The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.
To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.
Since the owner wants the total cost to be under $2000, we can set up the inequality:
43H + 750 < 2000
Now, let's solve this inequality for H, the number of hours:
43H < 2000 - 750
43H < 1250
Dividing both sides of the inequality by 43:
H < 1250/43
To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.
Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:
H < 29
Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.
By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.
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What the meaning of "well-ordered by ∈"?
The phrase "well-ordered by ∈" refers to a specific kind of ordering or relation on a set using the element-of symbol (∈). In set theory, the symbol "∈" represents membership, indicating that an element belongs to a set.
The meaning of "well-ordered by ∈"A well-ordering is a particular type of total order, where every non-empty subset of the set has a least element. In other words, for any subset of the set, there is always a smallest element in that subset according to the ordering relation.
When we say that a set is "well-ordered by ∈," it means that the elements of the set are arranged in a specific order such that the membership relation (∈) satisfies the properties of a well-ordering. This implies that every non-empty subset of the set has a smallest element with respect to the membership relation (∈).
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FInd the rate oifd change for thgis said function . pleaser
The average rate of change of the function over the interval is 4x + 2h
Finding the average rate of changeFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2x² + 9
The interval is given as
From x = x to x = x + h
The function is a quadratic function
This means that it does not have a constant average rate of change
So, we have
f(x) = 2x² + 9
f(x + h) = 2(x + h)² + 9
Next, we have
Rate = (2(x + h)² + 9 - 2x² - 9)/(x + h - x)
Evaluate
Rate = 4x + 2h
Hence, the rate is 4x + 2h
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answer the question in the picture
Answer:
The answer is 692
Step-by-step explanation:
a₁₇ = 72, a₅₁ = 208
aₙ = a + (n-1)d
a₁₇ =a + 16d = 72→ 1
a₅₁ = a + 50d = 208 →2
2-1
34d = 136
d= 4
a₁₇ = a + 16d = 72
72 = a + 64
a = 8
a₁₇₂ = a + (172-1)4
a₁₇₂ = 692
If the multiplication expression below were written in exponential form, what
number would form the base?
23 x 23 x 23 x 23 x 23 x 23 x 23
Answer here
Answer:
23 would form the base
7 would form the exponent
Step-by-step explanation:
23 is being multiplied by itself 7 times, so you can write it as [tex]23^7[/tex] where 23 is the base and 7 is the exponent
Simplify the product need help ASAP!!
The algebraic expression (3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4) can be simplified to give 3x/(x - 3) which makes the option D correct.
Simplifying Algebraic expressionSimplification of an algebraic expressions is the process of writing an expression in the most efficient and compact way, that is in their simplest form, without changing the value of the original expression.
Simplifying the algebraic expression we have:
(3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4)
by factorization;
3x² - 6x = 3x(x - 2)
x² - 6x + 9 = (x - 3)(x - 3)
x² - x - 6 = (x - 3)(x + 2)
x² - 4 = (x + 2)(x - 2)
(3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4) = 3x(x - 2)/(x - 3)(x - 3) × (x - 3)(x + 2)/(x + 2)(x - 2)
cancel out common factors we have;
(3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4) = 3x/(x - 3)
Therefore, the algebraic expression (3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4) can be simplified to give 3x/(x - 3)
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subtraction 8(1/2)-2(2/3)
Answer:
Exact Form:
35/6
Decimal Form:
5.83
Mixed Number Form:
5 5/6
Answer:8/3
Step-by-step explanation:
4-4/3
=12-4/3
=8/3
two third of 15 is equal to 2/5 of what number?
A. 20
B. 12
C. 25
D. 60
See the attached math problem.
The solutions to the matrices are
A = 2 by 3B = 3 by 2A₂₁ = 4B₁₂ = 8How to determine the solutions to the matricesFrom the question, we have the following parameters that can be used in our computation:
The matrices
The dimensions of the matrices are
A = 2 by 3 i.e 2 rows and 3 columns
B = 3 by 2 i.e 3 rows and 2 columns
For the positions of the matrices, we have
A₂₁ = 4
B₁₂ = 8
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5.5 m
5.5 m
+2m+2m+
What is the area of the rhombus?
O 11 m²
O 15 m²
O 22 m²
O 44 m²
The best answer choice among the given options is O 15 m², as none of the provided options match the correct Ccalculation.
