find three positive numbers whose sum is 21 and whose product is maximal. (enter your answers as a comma-separated list.)
Answers
The three positive numbers whose sum is 21 and whose product is maximal are 7, 7, and 7. So, the answer is: 7, 7, 7.
To find three positive numbers whose sum is 21 and whose product is maximal, we have to use the concept of AM-GM inequality.
The AM-GM inequality states that for any set of positive real numbers, the arithmetic mean of these numbers is always greater than or equal to the geometric mean of these numbers. To maximize the product of the three positive numbers whose sum is 21, we let all three numbers be equal. Therefore:
Let the three numbers be a, b, and c.
So, a = b = c.
The sum of the three numbers is 21,
so: a + b + c = 21
We have a = b = c.
Then we substitute to obtain:
3a = 21
a = 7
Therefore, the three positive numbers whose sum is 21 and whose product is maximal are 7, 7, and 7. So, the answer is: 7, 7, 7.
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Related Questions
Determine whether the selection process for each sample was random or nonrandom.
Answers
The selection process for each sample was Random, Hence, Random sampling
This is further explained below.
Determine whether the selection process for each sample was random or nonrandom.?Generally, During physical education classes, students are randomly assigned to teams by selecting names from a hat or bag containing their names on individual pieces of paper.
There is a designated area at a supermarket for shoppers to leave comments. Each week, a satisfied customer will be randomly selected from the feedback forms submitted to win a gift certificate.
Selection bias
For a research project, physicians must first compile a list of patients. The first ten people on the list will be placed in the placebo group.
A clothes retailer conducts surveys of clients who use its store credit card to better understand its clientele.
We collect five soil samples from the biggest farm in a given area to determine the quality of the soil there.
The distinction between random and non-random sampling is explained.
In random sampling, each sample has the same chance of getting the target variable. When a researcher uses a sampling strategy that is not random, the features of the sample chosen are not based on chance but on factors like their own convenience, their own professional judgment, and their own prior experience.
In conclusion, During physical education classes, students are randomly assigned to teams by selecting names from a hat or bag containing their names on individual pieces of paper.
There is a designated area at a supermarket for shoppers to leave comments. Each week, a satisfied customer will be randomly selected from the feedback forms submitted to win a gift certificate.
Selection bias
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If 4u-5v=23 and 2u+4v=-8, find the value of u+v
Answers
Answer:
-1
Step-by-step explanation:
4u-5v=23
-2(2u+4v=16) We multiply by -2 here to destroy u's.
4u-5v=23
-4u-8v=16 we addition both processes
-13v=39 so, v=-3
4u-5(-3)=23, 4u=8 so, u=2
u+v= -3+2= -1
Last month,simon 's neighbors paid him to take care of their dog when they went on vacation.he spent 4$ of h earnings on an afternoon snack and12 $ on a new book. Afterward, had 6$ left. How can you best describe how much 's neighbors paid ?
Answers
The amount that the neighbor paid for taking care of the dog is $22.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
From the information, Simon's neighbors paid him to take care of their dog when they went on vacation and he spent $4 of his earnings on an afternoon snack and $12 on a new book. Afterward, hhl $6 left.
It should be noted that the total amount will be the addition of the money. This will be:
= $4 + $12 + $6
= $22
The amount is $22.
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A farmer uses 920 grams of grain to feed his 8 chickens. At this rate how many grams of grains does he use to feed 100 chickens
Answers
Answer: 11,500 grams
Step-by-step explanation: 920/8=115 115*100= 11,500
$2.00 $2.00 $5.00 $3.00 $6.00 $3.00 $3.00 What was the median winning bid?
Answers
To find the median winning bid, we need to first arrange the bids in order from lowest to highest:
$2.00 $2.00 $3.00 $3.00 $3.00 $5.00 $6.00
There are seven bids in total, which means that the median is the fourth value when the bids are arranged in order. In this case, the fourth value is $3.00.
Therefore, the median winning bid is $3.00.
the geometric series $a ar ar^2 \cdots$ has a sum of $12$, and the terms involving odd powers of $r$ have a sum of $5.$ what is $r$?
Answers
The sum of an infinite geometric series is given by a+ar+ar^2 where a is the first term and r is the common ratio.
