If a bundle of strip flooring has 25 sq ft and 30% extra is provided for side and end matching, 12.2 bundles of strip flooring are required to cover a rectangle floor space 16 ft by 14 ft 6 in size.
How do you find the area of the rectangle?Once the length and breadth of a rectangle are determined, the area is computed. The area of a rectangle may be calculated by multiplying its length and width.
In this question, because the rectangular floor has an area of 16 ft by 14 ft 6 in, we can compute the total area of the floor by multiplying 16 ft by 14 ft 6 in, which is 234 [tex]ft^{2}[/tex]. We also know that a strip flooring bundle comprises 25 square feet. As a result, we must determine how many bundles of strip flooring are required to cover the floor.
We must account for side and end matching, which is computed by increasing the total floor area by 30%. To determine the extra space required for side and end matching, multiply 234 ft2 by 0.3. This equates to 70.2 [tex]ft^{2}[/tex].
We can now compute the total area required to cover the floor. This is 234 [tex]ft^{2}[/tex] + 70.2 [tex]ft^{2}[/tex] = 304.2 [tex]ft^{2}[/tex].
Because each strip flooring bundle includes 25 square feet, we can divide 304.2 [tex]ft^{2}[/tex] by 25 to determine the total number of bundles required to cover the floor.
This corresponds to 12.2 bundles.
Therefore, 12.2 bundles of strip flooring are needed to cover a rectangular floor area 16 ft by 14 ft 6 in size, with 30% extra for side and end matching.
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? - 85 ÷ 641 = 650
Need help
Answer:
416,`735
Step-by-step explanation:
Do inverse operations
The polynomial function f(x) = x³ - 4x²-3x + 18 has (x+2) as one of its linear factors. Use long division to find the other linear factors.
Separate multiple factors with a comma. If there are any repeated factors, only write them once.
The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).
What is a polynomial ?
A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) multiplied by coefficients.
where n is a non-negative integer (the degree of the polynomial), x is the variable, and (the coefficients of the polynomial). The highest power of x in the expression is n, and this term is called the leading term. The coefficient of the leading term, a_n, is called the leading coefficient.
To find the other linear factors of the polynomial function f(x) = x³ - 4x² - 3x + 18, we can use long division by dividing the polynomial function by (x + 2).
Here's how the long division would look like:
x³ - 4x² - 3x + 18
÷ x + 2
__________________________
x² - 6x - 20
÷ x + 2
__________________________
x - 22
÷ x + 2
__________________________
-20
here -20 is the remainder.
The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).
So, the other linear factors are x - 22.
Therefore, The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).
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work and solution. Identify the error and descr
problem correctly.
Incorrect Work/Solution
m = the number of messages Nigel sent
644 = 7m
-7 -7
637 =m
Nigel sent an average of 637 messages
each day last week.
Correct Work/Solution
The correct solution to the problem is m = 92 and the error made was subtracting 7 from both sides of the equation instead of dividing both sides by 7
How to solve algebra correctly?Incorrect Work/Solution:
m = the number of messages Nigel sent
644 = 7m
subtract 7 from both sides
644 - 7= 7m - 7
637 = m
Nigel sent an average of 637 messages
each day last week.
Correct solution:
644 = 7m
divide both sides by 7
m = 644/7
m = 92
Therefore, Nigel sent an average of 92 messages
each day last week.
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The table shows a linear relationship between the variables x and y. What is the slope? X y 3 6 9 24 12 6 12 288 18 8
The slope of the line with the points (6, 3) and (12, 6) is equal to 1/2.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (6, 12).
Points on y-axis = (3, 6).
Substituting the given data points into the slope formula, we have the following;
Slope, m = (6 - 3)/(12 - 6)
Slope, m = 3/6
Slope, m = 1/2.
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Consider the graph of the function f(x)=log4(x-2)+2. What are the domain and the range of function f?
Answer:domain is (2, ∞), range is (-∞,∞)
Step-by-step explanation:
domain is (2, ∞) as it aproaches 2 but never reaches and range is (-∞,∞)
Analyzing Functions Using an Equation and a Table
The function f(x)=x+is used to complete this
table.
-1
0
2
f(x)
1
312
2
512
2
Which statements are true of the given function?
Check all that apply.
머글)=-2
Of(0) = 2/1/2
Of(1) = -1
Of(2)=1
f(4) = 글
Answer:
2 . of(0)=2/1/2 this is answer number 2
The solution is, option 2 neither linear nor exponential.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
The given function is
x : -5 -3 -1 1 3
f(x) :8192 512 32 2 18
when we plot this function in the excel we get to know that it a regression as shown in the figure attached
because value of lies between (0,1)
which shows regression
therefore it is neither linear nor exponential.
