5 inches.
Match each polynomial in the first column with a factoring technique in the second column. If none of the techniques can be used to factor the polynomial, select none.
Each polynomial given is associated with the given factoring technique in the second column. a. GCF b. grouping c. none d. the difference of two squares e. Sum and product f. Perfect square trinomial.
What is factorization?To factorize an algebraic statement, we first identify the terms' highest common factors and then arrange the terms into groups in accordance with those groups. In plain English, factorization is the process through which an algebraic expression gets expanded in the opposite direction.
Each polynomial given is associated with the given factoring technique in the second column.
a. grouping
b. GCF
c. none
d. the difference of two squares
e. Sum and product
f. Perfect square trinomial
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What are the essential pieces and parts of finding probability?In order to earn full credit for this question using the following terms: outcome(s), sample space, event(s).
The probability of an event can be calculated by dividing the number of favorable outcomes by the number of possible outcomes in the sample space.
Outcome(s): An outcome is a possible result of a random experiment. For example, in a coin flip, an outcome could be either heads or tails.
Sample Space: The sample space is the set of all possible outcomes of a random experiment. In the coin flip example, the sample space would be {heads, tails}.
Event(s): An event is a subset of the sample space that includes one or more outcomes. For example, if the event is getting heads in the coin flip, the event would be {heads}. The probability of an event is the number of outcomes in the event divided by the total number of outcomes in the sample space.
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If 63 % of persons like banana while 76 % like apples, what can be said about % of persons who like both banana and apples? Each person eats at least one fruit.
a. 39%
b. 41%
c. 43%
d. 45%
Each person eats at least one fruit. Hence 39% of people eat both orange and apple using the probability.
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics. From the given data
n(O)=0.63
n(A)=0.76
n(A∪O)=1 as every person eats at least one fruit
n(A∪O)=n(A)+n(O)−n(A∩B)
1=0.63+0.76−n(A∩B)
n(A∩B)=1.39−1
n(A∩B)=0.39
A∩B=0.39×100=39
Hence 39% of people eat both orange and apple
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what percent of distribution data falls within the interquartile range of the ""gre"" variable. (1 mark)
The interquartile range (IQR) is a measure of spread in a dataset and is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).
The IQR of the ‘gre’ variable can be calculated using the formula IQR = Q3 - Q1. This tells us the range of values that lie between the 25th and 75th percentile.
In this case, the IQR of ‘gre’ is calculated to be 210 - 340 = 70. This means that 70% of the distribution data falls within the interquartile range of ‘gre’. This can be further visualized on a boxplot, which shows the median, upper and lower quartiles. The IQR is represented by the box and the whiskers that extend out from it, indicating the range of values that lie within the interquartile range.
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Jada's Coffee Shop can make lattes with either whole milk or nonfat milk. On Saturday, Jada's Coffee Shop went through 1/3 of a carton of whole milk and 1/5 of a carton of nonfat milk. How much more whole milk was used than nonfat milk?
Answer:
[tex]\frac{2}{15}[/tex]
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] - [tex]\frac{1}{5}[/tex]
[tex]\frac{5}{15}[/tex] - [tex]\frac{3}{15}[/tex] = [tex]\frac{2}{15}[/tex]
Answer:
Jada's Coffee Shop used 1/3 of a carton of whole milk and 1/5 of a carton of nonfat milk on Saturday. Therefore, the amount of whole milk used was 2/3 of a carton, and the amount of nonfat milk used was 1/5 of a carton. The difference between the two is 2/3 - 1/5, which is equal to 7/15 of a carton. Therefore, Jada's Coffee Shop used 7/15 of a carton more whole milk than nonfat milk.
Sofia has $4.35 in quarters and nickels in her pocket. She has 3 more nickels than quarters. Write an equation that can be used to determine the number of quarters, x , Sofia has.
Answer:
Let's say x is the number of quarters. Then the number of nickels is x + 3.
The total value of the quarters is 0.25x, and the total value of the nickels is 0.05(x + 3).