To find the area of a rhombus, we need the lengths of the diagonals. In this case, the lengths of the diagonals are not provided. However, we can use the given information to determine the area based on the side lengths.
A rhombus is a quadrilateral with all sides of equal length, so the given side lengths of 5.5 m and 2 m can help us find the area.
We know that the diagonals of a rhombus bisect each other at right angles, dividing the rhombus into four congruent right triangles. Each side of the rhombus is the hypotenuse of one of these triangles.
Given that the side length is 5.5 m, we can consider one of these right triangles. One leg of the right triangle is half of the side length, which is (5.5 m)/2 = 2.75 m. The other leg of the triangle is the length of the diagonal, which is unknown.
Using the Pythagorean theorem, we can find the length of the diagonal:
(diagonal)^2 = (leg)^2 + (leg)^2
(diagonal)^2 = (2.75 m)^2 + (2 m)^2
(diagonal)^2 = 7.5625 m² + 4 m²
(diagonal)^2 = 11.5625 m²
diagonal ≈ √11.5625 m ≈ 3.4 m (rounded to the nearest tenth)
Since the diagonals of a rhombus are perpendicular bisectors of each other, the length of the other diagonal would also be approximately 3.4 m.
Now, we can calculate the area of the rhombus using the formula: area = (diagonal1 * diagonal2) / 2
area = (3.4 m * 3.4 m) / 2
area = 5.8 m²
The area of the rhombus is approximately 5.8 m².
The best answer choice among the given options is O 15 m², as none of the provided options match the correct area calculation.
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If 5x = 1/5 then x = ?
A. 2
B. -1
C. -0.2
D. 1
The value of x in the given expression is 1/25
Given the expression :
5x = 1/5To solve for x, we make x the subject of the expression
5x = 1/5
multiply both sides by 5
25x = 1
divide both sides by 25 to isolate x
x = 1/25
Therefore, the value of x in the expression is 1/25
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Combine like terms to create an equivalent expression.
7.4z-5(-1.6z+2.4)
The equivalent expression after combining like terms is 15.4z - 12.
To combine like terms and simplify the given expression, let's distribute the -5 to the terms inside the parentheses and then combine the like terms:
Expression: 7.4z - 5(-1.6z + 2.4)
Distributing -5 to the terms inside the parentheses:
7.4z - 5(-1.6z) - 5(2.4)
Simplifying the distributed terms:
7.4z + 8z - 12
Combining the like terms:
(7.4z + 8z) - 12
(7.4 + 8)z - 12
15.4z - 12
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match their terms to their definition
The correct match of the following item to their definitions are:
Reasoning or argument that explains how come, or in what way your evidence supports your position - warrant.Statement of your topic - what your paragraph is about AND your specific opinion or observation about it - claim.Common knowledge provided to orient your reader - contextAny information that is not common knowledge - data.What is a warrant?A writ authorizing or ordering someone to do something. The term frequently refers to a judge's writ authorizing law enforcement to conduct certain actions, such as making an arrest, searching a place, or seizing property.
A claim is to declare or insist that something is true, usually without giving any support or proof.
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What is the slope of a line that is parallel to the line shown
(-3, 1 ) (3,3)
2/3
3/2
-2/3
-3/2
Answer:
2/3
Step-by-step explanation:
You set up the formula then come out with 2/3
Its also positive because the arrows are facing to the right.
A manufacturer of light-emitting diode (LED) lights has tested its lights and found that the percent chance P that a light will fail after t hrs of use can be approximated by the following.
P = 100(1/2)^t/30,000
(a)
What is the percent chance that one of the company's LED lights will fail after 20,000 hrs? Round to the nearest tenth.
(b)
In how many hours will the chance of an LED light failing reach 40%? Round to the nearest thousand.