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the company bought $15000 worth of equipment beginnning of year 2018 the equipment is est. to increase in value at a rate of 15.9% per year how many yers, t , after which the value of the company's new equipment will be less than 7500 what formula would be used
Answer:
To solve this problem, we can use the formula for exponential growth:
V(t) = V0 * (1 + r)^t
where:
V(t) is the value of the equipment at time t
V0 is the initial value of the equipment ($15,000)
r is the annual growth rate (15.9% or 0.159)
t is the time in years
We want to find the time t when the value of the equipment will be less than $7500. So we can set up the following inequality:
V(t) < 7500
Substituting the formula for V(t), we get:
V0 * (1 + r)^t < 7500
Substituting the given values, we get:
15000 * (1 + 0.159)^t < 7500
Simplifying and solving for t,
we get:(1 + 0.159)^t < 0.5
t * log(1 + 0.159) < log(0.5)
t > log(0.5) / log(1 + 0.159)
Using a calculator, we get:
t > 2.64
So the company's new equipment will be worth less than $7500 after about 2.64 years.
Step-by-step explanation:
Lenart Corporation has provided the following data for its two most recent years of operation: Manufacturing costs: Variable manufacturing cost per unit produced: Direct materials $ 13 Direct labor $ 5 Variable manufacturing overhead $ 5 Fixed manufacturing overhead per year $ 90,000 Selling and administrative expenses: Variable selling and administrative expense per unit sold $ 6 Fixed selling and administrative expense per year $ 61,000 Year 1 Year 2 Units in beginning inventory 0 1,000 Units produced during the year 10,000 9,000 Units sold during the year 9,000 8,000 Units in ending inventory 1,000 2,000
Answer: To calculate the total cost of the units in beginning inventory for each year, we need to multiply the number of units by the per-unit cost:
Year 1: Cost of units in beginning inventory = 0 units * $13 + $5 + $5 = $0
Year 2: Cost of units in beginning inventory = 1,000 units * ($13 + $5 + $5) = 1,000 * $23 = $23,000
To calculate the total cost of the units produced during each year, we need to multiply the number of units by the per-unit cost:
Year 1: Cost of units produced = 10,000 units * ($13 + $5 + $5) = 10,000 * $23 = $230,000
Year 2: Cost of units produced = 9,000 units * ($13 + $5 + $5) = 9,000 * $23 = $207,000
To calculate the total cost of the units sold during each year, we need to multiply the number of units sold by the per-unit cost:
Year 1: Cost of units sold = 9,000 units * ($13 + $5 + $5 + $6) = 9,000 * $29 = $261,000
Year 2: Cost of units sold = 8,000 units * ($13 + $5 + $5 + $6) = 8,000 * $29 = $232,000
To calculate the total variable manufacturing costs for each year, we need to sum the costs of the units in beginning inventory, units produced, and units sold:
Year 1: Total variable manufacturing costs = $0 + $230,000 + $261,000 = $491,000
Year 2: Total variable manufacturing costs = $23,000 + $207,000 + $232,000 = $462,000
To calculate the total fixed manufacturing overhead costs for each year, we need to add the fixed manufacturing overhead per year to the total variable manufacturing costs:
Year 1: Total manufacturing costs = $491,000 + $90,000 = $581,000
Year 2: Total manufacturing costs = $462,000 + $90,000 = $552,000
To calculate the total variable selling and administrative expenses for each year, we need to multiply the number of units sold by the variable selling and administrative expense per unit:
Year 1: Total variable selling and administrative expenses = 9,000 units * $6 = $54,000
Year 2: Total variable selling and administrative expenses = 8,000 units * $6 = $48,000
To calculate the total selling and administrative expenses for each year, we need to add the fixed selling and administrative expenses per year to the total variable selling and administrative expenses:
Year 1: Total selling and administrative expenses = $54,000 + $61,000 = $115,000
Year 2: Total selling and administrative expenses = $48,000 + $61,000 = $109,000
Step-by-step explanation:
Mrs, Hansen usually makes a disinfecting solution by adding 1 2/3 cups of bleach to 5 gallons of water. Today, however, she is using only 3 1/2 gallons of water. She wants to make the solution so that it has the same disinfecting strength. How much bleach should she use?
Answer:
1 1/6 cups
Step-by-step explanation:
You want to know the amount of bleach to use with 3 1/2 gallons of water to obtain the same strength as 1 2/3 cups of bleach in 5 gallons of water.
