Answer:
The solution has infinitely many solutions
Step-by-step explanation:
Let's simplify the equation first by combining like terms on both sides and then solving for x:
4x - 7 + 2x = 2(3x - 3) - 1
Simplifying the right-hand side:
4x - 7 + 2x = 6x - 6 - 1
Combining like terms on the right-hand side:
4x - 7 + 2x = 6x - 7
Combining like terms on the left-hand side:
6x - 7 = 6x - 7
The equation simplifies to an identity, meaning that it is true for all values of x. Therefore, there are infinitely many solutions to this equation.
example of two nonlinear functions that dont dominate each other
An example of two nonlinear functions that don't dominate each other is the sin function (f(x) = sin(x)) and the exponential function (g(x) = e^x).
For any given value of x, the sin function oscillates between -1 and 1, taking on both positive and negative values. It has a periodic nature and does not grow or decay exponentially as x increases or decreases.
On the other hand, the exponential function grows or decays exponentially as x increases or decreases. It is characterized by a constant positive growth rate. The exponential function increases rapidly when x is positive and approaches zero as x approaches negative infinity.
The key characteristic here is that the sine function oscillates while the exponential function grows or decays exponentially.
Due to their fundamentally different natures, neither function dominates the other over their entire domains.
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Gym A has an membership
fee of $100 and a monthly
cost of $30. Gym B has a
membership fee of $70 and a
monthly cost of $40. How
many months until both cost
the same?
Answer: 3months
Step-by-step explanation:
130 160 190 220 250 280 310 340 370 400
110 150 190 230 270 310 350 390 430 470 510
After 3 months they will both be at 190
Answer:
3 months until both costs are the same
Step-by-step explanation:
30x+100 = 40x+70
-30 -30
100 = 10x+70
-70 -70
30 = 10x
30/10 10x/10
30/10 = 3
How many unique triangles can be drawn with side lengths 8 in., 12 in., and 24 in.? Use the drop-down menus to explain your answer.
The side lengths can be used to draw
Choose...(an infinite number, 1, 2 or 0)
unique triangles because the two side lengths
Choose...(8&24, 24&12, 12&8)
add together to a sum that is
Choose...(less than, greater than)
the third side length.
Answer:
The side length can be used to draw (0) unique triangles because the two side lengths (8 and 12) add together to a sum that is (less than) the third side length
Step-by-step explanation:
Mrs. Trobiano regularly works 40 hours per week, at a rate of d dollars
per hour. Last week she worked h overtime hours at double time.
Express her total weekly salary algebraically.
Answer:
d = 40w x 2
Step-by-step explanation:
evaluate \int_c 2xy \, ds∫ c 2xyds where cc is the straight line between the points (1,1)(1,1) and (2,1)(2,1)
The value of the integral ∫c 2xy ds along the line segment between the points (1,1) and (2,1) is 3.
What is integral?
In mathematics, an integral is a fundamental concept that represents the accumulation or sum of infinitesimal quantities.
To evaluate the integral ∫c 2xy ds along the line segment between the points (1,1) and (2,1), we need to parameterize the curve and calculate the line element ds.
The line segment between the two given points can be parameterized as follows:
x = t, where t ∈ [1, 2]
y = 1
The line element ds can be calculated using the arc length formula:
\(ds = \sqrt(dx^2 + dy^2)\)
Substituting the parameterization into the formula, we have:
dx = dt
dy = 0
\(ds = \sqrt(dt^2 + 0) = dt\)
Now, we can rewrite the integral in terms of the parameter t:
∫c 2xy ds = ∫[1, 2] 2xy ds = ∫[1, 2] 2(t)(1)(dt)
Simplifying:
\(\int[1, 2] 2t dt = [t^2] |[1, 2]\)
Evaluating the limits:
\([2^2] - [1^2] = 4 - 1 = 3\)
Therefore, the value of the integral ∫c 2xy ds along the line segment between the points (1,1) and (2,1) is 3.