[tex]P=100\left( \frac{1}{2} \right)^{\frac{t}{30000}} \\\\[-0.35em] ~\dotfill\\\\ \boxed{A}\\\\ t=20000\hspace{5em}P=100\left( \frac{1}{2} \right)^{\frac{20000}{30000}}\implies P=100\left( \frac{1}{2} \right)^{\frac{2}{3}}\implies P\approx 63.0 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\\\\ P=40\hspace{5em}40=100\left( \frac{1}{2} \right)^{\frac{t}{30000}}\implies \cfrac{40}{100}=\left( \cfrac{1}{2} \right)^{\frac{t}{30000}}\implies \cfrac{2}{5}=\left( \cfrac{1}{2} \right)^{\frac{t}{30000}}[/tex]
[tex]\cfrac{2}{5}=\left( \cfrac{1}{2} \right)^{\frac{1}{30000}t}\implies \log\left( \cfrac{2}{5} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{30000}t} \right] \\\\\\ \log\left( \cfrac{2}{5} \right)=t\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{30000}} \right]\implies \cfrac{\log\left( \frac{2}{5} \right)}{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{30000}} \right]}=t\implies 40000\approx t[/tex]
-
Number of Weeks
9 s
Alexandra kept track of her salary for 15 weeks and created the histogram below.
4
O
1-10
S
Weekly Wages
Mark this and return
10
11-20
21-30
31-40
Amount of Wages in Dollars
A
41-50
What does the gap from 21-30 tell Alexandra about her weekly salary?
She did not work that week
Save and Exit
Next
4
Submit
The gap in the histogram tells her that she did not earn any wages that week.
What is histogram ?A histogram is a graphical data representation that reveals a dataset's distribution. It consists of a sequence of bars, where the height of each bar denotes the frequency or count of data points falling inside a given range and the width of each bar denotes a range of values.
Alexandra's pay histogram shows a gap from 21 to 30, which indicates that she did not work that week. This is so because no wages in the range of 21 to 30 are recorded in the histogram, which displays the amount she made each week.
It's possible that Alexandra was on vacation or ill and unable to work that week. Whatever the cause, the histogram gap indicates that she did not get any pay that week.
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Colin borrowed 4200 at 8% simple interest to be paid back in 3 years. How much interest will he pay
Answer:
Answer 1008
Step-by-step explanation:
HELP WITH CALCULATING AREA OF A CYLINDER AND SURFACE AREA.
These methods can be used in the construction of water tanks, oil storage tanks, cans, and tubes. They can also be used in the engineering sector to determine the Volume of certain cylinders like pipes and cylinders.
The cylinder is a geometrical figure which is three-dimensional with two parallel circular bases. There are different ways to calculate the area of a cylinder and the surface area of a cylinder.
The methods and formulas of calculating the area of a cylinder and the surface area of a cylinder are explained below.Area of a CylinderThe area of a cylinder is defined as the region occupied by the cylinder on a two-dimensional plane.
The formula used to calculate the area of a cylinder is A = 2πr² + 2πrh. Here, r denotes the radius of the circular base, and h denotes the height of the cylinder. The area of curved surface area of a cylinder is 2πrh. Surface Area of a Cylinder
The surface area of a cylinder refers to the total area of the figure including the area of the two bases of the cylinder.
The formula for calculating the surface area of a cylinder is A = 2πr(h + r). Here, r denotes the radius of the circular base, and h denotes the height of the cylinder. The surface area of the two circular bases of a cylinder is 2πr².
The two methods of calculating the area of a cylinder and the surface area of a cylinder are very essential in solving real-life problems.
For instance, these methods can be used in the construction of water tanks, oil storage tanks, cans, and tubes. They can also be used in the engineering sector to determine the volume of certain cylinders like pipes and cylinders.
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Determine the value of x in the equation. five sevenths times the quantity x plus 2 end quantity minus three sevenths times x equals two sevenths times the quantity x plus 5 end quantity
PLS HURRRY NEED THIS DUE BY 12 PM EDT
The equation does not have a unique solution for x. It is true for any value of x.
The given equation is:
(5/7)(x + 2) - (3/7)x = (2/7)(x + 5)
To solve for x, we'll first simplify both sides of the equation using the distributive property and combining like terms:
[(5/7)x + (5/7)(2)] - (3/7)x = [(2/7)x + (2/7)(5)]
Simplifying further:
(5/7)x + 10/7 - (3/7)x = (2/7)x + 10/7
Next, we'll collect the x terms on one side and the constant terms on the other side of the equation:
(5/7)x - (3/7)x - (2/7)x = 10/7 - 10/7
Combining like terms:
[(5/7) - (3/7) - (2/7)]x = 0
Simplifying further:
(0/7)x = 0
Any value of x will satisfy this equation since (0/7)x will always be zero.