The sum of the series can be represented by :
a / ( 1 - r) = 12
a = 12 ( 1- r ) (1)
So....note that the sum of the terms with odd powers of r can be represented by :
ar + ar^3 + ar^5 + ar^7 + ..... + ar^(2n - 1) = 5 (2)
And note that the sum of the terms with even powers of r can be represented by :
a + ar^2 + ar^4 + ar^6 + ar^8 + ..... + ar^(2n) = 7 (3)
Multiply (2) by r on both sides
ar^2 + ar^4 + ar^6 + ar^8 + ..... + ar^(2n ) = 5r (4)
Subtract (4) from (3)
a = 7 - 5r (5)
Sub (5) into (1)
7 - 5r = 12(1 - r)
7 - 5r = 12 - 12r
7r = 5 → r = 5/7
Check
a = 7 - 5(5/7) = 24/7
a / ( 1 - r) =
(24/7) / ( 1- 5/7) =
(24/7) / ( 2/7) =
24 / 2 =
12
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Determine the domain of the function f(x)= 1/2x^2 +11x +15
Answers
The domain of the function is expressed as D = (-∞, ∞)
The domain of a function is the value of the input 'x' for which the given function exists.
Given the function f(x)= 1/2x^2 +11x +15;
the domain of the function exists on all real numbers. That is the function will exist for any given value of x.Hence the domain of the function is expressed as D = (-∞, ∞)
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pls help need it plsssssssssss
Answers
Answer:
a. r² = 0.8555148135 so...
r = 0.9249... or 0.92
b. a correlation coefficient of 0.92 indicates a strong positive association between the two data sets
if m, r, x, and y are positive, is the ratio of m to r equal to the ratio of x to y ? (1) the ratio of m to y is equal to the ratio of x to r . (2) the ratio of m x to r y is equal to the ratio of x to y.
Answers
Yes the ratio of m to r is equal to the ratio of x to y
Given m, r, x and y are positive numbers.
m>0,r>0 x>0 ,y>0
(1) The ratio of m to y is equal to the ratio of x to r
\(m/y = x/r\)
(2) The ratio of m + x to r + y is equal to the ratio of x to y
\((m+x) / (r+y) = x/y\)
by solving this equation
my + xy = rx + xy
both side xy will be cancelled.
my = rx
m/r = x/y
in question it is asking is the ratio of m to r equal to the ratio of x to y?
yes the ratio of m to r is equal to the ratio of x to y that statement is correct.
Given Question is incomplete Complete Question here:
If m, r, x, and y are positive, is the ratio of m to r equal to the ratio of x to y?
(1) The ratio of m to y is equal to the ratio of x to r
(2) The ratio of m + x to r + y is equal to the ratio of x to y
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2. Your friend wants to write the equation of a quadratic function 1 5. 3.r = 1) that has zeros at 3 and 3. They want to use the binomials (3.7" – 5) and You insist that they must use the binomials 3 and (3) Who is correct? Explain.
Answers
Let's expand both options, your friend's and yours, as shown below
\(\begin{gathered} y=(3x+1)(3x-5)=9x^2-12x-5=9(x^2-\frac{4}{3}x-\frac{5}{9}) \\ \text{and} \\ y=(x+\frac{1}{3})(x-\frac{5}{3})=x^2-\frac{4}{3}-\frac{5}{9} \end{gathered}\)Then, both equations are the same besides a constant that will not affect the zeros of the functions, as shown below
\(\begin{gathered} y=(3x+1)(3x-5) \\ x=-\frac{1}{3} \\ \Rightarrow y=(-1+1)(-1-5)=0 \\ \text{and} \\ x=\frac{5}{3} \\ \Rightarrow y=(5+1)(5-5)=0 \\ \end{gathered}\)And
\(\begin{gathered} y=(x-\frac{5}{3})(x+\frac{1}{3}) \\ x=-\frac{1}{3} \\ \Rightarrow y=(-\frac{1}{3}-\frac{5}{3})\cdot0=0 \\ x=\frac{5}{3} \\ \Rightarrow y=0\cdot(\frac{6}{3})=0 \end{gathered}\)Both your friend and you are correct. The functions are the same with exception of a constant that multiplies the whole function (a scale factor); despite that, the zeros are the same for both functions
\((3x-5)(3x+1)=9(x+\frac{1}{3})(x-\frac{5}{3})\)A truck traveling East at a velocity of 40.0 m/s comes to a complete stop. How much time it will take for the truck to stop if it decelerates at -5.0 m/s2
Answers
Question 1 - Write an equation in Standard Form of a line that passes through (-3,-7) and has a slope of 4.