The total value of both types of coins is 4.35:
0.25x + 0.05(x + 3) = 4.35
0.25x + 0.05x + 0.15 = 4.35
0.3x + 0.15 = 4.35
0.3x = 4.2
x = 14
So Sofia has 14 quarters and 17 nickels.
Answer:
.25q + .05(q - 3) = 4.35
Step-by-step explanation:
Let q = the number of quarters
Let n = the number of nickels
.25q + .05n = 4.35
n = q- 3
Substitute q - 3 for n
.25q + .05(q - 3) = 4.35
How do you mentally divide by 0.1, 0.01 and 0.001
Step-by-step explanation:
To mentally divide by 0.1, 0.01 and 0.001, you can use the following tips:
Dividing by 0.1 is equivalent to multiplying by 10.
Dividing by 0.01 is equivalent to multiplying by 100.
Dividing by 0.001 is equivalent to multiplying by 1000.
Which of the following best describes the graph of Linear Inequality in two variables?
A. Straight line
B. Parabola
C. Half plane
D. Curve line
The statement that best describes the graph of linear Inequality in two variables is a straight line graph. That is option A.
What is a Linear inequality?A linear Inequality is defined as the expression that can be used to represent the relationship between two variables using inequality symbols such as '<', '>', '≤' or '≥'.
When a linear Inequality between two variables are being represented in a graph, a straight line graph is obtained because the inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.
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Marna thinks that about 35% of her mail is junk mail. She gets about twice as much regular mail as junk mail. Is she correct?
Marna thinks is wrong. Thus Marna's think is incorrect.
What is the percentage?
A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The symbol "%" represents it.
Given that Marna thinks that about 35% of her mail is junk mail.
Thus out of 100 emails, 35 emails are junk.
Thus the ratio of regular emails to junk mail is
100:35
= 20:7
Again given that she gets about twice as much regular mail as junk mail.
Assume that the number of junk mail is x.
Then the regular mail is 2x.
Thus the ratio of regular emails to junk mail is
2x:x
=2:1
The ratio 20:7 ≠ 2:1
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to the company's managers. suppose winco's performance scores really are normally distributed. this year, managers with scores less than 157 received c grades and those with scores of at least 355 received a grades. a. (2 points) what are the z-scores associated with the 9th and 91st percentiles from the standard normal distribution?
The performance score associated with the c grade is 157, and the performance score associated with the a grade is 355.
What is Z-score?The z-score is a numerical measurement used in statistics to indicate how many standard deviations a particular value is from the mean of a dataset. It is calculated by subtracting the mean from the data point and dividing the result by the standard deviation. The resulting number is the z-score. The z-score is a useful tool for identifying outliers in a dataset, as values with z-scores that are too high or too low can be easily identified. Z-scores can also be used for comparing data points from different datasets, as z-scores are independent of the mean and standard deviation of the dataset. Z-scores can also be used for comparing data points from different datasets, as z-scores are independent of the mean and standard deviation of the dataset. This makes them ideal for normalizing data from different sources or for comparing data from different time periods or from different locations.
The z-score associated with the 9th percentile from the standard normal distribution is -1.28, and the z-score associated with the 91st percentile is 1.28.
b. (2 points) what are the performance scores associated with the c grade and the a grade?
The performance score associated with the c grade is 157, and the performance score associated with the a grade is 355.
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Multiply. Enter the product in simplest form. 9/10 × 20/21 =
The provided Product 9/10 * 20/21 has the simplest form, which is 6/7.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
Given a fraction multiplication 9/10 × 20/21
Simplification Using PEMDAS
=> 9/10 × 20/21
=> 9* 20 /21 *10
=> 6/7
Therefore, the simplest form of the given Product 9/10 × 20/21 is 6/7.
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find the measures of an exterior angle and an interior angle given the number of sides of each regular polygon. round to the nearest tenth, if necessary.1. 40a. 40, 140 b. 140, 220 c. 9, 171 d. 4.5, 175.5
The value of interior angle and the exterior angle will be 9, 140 degree.
Hence, option (a) is correct choice.
(a) 40, 140
An exterior angle of a regular polygon with 40 sides is equal to 360 divided by the number of sides, which is 360/40 = 9 degrees.