Therefore, the equation does not have a unique solution for x. It is true for any value of x.
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Solve for x
8,10,12,3
Answer:
10
Step-by-step explanation:
2x = 2(-10 + 2x)
x = -10 + 2x
-x = -10
x = 10
Answer:
10
Step-by-step explanation:
Multiply the smaller line by 2
which is RS
2x = -20 + 4x
-2x = -20
x = 10
5. Find an expression to represent the area that is shaded
r
Answer:
(4 - π)r²
= 0.86 r²
Step-by-step explanation:
The radius of the circle = r
The diammeter of the circle = 2r
Area of circle = πr²
The side of the square = diammeter of the circle = 2r
The area of the square = (2r)² = 4r²
Area of shaded region = ar(square) - ar(circle)
= 4r² - πr²
= (4 - π)r²
= (4 - 3.14)r²
= 0.86 r²
Evaluate f(x)=7cos2x f(-pi/4)
[tex]f(x)=7\cos(2x)\hspace{5em}f\left( -\frac{\pi }{4} \right)=7\cos\left( -\frac{\pi }{4} \right) \\\\\\ f\left( -\frac{\pi }{4} \right)=7\left( \frac{\sqrt{2}}{2} \right)\implies f\left( -\frac{\pi }{4} \right)=\cfrac{7\sqrt{2}}{2}[/tex]
Please help me out with this
Answer:
I would say D
Step-by-step explanation:
since it already tells you what y equals it makes it easier to substitute the others take more work so the best first step is substituting for y
Answer:
Option D) Substitute for y in the first equation
Step-by-step explanation:
When solving for a system of equation, we always need 1 equation to have x or y already isolated by itself. This makes it easy to substitute that variable into the other equation, solve, then substitute the other variable into another equation.
This will give us an ordered pair, known as the solution.
In this system, we have 2 equations. In the first one, we have no variables isolated. In the second one, we have y isolated on the left side of the equal sign. This means we can take what y equals (3x+2) and substitute that in for y in the first equation.
Hope this helps! :)
What is the range of the function y=e^4x
The function [tex]y = e^4x[/tex] has a range of (0,∞). Here's why: The range of a function is the set of all possible output values.
To determine the range of a function, you must examine its graph or find the output for every input value.
In this case, [tex]y = e^4x[/tex] is an exponential function with a base of e, which is a constant that is approximately equal to 2.71828.
The exponential function [tex]y = e^x[/tex] is always positive.
Therefore, [tex]y = e^4x[/tex] will also be positive for all values of x.
As a result, the function's range will start at 0 and continue up to positive infinity, but will not include 0.This can be shown by graphing the function or plugging in various values of x to see what output values result. However, by knowing the properties of exponential functions, you can determine the range of[tex]y = e^4x[/tex] without graphing it.
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Khalid wrote the sequence below.
x-1,-2x+2,4x-4,-8x+8
Which formula can be used to find the 10th term of the sequence?
The formula to find the 10th term of the sequence is -512(x-1).
How to find sequenceThe given sequence is generated by starting with the term x-1 and then multiplying each term by -2 to get the next term.
Therefore, the nth term of the sequence can be expressed as:
[tex](-2)^(n-1) * (x-1)[/tex]
To find the 10th term of the sequence, we substitute n = 10 into the formula
[tex](-2)^(10-1) * (x-1) = (-2)^9 * (x-1)[/tex]
= -512(x-1)
So the formula to find the 10th term of the sequence is -512(x-1).
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cm² What is the area of this shape? Give your answer in cm 3 cm 2cm 6cm 2cm Not to scale
Based on the information provided, the total area of the shape given is 25 square centimeters.
How to calculate the area of this shape?The shape given is made up of two different shapes or two different rectangles. Due to this, to calculate the area, let's calculate the area of each of the rectangles, and then let's add the areas obtained.
First rectangle:
area = side x side
area = 2 cm x 3 cm
area = 6 square centimeters
Second rectangle:
area = side x side
area = 4 cm x 2 cm
area = 8 square centimeters
Total area: 6 square centimeters + 8 square centimeters
Total area = 14 square centimeters
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2. Bob said 5 x 800 = 400. Explain his error.
Answer:
Step-by-step explanation:
Bob made a little mistake there. 5 multiplied by 800 is actually equal to 4,000.