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A lawn is in the shape of a regular pentagon. It is made from 5 pieces of turf that are congruent triangles. Each triangle has an area of 19 in.2. What is the area of the lawn?
Answer:
The answer is 95 in^2
Step-by-step explanation:
The lawn is made up of 5 congruent triangles.
Since we know the area of the triangles we can add or multiply them.
5 * 19 = 95 so the area is 95 in^2
UPS charges $7 for the first pound and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each additional pound.
How many additional pounds, p, will it take for UPS and FedEx to cost the same? What is the cost? Write and solve an equation to show your work.
Answer:
1. 20 pounds
2. $11
Step-by-step explanation:
To set this up, you have to use a system of equations. It would look like this, where is pounds and is total cost:
UPS:
FedEx:
In order to solve a system of equations you must either a.) graph it, or b.) set them equal to each other.
If you graph it, the answer is where the two lines intersect.
If you set them equal to each other, solve it.
I will set them equal to each other in this:
The first step in a problem like this, where there's the same variable on both sides, is to subtract the smaller variable from both sides. In this case, it is . That would turn the equation into:
After that, you must solve it like a regular two-step equation.
Start by subtracting 5 from both sides:
Now, you must divide both sides by .
That would give us:
This means that in order for the prices to be the same, the package must be 20 pounds.
Now in order to find the total cost, you must plug 20 into one of the equations. It doesn't matter which, since they both equal the same. I will plug it into the FedEx equation:
Now you can just use a calculator and solve that or do it by hand. Multiply 0.30 by 20, to get 6, then add 5, which equals 11.
You should get: .
This means that the total cost, when the costs are the same for both FedEx and UPS, is $11.
Need 6 and 7 done please and thank you
Answer:
black
black
Step-by-step explanation:
Kendra was 46¼ inches tall. Three and a half years later, she was 49¾ inches tall. What was Kendra’s average yearly growth rate?
Answer:
Step-by-step explanation:
1 inch
Sydney spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -12.3°F. Between 9am and noon, the temperature rose 12°F. Between noon and 3pm, the temperature went up 11.5°F. Between 3pm and 6pm, the temperature dropped 16.3°F. What was the temperature at 6pm?
The temperature at 6pm was of -5.1ºF.
This problem can be solved by using system of equations.
A system of equations means when there are two or more variables that are related, and equations are made to find the values of each variable of the problem.
It is given that at 9 am, the temperature was -12.3°F. Between 9am and the noon, the temperature rose 12°F. So, the temperature at noon was of -12.3 + 12 = -0.3ºF.
Also, between the noon and 3pm, the temperature went up 11.5°F. So, at 3 pm, the temperature was of -0.3 + 11.5 = 11.2 ºF.
Further, between 3pm and 6pm, the temperature dropped 16.3°F.So, the temperature at 6 pm was of 11.2 - 16.3 = -5.1 ºF.
Hence, the temperature at 6pm was -5.1°F
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depending on the circumstances, the dequeue method of our linkedqueue class sometimes throws the queueunderflowexception. True or false?
True. depending on the circumstances, the dequeue method of our linkedqueue class sometimes throws the queueunderflowexception
The dequeue method of a LinkedQueue class throws a QueueUnderflowException when the queue is empty, and the user attempts to remove an element from it. This is because removing elements from an empty queue is not allowed and violates the basic properties of a queue data structure. Therefore, depending on the circumstances, the dequeue method may throw a QueueUnderflowException to indicate that the operation is invalid.
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Standard form of a linear equation -2x+3=4y
Answer:
y=-1/2x+3/4
Step-by-step explanation:
just divide the entire equation by 4, so that y is isolated.
The standard form equation of a line is y=mx+b
Question
You work with a carpenter who asks you to cut 4 boards to the following lengths: 7½ inches, 10½ inches, 9 inches, and 5½ inches. What is the total length, in inches, of the cut boards?
The total length, in inches, of the four cut boards is 130 inches.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum.
Given that, the length of each of the cut pieces of the board are 7½ inches, 10½ inches, 9 inches, and 5½ inches.
