Answer:
Your answer is 4cm.
Step-by-step explanation:
simple calculation
x (12+x) π = 32 π
x = 4cm
On June 10, Metlock, Inc. purchased $7,400 of merchandise on account from Monty Company, FOB shipping point, terms 3/10, n/30. Metlock, Inc. pays the freight costs of $560 on June 11. Goods totaling $600 are returned to Monty for credit on June 12. On June 19, Metlock, Inc. pays Monty Company in full, less the purchase discount. Both companies use a perpetual inventory system.
Prepare separate entries for each transaction on the books of Metlock, Inc.
According to the given data in question below given are the separate journal entries for each transaction on the books of Metlock, Inc.
What is entries?"Entries" typically refers to the individual values in a matrix or table. A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns, while a table is an arrangement of data in rows and columns with each intersection representing a single piece of data.
1.On June 10, Metlock, Inc. made an account-based purchase from the Monty Company for $7,400 in goods, FOB shipping point, 3/10, n/30.
Inventory (asset) $7,400
Accounts payable (liability) $7,400
2. On June 11, Metlock, Inc. pays the freight costs of $560:
Freight expense (expense) $560
Cash (asset) $560
3. On June 12, goods totaling $600 are returned to Monty for credit:
Accounts payable (liability) $600
Inventory (asset) $600
4. On June 19, Metlock, Inc pay Monty Company in full, less the purchase discount:
Accounts payable (liability) $7,400
Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]
Cash (asset) $7,178
Note that the purchase discount is calculated as $7,400 x 3%, or $222.
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The information in issue below is taken from Metlock, Inc.'s books, which include separate journal entries for each transaction.
Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]
Cash (asset) $7,178
What is entries?1.On June 10, Metlock, Inc. made an account-based purchase from the Monty Company for $7,400 in goods, FOB shipping point, 3/10, n/30.
Inventory (asset) $7,400
Accounts payable (liability) $7,400
2. On June 11, Metlock, Inc. pays the freight costs of $560:
Freight expense (expense) $560
Cash (asset) $560
3. On June 12, goods totaling $600 are returned to Monty for credit:
Accounts payable (liability) $600
Inventory (asset) $600
4. On June 19, Metlock, Inc pay Monty Company in full, less the purchase discount:
Accounts payable (liability) $7,400
Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]
Cash (asset) $7,178
Note that the purchase discount is calculated as $7,400 x 3%, or $222.
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Find the measure of x
Answer:
≈ 11,88
Step-by-step explanation:
Use trigonometry:
cos (62∘) = 8 / x
x = 8 / cos (62∘) ≈ 11,88
I need help with this please
Yolanda will spend a total of 3 hours / 9 tables,
or **1/3 hour per table**, if she spends an equal amount of time at each table.
How many guests can Yolanda accommodate in total?Yolana can serve a total of 36 people if she has to serve 9 tables, each of which can hold 4 guests, and she must serve a total of 4 guests per table.
How long does each visitor spend on average?
We need to know the entire length of time Yolana will spend serving all 36 guests in order to calculate the average time spent per guest.
If the entire time is divided by the number of guests,we get:
36 people in 3 hours equals 5 minutes each person.
Thus, each visitor spends 5 minutes on average.
What is the average time?
A measurement of a set of time values' central tendency is the average time. It is determined by multiplying the total number of values in the set by the sum of all the time values.
As an illustration, if you have a series of times of 5, 10, and 15, you would add them all up to reach 30 minutes, divide that number by 3, and get an average time of 10 minutes.
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How many solutions does this nonlinear system of equations have?
Answer:
the answer is 0
Step-by-step explanation:
Practice
Use the following data sets for 1 and 2.
Company A sales: $1,000; $5,000; $5,500;
$6,000; $6,000; $7,000; $7,000; $7,000; $8,000;
$8,500; $9,000
Median: 7,000 IQR: 2,500
Company B sales: $3,000; $4,000; $4,000;
$5,000; $5,500; $6,000; $6,500; $6,500; $7,000;
$7,000; $10,000
Median: 6,000 IQR: 3,000
1. How can you use the median to interpret the
amounts of sales?
After answering the presented question, we can conclude that Yet, we equation cannot make final decisions based just on the median.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
Whether data is sorted in ascending or descending order, the median is the midway value. In this situation, the median sales amount for Company A is $7,000, which suggests that half of the sales are greater than $7,000 and half are less. The median sales amount for Business B is $6,000, which means that half of the sales are greater than $6,000 and half are less.