Calculate the values in these expressions:
A+B+C=196. A=82, B=2C B=__? C=__?
Answer:
B = 76, C = 38
Step-by-step explanation:
A + B + C = 196
substitute A = 82 and B = 2C into the equation
82 + 2C + C = 196
82 + 3C = 196 ( subtract 82 from both sides )
3C = 114 ( divide both sides by 3 )
C = 38
B = 2C = 2 × 38 = 76
The average weight of 12 eggs is 32 gms. Two of them weighing 35 and 37 gms respectively are broken. Find the average weight of the remaining 10.
Answer:
31.2 g
Step-by-step explanation:
You want to know the average weight of the remaining eggs if two from a dozen with average weight 32 g are broken, and their weights are 35 and 37 g.
Relative to averageThe two broken eggs differ from average by ...
(35 -32) +(37 -32) = 3 +5 = 8 . . . . . grams
The remaining eggs must differ from that average by the opposite amount, a total of -8 g.
Distributed over 10 eggs, this difference is -0.8 g, so the average weight of the remaining eggs is 32 -0.8 = 31.2 g.
The average weight of the remaining 10 is 31.2 g.
New sumThe average weight is the sum of all weights divided by the number of eggs:
avg = W/N
W = N·avg = 12·32 g = 384 g
The new sum of weight will be this amount less the weights of the broken eggs:
W' = 384 g -35 g -37 g = 312 g
The new number of eggs is 2 fewer: N' = 12 -2 = 10.
So, the new average weight is ...
avg' = W'/N' = 312 g/10 = 31.2 g
__
Additional comment
By working with the differences from average, we don't have to figure the old and new sums. We're only concerned with the way that sum changes, and the average amount of that change. Often, this means we can solve the problem using only mental arithmetic.
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Here is a table of values for y= f(x).
x -2 -1 0 1 2 3 4 5 6
f(x) 5 6 7 8 9 10 11 12 13
Mark the statements that are true.
A. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6).
B. The range for f(x) is all real numbers.
C. f(-1) = 6
D. f(5) = -2
The statements that are true are:
A. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6).
C. f(-1) = 6
To determine the truth of each statement, we need to analyze the given table of values for the function f(x).
A. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6).
The x-values listed in the table are -2, -1, 0, 1, 2, 3, 4, 5, and 6. These are the inputs for the function, and therefore, they represent the domain of f(x). Thus, statement A is true.
B. The range for f(x) is all real numbers.
Looking at the y-values listed in the table for f(x), we can see that the range of f(x) is from 5 to 13. It does not include all real numbers, so statement B is false.
C. f(-1) = 6
From the table, we can see that when x = -1, f(x) = 6. Thus, statement C is true.
D. f(5) = -2
There is no entry in the table for f(5), so we cannot determine the value of f(5) from the given information. Therefore, statement D is false.
In conclusion, the true statements are A and C.
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PLEASE HELP WILL MARK BRAINLIEST! PLEASE GIVE A LONG EXPLANATION!
Answer:
Both are incorrect
Step-by-step explanation:
In the right triangle ΔABC, ∠ABC = 90 and two angles = 45,
∠ACB = ∠BAC = 45
Therefore, the sides opposite to these angles are equal
⇒ x = z
By Pythagorean theorem,
x² + z² = y²
⇒ x² + x² = y²
⇒ 2x² = y² -----eq(1)
In the right triangle ΔABD,
∠ADB = 90
∠BAD = 45 (since ∠BAC = 45)
⇒ ∠ABD = 180 - 90 - 45
⇒ ∠ABD = 45
Since ∠BAD = ∠ABD = 45, the sides opposite to these angles are equal
⇒ AD = 3
Also since ΔABC is an isoceles triangle, BD bisects AC
⇒ AD = DC = AC/2 = y/2
⇒ y/ 2 = AD
⇒ y = 2AD
⇒ y = 2(3)
⇒ y = 6
From eq(1)
2x² = y²
⇒ 2x² = 6²
⇒ x² = [tex]\frac{6^2}{2}[/tex]
⇒ [tex]x = \sqrt{\frac{6^2}{2} }[/tex]
⇒[tex]x = \frac{6}{\sqrt{2} }[/tex]
and
[tex]z= \frac{6}{\sqrt{2} }[/tex]
