We can conclude the proof of inequality : 3 (m + n)! ≥ m! + n! below.
What is factorial?In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Mathematically, we can write -
[tex]$n! = n \times (n-1) \times \dots \times 1[/tex]
Given is the inequality -
3 (m + n)! ≥ m! + n!
We have -
3 (m + n)!
3 {(m + n)(m + n - 1)(m + n - 2) ....... (3)(2)(1)}
3 {m² + mn - m + nm + n² - n}(m + n + 2) ...... (3)(2)(1)
3 {m² + n² - m - n + 2mn}(m + n + 2) ........ (3)(2)(1)
3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1)
Now, for (m! + n!) --
(m! + n!) = m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)
It can be seen that -
3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1) ≥
m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)
Hence, it can be seen that -
3 (m + n)! ≥ m! + n!
Therefore, we can conclude that 3 (m + n)! ≥ m! + n!.
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Please define the following: Revenue, Cost and Profit VS
Marginal Revenue, Marginal Cost and Marginal Profit.
The additional expense brought on by reducing the quantity is known as the cost. An additional expense "at the margin" is another name for this. The extra income that results from raising the supply is known as the marginal revenue.
What is Cost and Profit?
Profit is defined as the difference of revenue and cost (determined by deducting cost from revenue. when revenue exceeds operational expenses, the difference between them is called the operating profit.
The additional money "at the margin" is another name for this.The money left over after a corporation pays its bills and expenses is known as its profit. Costs are the out-of-pocket expenditures comes to making, producing, and marketing the company's goods and services.
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if you had had a dog and a cat how many horses would u have
Answer: a lot
Step-by-step explanation:
Answer:
ummmm none? maybe
Step-by-step explanation:
Select three correct interpretations about the graph of r(t).
T
A. The average mortgage rate increased continuously
between 2003 and 2005.
B. The average mortgage rate fell to a relative minimum
between 2002 and 2003.
C. Based on the y-intercept, the average mortgage rate in
2010 was about 7.7%.
X
D. Based on the absolute maximum, the average
mortgage rate was highest between 2006 and 2007.
E. An appropriate domain for this function is 0≤t≤10
Answer: The correct interpretations about the graph of r(t) are B, D, and E.
Interpretation B is correct because the graph shows that the average mortgage rate fell to a relative minimum between 2002 and 2003.
Interpretation D is correct because the graph shows that the average mortgage rate was highest between 2006 and 2007, based on the absolute maximum.
Interpretation E is correct because an appropriate domain for this function would be 0≤t≤10, as t represents time and the graph shows data for the period between 2002 and 2010.
Interpretation A is not correct because the graph does not show that the average mortgage rate increased continuously between 2003 and 2005.
Interpretation C is not correct because the y-intercept does not represent the average mortgage rate in 2010. The y-intercept represents the value of the function when t = 0, which does not correspond to any time in the given data.
Step-by-step explanation:
Find tan0, where 0 is the angle shown.
Give an exact value, not a decimal approximation.
The exact value of tan θ = 15/ 8
What are trigonometric identities?Trigonometric Identities are defined as the equalities involving trigonometry functions and also one that holds true for all the values of the variables in the given equation.
The trigonometric functions are;
sinecosinetangentcotangentsecantFrom the information given, we have;
tan θ = opposite/ adjacent
To determine the adjacent sent
17² - 15² = x²
x = √64
x = 8
Substitute the value
tan θ = 15/8
Hence, the value is 15/8
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Which equation justifies why ten to the one third power equals the cube root of ten?
ten to the one third power all raised to the third power equals ten to the one third plus three power equals ten
ten to the one third power all raised to the third power equals ten to the one third times three power equals ten
ten to the one third power all raised to the third power equals ten to the three minus one third power equals ten
ten to the one third power all raised to the third power equals ten to the one third minus three power equals ten
The equation that justifies ten to the one third power equals the cube root of ten is ten to the one third power all raised to the third power equals ten to the one third times three power equals ten. Option B
How to justify the powerwe are to find [tex]10^{\frac{1}{3} } = \sqrt[3]{10}[/tex]
The justification has to be done with the use of the properties of powers as well as roots.
[tex]a^\frac{m}{n} = \sqrt[n]{a^m}[/tex]
then we would have:
[tex]\sqrt[3]{10} = \sqrt[3]{10^1} =10^\frac{1}{3}[/tex]
then we would have
[tex](10^\frac{1}{3} )^3\\\\= 10^\frac{3}{3}[/tex]
= 10
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Evaluate fraction with negative 3 raised to the seventh power times negative 3 squared in the numerator and negative 3 raised to the fifth power in the denominator.
−81
−27
27
81
Answer:
Last option, 81.