The median can be a useful approach to summaries a data set's core tendency. For example, we can see that Company A has a greater median sales amount than Company B, implying that Company A generates more money each sale on average. Yet, we cannot make final decisions based just on the median.
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Please help with number 3!! Thank you so much!
Answer:
[tex]\cos^2x+\cos x-1+\sin^2x[/tex] can be simplified to [tex]\cos x[/tex]
Step-by-step explanation:
Given
[tex]\cos^2x+\cos x-1+\sin^2x[/tex]
We need to use the Pythagorean trig identity in this example.
[tex]\sin^2x+\cos^2x=1[/tex]
Lets simplify.
We can use the Commutative and Associative Properties of Addition to reorder the equation.
[tex]\sin^2x+\cos^2x+\cos x-1[/tex]
Apply the Pythagorean trig identity to [tex]\sin^2x+\cos^2x[/tex].
[tex]1+\cos x-1[/tex]
Group like terms.
[tex]\cos \left(x\right)+\left(1-1\right)[/tex]
1 minus 1 is zero.
That leaves us with
[tex]\cos x[/tex]
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Points Scored by Teams
Team Points
A 30
B 35
C 20
D 30
E 15
mean of points=____
-21
-26
-22
To find the mean of the points scored by the teams, we need to add up all the points and divide by the number of teams:
Mean = (30 + 35 + 20 + 30 + 15) / 5
Mean = 130 / 5
Mean = 26
Therefore, the mean of the points scored by the teams is 26.
Answer:
answer is 26
Step-by-step explanation:
add the five numbers and divide them by the number you add them(that means by 5) and it comes
[tex] \frac{30 + 35 + 20 + 30 + 15 \\}{5} = \frac{130}{5} = 26[/tex]
two students sit in the first row and in the second row, 2 students sit behind each of those students how many students sit in the second row?
Answer: 4
Step-by-step explanation:
If there are two students in the first row and two students sit behind each of those students in the second row, then there are a total of 2 x 2 = 4 students in the second row.
Th ee even numbers sum up to 108. The smaller
is half the larger and the middle number is 3/4 the larger. What are the three numbers
Answer:
24, 36, 48.
Step-by-step explanation:
Represent the three even numbers as 2x, 2y, 2z, where x,y,z are integers.
2x+2y+2z = 108
x+y+z = 54
Let x≤y≤z
x = z/2
y = ¾z
z/2 + 3z/4 + z = 54
2z/4 + 3z/4 + 4z/4 = 54
2z + 3z + 4z = 216
9z = 216
z = 24
x = z/2 = 12
y = ¾z = 18
Therefore, The numbers are 24, 36, 48.
Find the EAR in each of the following cases: 10% compounded monthly
Answer:
Step-by-step explanation:
ear
13) Jason is 9 miles ahead of Joe running at 5.5 miles per hour and Joe is
running at the speed of 7 miles per hour. How long does it take Joe to catch
Jason?
A. 3 hours
B. 4 hours
C. 6 hours
D. 8 hours
Joe will catch Jason in 6 hours running at 7mph while Jason is running at 5.5 mph .
Given,
Jason is 9 miles ahead of Joe running at 5.5 miles per hour and Joe is running at the speed of 7 miles per hour.
Now,
Joe speed is more than Jason.
So,
Differences in speed:
(7 - 5.5) = 1.5 miles per hour.
Now,
Jason is ahead of joe by 9 miles.
To cover 9 miles of distance by joe to catch jason,
Distance = Speed * Time
9 miles = 1.5mph* Time
Time = 6hours.
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A 15-foot ladder is leaning against a wall. If we pull the ladder away from
the wall at a rate of 2 ft/s, how fast is the top of the ladder moving down
the wall when the bottom of the ladder is 12 ft from the wall?
Answer:
Step-by-step explanation:
Inductive logic---
State the two characteristics that tend to make a sample representative of the population from which it is taken:
The size of the sample required to be representative depends on the variability of the population and the level of precision required in the analysis.
What is Inductive logic ?
Inductive logic, also known as induction, is a type of reasoning that involves drawing general conclusions based on specific observations or examples.
In inductive logic, a sample is considered representative of the population from which it is taken if it possesses the following two characteristics:
Randomness: The sample should be selected randomly from the population. This means that every individual in the population should have an equal chance of being selected for the sample. A random sample helps to reduce the potential for bias in the selection process.