ProportionThe quantities are proportional, so the amount of bleach (b) will need to be ...
b/(3 1/2 gal) = (1 2/3 cups)/(5 gal)
Multiplying by 3 1/2 gal, we get ...
b = (3 1/2)(1 2/3)/5 cups = 1 1/6 cups
Mrs. Hanson should use 1 1/6 cups of bleach in 3 1/2 gallons of water.
North A North 110% B
Answer:
Step-by-step explanation:
I do not know bro. If I was a robot i'd know. I don't. I'm different.
What might the composer do to write a piece with a carefree and ecstatic mood?
A. A lively accompaniment
B. Dissonant chords
C. A slow tempo
D. A minor key
Answer:
A. A lively accompaniment
Step-by-step explanation:
B. Dissonant - would most likely result in a eerie mood
C. A slow tempo - could result in melancholy or calm emotions
D. A minor key - could also result in melancholy emotions
Alicia drew these same size game boards
Please help fast!! Which of the following equations represents a linear function? Please show the steps of the answer! Thank you
one night a movie theater sold 124 tickets. an adult ticket cost $12.50 and a child ticket cost $6.50. in all, $1298 was taken in. how many of each kind of ticket were sold?
Using the system of equations, we found the number of adult tickets sold as 82 and the number of child tickets sold as 42.
What is the system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
Given,
Number of tickets sold = 124
Cost of one adult ticket = $ 12.50
Cost of one child ticket = $ 6.50
Total money received = $ 1298
We can write a system of equations using the above information.
Number of adult tickets sold = x
Number of child tickets sold = y
x + y = 124
12.5x + 6.5y = 1298
Solving the above equations, we can find x and y.
Multiplying the first equation by 6.5
6.5x+ 6.5y = 806
12.5x + 6.5y = 1298
Subtracting the equations,
-6x = -492
x = 82
Substituting the above value in any one of the equation
82 + y = 124
y = 42
Therefore from the system of equations, the number of adult tickets sold is 82 and the number of child tickets sold is 42.
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Which equation is quadratic in form?
3x5 + 8x3 + 6 = 0
6x4 + 7x2 – 3 = 0
5x6 + x4 + 12 = 0
x9 + x3 – 10 = 0
The equation which is in the quadratic form is 6x⁴ + 7x² - 3 = 0. So Option B is correct.
What is a quadratic equation ?An equation is quadratic in form if it can be written in the form of ax + bx + c = 0, where a, b, and c are constants and x is the variable.
Among the given equations, we can see that the first, third, and fourth equations are not quadratic in form, since they contain x raised to powers other than 2.
The second equation, 6x⁴ + 7x² - 3 = 0, can be written in quadratic form by making a substitution.
If we let y = x², then we can write the equation as 6y² + 7y - 3 = 0,
which is a quadratic equation in y. Substituting back x² for y,
we get:
6x⁴ + 7x² - 3 = 0
So the second equation is quadratic in form.
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Answer:
Step-by-step explanation:
answer b, trust
Here is a number machine.
input
x 4
a) Work out the output when the input is 6
b) Work out the input when the output is 31
- 5
output
The solution is,
(a) Output = 37
(b) Input = 9
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
Given
y=5x -3
Solving (a): Output, when input = 8
This means that, we solve for y when x = 8
So, we have:
y=5x -3
=5*8 -3
=40 - 3
= 37
Solving (b): Input, when output = 42
This means that, we solve for x when y = 42
So, we have:
y=5x -3
5x = 42+3
= 45
Collect like terms
Divide both sides by 5
x = 9
Hence, The solution is,
(a) Output = 37
(b) Input = 9
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15. Which set is an example of like fractions?
A. 7/4 and 4/7
B. 10/10 and 5/5
C. 2/1 and 2/3
D. 1/2 and 3/2
A rectangular room is 2 meters longer than it is wide, and its perimeter is 24
meters. Find the dimension of the room.
The length is : _____ meters and the width is _____
meters.
If a rectangular room is 2 meters longer than it is wide, and its perimeter is 24 meters then the dimensions of the room: 7 meter x 5 meter
What is the perimeter?Perimeter is a mathematical term, it indicates total outer boundary of a figure, we define it only for two dimensional figures.
Perimeter = Sum of length of the all the sides
Let x be the width of the room in meters.
Then the length of the room is 2 meters longer, which means it is x+2 meters.
In this case, we know that the perimeter is 24 meters.
So we can set up an equation:
Perimeter = 2Length + 2Width
Substituting the values we know:
24 = 2(x+2) + 2x
Simplifying the equation:
24 = 2x + 4 + 2x
24 = 4x + 4
20 = 4x
x = 5
So the width of the room is 5 meters, and the length is x+2 = 7 meters.