We have to find the total length of the board.
Total length of the board is found by adding each length.
Total length = 7½ + 10½ + 9 + 5½
Mixed fraction can be converted to improper fraction by cross multiplication.
7½ = (7 * 2 + 1) / 2, 10½ = (10 * 2 + 1) / 2 and 5½ = (5 * 2 + 1) / 2
Total length = 15/2 + 21/2 + 9 + 11/2
= (15/2 + 21/2 + 11/2) + 9
= 47/2 + 9
= 65/2
Again improper fraction can be converted to mixed fraction.
Total length of a board = 32 1/2 inches
But there are 4 boards.
Total length of the 4 boards = 4 × 65/2 = 130 inches
Hence the total length is 130 inches.
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Ifwe take the following list of functions f1,f2,f},f4, and f5. Arrange them in ascending order of growth rate. That is, if function g(n) immediately follows function f(n) in your list, then it should be the case that f(n) is O(g(n)). 1) f1(n)=10n 2)f2(n)=n1/3 3) 73(n)=nn 4) f4(n)=log2n 5)(5(n)=2log2n
Arranging the given functions in ascending order of growth rate, we have:
f4(n) = log2(n)
f5(n) = 2log2(n)
f2(n) = n^(1/3)
f1(n) = 10n
f3(n) = n^n
The function f4(n) = log2(n) has the slowest growth rate among the given functions. It grows logarithmically, which is slower than any polynomial or exponential growth.
Next, we have f5(n) = 2log2(n). Although it is a logarithmic function, the coefficient 2 speeds up its growth slightly compared to f4(n).
Then, we have f2(n) = n^(1/3), which is a power function with a fractional exponent. It grows slower than linear functions but faster than logarithmic functions.
Next, we have f1(n) = 10n, which is a linear function. It grows at a constant rate, with the growth rate directly proportional to n.
Finally, we have f3(n) = n^n, which has the fastest growth rate among the given functions. It grows exponentially, with the growth rate increasing rapidly as n increases.
Therefore, the arranged list in ascending order of growth rate is: f4(n), f5(n), f2(n), f1(n), f3(n).
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I dont know how to do this help!
Answer:
4\(\sqrt{3}\)
Step-by-step explanation:
\(\sqrt{48}\) is not in simplest form, however, 48 contains a perfect square as a factor, that is 16 × 3
using the rule of radicals
\(\sqrt{ab}\) ⇔ \(\sqrt{a}\) × \(\sqrt{b}\) , then
\(\sqrt{48}\)
= \(\sqrt{16(3)}\)
= \(\sqrt{16}\) × \(\sqrt{3}\)
= 4\(\sqrt{3}\) ← in simplest form
21) Eric buys a new hat for the price of $34.99. What
was the sales tax amount if the sales tax rate is 6%?
Answer: The sales tax is $2.10! Or to be very exact it is 2.0994!
Step-by-step explanation:
Running at a constant rate, Miguel ran 12 miles in a time of 120 minutes. How many minutes does it take Miguel to run 6 miles?
Answer:
60 min
Step-by-step explanation:
120 divided by 2= 60
Refer to Scenario 15-1. Vincent uses a pricing practice called?
QUESTION 14
Scenario 15-1
Vincent operates a scenic tour business in Boston. He has one bus which can fit 50 people per tour and each tour lasts 2 hours. His total cost of operating one tour is fixed at $450.
Vincent's cost is not reduced if he runs a tour with a partially full bus. While his cost is the same for all tours, Vincent charges each passenger his/her willingness to pay: adults $18 per
trip, children $10 per trip, and senior citizens $12 per trip. At those rates, on a typical day Vincent's demand is:
Passenger Type
Willingness to Pay
Demand per day
Adults
$18
70
Children
$10
25
Senior Citizens
$12
55
Assume that Vincent's customers are always available for the tour, therefore, he can fill his bus for each tour as long as there is sufficient total demand for the day.
Each customer who requests a tour on a regular day costs Vincent $1350.Vincent often makes $820 a day in profit. Vincent will make more money because he charged each consumer $18.