Size: The sample size should be large enough to accurately represent the population. A larger sample size helps to reduce the impact of chance variation and provides a more accurate estimate of the characteristics of the population.
Therefore, The size of the sample required to be representative depends on the variability of the population and the level of precision required in the analysis.
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Every week at the Cougar Scouts meeting, Caden is in charge of the craft activity. This week, he decides to make pinecone bird feeders. At the meeting, Caden divides a bag of birdseed evenly among 12 Cougar Scouts, and each scout gets 1/2 of a cup of birdseed
There are 4 cups of birdseed in the bag.
Describe Algebra?Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols to solve equations and understand mathematical relationships. It involves the use of letters and symbols to represent variables and numbers, and the manipulation of these variables and numbers using rules and operations such as addition, subtraction, multiplication, and division. The main goal of algebra is to solve equations, which involves finding the value of an unknown variable that satisfies the given equation.
In algebra, equations are often represented graphically as lines or curves on a coordinate plane, which allows for a visual representation of mathematical relationships. Algebraic equations are used in a variety of fields, including physics, engineering, finance, and computer science.
The study of algebra starts with basic arithmetic concepts and progresses to more complex topics such as linear equations, quadratic equations, and functions. The ability to understand and manipulate algebraic expressions is an essential skill in many areas of life, from solving practical problems to understanding complex mathematical theories.
If each of the 16 Cougar Scouts gets 1/4 of a cup of birdseed, then the total amount of birdseed in the bag can be found by multiplying the amount given to each scout by the number of scouts:
Total birdseed = (1/4) x 16 = 4 cups
Therefore, there are 4 cups of birdseed in the bag.
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The complete question is:
Frank is 5 years older than Mary. In 5 years, Frank will be twice as old as Mary is now. How old is Frank now?
A. 10
B. 15
C. 20
D. 25
E. 30
Answer:
Step-by-step explanation:
Line plot titled, Width of Crocus Plants. There is a line labeled, Width in Centimeters. There are tick marks representing values from 8 to 10, partitioned into tenths. Each fifth tick mark is labeled with a decimal number, 8, 8 and 5 tenths, 9, 9 and 5 tenths, and 10. There is one mark above the first tick mark after 8. There are two marks above the third tick mark after 8. There is one mark above the second tick mark after 8 and 5 tenths. There are 3 marks above the first tick mark after 9. There is one mark above the first tick mark after 9 and 5 tenths. There is one tick mark above the third tick mark after 9 and 5 tenths. There is one mark over 10. What is the total width of the plants that are 8.5 cm or less? 3 centimeters 24 centimeters 24.7 centimeters 30 centimeters
George is given two circles, Circle O and circle X, as shown. If he wants to prove that the two circles are similar, what would be the correct second step in his proof? Given: The radius of circle O is r, and the radius of circle X is r'. Prove: Circle O is similar to circle X.
Answer:
Step-by-step explanation:
you need to show us what circle x looks like
Find A×A if,
A={x: 4 ≤ x ≤ 7, x ∈ W }
Note: W means whole number!
A×A is the set {16, 20, 24, 28, 20, 25, 30, 35, 24, 30, 36, 42, 28, 35, 42, 49}
To find A×A, we need to first understand what A represents.
In mathematics, a set is a well-defined collection of distinct objects, called elements or members of the set. These objects can be anything, such as numbers, letters, or even other sets. The elements of a set are typically enclosed in curly braces { } and are separated by commas.
A is a set defined as the set of all whole numbers, x, where 4 ≤ x ≤ 7. In other words, A contains the elements 4, 5, 6, and 7.
To find A×A, we need to take each element in A and multiply it by every other element in A. This means that we need to find the product of (4, 4), (4, 5), (4, 6), (4, 7), (5, 4), (5, 5), (5, 6), (5, 7), (6, 4), (6, 5), (6, 6), (6, 7), (7, 4), (7, 5), (7, 6), and (7, 7).
When we do the multiplication, we get the set {16, 20, 24, 28, 20, 25, 30, 35, 24, 30, 36, 42, 28, 35, 42, 49}.
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A pizza restaurant offers thin crust or deep dish pizzas. This weekend, they have a special offer that includes 1 meat topping of
either pepperoni or sausage, and 2 vegetable toppings chosen from onions, black olives, and peppers. The different pizzas are
listed in the table shown.