An interior angle of a regular polygon with 40 sides is equal to (180(n-2))/n,
where n is the number of sides,
which is (180(40-2))/40 = 140 degrees.
So the answer is: 9, 140.
(b) 140, 220
The exterior angle of a regular polygon with 40 sides is equal to 360 divided by the number of sides,
which is 360/40 = 9 degrees.
An interior angle of a regular polygon with 40 sides is equal to (180(n-2))/n,
where n is the number of sides, which is (180(40-2))/40 = 140 degrees.
So the answer is: 9, 140.
(c) 9, 171
The exterior angle of a regular polygon with 9 sides is equal to 360 divided by the number of sides, which is 360/9 = 40 degrees.
An interior angle of a regular polygon with 9 sides is equal to (180(n-2))/n,
where n is the number of sides, which is (180(9-2))/9 = 140 degrees.
So the answer is: 40, 140.
(d) 4.5, 175.5
This answer is incorrect.
The exterior angle of a regular polygon with 4.5 sides is not possible since the number of sides in a polygon must be a positive integer.
The interior angle of a regular polygon with 4.5 sides is not possible since the number of sides in a polygon must be a positive integer.
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Please help me I need to get my grade up!
The measure of ∠XYZ is 130°. Option C is the correct option.
What is an isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. Sometimes it is stated to have exactly two sides that are the same length, and other times it is stated to have at least two sides that are the same length, with the latter version including the equilateral triangle as an exception.
Given that the length of YZ = YX and ∠YZX = 25°.
There is an agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.
According to the property of the isosceles triangle:
∠YXZ = ∠YZX = 25°
The sum of all angles of a triangle is 180°.
Therefore,
∠YXZ + ∠YZX + ∠XYZ = 180°
25° + 25° + ∠XYZ = 180°
50° + ∠XYZ = 180°
∠XYZ = 180° - 50°
∠XYZ = 130°
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The size of a certain cell is 2.5 x 10-° m. Another cell is 1.5 x 103 times larger. How large is the larger cell in scientific notation?
The correct option: C.) 3.75 x 10^6 m. The size of other larger cell is found as the 3.75 x 10^6 m , written in the scientific notation.
Explain the term scientific notation?In scientific notation, a number is written as the outcome of two other numbers: the coefficient and a power of 10. It is an excellent tool for handling extremely huge or extremely small quantities.The power-of-10 notation, often known as scientific notation, is a way to express exceedingly big and small numbers.The size of one smaller cell : 2.5 x 10^-9 m.
The size of other larger ball: 1.5 x 10^3 times larger than first ball.
For the size of other larger ball:
Size = 2.5 x 10^-9 x 1.5 x 10^3
Size = 2.5 x 1.5 x 10^(-9+3)
Size = 3.75 x 10^6 m
Thus, the size of other larger cell is found as the 3.75 x 10^6 m , written in the scientific notation.
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The correct question is-
The size of a certain cell is 2.5 x 10^-9 m. Another cell is 1.5 x 10^3 times larger. How large is the larger cell in scientific notation?
A.) 4 x 10^-27m
B.) 4 x 10^-12m
C.) 3.75 x 10^6m
D. 3.75 x 10^-6m
How to solve 3x+4y=10, 2x+5y=9 in using graphical method.
Answer:(-2,4) (6,-2)
Step-by-step explanation: 1.We solve the equation with x = -2 and get y = 4 , (-2,4) which is a coordinate
2. we solve the equation with x=6 and gets y= -2 (6,-2) is a coordinate
Mark these two coordinates to get a line in the graph!
Expand this equation to write an identity: (a-b)^3
The equation using the identity rule is a^3 - 3a^2b + 3ab^2 - b^3
How to expand the equation using the identity ruleThe equation (a-b)^3 can be expanded using the binomial theorem, where the variables are the two numbers (a and b),
From the question, we have the following parameters that can be used in our computation:
(a-b)^3
When expanded, we have
a^3 - 3a^2b + 3ab^2 - b^3
Hence, the expansion is a^3 - 3a^2b + 3ab^2 - b^3
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Help me please you will be blessed
Answer:
3+[tex]\frac{1}{4}w[/tex] represents the distance ran on week w
Identify the initial amount a
and the rate of decay r
(a a percent) of the exponential function h(t)=1250(0. 865)t. Evaluate the function when t=3. Round your anwer to the nearet tenth
The initial amount a is 1250 and the rate of decay r is 0.865 (86.5%). When t = 3, the function h(t) = 1250(0.865)3 = 587.356. Rounded to the nearest tenth, the answer is 587.4.
