The required equation is x × 3 = 528.75 - 60.
The cost of the labor per hour is $156.25
How do equations work?
The definition of an equation is a mathematical statement with at least two terms that contain variables or equal numbers.
Let x be the cost of the labor per hour.
We know that
x × 3 = labor cost
60 + x × 3 = total cost
We also know that the total cost is $528.75
So we can write the equation:
60 + x × 3 = 528.75
Solving for x:
x × 3 = 528.75 - 60
x × 3 = 468.75
x = 468.75/3
x = 156.25
Therefore, the cost of the labor per hour is $156.25
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The area of this rectangle is given by the quadratic function
A = 50W - W2
.
What is the reasonable domain for this function?
The reasonable domain for this function is 0 < x < 50
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
Given;
A = 50W - W2
The area of a rectangle cannot be negative;
The practical domain of A is determined when;
50W-W^2>0
Taking common factor W
W(50-W)>0
Since W must be positive W>0
50-W>0
Or equivalently
50>w
W<50
The total interval is
0<W<50
Therefore, the domain of the function will be 0 < x < 50
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PLSSSS HELP IF YOU TURLY KNOW THISSS
[tex] \pmb{ \underline{\color{green} \huge{Αηςωεr : ∼}}}[/tex]
[tex] \large \frak{ \red{x } - 4 = 8}[/tex]
[tex] \: [/tex]
[tex] \large \frak{ \red{x } = 8 + 4}[/tex]
[tex] \: [/tex]
[tex] \underline{ \boxed{ \large \frak{ \red{x } = \green{12}}}}[/tex]
[tex] \: [/tex]
hope it helps!
Vanessa and Jo share £128 in the
ratio 5: 3. Work out how much money
Vanessa receives.
Answer:
vanessa gest 80
Step-by-step explanation:
128/8 =16
5 * 16 =80
3*16. =48
Answer: £80
Step-by-step explanation:
Step 1:
Make a proportion:
5 - 8
x - 128
Step 2:
Cross multiply:
5*128=8x
640=8x
Step 3:
Divide by 8:
80=x or x=80
Helppppp!!!! Question: Jimmy’s friend Tom also wants to save money to buy concert tickets. He draws up the following savings plan. Each week Tom will raise $4 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job. Use summation notation to write the sum and find the total amount Tom will save in three weeks.
The summation notation of the sum is:
[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]
The total amount is $84.
How to use summation notation to write the sum?Summation notation, also known as sigma notation, is a mathematical notation used to represent the sum of a sequence of numbers. The notation typically uses the Greek letter sigma (∑) to represent the operation of summation.
Since each week Tom will raise $4 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job.
Let n represent the number of weeks
Thus, this can be written using summation notation as:
[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]
Thus, the total amount = 4¹ + 4² + 4³ = $84
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Brown's Tree Farm Company is going to plant pine trees and birch trees this planting season. On Farm A, the land type allows for them to plant 25 pine trees per acre and 75 birch trees per acre. On Farm B, the land type allows for them to plant 50 pine trees per acre and 75 birch trees per acre. There are a total of 200 pine trees and 450 birch trees available for planting.
1. Write and solve a system of equations to determine how many of each tree the company will plant on each farm.
Let x be the number of acres of Farm A planted with pine trees and birch trees, and let y be the number of acres of Farm B planted with pine trees and birch trees.
The system of equations would be as follows:
25x + 50y = 200 (the total number of pine trees planted)
75x + 75y = 450 (the total number of birch trees planted)
To solve this system of equations, we can use the method of substitution. Solving the first equation for x in terms of y:
x = (200 - 50y) / 25
We can substitute this expression for x into the second equation:
75((200 - 50y) / 25) + 75y = 450
Simplifying and solving for y:
(200 - 50y) + 75y = 450
25y = 250
y = 10
So 10 acres of Farm B are planted with pine and birch trees. To find the number of acres of Farm A that are planted with pine and birch trees, we can substitute this value of y back into the first equation:
25x + 50(10) = 200
25x = 50
x = 2
So 2 acres of Farm A are planted with pine and birch trees.
Therefore, the company will plant 25x = 50 pine trees and 75x = 225 birch trees on Farm A, and 50y = 500 pine trees and 75y = 750 birch trees on Farm B.
Divide 3x^2 + 6 by 3x – 3.
Which expression represents the quotient and remainder?
because i couldn't find it anywhere
the answer is c
The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.
Division of Polynomials :To divide polynomials by a polynomial, we use the long division method.
When there is no common factor in both the numerator and the denominator, we can use the long division.
It may be used to find reminders and quotients while dividing.