Answer:
25%
Step-by-step explanation:
Randall recorded the total number of comic books in five different school libraries.
Rank the libraries from 1 having the
GREATEST total number of comic books to 5 having the LEAST total number of comic books.
Library A: 30 comic books are 2% of its total books.
Library B: 45 comic books are 5% of its total books.
Library C: 65 comic books are 2% of its total books.
Library D: 75 comic books are 10% of its total books.
Library E: 90 comic books are 3% of its total books.
To rank the libraries from 1 having the greatest total number of comic books to 5 having the least total number of comic books, we need to first calculate the total number of books in each library.
Let's start by using the information given to find the total number of books in each library:
For Library A, we know that 30 comic books are 2% of its total books. So, we can set up the following equation:
30 = 0.02x
where x is the total number of books in Library A. Solving for x, we get:
x = 1500
Therefore, Library A has a total of 1500 books.
For Library B, we know that 45 comic books are 5% of its total books. So, we can set up the following equation:
45 = 0.05x
where x is the total number of books in Library B. Solving for x, we get:
x = 900
Therefore, Library B has a total of 900 books.
For Library C, we know that 65 comic books are 2% of its total books. So, we can set up the following equation:
65 = 0.02x
where x is the total number of books in Library C. Solving for x, we get:
x = 3250
Therefore, Library C has a total of 3250 books.
For Library D, we know that 75 comic books are 10% of its total books. So, we can set up the following equation:
75 = 0.1x
where x is the total number of books in Library D. Solving for x, we get:
x = 750
Therefore, Library D has a total of 750 books.
For Library E, we know that 90 comic books are 3% of its total books. So, we can set up the following equation:
90 = 0.03x
where x is the total number of books in Library E. Solving for x, we get:
x = 3000
Therefore, Library E has a total of 3000 books.
Now that we have the total number of books in each library, we can rank them based on the number of comic books they have:
Library C: 65 comic books
Library E: 90 comic books
Library B: 45 comic books
Library A: 30 comic books
Library D: 75 comic books
Therefore, the libraries ranked from 1 having the greatest total number of comic books to 5 having the least total number of comic books are: C, E, B, A, D.
Help me with this question
Step-by-step explanation:
gradient= 12-10/10-9
= 2
y=mx+c
c= -8
y= 2x-8
when x= -1,
y= 2(-1)-8
= -2-8
= -10
when x= 5,
y= 2(5)-8
= 10-8
= 2
Calculate 7 × 3 1/4 The answer is Choose... and Choose... fourths.
The value of the product 7 × 3 1/4 is 22 3/4
How to determine the valueIt is important to note that fractions are defined as the part of a whole variable, element or number.
There are different types of fractions, such as;
Mixed fractionsSimple fractionsProper fractionsImproper fractionsComplex fractionsFrom the information given, we have;
7 = A whole number
3 1/4 = a mixed fraction
Let's convert it to an improper fraction by multiplying the denominator by the whole number, then adding the numerator
13/4
Multiply the values
7 × 13/4
91/4
Divide the values
22 3/4
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A party hat is shape of a cone has a volume of 199 cubic inches which of the following is the closest to height
Answer:
200
Step-by-step explanation:
199+1
An investor needs $19,000 in 12 years.
(a) What amount should be deposited in a fund at the end of each quarter at 7% compounded quarterly so
that there will be enough money in the fund?
(b) Find the investor's quarterly deposit if the money is deposited at 7.2% compounded quarterly.
The solution of the given problem of percentage comes out to be $19,000 in 12 years, they should deposit $170.89 at the conclusion of each quarter.
What is percentage?The abbreviation "a%" is used to indicate a value or number in statistics that is expressed as a percentage of 100. Versions with "pct," "pct," or "pc" as the initials are also rare. However, the most popular method to do this is to use the percentage symbol ("%"). Additionally, both hints nor a constant ratio of every element to the overall amount exist. Since numbers commonly add up to 100, they are essentially integers.
Here,
=> [tex]FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n)[/tex].
By entering these numbers, we obtain:
[tex]= > 19000 = PMT * [(1 + 0.07/4)^(4*12) - 1] / (0.07/4)[/tex]
Upon solving for PMT, we obtain:
[tex]= > PMT = 19000 * (0.07/4) / [(1 + 0.07/4)^(4*12) - 1][/tex]
=> PMT = $174.58 (rounded to the nearest cent)
In order to have $19,000 in 12 years, the investor needs to deposit $174.58 at the conclusion of each quarter at a rate of 7% compounded quarterly.