Question 2 - Write an equation in Standard Form of a line that passes through (10,-2) and has a slope of -1/2
Question 3 - Write an equation in Point Slope Form of a line that passes through (-1,8) and has a slope of -3/4
Question 4 - Write an equation in Slope Intercept Form that passes through (-3,11) and (6,-7).
Answers
The equation is, 4x - y = -5
The equation is, x + 2y = 6
The equation is, \(\(y = -\frac{3}{4}x + \frac{29}{4}\)\)
The equation is, y = -2x + 5
What is standard form of equation of line?
When A and B are not both zero, a line has the usual form Ax + By = C. The standard form of equation with slope and the point is,\(\(y - y_{1} = m(x - x_1)\)\) ...(1)
1. Given:\(\(x_1 = -3, y_1 = -7, m = 4\)\)
Plug these values in the above equation,
\(\(y - (-7) = 4(x - (-3)\\ y + 7 = 4(x + 3)\\\\y + 7 = 4x + 12\\y = 4x + 5\\\\4x - y = -5\)\)
This is the equation in standard form of line.
2. Given:
\(\(x_1 = 10, y_1 = -2, m = -\frac{1}{2}\)\)
Plug these values in the equation (1),
\(\(y - (-2) = -\frac{1}{2} (x - 10)\\y + 2 = -\frac{1}{2} x + 5\\\)\)
Multiply both sides by 2.2y + 4 = -x + 10x + 2y = 6
This is the equation in standard form of line.
3. Given:
\(\(x_1 = -1, y_1 = 8, m = -\frac{3}{4}\)\)
Plug these values in the equation (1),\(\(y - 8 = -\frac{3}{4}(x - (-1))\\ y -8 = -\frac{3}{4}(x + 1)\\ y - 8 = -\frac{3}{4}x - \frac{3}{4}\)\(y = -\frac{3}{4}x -\frac{3}{4} + 8\\ y = -\frac{3}{4}x + \frac{29}{4} \\\)\)
This is the equation in point slope form.
4. Given:\(\((x_1, y_1) = (-3, 11), (x_2, y_2) = (6, -7)\)\)
First to find the slope from the given two points.
\(\(m = \frac{y_2 - y_1}{x_2 - x_1} \\m = \frac{-7-11}{6-(-3)}\\ m = \frac{-18}{9\\}\\ m = -2\)\)
Now plug m = -2 and one of the given point in the equation (1), we ge\(t\(y - 11 = -2(x - (-3))\\y - 11 = -2(x + 3)\\y - 11 = -2x - 6\\y = -2x + 5\)\)
This is the equation in slope intercept form.
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Find at least three different sequences beginning with the terms 3, 5, 7 whose terms are generated by a simple formula or rule.
Answers
Answer:
3 5,7,9,11,13,16,17 19,21,23,25,27,29
For each question below, determine True or False: If a simple random sample is chosen with replacement, each individual has
the same chance of selection on every draw.
Answers
The statement If a simple random sample is chosen with replacement, each individual has the same chance of selection on every draw is True.
If a simple random sample is chosen with replacement, it means that after each selection, the chosen individual is placed back into the population before the next selection is made. In this case, each individual in the population has the same chance of being selected for every draw.
The process of replacing the selected individual ensures that the selection probabilities remain constant throughout the sampling process. As a result, each individual has an equal probability of being chosen on each draw, making the statement true.
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(-1.5) + 3.5+2=
Show your work
Answers
Answer:
4
Step-by-step explanation:
(-1.5) + 3.5+2
-1.5 + 3.5 + 2
2 + 2
= 4
4
Step-by-step explanation:
(-1.5) + 3.5 + 2 =
2 + 2 =
4
I need help with this without links
Answers
Answer:
36°
Step-by-step explanation:
I used an online protractor to solve it
Work out (7 x 10°) (2 × 10²) 4 Give your answer in standard form.