Therefore, the dimensions of the room are 7 meters by 5 meters.
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PLS HELP ME MY GRADE DEPENDS ON IT
The constant of proportionality for the given graph is 6.
What is a constant of proportionality?The two sequences of numbers are proportional or directly proportional if the ratio between the corresponding elements of two sequences of numbers, typically experimental data, is constant and is known as the coefficient of proportionality or proportionality constant.
From the given graph the point is (5,30) from which the line is passing.
The equation for the constant of proportionality is written as below,
y = kx
Substitute the points in the above equation,
y = kx
30 = k x 5
k = 30 / 5
k = 6
Therefore, the proportionality constant for the displayed graph is 6.
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4) Marla is jumping rope in her school's jump-a-thon to raise money for the school library.
Marla's parents pledge $0.25 for each time Marla jumps rope and write a check for $63.25. This
situation is modeled by the equation 0.25c = 63.25, where c represents the number of times that
Marla jumps rope in the jump-a-thon. What is the value of c in the equation?
A. 16
B. 64
C. 63
D. 253
Step-by-step explanation:
0.25c = 63.25
We would just get c alone by dividing by 0.25 on both sides of the equal sign
c = 253
Answer: C = 253
Step-by-step explanation:
Determine the Domain and Range for the graph below. Write your answer in interval notation and as an inequality.
Domain written in Interval Notation:
Domain written as an Inequality:
Range written in Interval Notation:
Range written as an Inequality:
Points on the graph are:
(0,1) (1,2) (2,3) (3,4) (4,5)
(-1,0) (-2,-1) (-3,-2) (-4,-3)
The domain and the range of the ordered pairs in interval notations are as follows: 1) Domain = [0,4], Range = [1,5] ; (2) Domain [-1,-4], Range =[0,-3]
Domain and Range of a set of Ordered pairsThe domain of a function is the collection of all conceivable values that may be used as inputs, or alternatively, it is the whole array of possible values for independent variables.
The range of a function is the set of every possible value for the dependent variable's outcomes, or the whole set of all possible values when the domain is substituted.
In a set of ordered pairs (x,y), the domain (input) refers to all the x-values and the range refers to all the y-values.
From the points on the graph given:
(0,1) (1,2) (2,3) (3,4) (4,5)
Domain: (0, 1, 2, 3, 4)
In interval notation: = [0,4]Range: (1, 2, 3, 4, 5)
In interval notation: = [1, 5](-1,0) (-2,-1) (-3,-2) (-4,-3)
Domain: ( -1, -2, -3, -4)
In interval notation: = [-1, -4]Range: (0, -1, -2, -3)
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3. What is the volume of this complex figure?
3 m
4 m
6 m
4 m
7m
The volume of the given complex structure would be = 56 m³
How to calculate the volume of the given structure?The structure is made up of the big and small cubes.
The volume of the big cube = length × breadth × width = 7 × 3 × 4 = 84 m³
The volume of the small cube cut out = length * breadth * width = 4 × 7 × (4 - 3) = 28 m³
Volume of the complex figure = 84 m³ - 28 m³ = 56 m³
The volume of the complex figure shown in the diagram is 56 m³.
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Metalworking Twelve equally spaced holes are to be drilled in a metal strip 3414-in. long, with 2 in. remaining on each end. What is the distance, to the nearest hundredth of an inch, from center to center of two consecutive holes.
Based on the given data, the distance from center to center of two consecutive holes is approximately 25.83 inches.
Calculating Distance Between Equally Spaced Holes in MetalworkingTo solve this problem, we need to divide the length of the metal strip (excluding the 2 inches on each end) by the number of holes to be drilled, and that will give us the distance from center to center of two consecutive holes.
So the length of the metal strip available for the 12 holes is:
3414 - 2 - 2 = 3410 inches
Dividing this length by the number of holes gives us:
3410 ÷ 12 = 284.166666... inches
To find the distance from center to center of two consecutive holes, we need to divide this value by the number of spaces between the holes, which is 11 (since there are 12 holes, but only 11 spaces between them). So:
284.166666... ÷ 11 = 25.833333...
Rounding this to the nearest hundredth of an inch, we get:
25.83 inches (to the nearest hundredth)
Therefore, the distance from center to center of two consecutive holes is approximately 25.83 inches.
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Find the perimeter of a triangle where the length of side one is 10x + 19. The length of
side two is 12x - 2 and the length of side three is x.
The perimeter of the triangle is 23x + 17.
What is the perimeter of the triangle ?Perimeter is simply the sum of all sides of a polygon.