(b) Using the same procedures as in (a), but with an interest rate of 7.2%, we arrive at:
[tex]= > 19000 = PMT * [(1 + 0.072/4)^(4*12) - 1] / (0.072/4)[/tex]
Upon solving for PMT, we obtain:
[tex]= > PMT = 19000 * (0.072/4) / [(1 + 0.072/4)^(4*12) - 1][/tex]
=> PMT = $170.89 (rounded to the nearest cent)
In order to have $19,000 in 12 years, they should deposit $170.89 at the conclusion of each quarter.
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At the annual school track meet, two sprinters will race for 80 meters.
Sprinter A runs 9 meters per second.
Sprinter B runs 9 meters per second.
Sprinter B is given a 14 meter head start.
Select all the statements that are true.
A. The graphs of these two functions never intersect before the race end.
B. Sprinter B will win the race.
C. Sprinter B is leading the race at the 4 second mark.
The statements that are true with regards to the graph of the functions and the sprinter that wins and lead the race are;
The true statements are; A, B, and C
What is the graph of a function?The graph of a function visually represents the rule of the function showing how the output values of the function changes as the input value varies.
The distance the two sprinter's will run = 80 meters
The speed of sprinter A = 9 meters per second
The speed of sprinter B = 9 meters per second
The head start of sprinter B = 14 meter
The analysis of the statements are as follows
A. The graph of the functions representing the speeds of the sprinters have the same slope of 9 which is the rate of change of distance with time, therefore, the graphs are parallel and will never intersect.
The statement is therefore; True
B. Sprinter B will win the race. - True
Sprinter B has a head start of 14 meters and both sprinters have the same speed, therefore, sprinter B will reach the finish line first and win the race.
C. Sprinter B is leading the race at the 4 seconds mark;- True
Sprinter A will cover a distance of 9 m/s × 4 s = 36 m at the 4 seconds mark, while sprinter B will cover a distance in the 80 m race of 9 m/s × 4 s + 14 m = 50 m at the 4 second mark, therefore, sprinter B will be leading at the 4 second mark
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The thermostat in an apartment is set to 75°F while the owner is awake and to 60°F while the
owner is sleeping. The function W gives the temperature W(z), in degrees Fahrenheit, in the
apartment 2 hours after midnight. When it is hot outside, the owner changes the settings to be
exactly 10 degrees warmer than W to save energy. The function H gives the temperature H(2),
in degrees Fahrenheit, z hours after midnight when it is hot outside.
a.
If W (6.5) = 75, then what is the corresponding point on H? Use function notation to
describe the point on H.
НО
b.
If W (2) = 60, then what is the corresponding point on H? Use function notation to describe
the point on H.
НО
c. Write an expression for H in terms of W.
H(x) =
Using expressions, we can get the following:
a. If W (6.5) =75, H (6.5) = 85
b. If W (2) = 60, H (2) = 70
c. W (x) + 10
Define expressions?Expressions are statements in mathematics that include variables, numbers, or both, as well as at least two terms connected by an operator. Addition, subtraction, multiplication, and division are examples of mathematical operations.
The equation x + y, which combines the terms x and y with an addition operator, serves as an illustration. Expressions can be classified into two categories in mathematics: algebraic expressions, which also contain variables, and numerical expressions, which only contain numbers.
W(x) gives the temperature W in the apartment x hours after midnight.
H(x) gives the temperature H x hours after midnight when it is hot outside.
When it is hot outside, the owner changes the settings to be exactly 10 degrees warmer than W.
So,
H (x) = W(x) + 10
If W (6.5) =75, then
H (6.5) =W (6.5) + 10
= 75+10
= 85
If W (2) = 60, then
H (2) = W (2) + 10
= 60+ 10
= 70
The expression of H in terms of W:
W (x) +10
Hence the equation:
H(x) = w(x) + 10
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How much do we need to invest each year at a rate of 8% compounded annually so that we have a total of $600,000 saved in 25 years?