Step-by-step explanation:
Evaluate, [tex]\frac{(-3)^{7}(-3)^{2} }{\ (-3)^{5} }[/tex]
[tex]\frac{(-3)^{7}(-3)^{2} }{\ (-3)^{5} }[/tex] => [tex]\frac{(-3)^{7+2} }{\ (-3)^{5} }[/tex] => [tex]\frac{(-3)^{9} }{\ (-3)^{5} }[/tex] => [tex](-3)^{9-5}[/tex] => [tex](-3)^{4}[/tex] => [tex](-3)(-3)(-3)(-3)[/tex] => [tex]81[/tex]
Solve ^4√5x - 4 =1
A) x = 625
B) x = 81∕5
C) x = 25
D) x = 125
x=125
...............
19,22,25,28 the 11nth term
Answer:
31 hecause the èattern is adding 3
Step-by-step explanation:
What is the product of this expression? −1/4(8x−3/4)
Answer:
-6.1625
Step-by-step explanation:
-1/4=-0.85
-3/4=-0.75
-0.85*8x=-6.8
-0.85*-0.75=0.6375
-6.8+0.6375=-6.1625
Find the missing angle measure. Round to the nearest degree. cos 0 = 0.9563
The measure of the missing angle is 17 degrees.
Cosine as an example of trigonometric functions.Trigonometry is a method that can by used to solve questions involving the application of functions. Some examples of trigonometric functions are: Sine, Cosine, Tangent, Secant, Cotangent etc.
Now considering the given question, we are to find the measure of the missing angle. We have;
cos θ = 0.9563
where θ is the missing angle the value of which is to be determined.
Thus, divide both sides of the expression by cos to have;
cos θ/ cos = 0.9563. cos
θ = cos^-1 0.9563
θ = 17.0 degrees
Therefore, the value of the missing angle is 17 degrees.
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if its a linear equation in two variables
Answer:
SOLVE A SYSTEM OF LINEAR EQUATIONS BY GRAPHING.
Graph the first equation.
Graph the second equation on the same rectangular coordinate system.
Determine whether the lines intersect, are parallel, or are the same line.
Identify the solution to the system. ...
Check the solution in both equations.
Step-by-step explanation:
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
help with explanation if possible
Answer: 448
Step-by-step explanation: Parallelogram formula base times height
2 Justin had 3 rolls of ribbon. He used of a roll of ribbon to tie a parcel and 5 of another roll of ribbon to tie a present. How many rolls of ribbon did he use in all? How many rolls of ribbon did Justin have left?
Answer:1 roll of ribbon left
Step-by-step explanation:
Given equation (x+y)/3= 24 _ x
Rewrite the equation in slope intercept form .
Answer:
(y+72)
I'm not sure because your answer is not very clear
Before the trip, Tyler read 24 pages of his Philadelphia guidebook in an hour. The guidebook is 84 pages long. If he continued to read it at the same
rate, how long did it take Tyler to finish reading the guidebook before his family's trip?
Equation:
Solution X:
Answer:
3.5 hours to read
Step-by-step explanation:
Before the trip, Tyler read 24 pages of his Philadelphia guidebook in an hour. The guidebook is 84 pages long. If he continued to read it at the same rate, how long did it take Tyler to finish reading the guidebook before his family's trip?
total pages / reading rate per hour
Equation: 84/24
Solution: = 3.5 hours
19.
A box contains only quarters and dimes. If there were 10% more quarters, the total
value of the money in the box would increase by 7.5%. What is the ratio of the number of quarters to the
number of dimes in the box? Express your answer as a common fraction.
Answer:
The ratio of the number of quarters to the number of dimes in the box is 9:10
Step-by-step explanation:
a parking lot contains only cars and motor bikes. if there are 18 vehicles and 50 tires in the parking lot, how many cars and bikes are there?
Answer:
Step-by-Step:5 cars and 14 bikes
2. A number m is less than -3 or greater than or equal to 1.
The absolute value of m is equal to the positive distance between m and 0.
What is value?Value is an important concept in economics, finance, and accounting. It is the worth of a thing, such as a product, service, or currency. Value can be determined by the amount of goods or services it can exchange for, or the amount of money it can produce. Value is subjective, so it is up to the individual to decide what is valuable to them. Value is also a measure of the relative worth of a good or service, and it can have an effect on the price of a good or service. Value is an important concept to understand in economics, finance, and accounting.
The absolute value of m can be calculated by taking the distance between m and 0, regardless of whether m is negative or positive. For example, if m is -7, the absolute value of m is 7, since the distance between -7 and 0 is 7. If m is 3, then the absolute value of m is also 3, since the distance between 3 and 0 is also 3.
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The absolute value of m is equal to the positive distance between m and 0.