What is meant by price discrimination?Price discrimination is a sales strategy that involves charging clients differently for the same commodity or service based on what the vendor believes they can persuade the customer to accept. When a company uses pure price discrimination, it charges the highest price that each customer will accept.
Given,
Bus capacity = Adult Demand + Child Demand + Senior Demand
= 70 + 25 + 55/50
= 150/50
= 3
$450 × 3 is the tour's total price.
= $1350
2. On a typical day, total revenue equals the sum of adult demand multiplied by willingness to pay, child demand multiplied by willingness to pay, and senior demand multiplied by willingness to pay.
= 70 × $18 + 25 × $10+ 55 × $12
= $2170
Total revenue minus total costs equals profit.
= $2170 - $ 1350
= $820
The following formula will be used to determine his profit if he charged each customer $18:
Total Sales for a given day are calculated as follows: Adult Demand × $18 + Child Demand × $18 + Senior Demand × $18
= 70 × 1 8 + 25 × 18 + 55 × 18
= $1260 + $450 + $990
= $ 2700
Total Revenue - Total Cost = Profit
= $ 2700 - $ 1350
= $ 1350
As a result, the profit on the price of $18 is $1350, which is more than the prior profit.
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Write an exponential growth model for each situation.
1. initial value: 2,000 2. initial value: 50
growth rate: 6%
growth rate: 75%
3. initial value: 40
growth rate: 100%
write an exponential decay model for each situation. the value of x for each
value of f(x) will lie between two consecutive whole numbers. list the whole
numbers.
4. initial value: 1,000
decay rate: 20%
f(x) = 500
5. initial value: 1,800
decay rate: 7%
f(x) = 400
6. initial value: 1,200
decay rate: 12.5%
f(x) = 450
Exponential growth model for initial value 2,000 and growth rate 6%: \(f(x) = 2,000 * (1 + 0.06)^x.\)
Exponential growth model for initial value 50 and growth rate 75%: \(f(x) = 50 * (1 + 0.75)^x.\)
Exponential growth model for initial value 40 and growth rate 100%: \(f(x) = 40 * (1 + 1)^x.\)
Exponential decay model for initial value 1,000 and decay rate 20%: \(f(x) = 1,000 * (1 - 0.20)^x\)(f(x) lies between 333 and 334).
Exponential decay model for initial value 1,800 and decay rate 7%: \(f(x) = 1,800 * (1 - 0.07)^x\) (f(x) lies between 363 and 364).
Exponential decay model for initial value 1,200 and decay rate 12.5%: \(f(x) = 1,200 * (1 - 0.125)^x\) (f(x) lies between 6 and 7).
What is rate?
Rate refers to the measurement of the change in one quantity relative to another quantity. It describes the amount of change that occurs in a certain unit of time or with respect to another variable.
Exponential Growth Models:
Initial value: 2,000
Growth rate: 6%
Exponential growth model: \(f(x) = 2000 * (1 + 0.06)^x\)
Initial value: 50
Growth rate: 75%
Exponential growth model: \(f(x) = 50 * (1 + 0.75)^x\)
Initial value: 40
Growth rate: 100%
Exponential growth model: \(f(x) = 40 * (1 + 1)^x\)
Exponential Decay Models:
Initial value: 1,000
Decay rate: 20%
Exponential decay model: \(f(x) = 1000 * (1 - 0.20)^x\)
Whole numbers between which f(x) lies: 333 and 334
Initial value: 1,800
Decay rate: 7%
Exponential decay model: \(f(x) = 1800 * (1 - 0.07)^x\)
Whole numbers between which f(x) lies: 363 and 364
Initial value: 1,200
Decay rate: 12.5%
Exponential decay model: \(f(x) = 1200 * (1 - 0.125)^x\)
Whole numbers between which f(x) lies: 6 and 7
Please note that the exponential decay models assume continuous decay over time and may not precisely match the given exact value of f(x) in all cases. The listed whole numbers represent the range of whole numbers between which the corresponding value of f(x) will fall.