Here we have
Divide 3x² + 6 by 3x – 3
On dividing 3x² + 6 by 3x – 3 in long division method
we get the remainder as 9 and the quotient as (x - 1)
For more understanding understand the long division in the given picture.
Therefore,
The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.
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HELP ME PLEAE ASAP!!!!!!!!!!!!
Lin is running in an election to be president of the seventh grade. She wants to predict her chances of winning. She has the following ideas for surveying a sample of the students who will be voting: a. Ask everyone on her basketball team who they are voting for. B. Ask every third girl waiting in the lunch line who they are voting for. C. Ask the first 15 students to arrive at school one morning who they are voting for.
Answer:
C
Step-by-step explanation:
Lets use process of elimination.
A would result in biased results as Lin is on the basketball team herself and thus, her teammates would be inclined to vote for her.
B would result in biased results as well. It doesn't say every third person in the line but rather every third girl. The girls might be inclined to vote for a female candidate.
That leaves C as the only viable option.
what is the domain of the function shown in the graph below?
The domain of the function shown in the graph above include the following: D. {x|x ≥ -4}.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
By using set builder notation, the domain of this function shown in the graph above can be written as follows;
Domain = {-4, ∞}
Domain = {x|x ≥ -4}
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The solution set to 6 + 2n> 12 is n> 3. Which are correct representations of this solution? Select two options.
{n\n<3}
{n\n≥3)
-5-4-3-2-1 0 1 2 3 4 5
-5-4-3-
(3,0⁰0)
0
2 3 4
5
-5-4-3- is the solution for {n\n<3} and 2-1-0 is the correct set for this solution {n\n≥3).
What is the set?A set is a well-defined collection of distinct objects, known as elements or members of the set. The objects can be anything, such as numbers, letters, words, animals, or even other sets. The defining feature of a set is that its elements are unique and distinct, meaning that no element can appear more than once in the set.
The solution set to 6 + 2n > 12 is n > 3. The correct representations of this solution are:
{n | n ≥ 3}
(3, ∞)
Option 1 {n | n < 3} is incorrect, as it represents the solution set of n being less than 3, which is the opposite of the solution set provided.
Option 2 -5-4-3- is Correct, as it is not in the correct format to represent a solution set.
Option 3 (3,0⁰0) is correct because it represents a point, not a set.
Option 4 and 5 -5-4-3-2-1 0 1 2 3 4 5 and 0 2 3 4 5 are also incorrect as they are not in the correct format to represent a solution set, and does not include the value 3.
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Use your formula to determine the height of a trapezoid with an area of
24 cubic centimeters and base lengths of 9 cm and 7 cm
Here is the formula: 1/2(a+b)h
Answer:
Step-by-step explanation:
Need help solving this question
Answer: Billy drives 171 miles in 3 hours, so he could drive 256.5 miles in 4.5 hours.
Step-by-step explanation:
Speed = Distance/Time
The number of miles driven varies directly with the number of hours in the car. Billy drives 171 miles in 3 hours. Then the number of miles he can drive in 4.5 hours will be. This meas that x will be the number of miles covered in 4.5 hours.
x / 4.5 = 171 / 3
x = 256.5 miles
I hope this helps!
Find the area of the shaded region.
13.
12
Geometry IF8763
12
2014
11
86
15, 1111717-74
27
12.5
27
10 mm
24
27
27
MCMXCIV Instructional Fair,
Answer: need photo
Step-by-step explanation:
The solution to an inequality is graphed on the number
line.
-5-4-3 -2 -1 0 1 2 3 4 5
What is another way to represent this solution set?
Oxx<4.5}
O {x|x≤4.5}
Oxx>4.5)
Ox|x24.5}
The term "solution set" refers to the collection of all possible solutions to an equation thus {x|x≤4.5} holds it . The value is a solution because the equation holds true if both sides are equal.
Option B is correct.
What is set?The distinct items that make up a set are referred to as the set's members or elements. Set notation is a method for representing a set using a combination of symbols and numbers, and it can be used to define sets. "x | -5 x 4.5" is another way to show the solution set of the inequality -5 x 4.5 on a number line. Interval notation is the method by which all real numbers between two given values can be represented. The solution set can be read as "x such that -5 is less than x and x is less than or equal to 4.5" because "|" denotes "such that" and the vertical line denotes "and."
Why is the set of solutions infinite?When the lines coincide and have the same y-intercept, the number of solutions to an equation system is infinite. If the slope and y-intercept of the two lines are the same, they are in fact on the same exact line.
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the shortest leg of a triangle is 2 centimeters shorter than the other leg. the hypotenuse of this triangle is 10 centimeters. what are the lengths of the two legs of this triangle?