Answer:
In this problem, we have to use the formula
[tex]P= \frac{A}{(1+\frac{r}{n})^{nt} }[/tex]
A = $600,000.00
n = 1 (annually)
t = 25 years
First, convert R as a percent to r as a decimal
r = R/100
r = 8/100
r = 0.08 per year,
Then, solve the equation for P
[tex]P= \frac{A}{(1+\frac{r}{n})^{nt} }[/tex]
[tex]P= \frac{6000000}{(1+\frac{0.8}{1})^{1*25} }[/tex]
P = $87,610.74
The principal investment required to get a total amount of $600,000.00 from compound interest at a rate of 8% per year compounded annually over 25 years is $87,610.74.
2x − 3y = -5 y = 2 + x The value of x in the system of equations is: x = -1. x = -3. x = 1. x = 3.
Answer: We can solve this system of equations by substituting the expression for y in terms of x from the second equation into the first equation, and then solving for x.
First, we substitute y = 2 + x from the second equation into the first equation, giving:
2x - 3(2 + x) = -5
Simplifying this expression by distributing the -3, we get:
2x - 6 - 3x = -5
Combining like terms, we get:
-x - 6 = -5
Adding 6 to both sides, we get:
-x = 1
Multiplying both sides by -1, we get:
x = -1
Therefore, the value of x in the system of equations is -1.
Step-by-step explanation:
Help really hard please
Answer:
[tex]\large\boxed{\tt x^{\frac{5}{6}} + 2x^{\frac{7}{3}}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to simplify the given expression.}[/tex]
[tex]\textsf{We should use the \underline{Distributive Property, and Rule of Multiplying Exponents.}}[/tex]
[tex]\boxed{\begin{minipage}{25 em} \underline{\textsf{\large Distributive Property;}} \\ \\ \textsf{Distributive Property is a property that allows us to multiply the term to the left of the parentheses with the terms inside the parentheses.} \\ \\ \underline{\textsf{\large Example;}} \\ \tt a(b+c) = \boxed{\tt ab+ac} \end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{25 em} \underline{\textsf{\large Rule of Multiplying Exponents;}} \\ \\ \textsf{Whenever we have to multiply 2 terms with exponents, it's important to know the Rule of Multiplying Exponents. This rule states that whenever 2 exponential terms multiply together, their exponents add together. }\\ \\ \underline{\textsf{\large Example;}} \\ \tt x^{3} \times \tt x^{4} = x^{3+4} = \boxed{\tt x^{7}} \end{minipage}}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\textsf{We should first use the Distributive Property, then use the Rule of Multiplying}[/tex]
[tex]\textsf{Exponents.}[/tex]
[tex]\tt x^{\frac{1}{3}} (x^{\frac{1}{2}} + 2x^{2})[/tex]
[tex]\underline{\textsf{Use the Distributive Property;}}[/tex]
[tex]\tt x^{\frac{1}{3}} (x^{\frac{1}{2}} + 2x^{2}) = (x^{\frac{1}{3}} \times x^{\frac{1}{2}}) + (x^{\frac{1}{3}} \times 2x^{2})[/tex]
[tex]\underline{\textsf{Use the Rule of Multiplying Exponents;}}[/tex]
[tex]\tt (x^{\frac{1}{3}} \times x^{\frac{1}{2}}) + (x^{\frac{1}{3}} \times 2x^{2}) = x^{\frac{1}{3} + \frac{1}{2}} + 2x^{\frac{1}{3} + \frac{2}{1} }[/tex]
[tex]\underline{\textsf{Find Common Denominators per fractions;}}[/tex]
[tex]\tt x^{\frac{1}{3} + \frac{1}{2}} + 2x^{\frac{1}{3} + \frac{2}{1}} = x^{\frac{2}{6} + \frac{3}{6}} + 2x^{\frac{2}{6} + \frac{12}{6}}[/tex]
[tex]\underline{\textsf{Add;}}[/tex]
[tex]\tt x^{\frac{2}{6} + \frac{3}{6}} + 2x^{\frac{2}{6} + \frac{12}{6}} = x^{\frac{5}{6}} + 2x^{\frac{14}{6}[/tex]
[tex]\underline{\textsf{Simplify Fractions;}}[/tex]
[tex]\large\boxed{\tt x^{\frac{5}{6}} + 2x^{\frac{7}{3}}}[/tex]
The average width of a movie theater seat is 23 inches. Thirty years ago, the typical movie theater seat was approximately 19 inches wide. Current movie theater seats are what percent of a theater seat from 30 years ago?