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Betty is making a quilt made of various patterns . She buys 3 sheets of fabric that each have an area of 30 square feet. She cuts them up into sections that are each 2/5 of a square foot . How many sections will she have total
Answer:
She will have 12 sections per fabric and 36 sections in all
Step-by-step explanation:
Betty buy 3 fabrics of 30 ft²
If she cut each to 2/5 of 1 ft²
Then she will have
30 × 2/5
= 6 × 2
= 12
She will have 12 for each fabric and for the 3 fabrics, she will have
12 × 3 = 36
Step-by-step explanation:
Answer:
225 sections
Step-by-step explanation:
Each fabric has an area of 30 sq ft.
All 3 fabrics have a total area of 3 * 30 sq ft = 90 sq ft.
Each sections has an area of 2/5 sq ft.
number of sections = total area of fabric / area of each section
90/(2/5) = 90 * 5/2 = 450/2 = 225
Answer: 225 sections
Help with numbers 6 and 8 please. :)
The required answers are 6) 150 degree 8) 215 degree.
What is Quadrant in trigonometry?If the terminal edge of an angle in standard position is on the x- or y-axis, the angle is referred to as a quadrantal angle. Quadrantal angles include 0, 90, 180, 270, and 360 degrees, among others. The images below show examples of some of these angles.
According to question:To convert radian to degree just multiply 180/π to radian.
6) 5π/6
= \($\frac{5\pi}{6}\times\frac{180}{\pi}\)
= 150 degree
8) to lie 35 degree in third quadrant add 180 degree to it
= 180 + 35
= 215 degree
Thus, required answers are 6) 150 degree 8) 215 degree.
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Determine the fundamental period of the following signal. Explain your steps in details. x[n]=8+cos(8πn/17)
Given signalx[n]= 8 + cos(8πn/17)The given signal is a sum of a constant and a cosine signal. The cosine signal is periodic with a period of 17, and a frequency of 8π/17 rad/sample.
To find the fundamental period of the given signal we need to consider both the constant and the cosine signal. Period of constant signal = ∞ Period of cosine signal = 2π/((8/17)π) = 17/4 samples. Now, we need to find the least common multiple (LCM) of the two periods, which will give us the fundamental period.
LCM (17/4, ∞) = 17/4 × 2 = 34/4 = 8.5The fundamental period of the given signal is 8.5 samples. Now, we need to find the least common multiple (LCM) of the two periods, which will give us the fundamental period.
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I would appreciate it if you can help me with this.
Answer:
\(450000 \leqslant 15000 + 4t\)
(3×10^-4)÷(1.2×10^7)
Answer: 2.5 x 10^-11
Step-by-step explanation:
R-3.15 Show that f(n) is O(g(n)) if and only if g(n) is Q2(f(n)).
f(n) is O(g(n)) if and only if g(n) is Q2(f(n)). This means that the Big O notation and the Q2 notation are equivalent in describing the relationship between two functions.
We need to prove the statement in both directions in order to demonstrate that f(n) is O(g(n)) only in the event that g(n) is Q2(f(n).
On the off chance that f(n) is O(g(n)), g(n) is Q2(f(n)):
Assume that O(g(n)) is f(n). This implies that for all n greater than k, the positive constants C and k exist such that |f(n)| C|g(n)|.
We now want to demonstrate that g(n) is Q2(f(n)). By definition, g(n) is Q2(f(n)) if C' and k' are positive enough that, for every n greater than k', |g(n)| C'|f(n)|2.
Let's decide that C' equals C and k' equals k. We have:
We have demonstrated that if f(n) is O(g(n), then g(n) is Q2(f(n), since f(n) is O(g(n)) = g(n) = C(g(n) (since f(n) is O(g(n))) C(f(n) = C(f(n) = C(f(n)2 (since C is positive).