Lengths of the legs of triangle are 6 cm and 8 cm by Pythagoras theorem of right triangle.
Let One short leg = x
then other = x+2
And hypotenuse is = 10 cm
so x²+(x+2)²=10²
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
From Pythagoras theorem : a^2 + b^2 = c^2
Where c is the hypotenuse and a,b are the other sides of a right angle triangle.
x²+ x²+4x+4=100
[(a + b)^2 = a^2 +2.a.b +b^2]
2 x²+4x-96=0
x²+2x-48=0
(x+8)(x-6)=0
x= -8 or 6
Neglecting - value x=6 as the length can not be negative.
So legs of triangle are 6 cm and 8 cm.
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true or false correlations are used both as a hypothesis test to check the relationship between two variables, and also as internal reliability check, again to check the relationship between two items
Correlations are used both as a hypothesis test to check the relationship between two variables, and also as internal reliability check, again to check the relationship between two items is true.
To evaluate a hypothesis about a population, hypothesis testing uses sample data. A hypothesis test evaluates the result's unusualness, determining if there is a reasonable amount of random variation or whether the result is too extreme to be accounted for by chance.
Reliability can be measured by internal consistency. When a measurement is said to be reliable, it means that it will always produce the same result, given all other factors being equal.
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here is an equation: 4x - 4 = 4x + _. What could you write in the blank so the equation would be true for:
a. No values of x
b. All values of x
c. One value of x
The value to write in the blank so the equation would be true is -4. Option A. no values of x
How to determine the valueIt is important to note that an algebraic expression is an expression comprising of coefficients, terms, factors, constants and variables.
These algebraic expression also consist of mathematical operations, such as;
MultiplicationDivisionFloor divisionSubtractionAdditionParenthesesBracketFrom the information given, we have the equation;
4x - 4 = 4x + _
To make the equation true, then, the values must be the same on both sides, the value to add is (-4) because expanding the bracket would give the same value. We have;
4x - 4 = 4x + (-4)
expand the bracket
4x - 4 = 4x - 4
0 = 0
Hence, the value is -4
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Identify the Constant of Proportionality From a Graph
The graph of constant of proportionality is determined and attached with a green check on the mark box
How to find the graph of constant of proportionalityThe ratio between two quantities that are directly proportional is the constant of proportionality.
When two quantities grow and shrink at the same rate, they are directly proportional. When y and x are two values that are directly proportional to one another, the proportionality constant k is defined as k=y/x.
The equation shows that y = kx and the y intercept is zero, because of this the graph will start from the origin
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Find the distance between the given points. Round your answer to the nearest tenth. ( 1 , 2 ) and (5, 9)
The distance between the given points is 8.1 units
How to find the distance between the given points?Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²)
From the given info, we have:
( 1 , 2 ) and (5, 9),
where x1 = 1, y1 = 2 and x2 = 5 and y2 = 9
d=√((x2 – x1)² + (y2 – y1)²)
d=√((5 – 1)² + (2 – 9)²)
d=√((4)² + (-7)²)
d = √65
d = 8.1 units
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*
The value of tan x is given. Find sin x and cos x if x lies in the specified
tan x=2, x 0,
xe
T
sinx=| (Type an exact answer, using radicals as needed.)
The value of sin and cosine of angle x are √2 and √2/2
How to determine the value of sin and cosinefrom the question, we have the following parameters that can be used in our computation:
tan(x) = 2
Also, we have the interval to be
x = (0, ¤/2)
This means that the value of the angle x is from 0 to 90 degrees
Mathematically, we have
tan(x) = sin(x)/cos(x)
This means that
sin(x)/cos(x) = 1/2
So, we have
cos(x) = 2sin(x)
Let cos(x) = √2
This means that
sin(x) = √2/2
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i need answers asap or pls
Answer:
see attached
Step-by-step explanation:
Pt.2 Can someone review my answers please? Thank you!
Answer:
Step-by-step explanation: Whats you answer? cant see it.
Help would be so appreciated!
Find the equation of the tangent line to the function f(x) = 3x3 − x2 + 2 at a = 0.
A.
y = 2
B.
y = 2x
C.
y = 2x + 2
D.
y = –2x + 2
Answer: To find the equation of the tangent line to a function at a specific point, we can use the following steps:
Find the derivative of the function f(x) = 3x3 − x2 + 2
f'(x) = 9x^2 - 2x
Substitute the point a = 0 into the derivative to find the slope of the tangent line at that point
f'(0) = 9(0)^2 - 2(0) = 0
Use the point-slope form of a linear equation, y - y1 = m(x - x1) to find the equation of the tangent line, where m is the slope and (x1, y1) is the point at which the tangent line touches the function.
y - f(a) = m(x - a)
y - (3*0^3 - 0^2 + 2) = 0(x - 0)
y - 2 = 0
So the equation of the tangent line to the function f(x) = 3x3 − x2 + 2 at a = 0 is:
y = 2
Therefore, the correct answer is A. y = 2
Step-by-step explanation:
1/2 x 2 please show your work .