Answers
Answer:
\( {1.4 \times 10}^{3} | \)
Step-by-step explanation:
*winks and runs off ;)*
A motorboat travels kilometers in hours going upstream and kilometers in hours going downstream. What is the rate of the boat in still water and what is the rate of the current
Answers
The rate of the motorboat in still water is 49 km/hr. The rate of the current is 6 km/hr.
We have, A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in the same amount of time. We have to calculate the rate of the boat in still water and the rate of the current. Let the speed of the boat in still water and rate of stream be "B" and "S" respectively.
Using the relative speed formula , the speed upstream is B - S and the speed downstream is B + S.
Use the distance , in speed/rate formula ,
Rate × Time = Distance
Upstream : (B-S)6 = 258
=> B - S = 43 --(1)
Downstream: (B+S)6 = 330
=> B + S = 55 --(2)
Solve the linear equations by elimination method. Add the two equations.
=> 2B = 98
=> B = 49 km/hr
Substitute this value of B in equation(2) and solve for S, B+S = 55
=> 49+S = 55
=> S = 6 km/hr
So, the rate of the current is 6 km/hr.
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Complete question:
A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in same amount of time. What is the rate of the boat in still water and what is the rate of the current.
The diagram below shows two
similar isosceles triangles.
Р P.
S
8 cm
8 cm
o
4 cm
Q R 2 cm T
What is the length of ST in Triangle
RST?
A 6 cm
B 4 cm
C 12 cm
D 16 cm
Answers
Answer:
4 cm
Step-by-step explanation:
\(\frac{8}{ST} = \frac{4}{2} \\\\ST = 8*2 / 4\\ST = 4\)
PLSSSSS HELP!!!!
I WILL GIVE BRAINLIEST!!!!
Answers
Answer:
2.924
Step-by-step explanation:
First you'll solve the parenthesis:
...- (5.5-5.5)
...-(0)
Now solve the equation:
\(\sqrt[3]{5^{2} - 0}\)
\(\sqrt[3]{25}\)
Now solve fully
I hope this helps :)
Answer:
the answer is 3 times the square root of 27
Step-by-step explanation:
What is mean and median?
Answers
Answer:
Mean is the average of all of the numbers. Median is the middle number, when in order.
Carolyn and her basketball team are traveling form Oak City to the beach for the championships. The distance to the beach is about 1,344 miles. The team plans to drive 50 miles per hour. About how many hours will it take for Carolyn and her team to get to the beach?
Answers
Answer:
It will take 26.88hours to get to the beach
Step-by-step explanation:
From the problem statement, we are asked to find the time required to reach the beach.
given data
distance s=1344 miles
speed v= 50 mph
time t=?
we know that the relationship between speed, distance and time is given as
velocity=distance/time
substituting our given data into the expression we have
50=1344/t
making t subject of the formula we have
t=1344/50
t= 26.88 hours
Therefore it will take 26.88hours to get to the beach
A garden measures 32 feet by 126 feet, and the owner of the garden wishes to divide the garden
into two parts by installing a fence from corner to corner. Find the cost of the total length of fence
if the fence costs $5.81 per foot.
Answers
The total cost of the fence is $1,144.66.
1. To find the length of the fence, you need to calculate the distance from one corner to the opposite corner of the garden, which is the hypotenuse of a right triangle formed by the garden's dimensions.
2. Use the Pythagorean theorem: a² + b² = c², where a = 32 feet, b = 126 feet, and c is the length of the fence.
3. Calculate the square of the two sides: a² = 32² = 1024, and b² = 126² = 15876.
4. Add the squares of the two sides: a² + b² = 1024 + 15876 = 16900.
5. Calculate the square root of the sum to find the length of the fence: c = √16900 = 130 feet.
6. Now, calculate the cost of the fence by multiplying its length by the cost per foot: 130 feet × $5.81/foot = $754.30.
The total cost of the fence, which measures 130 feet in length, is $1,144.66.
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A flashlight has a parabolic cross section with a diameter of 10 inches and a depth of 2 inches. How far from the vertex is the focus?
Answers
The focus of the parabolic cross-section is 3.125 inches from the vertex.
How to solve for the parabolic cross-sectionA parabolic cross-section is defined by the equation:
y^2 = 4px
The depth, or the distance from the vertex to the widest point, is 2 inches. These are data from the question. We can use these dimensions to find the value of p.