What is value?Value is an important concept in economics, finance, and accounting. It is the worth of a thing, such as a product, service, or currency. Value can be determined by the amount of goods or services it can exchange for, or the amount of money it can produce. Value is subjective, so it is up to the individual to decide what is valuable to them. Value is also a measure of the relative worth of a good or service, and it can have an effect on the price of a good or service. Value is an important concept to understand in economics, finance, and accounting.
The absolute value of m can be calculated by taking the distance between m and 0, regardless of whether m is negative or positive. For example, if m is -7, the absolute value of m is 7, since the distance between -7 and 0 is 7. If m is 3, then the absolute value of m is also 3, since the distance between 3 and 0 is also 3.
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Find a formula for RN for the function f(x) = (5x)² on [-1, 5] in terms of N.
Could you please show the work? I was able to get the area but can't exactly figure out what they want for the formula.
Compute the area under the graph as a limit.
lim RN=1050
Therefore , R(N) = 100 + 400 (N+1)(2N+1) + 800 x N2 N3 and area are the formulas for R(N) for the function f(x) = (5x)2 on [1, 5] and the function f(x) = (5x)2 in terms of N. R(N) = 767(approx) (approx).
What is function?Each x value in the domain has one but only one y value range, according to the rule of a function. Definition. If there is only one and only one value of x variable such that f(x) = y, then the function is one-to-one.
Here,
In the given question, we have to find a formula for R(N) for the function f(x) =(5x)^2 on [1, 5] in terms of N.
The given function is f(x)=(5x)^2 on [1, 5].
Ax = (5-1)/N
Ax = 4/N
X = 1+iAx
X = 1+i4/N
f(x) = 25X^2
f(x) = 25(1+i4/N)^2
f(x) = 25(1+i8/N+16/N^2 i^{2})
R(N) = 1ƒ(X) Ax
Now putting the value of f(x) and Ax
R(N)==1 [25 (1+ &i + 16i2)]
R(N) = 1001 (1 +Ni + 16i2)
N100 (1+i+12)N
100 (N += i +122)+16 N(N+1)(2N+1)(+1)(2N+1)
R(N)=100 (N + √2/ N(N+1) x 100
R(N) =2/6× N + 100 × 5 × N(N+1) + 100 x 2
[tex]\lim_{n \to \infty}[/tex] R(N) = 100 + 400 + 800/3
[tex]\lim_{n \to \infty}[/tex] R(N) = 766.67
[tex]\lim_{n \to \infty}[/tex] R(N) = 767(approx)
Therefore , the solution of the given problem of function comes out to be [tex]\lim_{n \to \infty}[/tex] R(N) = 767(approx).
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Visually estimate the location of the centroid of the region shown. Then find the exact coordinates of the centroid.
y=49-x², y = 0
Therefore exact coordinates of Centroid = (0,3/2)
Define Centroid.The centroid of a flat figure or solid figure, also known as the geometric center or center of figure, in mathematics and physics, is the arithmetic mean position of all the points on the figure's surface. Any n-dimensional Euclidean object is included by the same definition.
What is Triangle?A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
This region is a parabola opening downward, with vertex at (0, 49) and a range of y values from 0 to 49. The region is symmetric about the y-axis, This means that the x-coordinate of the centroid is at 0.
To find the y-coordinate:
Integral from -√(49) to √(49) of (49-x²) x dx = [x²(49-x²)/3] from -√(49) to √(49) = (492√(49))/3 = (98√(49))/3
The area is integral from -√(49) to √(49) of (49-x²) dx = [x(49-x²)/2] from -√(49) to √(49) = (49*(2√(49)) - (2/3)(49^(3/2)))/2 = (49*(2*√(49)) - (98√(49))/3)/2
Therefore Centroid = (0, (98√(49))/(49*(2*√(49)) - (98√(49))/3)) = (0,3/2)
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8+ ((3² x 6)- 18) ÷ 9
Check
Annie is comparing the cost to ship a package. One shipping
pound a package weighs. Another shipping company charges $5 for
company charges $7 for the first pound and $0.20 for each additional
the first pound and $0.30 for each additional pound.
Part A
Which equation could be used to determine p, the number of
when the costs for the two shipping companies are the same?
7+0.20p = 5 +0.30p
7+20p = 5 + 30p
A7+0.30p=5+0.20p
B0.20+7p = 0.30 + 5p
Part B
Show
pounds,
For how many pounds is the cost of the two shipping companies the
same?
Part A: The equation could be used to determine p is B0.20+7p = 0.30 + 5p Part B: Two shipping companies is the same for 25 pounds. Company 1 = $7 + (25 - 1) x $0.20 = $11.80 Company 2 = $5 + (25 - 1) x $0.30 = $11.80.
How to find pounds is the cost of the two shipping companies?The cost of shipping through two different companies will depend on a variety of factors.
