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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Tell whether the angles are complementary or supplementary. Then find the value of x.
Answer:
Complementary
x = 15
Step-by-step explanation:
Given angles are complementary, because their sum is 90°.Now, let us find the value of x.-> 3x° + 45° = 90°-> 3x° = 90° - 45°-> 3x° = 45°-> x = 45/3-> x = 153 3/10 minus 2 1/5 as improper fraction
Answer:
11/10
Step-by-step explanation:
33/10 - 22/10
A person is using a new teenis ball launching machine that is 15 inches by 14. Assuming the machine uses tennis balls that are spherical and 2.7 inches in diameter, how many tennis balls should fit in one of the top of the machine?
The number of tennis ball fit in the machine are 305 balls.
What is volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.
given dimensions of machine 15 x 15 x 14
volume of machine is 15 x 15 x 14 = 3150 cubic inches
and shape of ball is spherical,
with dia = 2.7 inches
radius of ball = 2.7/2 = 1.35 inches
volume of sphere is 4/3πr³
V = 4/3πr³
V = 4/3(3.14)(1.35)³
V = 4/3(3.14)(2.46)
V = 10.30 cubic inches
the area covered by 1 ball is 10.30 cubic inches
the number of ball in machine is 3150/10.30
the number of ball in machine = 305.82 = 305 approx
Hence 305 balls can be fit in machine.
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What is 6,789,694,976 x 9,452,569,132
*Can not use calculator
The product of the given numbers can be represented in a scientific notation form as = 6418 × 10^19 (approximately)
What is multiplication?Multiplication can be defined as the repeated addition of a given value with the purpose of arriving to an expected value.
The multiplication of two given numbers is the same thing as the products of the given number and it's represented by the sign (X)
The product of 6,789,694,976 x 9,452,569,132 = 6418 × 10^19
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1/4×1/12 ÷ 1 page = blank
1page
Answer:
0.02083333333
BRAINLIST! Please help
In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.
what is triangle ?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. Triangle angles add up to 180 degrees when combined together.
given
Use similar triangles,
BAC and DAB are similar
therefore
CA/AB = BA/AD
CA/20 = 20/10
cross multiply
AC = CA = 20*20/10 = 40
Or use metric relations
CA*AD = BA^2
CA = BA^2/AD = 20^2/10 = 40
In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.
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Malia signed up for a gym membership 14 weeks after Jane.
Let a represent the number of weeks Malia has been a member and b represent
the number of weeks Jane has been a member.
Find the value of b when a = 9.
When Malia joined a gym 14 weeks after Jane did, the value of b was 5.
What does "proportional relationship" mean?Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them.
What is a good illustration of an unproportional relationship?A car's fuel capacity and efficiency, as well as how far it can go on a single charge of its electric battery, are important considerations. A nonproportional connection can be used to describe this.
a + b = 14
9 + b = 14
b = 14-9 = 5
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You want to compare the ratios 3:12 and 7:28 to see if they're equal. You know that you need to compare the products of the extremes against the product of the means. Which two values are the means for this comparison? A. 3 and 7 B. 12 and 28 C. 3 and 28 D. 12 and 7
Answer:
Step-by-step explanation:
3:12 7:28
The means are the second and third terms in the proportion.
The extremes are the two outside terms.
12 and 7 are the means.
(3 and 28 are the extremes.)
So thre answer is D. 12 and 7.
Which equation has two solutions? A. W=-1. B. W=1. C. W=-2. D. W=0
Answer: An equation has two solutions when it has two distinct values that can be assigned to the variable to make the equation true.
In this case
equation A. W=-1 is a single solution
equation B. W=1 is a single solution
equation C. W=-2 is a single solution
equation D. W=0 is a single solution
So none of the given equations have two solutions. they all have only one solution.
It's worth mentioning that, if the equation is a quadratic equation (in the form of ax² + bx + c = 0) and it has a non-zero discriminant (b² - 4ac) then the equation will have two distinct real solutions.
In this case the equations are not in that form, and also doesn't show any signs of having two solutions.
Step-by-step explanation:
Below are graphs of several functions. Which functions have the specified domain and range ? There may be more than one correct answer
For the given value of domain and range , By observing the figure, The correct answer are options B,C and E.
What do you mean by function?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
What are domain and range of the function?A function's domain and range are the set of all possible inputs and outputs, respectively. A function's domain and range are crucial components. The range includes all of the function's output values, whereas the domain includes all potential input values from the set of real numbers.
domain : (x | x 3/2)
range : (-∞ , 2)
For these values, Option B , C and E holds that they exists when x 3/2 and it's output that is y exists between (-∞ , 2).
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Complete the following indirect proof (proof by contradiction).
Given: Adjacent angles LA and ZB, formed by the intersection of two lines
Prove: At least one of the angles LA and B has measure 90° or greater
First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.
The assumption is equivalent to the following two statements:
(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]
(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]
Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].
On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].
Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.
the loving lemon company sells a 4-gallon jug of lemonade for $24. The sweet and sour company sells an eight pack of 1-quart bottles of lemonade for $16.00. Witch company has a higher unit price please explain your answers
Answer:
The Sweet and Sour company
Step-by-step explanation:
Convert both types of lemonades into gallons and divide by the price.
For the loving lemon company you divide 24 by 4 and get a unit price of $6 per gallon
For the sweet and sour company change the 8 quarts into 2 gallons and divide 16 by 2, which gets you a unit price of $8 per gallon
When fitting a pipe into an existing fitting it allows a diameter variance of 0.001". If the interior diameter of the pipe is 0.49" and the pipe thickness is 0.005" what's the maximum allowable pipe diameter? a. 0.496, b. 0.501, c. 0.499, d. 0.541
Considering that the diameter variance of 0.001". If the interior diameter of the pipe is 0.49" and the pipe thickness is 0.005". the maximum allowable pipe diameter is 0.501''
How to find the maximum allowable pipe thicknessThe maximum allowable pipe diameter is calculated by
finding the total thickness of pipe
= interior diameter + 2 * pipe thickness
= 0.49 + 2 * 0.005
= 0.49 + 0.01
= 0.50
The diameter variance gives the range of the allowable diameter to ± 0.001 for maximum allowable pipe diameter we use + 0.001
hence
= 0.50 + 0.001
= 0.501
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If the equation of a circle is (x + 5)2+(y-7)2=36, its radius is
06
016
0 36
Therefore , the solution is circle Part 1: The central idea ( -5 , 7 ). 2nd part: Radius is 6 in part 2,3rd part: FALSE and Parts 4. There are 10 miles between A and B.
What is circle?A circular shape called a circle is created by following a moving point in a plane so that its distance from a particular point remains constant. The Greek word kirkos, which means hoop or ring, distance is the source of the English word circle.
Here,
The common circle equation is,
( x - h )² + ( y - k ) ( y - k )
6² = r²
where the circle's radius is r and the center's coordinates are (h, k).
Part 1.
Using the common circle equation, we obtain,
Circle's circumference's coordinate is ( -5 , 7 )
Consequently, the second choice is the right one.
Part 2.
Using the common circle equation, we obtain,
circle radius is six.
Consequently, the first choice is the right one.
Part 3.
Using the common circle equation, we obtain,
Circle's circumference's coordinate is ( 2 , 3 )
Therefore False.
Part 1.
In comparison to the common circle equation, we obtain,
Circle's center's coordinates are: ( -5 , 7 )
As a result, the second choice is the right one.
Part 2.
In comparison to the common circle equation, we obtain,
circle's diameter is six.
As a result, the first choice is right.
Part 3.
In comparison to the common circle equation, we obtain,
Circle's center's coordinates are: ( 2 , 3 )
So, False.
Part 1.
Giving the distance between two points,
Distance between A(-5, 3) and B (5, 3), expressed as:
=> [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} )}[/tex]
= > [tex]\sqrt{(-5-5)^{2} + (3-3)^{2} )}[/tex]
=> 10
Thus, 3rd Option is correct.
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A moving company wants to buy a new type of truck and needs to know the volume of the storage compartment before they can decide if they should purchase the truck. What’s is the volume of the storage compartment
Answer: jump off a cliff and shatter your bones
Step-by-step explanation:
Audrey mowed 12 lawns in 9 hours. What was her rate of mowing in hours per lawn?
On solving the provided question, we got to know that - arbitrary number So the money she earns is equal to 10 times w plus 15, which can be expressed as: 10w + 15
what is arbitrary number?A number is considered arbitrary if its only unique characteristic is that it has a high value. You can think of them informally as the numbers that your opponent picked. Any number appears to be worthless intuitively.
Since the question allows us to use any number, we decide to make the money she makes from washing the car equal $10. We'll also assume that she gets paid $15 to wax the car.
So the money she earns is equal to 10 times w plus 15, which can be expressed as:
10w + 15
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It snowed 3 inches each day for a week. By
the next Monday, 6 inches had melted away.
How many inches of snow were still on the
ground?
Answer:
3 × 7 = 21
21 - 6 = 15
15 is the answer
Whoever answers the previous question after this gets 50 points and brainliest if correct.
Step-by-step explanation:
I said it I knew it I did it I submit for you so I'm the one that is if if you know me.
Bookerville has a record of 12 inches of rain in 5 days. How much will it have to rain on Friday to beat the record by one tenth of an inch
The amount of rain required would be 2.5 inches.
What is the addition?
Addition is a mathematical operation that represents the process of combining two or more numbers together. The result of this operation is called the sum. The addition operation is often represented using the symbol "+", and it can be used to add any two or more numbers together.
To beat the record by one-tenth of an inch, an additional 0.1 inches of rain must fall.
Currently, the average amount of rain per day is 12 inches / 5 days = 2.4 inches per day.
So, the amount of rain that must fall on Friday to beat the record by one-tenth of an inch is 2.4 inches + 0.1 inches = 2.5 inches
Hence, the amount of rain required would be 2.5 inches.
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use partial quotients to solve
5,140÷9=
Answer: 571.11111...(Fraction: 9/28)
Step-by-step explanation:
5,140÷9 = 571.11111...
The student council is responsible for setting up the tables for
an awards banquet at the end of the year.
There are 144 people
who confirmed that they would attend the banquet.
The equation
8x +12y = 144 models this situation, where x is the number of
circular tables and y is the number of rectangular tables.
Find the x- and y-intercepts.
On solving the provided question, we can say that - here in the slope intercept [tex]2y / 2 = -4x /2 + 24 / 2 = > y = -2x + 12\\[/tex]
what is slope intercept?The point on the y-axis where the slope of the line passes is known as the intersection point in mathematics. the location on a line or curve where the y-axis crosses that point. This is demonstrated by putting y = mx+c as the equation for the straight line, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the slope (m) and y-intercept (b) of the line are highlighted. The slope is m, and the y-intercept is b for equations in the intercept form (y=mx+b). Additionally, certain equations may be recast to seem like slope intercepts. For instance, if y=x is rewritten as y=1x+0, the slope becomes 1 and the y-intercept becomes 0.
y = mx + c
m = slope, c = y-intercept
[tex]4x + 2y = 24\\2y = -4x + 24\\2y / 2 = -4x /2 + 24 / 2\\y = -2x + 12\\[/tex]
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Every time an insect jump forward the distance covered is half of previous jump. if the insect initially jumped 8.4cm calculate to the nearest two decimal places distance of sixth jump
The distance that he jumped in the sixth jump nearest to two decimal places will be 0.13.
What is a geometric sequence?Let a₁ be the first term and r be the common ratio.
Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
Every time an insect jump forward, the distance covered is half of the previous jump. If the insect initially jumped 8.4 cm.
The equation is given as,
aₙ = 8.4 · (1/2)ⁿ⁻¹
The distance that he jumped in the sixth jump will be given as,
a₆ = 8.4 · (1/2)⁶⁻¹
a₆ = 8.4 / 64
a₆ = 0.13125
a₆ ≈ 0.13
The distance that he jumped in the sixth jump nearest to two decimal places will be 0.13.
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salve for y √(7-x)²+(9-y)²
The solution for y in the equation √(7 - x)² + (9 - y)² is infinite many solutions
How to determine the solution for yFrom the question, we have the following parameters that can be used in our computation:
√(7-x)²+(9-y)²
Express tthe equation properly
So, we have the following representation
√(7 - x)² + (9 - y)²
The above is an expression, not an equation
This means that the value of the variable y can take any value and the equation will be true
In other words, it means that the variable y has infinite many solutions because it is not an equation but it is an expression
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In 8 hours, Badria reads 48 chapters of a book. What is her rate in chapters per hour?
Answer:
6chapters per hour
Step-by-step explanation:
Take 48 chapters divided by the no hrs which are 8
HELP with this equation
Answer:
83°
Step-by-step explanation:
-4m+51-4m+42= 158°
-8m+94= 158
-8m= 64
m= -8
JMK= -4m+51
= -4(-8)+51
= 32=51
= 83°
4. There are 36 units in a case. You have 90 loose units of stock in the store. The store manager has requested a stock count in CASES. How many cases of stock will 90 units fill? CALCULATION:
There are 36 pieces in one case. The store has 90 loose storage units. The store manager requested an inventory count where 2.5 units would fill her 90 units.
What is the inventory process like?Typically, this process involves the retailer (or team of employees) walking through the retailer's warehouse and storefront, counting each item. Information is captured manually using pen and paper or electronically using a mobile device.
Create a storage location map showing each shelf, bin, drawer, receiving dock, and return area. Place geographic divisions, not product lines, between each storage area. Let's start counting! After each counter completes a certain range, allow a manager or someone else to check the count.
90/36 = 2.5
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‼️PLEASE HELP ASAP!!!!‼️
Select the table that represents a linear function. (Graph them if necessary.)
Consider the line y = 8x-2.
Find the equation of the line that is parallel to this line and passes through the point (3, -2).
Find the equation of the line that is perpendicular to this line and passes through the point (3,-2).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Answer:
parallel line: y = 8x - 26
perpendicular line: y = -1/8 x - 13/8
Step-by-step explanation:
1.
Lines are parallel, so slopes are equal, and y-intercepts are different.
Given line:
y = 8x - 2
New line:
y = 8x + b
Use point (3, -2) and solve for b.
-2 = 8(3) + b
-2 = 24 + b
b = -26
Equation: y = 8x - 26
2.
Lines are perpendicular, so slopes are negative reciprocals.
Given line:
y = 8x - 2
New line:
m = -1/8
y = -1/8 x + b
Use point (3, -2) and solve for b.
-2 = -1/8 × 3 + b
-2 = -3/8 + b
b = -16/8 + 3/8
b = -13/8
Equation: y = -1/8 x - 13/8
2 Log y= 1/2 Log 16-Log 2 + 2 Log 3
Answer:
Based on the given equation, the function g is an exponential function with base 2. The y-intercept of the function g is at (0, 4).
The graph of function f is not described, so it is not possible to accurately compare the two functions. In order to accurately compare the two functions, it would be helpful to have more information about the graph of function f, such as the vertex and any other points that the graph passes through.
The table below shows the number of bacteria in a laboratory sample after x minutes. Fill in the missing blanks (HELP!!!)
Answer:
2.25
4.5
9
18
36
72
144
288
Step-by-step explanation: you take the number and multiply it by itself. but went it comes to the negative numbers you have to divide the number by 2 then take the answer you get from that and add it by itself so 4.5+4.5=9. its pretty simply when you under stand how to do it.