Since the width is 10 inches, the distance from the vertex to the widest point along the y-axis is 5 inches (half of the diameter). So, we have:
(5)^2 = 4p(2)
Now, we can solve for p:
25 = 8p
p = 25 / 8
p = 3.125 inches
So, the focus of the parabolic cross-section is 3.125 inches from the vertex.
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2. The diagram shows a circle inside a rectangle. Work out the shaded region,
Give your answer to 3 significant figures.
8 cm
17 cm
32 cm
Answers
Answer:
342.938 cm²
Step-by-step explanation:
Area of shaded region = area of rectangle - area of circle
= (length*width) - (π*radius²)
= (32*17) - (π8²)
= 544 - 201.06192983
= 342.93807017 ≈ 342.938 cm²
Evaluate yz + x² x=3.2, y=6.1, z=0.2
Answers
Answer:
Step-by-step explanation:
To evaluate the given expression, we need to substitute the given values for x, y, and z. The expression becomes:
yz + x²
Substituting the given values, we get:
(6.1 * 0.2) + (3.2^2)
This simplifies to:
1.22 + 10.24
Therefore, the value of the expression is approximately 11.46.
11.46
gimme brainlyest gang
anova df ss ms f regression 1 12,323.60 12,323.60 90.0481 residual 8 1,154.802 136.8550 total 9 13,478.4 what is the correlation coefficient?
Answers
The correlation coefficient is 0.9541. This can be determined from the information provided in the ANOVA table, specifically the regression sum of squares (SSR) and the total sum of squares (SST).
The correlation coefficient, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where values closer to -1 or 1 indicate a stronger relationship, and values closer to 0 indicate a weaker relationship.
To calculate the correlation coefficient, we can use the formula:
r = sqrt(SSR/SST)
From the ANOVA table provided, we can see that SSR = 12,323.64 and SST = 13,538.4. Plugging these values into the formula gives:
r = sqrt(12,323.64/13,538.4) = 0.9541
Therefore, the correlation coefficient for this model is 0.9541, indicating a strong positive linear relationship between the independent variable and the dependent variable
Complete Question:
Using the following information. Coefficients -12.8094 Intercept Independent variable 2.1794 ANOVA df SS MS F 1 90.0481 Regression Residual Total 12,323.64 1,214.762 13,538.4 12,323.64 136.8550 8 1° 9 What is the correlation coefficient? Multiple Choice 0.9103 0.9541 -0.9541
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A one-way ride on a subway costs $0.90.A monthly pass costs $24.Write an inequality that represents how many one-way rides you can buy before it is cheaper to buy the monthly pass.Is it cheaper to buy the monthly pass?Is it cheaper to pay the one-way fare for 25 rides? Explain.
Answers
Answer:
35$ : 1,25$ = 28 Trips
Step-by-step explanation:
From 29 Trips you have a better deal.
Step-by-step explanation:
To write the inequality, let x be the number of trips:
As we are finding how many rides until it is cheaper, we will be using the greater than sign:
0.90 * x > 24
To isolate x, we need to divide both sides by 0.9:
\(x > \frac{24}{0.9}\)
x > 26.66 or
x > 26 \(\frac{2}{3}\)
Rounding down as too little money will result in no trip:
x > 26
This means that it is cheaper to buy individual tickets until 26 rides which are when the monthly pass will be better.
Hope this helps!
(0, 2), (1,7) create a equation that passes through each pair of points
Answers
Answer:
y = 5x + 2
Step-by-step explanation:
Given the equation 5x + 2
Plug in 0
y = 5(0) + 2
y = 2
(0,2)
Given the equation 5x + 2
Plug in 1
y = 5(1) + 2
y = 7
(1,7)
Jeremiah opened a savings account with a one-time deposit of $500. His savings account will pay a 5% simple interest per year. His brother, Brian, opened another savings account with a one-time deposit of $200. Brian’s savings account will pay 3% compounded annually. Who would earn more interest, to the nearest dollar, in 2 years?
A. Brian will make $12.00 more than Jeremiah.
B. Jeremiah will make $38 more than Brian.
C. Jeremiah will make $50 more than Brian.
D. Brian will make $212 more than Jeremiah.
Answers
Answer:
b
Step-by-step explanation:
Answer:
jhkunubnui
Step-by-step explanation: