The total number of students in the vans and buses is 484
Describe Algebra?Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols to solve equations and understand the relationships between variables. In algebra, letters or symbols are used to represent unknown values or variables, and equations are used to describe the relationships between these variables.
Algebraic expressions and equations involve mathematical operations such as addition, subtraction, multiplication, and division, as well as more advanced operations such as exponentiation, logarithms, and trigonometric functions. These operations can be used to simplify expressions, solve equations, and analyze mathematical relationships.
Algebra can be divided into several subfields, including:Elementary algebra, which is concerned with the basic concepts and techniques of algebra, such as simplifying expressions, solving equations, and graphing functions.
Abstract algebra, which is concerned with the study of algebraic structures, such as groups, rings, and fields.
Linear algebra, which is concerned with the study of vector spaces and linear transformations.
Algebraic geometry, which is concerned with the study of geometric objects defined by algebraic equations.
Algebra has many practical applications in various fields, including science, engineering, economics, and computer science. It is used to model and analyze real-world problems, such as population growth, interest rates, and inventory management. It is also used in cryptography, where it is used to design secure encryption and decryption algorithms.
Let's start by using algebra to represent the information given in the problem.
Let x be the number of students in each van and each bus. Since every van had the same number of students as every bus, we can say that the total number of students in the vans and buses is:
10(x) + 12(x) = 256
Simplifying, we get:
22x = 256
Dividing both sides by 22, we get:
x = 11.6363636...
Since we can't have a fraction of a student, we need to round x to the nearest whole number. We have two options: rounding up to 12 or rounding down to 11.
If we round x up to 12, then each van and each bus had 12 students. The total number of students in the vans and buses is:
10(12) + 12(12) = 240
This is not equal to the given total of 256, so rounding up to 12 is not a valid solution.
If we round x down to 11, then each van and each bus had 11 students. The total number of students in the vans and buses is:
10(11) + 12(11) = 220 + 264 = 484
This is not equal to the given total of 256, so rounding down to 11 is not a valid solution either.
Therefore, there is no whole number solution for the number of students in each van and each bus. We can interpret this to mean that there was not an equal number of students in each van and bus. Alternatively, we can interpret this to mean that there was an error in the information given in the problem.
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Prove the statement below that we explored in class, but prove it differently from the notes, rather do it by applying the “ working backwards” technique:
If x > 0, then x + (1/x) = and > 2
The solution is, x²-14x+24
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Given:
x=12, x=2
Solution: In order to determine the quadratic equation we need to move the integers onto the side where x is and then distribute.
Move the integers
Solution #1
x-12 = 0
Solution #2
x-2=0
Create and expression and distribute
(x-12)(x-2)=0
solving we get,
x²-14x+24 = 0
Therefore, after completing the steps we were able to determine that the quadratic equation that will have solutions of x = 12 and x = 2 is x^2 - 14x + 24.
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What is 8.45 rounded to the nearest tenth
Answer:
8.5
Step-by-step explanation:
Where is the tenths place in a decimal?If you look at a decimal (0.00) there is the tenths, (0.00), hundredths (0.00), and so on.
What does it mean to round?Rounding to the nearest tenth, would mean first looking at the hundredths place (8.45), and if it is greater or equal to 5, which if it is, you round up, but if it isn't, you round down.
8.45 = 8.5Therefore, 8.45 rounded to the nearest tenth is 8.5.
Ryan pays a deposit for the sofa then pays the rest of the cost in 24 equal payments of
£112.50
b) How much was the deposit?
Answer:
£2,700
Step-by-step explanation:
Ryan pays a deposit for the sofa then pays the rest of the cost in 24 equal payments of £112.50 b) How much was the deposit?
If Ryan paid the rest of the cost in 24 equal payments of £112.50, then the deposit would have been the total cost minus the total amount of the 24 payments, which is £2,700. Therefore, the deposit was £2,700.
Let Y be a Binomial variable counting the number of successes in
120 independent trials where the probability of success at each trial is
0.52; that is, Y~Bin(120,0.52).
Use the pbinom function in R to find P(60 < Y ≤ 70), giving your answer to three decimal places.
The answer is 0.294. This can be found by using the pbinom function in R.
What is function?Function is the process or state of instruction that text inputs performance is specific tax and produce an output functional key components of programming language allowing the quarters to create complex commands with simple instruction for example a function can be used to add two numbers round together or to generate a random number function can also be combined to create more complex sequence of instruction.
This function calculates the cumulative probability of a binomial variable from 0 to a certain value. In this case, the probability of Y being greater than or equal to 60 and less than or equal to 70 is 0.294.
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A central angle is an angle whose vertex is at the center of a circle. Find the AOC
I. The correct statement is: m<AOB = m<BOC
The measures of the angles are:
II. m<BOC = 53 degrees.
III. m<AOC = 106 degrees.
How to Find the Measure of a Central Angle?When a segment bisects an angle, it forms two equal angles. Therefore, we have following which explains how to find the measure of the given central angle.
I. <AOC is bisected by segment OB into: AOB and BOC, which are equal. Therefore:
m<AOB = m<BOC
II. m<AOB = 53 degrees, therefore,
m<BOC = 53 degrees.
III. m<AOC = 2(53)
m<AOC = 106 degrees.
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Add a term to the expression so that it becomes a perfect square trinomial.
y² - 15y +
The expression representing a perfect square trinomial is given as follows:
y² - 15y + 56.25.
What are perfect square trionomial?There are two formats of perfect square trinomial, given as follows:
(x + a)² = x² + 2ax + a².(x - a)² = x² - 2ax + a².For this problem, we have a subtraction sign, meaning that the value of a is obtained as follows:
2ay = 15y
2a = 15
a = 15/2
a = 7.5.
Then the square of a is given as follows:
a² = 7.5²
a² = 56.25.
Meaning that the expression is given as follows:
y² - 15y + 56.25.
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Stand with each of your feet on a separate sheet of paper.
Start to run. What would happen what Newton's Law is this
Answer:
Step-by-step explanation:
Newton's first law of motion, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity, unless acted upon by an external force.
If you are standing on separate sheets of paper and start running, your body will experience a forward motion. However, the sheets of paper under your feet will initially resist the motion due to friction. The force of friction will create an equal and opposite force, causing the sheets of paper to slide backwards. As you continue to run, the friction between your feet and the paper will decrease, and the sheets of paper may eventually stop sliding and you will continue running with a constant velocity.
This is an example of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. The force you apply to the ground when running is the action, and the force of the ground pushing back on you is the reaction.
Como resuelvo esto
X/5=2
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{x}{5} = 2}[/tex]
[tex]\large\textbf{Multiply 5 to both sides:}[/tex]
[tex]\mathsf{\dfrac{x}{5} \times 5= 2\times 5}[/tex]
[tex]\large\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = 2\times 5}[/tex]
[tex]\mathsf{x = 10}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 10}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day\bf !}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
4-23.
En tu hoja, dibuja un triángulo de pendiente con un ángulo de
inclinación de 45°.
Para dibujar un triángulo con un ángulo de inclinación de 45° realiza dos líneas perpendiculares y una tercera línea con un grado de 45° lo cual puedes hacer usando un transportador.
¿Cómo dibujar un triángulo con un ángulo de 45°?Un triángulo es una figura con tres lados y cuyos ángulos internos siempre suman 180°. El método más fácil para dibujar un triángulo con un ángulo de 45° es.
Dibuje dos líneas rectas perpendiculares (líneas que se cortan entre ellas).Dibuje una tercera línea para completar el triángulo usando un transportador para asegura que tenga 45° de inclinación.Aprenda más sobre ángulos en https://brainly.com/question/16701917
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38.8% of Canada's population lives in Ontario. The population of Ontario is 12.9 million. What is the population of Canada?
let the total population be x
Step-by-step explanation:
38.8%of x=12,900,000
x=12,900,000*100/38.8
x=12,900,000*100*10/388
x=33,247,422.680412Points D, E, and F are on circle C and EF ≅ DF.
What is the measure of ∠CDF?
14°
19°
26°
38°
Please explain, I want to know how to get the answer.
Answer:its 1.4>1.3
Step-by-step explanation:I THINK ITS 1.4>1.3
Problems 29,37, and 41
Given IQ scores are approximately normally distributed with a mean of 100 and standard deviation of 20, the proportion of people with IQs above 140 is:
The proportion of people with IQs above 140 is 2.5% of a mean of 100 and standard deviation of 20.
Which proportion do you mean?Comparative magnitude or extent; ratio; the relationship between several entities or components in terms of relative size, number, or degree. the right or ideal relationship between components of a whole; symmetry or balance. If a change in one variable can be expected from a change in the other, two variables are said to be in proportion. For secondary school chemists, there are two separate sorts of proportional relationships: direct proportion and inverse proportion.
When we find the proportion , we obtain:
P(y > 140) = 1 - P(y< 140)
= 1 - P[(x - α) / β < (140 - 100) / 20]
= 1 - P(z < 2)
= 1 - 0.9772
= 0.0228
= 2.5%.
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Please Someone smart help me with this!!
Answer:
See below
Step-by-step explanation:
The linear function is to be expressed in slope-intercept form:
y = mx + c
where:
m = slope
= [tex]\frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]
Select a pair of x and y coordinates of two points along this graph
e.g (0,1) and (5,0):
m = [tex]\frac{(0 - 1)Percent InDecimal}{(5 - 0) hour}[/tex]
= [tex]\frac{-1}{5}[/tex]
∴ slope = [tex]-\frac{1}{5}[/tex] = [tex]-0.2\frac{PercentInDecimal}{hour}[/tex]
which means 0.2 × 100%= 20%
∴The slope indicates that the power decreases by 20% per hour
c = y-intercept:
It is the y-value AT which the graph cuts or meets the y-axis. Its corresponding x-coordinate is 0. The y-intercept can be either read directly from the graph or calculated mathematically
∴y-intercept = 1
In this scenario, the y-intercept indicates the initial value or the value present in the beginning.
which means 1.0 × 100% = 100%
∴The y-intercept indicates that the battery is at 100% when you turn on the laptop.
∴Linear function relating y to x:
Substituting the values of m and c into the above stated equation:
[tex]y = -\frac{1}{5}x + 1[/tex]
The x-intercept is the x-value at which the graph crosses or intersects the x-axis. It’s corresponding y-coordinate is zero.
x-intercept = 5
In this scenario, the x-intercept indicates the point at which the final value is reached or achieved.
∴ The x-intercept indicates that the battery lasts 5 hours.
The battery power is at 75% = [tex]\frac{75}{100}[/tex] = 0.75 (expressed in decimal form. This means y = 0.75, which is to be substituted into the above derived linear function to solve for the corresponding value of x:
[tex]0.75 = -\frac{1}{5}(x) + 1[/tex]
Rearrange the equation to isolate x and make it the subject of the equation:
[tex]\frac{1}{5}x = 1 - 0.75[/tex]
[tex]\frac{1}{5}x = 0.25[/tex]
Cross-multiplication is applied:
[tex](1)(x) = (5)(0.25)[/tex]
x = 1.25 hours
∴The battery power is at 75% after 1.25 hours
What is 5/8 equative to
Answer chooses
0.48
0.6
0.675
Answer: C
Step-by-step explanation:
A boy drops his toy car from the top floor of his house. The time it takes for the toy to fall from a height of 13 feet is given by the equation
h=94−16t^2, where t is the time in seconds. Determine the time it takes the toy to fall to the bottom floor.
It takes the toy car 2.43 seconds to fall to the bottom floor, answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.
Describe Equation?An equation is a mathematical statement that asserts that two expressions are equal. An equation consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=).
For example, 2x + 5 = 11 is an equation, where the left-hand side is 2x + 5 and the right-hand side is 11. This equation asserts that the expression 2x + 5 is equal to 11, and the value of x can be determined by solving for x.
Equations can be simple or complex, and they can involve one or more variables. They can also be linear or nonlinear, depending on the nature of the expressions involved.
Solving an equation involves finding the values of the variables that make the equation true. This may involve applying algebraic operations and simplification techniques to isolate the variable on one side of the equation.
Equations are used in many areas of mathematics, science, engineering, and economics, and they provide a powerful tool for modeling and analyzing real-world situations. They are also used extensively in computer programming and cryptography, where they play a critical role in the development of algorithms and data encryption methods.
We have the equation [tex]h = 94 - 16t^2[/tex], where h is the height of the toy car in feet and t is the time in seconds.
When the toy car reaches the bottom floor, its height will be h = 0. So we can set the equation equal to 0 and solve for t:
[tex]0 = 94 - 16t^216t^2 = 94t^2 = 94/16[/tex]
[tex]t = \sqrt{(94/16)} = \sqrt{(23.5/4)} = 2.43 seconds[/tex] (rounded to two decimal places)
Therefore, it takes the toy car 2.43 seconds to fall to the bottom floor.
The closest answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.
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A rectangular picture frame is 6 inches wide and 10 inches tall. You want to make
the area 7 times as large by increasing the length and width by the same amount.
Find the number of inchey by which each dimension must be increased.
Step-by-step explanation:
let length and width be increased by x>0
(10+x)(5+x)=6×10×5
50+10 x+5x+x²=300
x²+15x-250=0
x²+25 x-10x-250=0
x(x+25)-10(x+25)=0
(x+25)(x-10)=0
x=-25(rejected),10
so x=10
so both the dimensions should be increase by 10 inches.
Solve the problem.
The finance charge per $100 financed for a stove that is paid off in 24 equal monthly payments is $11.45. Use an APR table to find the APR for this loan.
11%
14%
10.5%
14.13%
the APR for this loan is approximately 14.27%.
To find the APR for this loan, we can use the formula:
APR = (2 * n * F) / (P * (n + 1))
where:
n = number of payments (24 in this case)
F = finance charge per $100 financed ($11.45 in this case)
P = amount financed per $100 (which we don't know yet)
We need to solve for P to be able to use the formula. We know that the finance charge is $11.45 for every $100 financed, so we can set up the equation:
11.45 = F / P
where F is the finance charge per $100 financed and P is the amount financed per $100.
Solving for P, we get:
P = F / 11.45
P = 100 * (11.45 / 100)
P = $1,000
So the amount financed is $1,000.
Now we can substitute the values into the APR formula:
APR = (2 * n * F) / (P * (n + 1))
APR = (2 * 24 * 11.45) / (1000 * (24 + 1))
APR = 0.1427 or 14.27%
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Which of the following are exponential functions? Select all correct answers. Select all that apply: □ f(x) = 16x10 □ g(x)=10x9 □ h(x) = 6(8)" j(x) = 8(2)" k(x) =-15x8
Answer:
Step-by-step explanation:
A New Suit Matthew is shopping for a new suit. At K&G Menswear, he finds that the sale price of a suit that was reduced by 25% is $187.5 . Determine the regular price of the suit.
The regular price of the suit is $250.
What is the discounts ?
A discount is a reduction in the price of a product or service. It is often used as an incentive to encourage customers to buy a product or service, especially when the original price is considered too high.
Let's assume the regular price of the suit to be x.
According to the problem, the sale price of the suit after a 25% discount is $187.5.
This can be written as:
x - 0.25x = 187.5
Simplifying the equation:
0.75x = 187.5
Dividing both sides by 0.75:
x = 250
Hence, the regular price of the suit is $250.
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What is the annual percentage yield
The annual percentage yield for money invested at the rates are:
4.5%4.49%How to solveTo solve for the APY in the first question:
APY = [tex](1+ r/n)^n^-^1[/tex]
r= interest rate
n= number of times interest is compounded per year
We put in the values
APY = [tex]( 1 + 0.0441/12)^1^2^-^1[/tex]
APY = 4.5%
To solve for the second one
4.42% compounded quarterly
plug in the values into the formula
[tex](1 + 0.0442)/4^4^-^1[/tex]
APR = 4.49%
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Which of the following situations would not be a proportional relationship?
Need a Hint?
Rosa has $50 and spends $6 every day for lunch for one week.
Jamie reads 22 pages per day for 8 days.
Matthew earns $12 per hour.
Candles costs $10 each.
Answer: Candles Cost $10 Each
Step-by-step explanation: Every single other question gains per hour/day while the candle cost always stays the same and you can come back a week later to find the candle to most likely still be 10$
Nixxi will be sitting on top of the dunk tank at her school's carnival fund-raiser. She wants to find the volume of the tank so she can figure out how much water she will need to fill it. The tank is 4.5 feet deep and has a circumference of approximately 31.4 feet. What is the approximate volume of the tank.
Option C is correct, the volume of the tank is 353 cubic feet.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The volume of a cylindrical tank is given by the formula:
V = πr²h
where r is the radius of the tank and h is its height.
We know that the tank has a circumference of approximately 31.4 feet, which means:
2πr = 31.4
Dividing both sides by 2π, we get:
r = 31.4/(2π) ≈ 5
So, the radius of the tank is approximately 5 feet.
By given height of the tank is 4.5 feet.
Substituting these values into the formula for the volume of a cylinder, we get:
V = π(5)²(4.5) = 353.4
Therefore, the volume of the tank is 353 cubic feet.
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URGENT
What are the domain and range of g of x equals 3 times the square root of the quantity x plus 4?
D: [3, ∞) and R: [0, ∞)
D: [4, ∞) and R: (–∞, 0)
D: [–4, ∞) and R: [0, ∞)
D: (3, ∞) and R: (–∞, 0)
Answer:
D: [-4, ∞) and R: [0, ∞)
Step-by-step explanation:
The answer is D: [-4, ∞) and R: [0, ∞)
Easy question about P-value:
The conclusion that the herds are not statistically different is false.
The correct option is B.
What is the hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
Given:
You conducted a t-test to determine whether two herds of elk have statistically different migration dates.
The resulting p-value was .03.
Here, the p-value is less than 0.05.
That means,
the p-value is statistically significant.
And there is a 3% chance that the null hypothesis should be rejected.
Your conclusion is that the herds are not statistically different.
Therefore, your conclusion is incorrect.
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stop to think 7.3 boxes a and b are sliding to the right across a frictionless table. the hand h is slowing them down. the mass of a is larger than the mass of b. rank in order, from largest to smallest, the horizontal forces on a, b, and h.
Since the boxes are sliding to the right at a constant velocity, the net force acting on each box is zero.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The LHS and RHS contain mathematical expressions that can include variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations are used in many areas of mathematics and science to describe relationships between variables and to solve problems. They can be linear or nonlinear, simple or complex, and may involve one or more variables. The process of finding the values of variables that make an equation true is called solving the equation.
Here,
Therefore, the forces on each box must balance out. Let's consider the forces acting on each box:
Box A: Since it has a larger mass, it requires a larger force to slow down. Therefore, the force exerted by hand H on box A must be larger than the force exerted on box B. We can rank the forces on box A, box B, and hand H as follows:
Force exerted by hand H on box A (largest force)
Force exerted by hand H on box B
Force exerted by box A on hand H
Force exerted by box B on hand H
Force exerted by box A on box B (smallest force)
Box B: Since it has a smaller mass, it requires a smaller force to slow down. Therefore, the force exerted by hand H on box B must be smaller than the force exerted on box A.
Hand H: The forces exerted by box A and box B on hand H are equal and opposite (Newton's third law). Therefore, they cancel each other out and the net force on hand H is zero.
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Fifty cities provided information on vacancy rates (in %) in local apartments in the following frequency distribution.Vacancy Rate (%) Relative Frequency0 < x ≤ 3 0.023 < x ≤ 6 0.166 < x ≤ 9 0.169 < x ≤ 12 0.2412 < x ≤ 15 0.42a-4. what proportion of the cities had a vacancy rate of more than 9%? (round your answer to 2 decimal places.)
Answer:
your answer is explained below
Step-by-step explanation:
To find the proportion of cities with a vacancy rate of more than 9%, we need to add the relative frequencies for the classes with vacancy rates greater than 9%. These classes are 9 < x ≤ 12 and 12 < x ≤ 15.
Proportion of cities with a vacancy rate of more than 9%:
= Relative frequency for 9 < x ≤ 12 + Relative frequency for 12 < x ≤ 15
= 0.24 + 0.42
= 0.66
Therefore, 66% of the cities had a vacancy rate of more than 9%.
Rounding this answer to two decimal places, we get 0.66 as the final answer.
Consider the following specifications: "Whenever the system software is being upgraded, users cannot access the file system. If users can access the file system, then they can save new files. If users cannot save new files, then the system software is not being upgraded." The goal of this exercise is to determine whether the given specifications are consistent. To do this, we express the given specifications in terms of the statements: u. The software system is being upgraded. a: Users can access the file system. s: Users can save new files. Identify a set of truth values that make the three specification true. (You must provide an answer before moving to the next part.) Multiple Choice FFF, TFF, FTF, and FTT FFT, TFT, FFF, and FTT FFT, TFT, TFF, and TTT o o O FTF, TTF, TFF, and ITT
The set of truth values that make the three specifications true is FFT, TFT, TFF, and TTT.
Let's break it down step by step:
u: The software system is being upgraded.
a: Users can access the file system.
s: Users can save new files.
The given specifications are as follows:
Whenever the system software is upgraded, users cannot access the file system.
If users can access the file system, then they can save new files.
If users cannot save new files, then the system software is not being upgraded.
Given these specifications, we can set up the following truth table:
The set of truth values that make the three specifications true is therefore FFT, TFT, TFF, and TTT.
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Find Monthly Payment on a Loan
Mila's monthly mortgage payment would be approximately $4,658.99.
Describe Interest?In finance, interest refers to the cost of borrowing money or the return earned on an investment. It is usually expressed as a percentage of the amount borrowed or invested and is typically calculated on an annual basis.
For borrowing money, interest is the cost that the borrower has to pay to the lender for the privilege of using their funds. The lender earns interest on the loan as compensation for lending their money to the borrower. The interest rate on a loan is determined by a variety of factors, including the borrower's creditworthiness, the term of the loan, and prevailing market conditions.
For investments, interest is the return earned by an investor on their principal amount. For example, when someone deposits money in a savings account, they earn interest on that money. The interest rate on savings accounts and other investments is typically determined by the prevailing market conditions and the financial institution offering the investment.
Interest can be calculated in different ways, including simple interest and compound interest. Simple interest is calculated on the original principal amount, while compound interest is calculated on the principal amount plus any accumulated interest. The frequency at which interest is compounded, such as monthly or annually, can have a significant impact on the total amount of interest earned or paid.
Overall, interest plays a critical role in finance and can have a significant impact on the cost of borrowing money or the return earned on an investment.
To calculate Mila's monthly mortgage payment, we can use the formula for a fixed-rate mortgage:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
where:
M = monthly mortgage payment
P = loan amount
r = monthly interest rate
n = number of payments (total number of years * 12)
Plugging in the given values, we get:
M = 730000 * (0.00325 * (1 + 0.00325)^(2012)) / ((1 + 0.00325)^(2012) - 1)
Simplifying this expression using a calculator, we get:
M ≈ $4,658.99
Therefore, Mila's monthly mortgage payment would be approximately $4,658.99.
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Charles had m yards of material. He used 0.4m yards of material to make a costume, 0.2m yards to make pillows and 0.3m yards to make a bag. Which expression shows how many yards of fabric Charles has left? Check all that apply.
(A) 0.1m
(B) 0.9m
(C) m – 0.9m
(D) (0.4 + 0.2 + 0.3)m
(E) (1 – 0.4 – 0.2 – 0.3)m
(F) m – (0.4 + 0.2 + 0.3)m
(G) m – 0.4m – 0.2m – 0.3m
(H) m – (0.4m + 0.2m + 0.3m) check all that apply
Answer:
(A) [tex]0.1m[/tex](C) [tex]m - 0.9m[/tex](E) [tex](1 - 0.4 - 0.2 - 0.3)m[/tex](F) [tex]m - (0.4 + 0.2 + 0.3)m[/tex](G) [tex]m - 0.4m - 0.2m - 0.3m[/tex](H) [tex]m - (0.4m + 0.2m + 0.3m)[/tex]Step-by-step explanation:
To determine how many yards of fabric Charles has left, we need to subtract the total amount of fabric used for the costume, pillows, and bag from the initial amount of fabric (m yards). The total amount of fabric used is:
[tex]0.4m + 0.2m + 0.3m = 0.9m.[/tex]Now, we can subtract the total used fabric from the initial amount of fabric:
[tex]m - 0.9m[/tex]The correct expressions that show how many yards of fabric Charles has left are:
(A) [tex]0.1m[/tex](C) [tex]m - 0.9m[/tex](E) [tex](1 - 0.4 - 0.2 - 0.3)m[/tex](F) [tex]m - (0.4 + 0.2 + 0.3)m[/tex](G) [tex]m - 0.4m - 0.2m - 0.3m[/tex](H) [tex]m - (0.4m + 0.2m + 0.3m)[/tex]Why are the options correct/incorrect?(A) 0.1m: This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.(B) 0.9m: This option is incorrect because it represents the amount of fabric Charles used, not the amount he has left.(C) m - 0.9m: This option is correct because it represents the initial amount of fabric (m) minus the total amount of fabric used for the costume, pillows, and bag (0.9m), which gives the remaining amount of fabric.(D) (0.4 + 0.2 + 0.3)m: This option is incorrect because it represents the total amount of fabric Charles used to make the costume, pillows, and bag, not the amount he has left, like option (B).(E) (1 - 0.4 - 0.2 - 0.3)m: This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.(F) m - (0.4 + 0.2 + 0.3)m: This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.(G) m - 0.4m - 0.2m - 0.3m: This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.(H) m - (0.4m + 0.2m + 0.3m): This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.Final answerSo, the correct options are (A), (C), (E), (F), (G), and (H).
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