If a, b, and c are different positive integers and a2+b3+c4=55, Then what is the greatest value for a*b*c=?
Answers
Answer:
Step-by-step explanation:
Given a^2 + b^3 + c^4 = 55, we need to find the greatest value for a * b * c.
To solve this problem, we can use the AM-GM inequality, which states that the arithmetic mean of a set of non-negative numbers is always greater than or equal to their geometric mean.
Using this inequality, we have:
(a^2 + b^3 + c^4) / 3 >= (a*b*c)^(2/3)
55/3 >= (a*b*c)^(2/3)
(55/3)^(3/2) >= a*b*c
The maximum value of a, b, and c occurs when they are as close together as possible. We can use the fact that a, b, and c are distinct positive integers to determine that the closest they can be is 1, 2, and 3.
So the greatest value for a * b * c is (1*2*3) = 6, and we have:
(55/3)^(3/2) >= 6
Approximately: 23.1 >= 6
Therefore, the greatest value for a * b * c is 6.
The greatest value for abc is 3,240.
What is the greatest value for abc?We want to find the greatest value of the product abc, given that a, b, and c are different positive integers and a + b + c = 55.
To maximize the value of abc, we want to maximize each individual factor, a, b, and c. We can do this by setting a to be as small as possible and c to be as large as possible, while ensuring that a, b, and c are still different positive integers.
Since a, b, and c are different positive integers, the smallest value for a is 1.
To maximize c, we set b = a + 1 and c = 55 - a - b.
Substituting b and c in terms of a, we get:
c = 55 - a - (a + 1) = 54 - 2a
Now we can express the product abc in terms of a:
abc = a x b x c = a (a + 1)(54 - 2a)
Expanding this expression, we get:
abc = -2a³ + 53a²+ 54a
To find the maximum value of abc, we can take the derivative of this expression with respect to a and set it equal to zero:
d(abc)/da = -6a² + 106a + 54 = 0
Solving for a, we get:
a = 8.93 (rounded to two decimal places)
Since a must be a positive integer, we round up to a = 9.
Using this value of a, we can find the corresponding values of b and c:
b = a + 1 = 10
c = 55 - a - b = 55 - 9 - 10 = 36
Therefore, the greatest value of abc is:
abc = 9 x 10 x 36 = 3,240
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The complete question is below:
If a, b, and c are different positive integers and a₂+ b₃ + c₄ = 55, Then what is the greatest value for abc= ?
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Graph the line with slope 3 and intercept 1 X
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Expand and simplify 2(3t+4)+3(2t+6)
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Answer:
∛4²
Step-by-step explanation:
A fraction exponent can be represented using a radical. The base number is the number in the radical. The numerator of the fraction is the exponent inside the radical. The denominator is the type of radical.
To write an exponent in radical form , the denominator, or index goes in front of the radical, and the numerator goes inside of the radical. We raise the base to the power of the numerator
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Also known as the last one hope i helped tell me if its right or not
1. Find the area.
7in
5in
3in
Answers
A2+B2=C2
5^2+3^2= x^2
25+9=x^2
34=x^2
You square booth sides and end up with a decimal of 5.831 rounded for the missing side.
Area for a rectangle is length times width so we multiply 7x5.831=40.817
Area of a triangle is the height times the base divided by 2 so 5.831x3= 17.493
Then you add those to together for the total area of the shape 40.817+17.493=58.31
58.31 is your approximate answer.
I Need help!!!
There are 36 students on the
school's student council. A special homecoming dance committee is to be formed by
randomly selecting 8 students from student council. How many possible committees can be formed?
1,043,460
27,907,200
30,260,340
Answers
Answer:
this is your answer 30,260,340
458 divided by eighty two
Answers
Answer: 5.5853658537
Step-by-step explanation:
You roll a die with the sample space S=(1,2,3,4,5,6]. You define A as (1,2,4),B as [1,2,4,5,6],C as [5,6) and D as [2,3,6) Determine which of the following events are exhaustive and/or mutually exclusive
Answers
- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.
To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.
To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.
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complete this item. (enter letter variables in alphabetical order.) rewrite the expression so that it has no denominator.
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The given expression is $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ and we need to rewrite this expression without any denominator in it. Step-by-step explanation: We can use the concept of the Least Common Multiple (LCM) of the denominators to remove the fractions in the expression. By taking the LCM of the denominators of the given expression, we have,$LCM\text{ of }t, u, v = t \cdot u \cdot v$ Now, multiplying each term of the given expression with the LCM $t \cdot u \cdot v$, we get,$\frac{6}{t}\cdot t \cdot u \cdot v+\frac{8}{u}\cdot t \cdot u \cdot v-\frac{9}{v}\cdot t \cdot u \cdot v$$6uv + 8tv - 9tu$$\therefore \text{The given expression without any denominator is } 6uv + 8tv - 9tu.$Thus, we can rewrite the given expression $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ without any denominator in it as $6uv + 8tv - 9tu$.
LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM. Take the positive integers 4 and 6 as an illustration.
There are four multiples: 4,8,12,16,20,24.
6, 12, 18, and 24 are multiples of 6.
12, 24, 36, 48, and so on are frequent multiples for the numbers 4 and 6. In that lot, 12 would be the least frequent number. Now let's attempt to get the LCM of 24 and 15.
LCM of 24 and 15 is equal to 222235 = 120.
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at a booth at the school carnival in past years, they've found that 28% of students win a stuffed toy ($3.65), 14% of students win a jump rope ($1.20), and 8% of students win a t-shirt ($7.50). the remaining students do not win a prize. if 250 students play the game at the booth, how much money should the carnival committee expect to pay for prizes for that booth?: *
Answers
The money the carnival committee expects to pay for prizes for that booth is $447.5
In previous years, they've discovered that 28% of students win a stuffed toy ($3.65).
14% of students win a jump rope ($1.20).
8% of students win a t-shirt ($7.50) at a booth at the school carnival.
There is no award for the remaining students. How much money should the carnival committee anticipate spending on prizes for that booth if 250 kids participate in the game at the booth.
percentage of students win a stuffed toy ( $3.65 ) = 28%
percentage of students win a jump rope ( $1.20 ) = 14%
percentage of students win a t-shirt ( $7.50 ) = 8%
Given 250 students playing the game.
Out of 250, 28% win a stuffed toy;
= 250 * (28/100)
= 70
14% win a jump rope;
= 250 * (14/100)
= 35
8% win a t-shirt;
= 250 * (8/100)
= 20
According to the total number of products sold for each quantity;
Amount of money the carnival committee expects to pay for prizes for that booth;
= ($3.65 * 70) + ($1.20 * 35) + ($7.50 * 20)
= 255.5 + 42 + 150
= $447.5
The money the carnival committee expects to pay for prizes for that booth is $447.5.
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If the following jobs are sequenced according to the SLACK rule then job A would be completed on day (assume zero for today's date)
Job - Processing Time (days) - Due Date
A 8 12
B 6 15
C 11 17
D 7 10
E 3 8
Select one: A. 7. B. 15. C. 8. D. 12.
Answers
If the jobs are sequenced according to the SLACK rule, Job A would be completed on day 12.
The SLACK rule involves calculating the slack time for each job, which is the difference between the due date and the completion time. The job with the least slack time is prioritized and scheduled first. In this case, the due dates for the jobs are as follows: Job A (12), Job B (15), Job C (17), Job D (10), and Job E (8).
Job A has a processing time of 8 days and a due date of 12, so the slack time is 12 - 8 = 4 days. Since Job A has the least slack time among all the jobs, it would be completed on day 12. Therefore, the answer is D. 12.
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PLS HELP I WILL MARK BRAINLIEST!!!
Answers
assume that t is a linear transformation. find the standard matrix of t. t: ℝ2→ℝ2 first reflects points through the line x2=−x1 and then reflects points through the origin.
Answers
the standard matrix of the linear transformation T: ℝ² → ℝ², which first reflects points through the line x₂ = -x₁ and then reflects points through the origin, is:
[ -1 0 ]
[ 0 1 ]
To find the standard matrix of the linear transformation T: ℝ² → ℝ², we can determine how the basis vectors of ℝ² transform under the given transformation.
The standard basis vectors of ℝ² are:
e₁ = (1, 0) (corresponding to the x-axis)
e₂ = (0, 1) (corresponding to the y-axis)
First, let's apply the reflection through the line x₂ = -x₁:
For e₁ = (1, 0), the reflection through the line x₂ = -x₁ maps it to (-1, 0).
For e₂ = (0, 1), the reflection through the line x₂ = -x₁ maps it to (0, 1).
Next, let's apply the reflection through the origin:
For (-1, 0), the reflection through the origin keeps it the same (-1, 0).
For (0, 1), the reflection through the origin keeps it the same (0, 1).
Now, we have the transformed basis vectors:
T(e₁) = (-1, 0)
T(e₂) = (0, 1)
The standard matrix of the linear transformation T is constructed by placing the transformed basis vectors as columns:
[ -1 0 ]
[ 0 1 ]
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Imani is buying a new cell phone for $800.00. She has to put down
20% and finance the rest at an exact interest rate of 6% for 275
days. How much is the maturity value of her loan?
Answers
Is the first side “WX and ZX” or “WX and XZ?”
This is sss congruence
Answers
Answer:
WX ZX
Step-by-step explanation:
If you fold it at the line of symmitry then w and x are at the same point
376×74 help and show work
Answers
Answer:
27,824
Step-by-step explanation:
i just calculated it.
here ya go! I hope this helps you! :)
1.) intersecting lines are _____ coplanar.
2.) two planes _____ intersect in exactly one point.
3.) three points are _____ coplanar.
4.) a plane containing two points of a line ____ contains the entire line.
5.) four points are ____ coplanar.
6.) two lines ______ meet in more than one point.
Answers
Answer:
1. Sometimes
2. Never
3. Always
4. Always
5. Sometimes
6. Never
Bob walks 8/10 of a kilometer to school each day. How many kilometers does bob walk to school in 5 days ?
Answers
Answer:
4 in 5 days
Step-by-step explanation:
diagrams that can convey both data and concepts or ideas are known as __________.
Answers
Diagrams that can convey both data and concepts or ideas are known as infographics.
Diagrams that can convey both data and concepts or ideas are known as "informational graphics" or "infographics". These graphics use visual elements such as charts, graphs, illustrations, maps, and diagrams to convey complex information and ideas in a concise and easy-to-understand way.
Infographics can be used in various fields, including business, education, journalism, and marketing, to present information in a visually appealing and engaging manner.
They are particularly useful when presenting large amounts of data or complex processes and can be designed to cater to different audiences, such as professionals or the general public. Overall, infographics are a powerful tool for communicating information and ideas effectively and efficiently.
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How many solutions does this system of equations have?
None
Exactly two
Exactly one
Infinitely many
Graph of a system of linear equations. Equation 1 is negative x plus 2y equals 6. Equation 2 is negative x plus 2y equals 0. The graphs of the lines are parallel.
Answers
Answer:
None
Step-by-step explanation:
If i'm being honest i don't remember why it was none when I took the quiz but I had a reason for choosing none and its correct. I promise
Answer:
none
Step-by-step explanation:
sorry I know everyone already knows but I could use the 20 points
likert-type scale response choices must be balanced at the ends of the response continuum.
Answers
that it is important for likert-type scale response choices to be balanced at the ends of the response continuum. This means that there should be an equal number of positive and negative response options to avoid any bias or skew in the results.
An explanation for this is that if there are too many positive or negative response options, respondents may feel pressured to choose a certain option even if it doesn't accurately reflect their true opinion. This can result in inaccurate data and can skew the results of the survey or study.
balancing the response choices on a likert-type scale is crucial for obtaining accurate and unbiased data. By having an equal number of positive and negative options, respondents are more likely to provide honest and accurate responses.
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Para comprar un edificio aportan Luis s/. 15489 mas que David y s/. 43968 menos que Cristian si David aportó s/. 189576 ¿cuánto pagaron por el edificio
Answers
The total amount paid for the building is the sum of the amounts contributed by all three people: Total amount = D + L + C= 189576 + (189576 + 15489) + 249033= s/. 703674 , the total amount paid for the building is s/. 703674
In this problem, the amounts contributed by Luis and Cristian are unknown, and we have to find them using the given information. We also need to find out the total amount paid for the building. Let us use algebraic expressions to represent the unknown amounts contributed by Luis and Cristian.We are given the following information: - Luis contributed s/. 15489 more than David. - Luis contributed s/. 43968 less than Cristian. - David contributed s/. 189576. Let us represent the unknown amounts contributed by Luis and Cristian as L and C, respectively. Using the given information, we can set up the following equations: L = D + 15489 C = L + 43968 = D + 15489 + 43968 (since L = D + 15489) = D + 59457Now, we can substitute the value of D in the second equation to get: C = 189576 + 59457 = 249033. the total amount paid for the building is s/. 703674
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Hi! I would like help on this, I’m a first-timer on brainly! The answer choices are:
A) multiplied by 4
B) decreased by 1/2
C) remains unchanged
D) increased by 1/2
E) None of the above
Thank you!☺️
Answers
Answer:
B
Step-by-step explanation:
No matter what value you multiply a, the fraction will remain unchanged. That is because you can divide an a out from the numerator and the denominator. Thus, doubling a has no affect on the fraction, and in fact, u can simplify it to just bc. Now, if you halve b, it will simply just halve the actual value. When you halve b, you are simply executing (1/2)(b)(c). Therefore, you can rearrange the expression to be (1/2)(bc), which is just halving bc. If you decrease by 1/2, it's the same thing as being half of the value it was before. Therefore, the answer is b.
Another word one! Please help only if you know, thank you!
Answers
Answer:
Step-by-step explanation:
if C is the right angle,
AB is the hypotenuse
AB^2=AC^2+BC^2
AC^2=13^2-5^2
AC^2=169-25=144
AC=\(\sqrt{144}\)=12
AC=12
2
What is the slope of the line y = 3-2/3x
Answers
Answer:
the slope is -3
Step-by-step explanation:
The number of cd's sold since april 8 at a music store can be modeled by the function n(d)=12d+35 and the price per cd can be modeled by p(d)=0.3d^2-d+5, where d is the number of days since april 8. according to this model,what is the total amount of revenue generated by the store's cd sales on april 18?
Answers
The total amount of revenue generated by the store's CD sales on April 18 is 21,144.2.
To find the total amount of revenue generated by the store's CD sales on April 18, we need to calculate the product of the number of CDs sold and the price per CD on that day.
First, let's find the number of CDs sold on April 18. We are given the function n(d) = 12d + 35, where d represents the number of days since April 8. Since we want to find the number of CDs sold on April 18, we substitute d = 18 into the function:
n(18) = 12(18) + 35
n(18) = 216 + 35
n(18) = 251
So, the store sold 251 CDs on April 18.
Next, we need to find the price per CD on April 18. We are given the function p(d) = 0.3d^2 - d + 5. Substituting d = 18 into the function:
p(18) = \(0.3(18)^2 - 18 + 5\)
p(18) = 0.3(324) - 18 + 5
p(18) = 97.2 - 18 + 5
p(18) = 84.2
So, the price per CD on April 18 is $84.2.
To find the total amount of revenue generated, we multiply the number of CDs sold by the price per CD:
Revenue = Number of CDs sold * Price per CD
Revenue = 251 * 84.2
Calculating this product, we find that the total amount of revenue generated by the store's CD sales on April 18 is 21,144.2.
In conclusion, the total amount of revenue generated by the store's CD sales on April 18 is 21,144.2.
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how to find
range
mode
median
mean
Answers
Answer:
- Mode-The most repetitive number! - Median:The number in the MIDDLE when they are IN ORDER! - Mean- The AVERAGE OF ALL NUMBERS: You add up all the numbers then you divide it by the TOTAL NUMBER of NUMBERS! - Range - THE BIGGEST minus the Smallest!
branliest?
Step-by-step explanation:
Answer:
RANGE = Highest number - lowest numberMODE = Total number of numberMEDIAN = {(n+1)÷2}th valueMEAN = €x/NQ.4 What is the difference between price floors and price ceiling? Give example and illustrate graphically in support of your answer.
Answers
A price floor is a law that limits the minimum price at which a good, service, or factor of production can be sold while a price ceiling is a regulation that limits the maximum price at which a good, service, or factor of production can be sold
Price floors are commonly implemented to support producers, while price ceilings are typically put in place to protect consumers from higher prices that might result from shortages or monopolies.
Example of Price Floor:Agricultural subsidies are a common example of price floors. Government price floors ensure that farmers receive a minimum price for their crops.
If the market price of wheat falls below the government-established price floor, the government may buy the excess supply at the guaranteed price, ensuring that farmers are able to make a profit. If there is a price floor, the minimum price is set above the equilibrium price.
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Which fraction comparison reasoning strategy can be used when both fractions have the same number of pieces?