F(n) is O(g(n)) if g(n) is Q2(f(n)):
Assume that Q2(f(n)) is g(n). This means that, by definition, there are positive constants C' and k' such that, for every n greater than k', |g(n)| C'|f(n)|2
We now need to demonstrate that f(n) is O(g(n)). If there are positive constants C and k such that, for every n greater than k, |f(n)| C|g(n)|, then f(n) is, by definition, O(g(n)).
Let us select C = "C" and k = "k." We have: for all n > k
Since C' is positive, |f(n) = (C' |f(n)|2) = (C' |f(n)||) = (C' |f(n)|||) = (C') |f(n)|||f(n)|||||||||||||||||||||||||||||||||||||||||||||||||
In conclusion, we have demonstrated that f(n) is O(g(n)) only when g(n) is Q2(f(n)). This indicates that when it comes to describing the relationship between two functions, the Big O notation and the Q2 notation are equivalent.
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Ms. Hernandez is taking her children and their friends to the movies. She will pay $10 for adult ticket and $7 for each child ticket. Ms. Hernandez does not want to spend more than $40. Which inequality can be used to find c, the number of child tickets Ms. Hernandez can purchase?
Look At Screenshot
Answer: 10 + 7x \(\leq \\\) 40
We can use exclusion method:
A and C is not correct because Ms Hernandez doesn't want to spend more than 40 dollars --> so it must be less than or equal to 40
What is the volume of a box with a height of 3/2 inches, a length of 7/2 inches, and a width of 5/2 inches.
Answer:
13.125 cubic inches
Step-by-step explanation:
Volume of box is 3/2 X 7/2 X 5/2 = 105/8 = 13 1/8 = 13.125 cubic inches
Select the correct answer.
Simplify the following expression.
view the picture
Answer: OPTION D ( \(6^{-67/28}\) )
Step-by-step explanation:
\(6^{-5/4} * 6^{-8/7}\)
\(6^{(-5/4) + (-8/7)}\)
\(6^{\frac{(-35-32)}{28} }\)
\(6^{-67/28} option D\)
Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane.
The volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane is V = xyz, where x, y, and z are the lengths of the sides of the rectangular box.
To find the largest volume, we need to maximize x, y, and z. Since we have three faces in the coordinate planes, one vertex will be at the origin (0, 0, 0). The other two vertices will lie on the coordinate axes.
Let's assume the vertex on the x-axis is (x, 0, 0), and the vertex on the y-axis is (0, y, 0). The third vertex on the z-axis will be (0, 0, z). Since the box is in the first octant, all the coordinates must be positive.
To maximize the volume, we need to find the maximum values for x, y, and z within the constraints. The maximum values occur when the box touches the coordinate planes. Therefore, the maximum values are x = y = z.
Substituting these values into the volume formula, we get V = xyz = x³. Therefore, the volume of the largest rectangular box is V = x³.
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What is the maximum volume of a rectangular box situated in the first octant, with three of its faces lying on the coordinate planes, and one of its vertices located in the plane?
there are 6 donut with sprinkles and 7 with filling. if there are 3 donut that have both sprinkles and filling, how many have sprinkles or filling?
There are 6 donut with sprinkles and 7 with filling. if there are 3 donut that have both sprinkles and filling, 10 have sprinkles or filling
What is Venn Diagram ?Circles that overlap or do not overlap each other are used in a Venn diagram to illustrate similarities and distinctions between objects or groups of objects.Objects that share characteristics are represented as overlapping circles, whereas objects that are unique stand alone.Venn diagrams are currently utilized in many academic and business settings as demonstrations.Let S represent the set for donut with Sprinklers.
Let F represent the set for donut with Filling.
To find :- How many have sprinkles or filling?
i.e. n ( S ∪ F )
Formula,
n ( S ∪ F ) = n ( S ) + n ( F ) + n ( S ∩ F )
Given,
n ( S ) = 6
n ( F ) = 7
n ( S ∩ F ) = 3
Putting in formula
n ( S ∪ F ) = n ( S ) + n ( F ) - n ( S ∩ F )
= 6 + 7 - 3
= 10
Donuts with Sprinklers or Filling = 10
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