To solve this exercise, you need to use the equation
h(t) = a(r)^t,
Where a is the initial amount and r is the rate of decay.
In this example,
a = 1250 and r = 0.865 (86.5%).Plugging in t = 3 into the equation gives
h(t) = 1250(0.865)^3 = 587.356.
To round this to the nearest tenth, you need to look at the number to the right of the decimal point, which is the 6 in 587.356. Since the 6 is 5 or greater, you need to round the 587.356 up to 587.4.
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A seedling Jeffery planted in 2009 was 5cm tall in 2010 it was 120 cm to find the percent increase in the height of the seedling
The percent increase in the height of the seedling is, 23%.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
A seedling Jeffery planted in 2009 was 5cm tall in 2010 it was 120 cm
i.e. increase in the height = 120-5
=115 cm
now,
the percent increase in the height of the seedling is,
115/5*100
=23%
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What are two numbers that multiply to -60 and add to -7
The two numbers that multiply to -60 and add up to -7 are:
[tex]-12,5[/tex]
We can multiply -12 by 5 and get -60:
[tex]-12\times5=-60[/tex]
We can also add -12 and 5 to get -7:
[tex]-12+5=-7[/tex]
So therefore, the two numbers that multiply to -60 and add to -7 are:
[tex]\fbox{-12 and 5}[/tex]
Which equation is equivalent to the given equation? x^2-6x=8
Answer:
Where are the choices?
Step-by-step explanation:
A pupil who scored 50 in his paper 1 exam got ill and missed paper 2 use the line of best fit and predict what his paper 2 mark would’ve been.
The marks in paper 2 would be 100.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a pupil who scored 50 in his paper 1 exam got ill and missed paper 2.
Assume the equation of the line of best fit is of the form -
y = mx + c
Let {c} = 0
Now, for the point (1, 50), we can write -
50 = m
So, the equation will be of the form -
y = 50x
Now, for {x} = 2, we can write -
y = 100
Therefore, the marks in paper 2 would be 100.
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what is the benefit of using a curve over a histogram?
The benefit of using a curve over a histogram is that, it is a useful tool for visualizing data distributions, curves provide a more detailed and flexible representation of the data and offer additional advantages in terms of resolution, flexibility, parametric modeling, and comparison.
Visualizing data is an essential aspect of understanding the underlying patterns and relationships. In data analysis, two popular ways of visualizing data are histograms and curves. While both of these visualization techniques serve the purpose of summarizing data, each of them has its unique benefits and limitations.
Resolution: One of the main benefits of using a curve over a histogram is that a curve provides a higher resolution representation of the data. A curve can capture finer details of the data distribution that might get lost in a histogram due to the binning process.
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5(
–
4+k)+
–
2(
–
3+
–
10k) can you help me please
Answer:
answer for the expression 5(–4+k) + –2(–3+–10k) is -5k - 6.
To arrive at this answer, we used the order of operations (PEMDAS) as follows:
Parentheses first: (–4+k) = k-4 and (–3+–10k) = –10k-3
Next, the multiplication: 5(k-4) = 5k-20 and -2(-10k-3) = 20k+6
Finally, the addition: -5k-20 + 20k+6 = -5k - 6 + 20k
And then we simplify further by combining the like terms:
-5k - 6 + 20k = -5k + 20k - 6 = 15k - 6
So the final answer is -5k -6
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The price of a camera is marked down
from $315 to $287. What is the
percent change for this camera?
The percent change for this camera is 9.756%.
What is Markdown Percentage?Markdown percentage is defined as the decrease in the price which is calculated as a percent of the selling price.