The solution of an expression 1/2 x 2 is 1.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
We have an expression 1/2 x 2.
We will apply the inverse property of multiplication.
= any number x its reciprocal
= 2 x 1/2
= 1
Therefore, 1 is the solution.
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PLEASE HELP E ASAP!!!!!!!!!!
Answer:
78.4 meters
Step-by-step explanation:
The line passes through the points (3,5) and (6,11).
Algebraic rule (slope-intercept form or point-slope
form):
When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b).
When should you use point-slope form?
When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.
One of the three ways we can express a straight line is using the point slope form, also known as the point-gradient form. By merely knowing one point on the line and the slope of the line, we may use this form to get the equation of the line.
The slope and y-intercept of the matching line can be rapidly determined when we have a linear equation in slope-intercept form. This enables us to graph it as well.
The equation of a line can be represented in either slope-intercept form or point-slope form.
Slope-intercept form:
The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the equation of the line passing through the points (3,5) and (6,11) in slope-intercept form, we can use the point-slope formula to find the slope and then use one of the points to find the y-intercept.
Point-slope form:
The point-slope form of a line is given by y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
To find the equation of the line passing through the points (3,5) and (6,11) in point-slope form, we can use the point-slope formula and one of the points.
Using the point-slope formula, the slope of the line is (11 - 5) / (6 - 3) = 6/3 = 2.
So, the equation of the line in slope-intercept form is:
y = 2x + b
We can use the point (3,5) to find the y-intercept:
5 = 2 * 3 + b
Solving for b, we get b = -1.
So the equation of the line in slope-intercept form is:
y = 2x - 1
In point-slope form, using the point (3,5), the equation of the line is:
y - 5 = 2(x - 3)
Both forms represent the same line, just in different ways.
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AOB is a line . Ray OP is perpendicular to AB OC is another ray between rays OA and OP . If ray OD is perpendicular to OC , prove ∠COP = ∠BOD.
The proof of ∠COP = ∠POD is below.
What is a ray?When viewed as a vector, a ray is a vector from a point to a point . In geometry, a ray is usually taken as a half-infinite line (also known as a half-line) with one of the two points and. taken to be at infinity.
Given is that AOB is a line. Ray OP is perpendicular to AB. OC is another ray between rays OA and OP. If ray OD is perpendicular to OC.
Refer to the figure attached.
In ΔOCP and ΔODP -
∠OPC = ∠OPD = 90° {right angles}
OP = OP {Common}
OC = OD
By SAS criteria, ΔOCP ≅ ΔODP.
So, we can write -
∠COP = ∠POD
Therefore, the proof of ∠COP = ∠POD is given above.
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Juwan makes 12 baskets in 40 minutes. If he continues making baskets at this rate, how many baskets will he make in 90 minutes?
The required number of baskets made in 90 minutes are 27 baskets.
It is given that Juwan makes 12 baskets in 40 minutes and continues to make the baskets for 90 minutes.
Number of baskets made in 90 minutes = ?
So, let us calculate the number of baskets made in 1 minute.
40 min - 12 baskets
1 min - 12/40 baskets
Now, we need to find out the number of baskets made in 90 minutes.
90 min - ?
1 × 90 min - 90 × 12/40 = 27 baskets
Thus, the required number of baskets made in 90 minutes are 27 baskets.
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When Landon moved into a new house he planted two trees in his backyard. At the time of planting tree a what 24 inches tall and tree B was 40 inches tall. Each year there after three A grew by 9 inches per year and tree B grew by 5 inches per year. Let A represent the height of tree A t years after being planted and let B represent the heights of tree B t years after being planted. Write an equation for each situation in terms of t, and determine the height of both trees at the time when they have an equal height.
Answer:
A=24+9t
B=40+5t
Step-by-step explanation:
see attached
what metric unit would be best to measure the amount of spices put into a batch of cookies? responses
Grams are the ideal unit for calculating the quantity of spices in a batch of cookies (g).
A system of measurements is called the metric system. It is employed in calculations and research across the globe. Here are some instances of measurements made with the metric system:
The unit used to measure lengths and distances is the meter. In daily life, we use this unit to measure things like the length of a piece of clothing, the distance from school to home, etc.
You may have noticed that the bag of your favorite food has a weight listed on it. 250 grams of potato chips, as an illustration. The unit of weight used here is the gram.
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