Given the sides of the triangle;
Side one = 10x + 19
Side two = 12x - 2
Side three = x
To find the perimeter, we add the sides
Perimeter = Side one + Side two + side three
Perimeter = 10x + 19 + 12x - 2 + x
Collect and add like terms
Perimeter = 10x + 12x + x - 2 + 19
Perimeter = 23x - 2 + 19
Perimeter = 23x + 17
Therefore, the perimeter is 23x + 17.
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Steve invests $2,100 in an account that earns 6.9% interest, compounded continuously. What is the value of the account after 13 years? Round your answer to the nearest hundredth.
The amount after 13 years with a compound interest of 6.9 % is given by the equation A = $ 5,149.69
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the amount after compound interest be represented as A
Now , the equation will be
The principal amount P = $ 2,100
The rate of interest r = 6.9 %
The number of years b = 13 years
when compounded continuously ,
The compound interest amount A = Pe^rt
Substituting the values in the equation , we get
A = 2,100.00 ( 2.71828 ) ^ ( 0.069 ) ( 13 )
A = 2,100 ( 2.71828 )^( 0.897 )
On further simplification , we get
A = $ 5,149.69
Hence , the amount after 13 years is $ 5,149.69
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Question is attached below!
Thanks! :)
The parameters for the home mortgage, and the monthly payment, PMT, for the mortgage are as follows;
Part 1;
P = $175,000, APR = 7%, n = 12, Y = 30
Part 2;
The monthly payment for the mortgage, PMT ≈ $1,164.28
What is a mortgage?A mortgage is a loan agreement, with the possession of the collateral presented for the loan such as a house being bought with the loan amount, being relinquished by the debtor, upon default
Part 1
The value of the mortgage = $175,000
The fixed Annual Percentage Rate, APR = 7%
The duration of the payment = 30 years
The principal amount of the mortgage, P = $175,000The annual percentage rate, APR = 7% = 0.07The number of payment (periods), per year, n = Monthly = 12The number of years of the loan, Y = 30Part 2; The monthly payment PMT loan formula can be presented in the following format;
[tex]PMT = \frac{P\times \frac{APR}{n} }{1-\left(1+\frac{APR}{n}\right)^{(-n\cdot Y)} }[/tex]Therefore;
[tex]PMT = \frac{175000\times \frac{0.07}{12} }{1-\left(1+\frac{0.07}{12}\right)^{(-12\times 30)} } \approx 1164.28[/tex]
The monthly payment for the mortgage is, PMT ≈ $1,164.28
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Please help me. I'll give brainliest.
Answer: interest= 670
Step-by-step explanation:
(1+r)^t*principal
The average rate of change of a function
f(x) = x2
between
x = 4
and
x = 6
is
average rate of change =
`
6 − 4
=
On solving the provided question we can say that The average rate of change between x₁ and x₂ and a function f(x), is 10.
What is function?The subject of mathematics includes quantities and their variatiοns, equations and related structures, shapes and their locations, and places where they can be fοund. The term "functiοn" refers to the relationship between a set of inputs, each of which has an assοciated output.
A connectiοn between inputs and οutputs in which each input leads tο a single, distinct result is known as a function. Each functiοn is given a domain and a codοmain, or scope. Usually, f is used to denοte functions (x). input is an x. There are fοur main types of functiοns accessible. based οn the following factors: on functiοns, one-to-one functiοns, many-to-one functions, inside functiοns, and on functions.
The average rate of change between x=x and a function f(x)
F(x₂) - F(x₁)/(x₂) - x₁
so,
f(x) = x²
average rate = f(6) - f(4) / 6-4 = 36-16 / 2 = 20/2 = 10
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Find the GCF of the terms of each polynomial 15x^2+18 and -18y^4+6y^3+24y^2
The GCF of the polynomials are
1. for 15x²+18 , the GCF is 3
2. for -18y⁴+6y³+24y² ,the GCF is 6y²
What is GCF?The GCF stands for the “greatest common factor”. The GCF is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.
The GCF is the highest factor that can be used to divide through 2 or more terms
1. For 15x²+18, 3 is a factor of 15 and 18 and it's the greatest factor, therefore the GCF is 3
2. For -18y⁴+6y³+24y², between 18,6 and 24, 6 is the greatest factor Ang between y⁴ ,y³, y², y² is the greatest factor. Therefore the GCF of the expression is 6y².
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What does the notation f(2) mean?
multiply fby 2
the output (y-value) when x = 2
O the value of x when the output is 2
Evaluate f(2)=
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
y = f(x) represents a function with output value as y and x as an input in the function.
Therefore, f(2) represents value of function (y) at x = 2
so the correct choice here would be : " the output (y - value) when x = 2 "