Given that,
Original selling price of the camera = $315
Selling price has been decreased to $287
Mark down percentage = (315 - 287) / 287
= 0.09756
= 9.756%
Hence the rate of the markdown percentage is 9.756%.
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luna sold 2 pairs of her old jazzy jumper sneakers at the step again secondhand store. before she left, luna spent $12 of her earnings on a used pair of dress shoes. she had $6 remaining. which equation can you use to find the amount of money, x, luna received for each pair of sneakers?
Luna received 9 dollar for each pair of sneakers. She got total 18 dollars for her 2 pairs of sneakers. The equation which we can use to find the amount of money x= total money spent+ money remained.
It is given that, total pair of jumper sneakers she sold at the secondhand market = 2 pairs.
So, total sneakers= 4
Let, she got total x dollar for her jumpy sneakers.
So, here, total money spent= 12 dollars
total money left with her= 6 dollars
Hence, x= 12+ 6 dollars = 18 dollars.
So, total money she got = 18 dollars.
Money for each pair of sneakers= 9 dollars.
Equation for x= total money spent+ money left with her.
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1. A fractions value is 4/5 when it’s numerator is increased by 9 the new fraction equals the reciprocal of the value of the original fraction. Find the fraction
The value of the original fraction is expressed as; 36/45
How to solve Fraction Problems?Let the numerator be x and let the denominator be y. Thus;
Original fraction = x/y
Reciprocal of fraction = y/x
x/y = 4/5
Cross multiply to get;
5x = 4y
4y - 5x = 0 -----(1)
The numerator is now increased by 9 and the new fraction equals the reciprocal of the value of the original fraction. Thus;
(x + 9)/y = 5/4
Cross multiply to get;
4x + 36 = 5y
5y - 4x = 36 ------(2)
Multiply eq 1 by 4 and eq 2 by 5 to get;
16y - 20x = 0 -----(3)
20y - 20x = 180 ----(4)
Subtract eq 3 from 4 to get;
4y = 180
y = 180/4
y = 45
5x = 4y
x = (4/5) * 45
x = 36
Original fraction is; 36/45
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given 2 3 2 3 ½sij¼ 4 5 and ½ai¼ 1 102 012 4 2 5; 303 3 evaluate (a) sii, (b) sijsij, (c) sjisji, (d) sjkskj, (e) amam, (f) smnaman, and (g) snmaman.
The evaluation of (a) sii, (b) sijsij, (c) sjisji, (d) sjkskj, (e) amam, (f) smnaman, and (g) snmaman was done by using the corresponding formulas and the given values. The results were 3, 6, 6, 6, 2, 6, and 24 respectively.
To evaluate (a) sii, we will use the formula sii = ai + bi. In this case, ai = 1 and bi = 2, so sii = 1 + 2 = 3.
To evaluate (b) sijsij, we will use the formula sijsij = ai × bi. In this case, ai = 2 and bi = 3, so sijsij = 2 × 3 = 6.
To evaluate (c) sjisji, we will use the formula sjisji = aj × bj. In this case, aj = 2 and bj = 3, so sjisji = 2 × 3 = 6.
To evaluate (d) sjkskj, we will use the formula sjkskj = ak × bk. In this case, ak = 3 and bk = 2, so sjkskj = 3 × 2 = 6.
To evaluate (e) amam, we will use the formula amam = ai × aj. In this case, ai = 1 and aj = 2, so amam = 1 × 2 = 2.
To evaluate (f) smnaman, we will use the formula smnaman = ai × aj × ak. In this case, ai = 1, aj = 2, and ak = 3, so smnaman = 1 × 2 × 3 = 6.
To evaluate (g) smnaman, we will use the formula smnaman = ai × aj × ak × bm. In this case, ai = 1, aj = 2, ak = 3, and bm = 4, so smnaman = 1 × 2 × 3 × 4 = 24.
The evaluation of (a) sii, (b) sijsij, (c) sjisji, (d) sjkskj, (e) amam, (f) smnaman, and (g) snmaman was done by using the corresponding formulas and the given values. The results were 3, 6, 6, 6, 2, 6, and 24 respectively.
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