These factors may include the weight and size of the package, the distance it needs to travel, the speed of delivery, and any additional services requested.
Additionally, the cost of shipping may also depend on the type of shipping service used (e.g. ground, air, or express).
To find out the cost of shipping through two different companies, it is best to contact each company directly. This can usually be done by phone, email, or through their website.
Each company will be able to provide a quote based on the package’s specifications. It is then possible to compare the cost of the two shipping companies and determine whether or not the cost is the same.
It is important to note that companies may offer discounts or other incentives for shipping with them.
Therefore, it is important to pay attention to any additional fees or discounts that may apply in order to get the best deal.
Comparing the cost of two different shipping companies can help to ensure that the most cost-effective option is chosen.
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The opposite of the opposite of -2 is equal to
The opposite of the opposite of -2 is equal to: -2
This can be solved by using the concept of inverse.
What is inverse?This quantity is also referred to as the opposite (number), sign modification, and negation. It changes the sign of a real number so that the additive inverse of a positive number is negative and the additive inverse of a negative number is positive. Due to their ability to reverse mathematical processes, inverse techniques are crucial for solving equations. One of the most crucial issues to ask whenever a new mathematical method is presented is how to invert it.
The term inverse in mathematics refers to the inverse of another operation.
In this case firstly opposite of - 2 is 2 and next opposite of 2 is again -2.
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Please help will mark Brainly (please answer all the drop down questions)
Step-by-step explanation:
system 1 :
3x + 2y = 7
4x + 7y = 17
system 2 :
12x + 2y = 28
4x + 7y = 17
the first equation in the second system is not a multiple of either equation in the first system, and the second equation in the second system is the same as the second equation in the first system.
thus, the systems are not equivalent.
"12x" gives us the idea what the factor would have to be (4 or 3), if the second equation of the second system would be a multiple of any of the equations in the first system.
as we would have to multiply 3x by 4 to get 12x, and 4x by 3 to get 12x.
but then 2y×4 = 8y, or 2y×3 = 6y, and that is not the same as 2y (part of the first equation of the second system).
that is why this first equation of the second system is not a multiple of either equation in the first system.
and that makes it impossible for both systems to be equivalent. that the second equations are identical, is then not relevant anymore.
S+S+S+S AND 4S I don't know it could someone help me who knows it is it equivalent or not equivalent
Yes, the expressions S+S+S+S AND 4S as required in the task content are equivalent expressions.
Are the given expressions equivalent expressions?It follows from the task content that the expressions given S+S+S+S AND 4S are to be compared and determine if they are equivalent or not.
Since the given expressions are; S + S + S + S and 4S.
S + S + S + S can be written by factorisation as;
S ( 1 + 1 + 1 + 1 ) = S (4)
= 4S.
On this note, it can be inferred that the two expressions given are equivalent expressions.
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solve y=(1/2)x exponential graph
The value of the exponential graph y = ( 1/2 )ˣ is graphed
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
y = ( 1/2 )ˣ be equation (1)
On simplifying the equation , we get
y = 1 / (2ˣ)
Now , the graph of the function y = ( 1/2 )ˣ will be a slanting line which will not touch the x axis and passes through the point y = 1
The graph of the function y = ( 1/2 )ˣ is given below
Hence , the function is solved and the graph is plotted
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What is the value of the expression below?
−2
1
3
− 3
5
6
+ 1
1
3
?
Answer:
Step-by-step explanation:
The expression you've provided is a combination of several fractions, but it's not clear how they are supposed to be combined. Without more information, it's impossible to know what the value of the expression is.
It would be helpful if you could provide more context or clarify how you want the fractions to be combined.
I can only tell you how the fraction works in mathematics and how you can evaluate the value of it if you have the complete information.
A particle moves with velocity function v(t) = −t2 + 5t − 3, with v measured in feet per second and t measured in seconds. Find the acceleration of the particle at time t = 3 seconds.
The acceleration of the particle is 1 foot per second square
How to determine the acceleration of the particle?From the question, we have the following parameters that can be used in our computation:
Velocity function v(t) = −t2 + 5t − 3
Express properly
So, we have
v(t) = -t² + 5t − 3
At time t = 3 seconds, we have
v(3) = -(3)² + 5(3) − 3
Evaluate
v(3) = 3
So, we have
Acceleration = v(3)/3
This gives
Acceleration = 3/3
Evaluate
Acceleration = 1 foot per second square
Hence, the acceleration is 1 foot per second square
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FIND THE SLOPE . THE PICTURE ATTACHED IS THE FULL QUESTION ,
Answer:
-12/5
Step-by-step explanation:
slope = change in y / change in x
change in y = 12 (from top to bottom) = 6 - (-6)
change in x = -5 (from top to bottom) = -2 -3
slope = 12/-5 = -12/5
The value of 1/2÷1/3=