Refer to the following breakdown of responses to a survey of room service in a hotel: Response - Frequency Not satisfied - 20 Satisfied - 40 Highly satisfied - 60 What percentage of the responses indicated that customers were satisfied?A. 40%B. 33%C. 50%D. 100%

Answer: kaeden brough 12 sammy brought 20

Step-by-step explanation:

i know that 16+16=32 and

15+17=32 and

14+18=32 and

13+19= 32 and

12+20=32. it’s gonna be 12 and 20 because those numbers add up to 32 and are 8 away from each other. since sammy had more fish he brought 20 and kaeden brough 12.

Final answer:

Kaden brought 12 shrimp and Sammy brought 20 shrimp to their fishing trip. This was determined by solving an algebraic equation set up based on the given information.

Explanation:

The question involves Sammy and Kaden, who went fishing and brought live shrimp as bait. Sammy brought 8 more shrimp than Kaden. Together, they had 32 shrimp. To solve for how many shrimp each boy brought, we can set up algebraic equations. Let the number of shrimp Kaden brought be represented by k, hence Sammy brought k + 8 shrimp. Adding together the shrimp both boys brought gives us:

k + (k + 8) = 32

Simplifying the equation:

2k + 8 = 32

2k = 32 - 8

2k = 24

k = 24 / 2

k = 12

Kaden brought 12 shrimp and Sammy brought 12 + 8 shrimp, which equals 20 shrimp.

So, Kaden brought 12 shrimp, and Sammy brought 20 shrimp.

Answer:

Step-by-step explanation:

The formula for determining the distance between two points on a straight line is expressed as

Distance = √(x2 - x1)² + (y2 - y1)²

Where

x2 represents final value of x on the horizontal axis

x1 represents initial value of x on the horizontal axis.

y2 represents final value of y on the vertical axis.

y1 represents initial value of y on the vertical axis.

From the points given,

x2 = 0

x1 = 9

y2 = - 33

y1 = 7

Therefore,

Distance = √(0 - 9)² + (- 33 - 7)²

Distance = √(- 9² + (- 40)² = √(81 + 1600) = √1681

Distance = 41

The formula determining the midpoint of a line is expressed as

[(x1 + x2)/2 , (y1 + y2)/2]

[(9 + 0) , (7 - 33)]

= (9, - 26]

The distance between the points (9, 7) and (0, -33) is 41 units, while the midpoint of the line segment joining them is (4.5, -13).

The subject of the question is Mathematics, specifically involving concepts in geometry. Given two points in 2-dimensional space - (9, 7) and (0, -33), we are asked to find the distance between these points and the midpoint of the line segment. The formula for the distance between two points (x1,y1) and (x2,y2) is  [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] applying the values,

[tex]\sqrt{ (0 - 9)^2 + (-33 - 7)^2 } = \sqrt{81 + 1600} = \sqrt{1681} = 41 \text{ units}[/tex] The midpoint of the line segment between two points (x1, y1) and (x2, y2) is ((x1+x2)/2, (y1+y2)/2). So that would be ((9 + 0)/2, (7 - 33)/2) = (4.5, -13).

https://brainly.com/question/18329129

#SPJ12

Answer:

36 men, 45 women

Step-by-step explanation:

36 men and 45 women attended the concert

Two or more expressions with an Equal sign is called as Equation.

Given,

There was a country concert held at the park.

For every 4 men there were 5 women that went to the concert

81 people attended the concert.

We need to find how many men and how many women each attended the concert.

4x+5x=81

9x=81

Divide both sides by 9

x=9

So 4(9)=36

5(9)=45

Hence, 36 men and 45 women attended the concert

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ5

Answer:

5° F

Step-by-step explanation:

According to Newton's law of cooling, the rate of change is proportional to the difference between the temperature and the ambient temperature.

dT/dt = k (T − T₀)

Solving this by separating the variables:

dT / (T − T₀) = k dt

ln (T − T₀) = kt + C

T − T₀ = Ce^(kt)

T = T₀ + Ce^(kt)

We're given that T₀ = 65.

T = 65 + Ce^(kt)

At t = 10, T = 35.

35 = 65 + Ce^(10k)

-30 = Ce^(10k)

At t = 20, T = 50.

50 = 65 + Ce^(20k)

-15 = Ce^(20k)

Squaring the first equation:

900 = C² e^(20k)

Dividing by the second equation:

-60 = C

Therefore:

T = 65 − 60e^(kt)

At t = 0:

T = 65 − 60e^(0)

T = 5

The initial temperature is 5° F.

Answer:

  see below

Step-by-step explanation:

The formula for the amount resulting from P earning interest at rate r continuously compounded is ...

  A = Pe^(rt)

for P=2500 and r=0.12, this becomes ...

  A = 2500e^(0.12t)

Answer:

Step-by-step explanation:

The measure of the floor of the rectangular room that is 12 feet by 15 feet. The formula for determining the area of a rectangle is expressed as

Area = length × width

Area of the rectangular room would be

12 × 15 = 180 feet²

The tiles are square with side lengths 1 1/3 feet. Converting 1 1/3 feet to improper fraction, it becomes 4/3 feet

Area if each tile is

4/3 × 4/3 = 16/9 ft²

The number of tiles needed to cover the entire floor is

180/(16/9) = 180 × 9/16

= 101.25

102 tiles would be needed because the tiles must be whole numbers.

Answer:

a = 50 houses

b = 45 houses

Step-by-step explanation:

Given

Number of houses called Model A = a

Number of houses called Model B = b

Total of single windows = 1800

Total of double windows = 375

then we have the system of equations

18a + 20b = 1800  (I)

3a + 5b = 375     (II)

Solving the system by whatever method we prefer, we obtain

(I)     a = (1800 - 20b)/18

then (II)

3((1800 - 20b)/18) + 5b = 375

⇒ 300 - (10/3)*b + 5b = 375

⇒ (5/3)*b  = 75

⇒ b = 45 houses

then

a = (1800 - 20*45)/18

⇒ a = 50 houses

50 model A homes and 45 model B homes will be built.

To solve the problem, let's define our variables:

We then create the following system of equations based on the given information:

1. For single windows:

18A + 20B = 1800

2. For double windows:

3A + 5B = 375

We can solve this system using the substitution or elimination method.

Step-by-Step Solution:

The solution to the system is A = 50 and B = 45, meaning that the construction company plans to build 50 model A homes and 45 model B homes.

You would do this:

 2x+8y=6

+ 3x-8y=9

5x=15

x=3

2x+8y=6

2(3)+8y=6

6+8y=6

8y=0

y=0

So x=3 and y=0

Very simple way to do that. Hope it helped.

Answer: x = 3, y = 0

Step-by-step explanation:

The given system of equations is expressed as

2x+8y = 6 - - - - - - - - - - - - - -1

3x -8y = 9- - - - - - - - - - - - - -2

We would eliminate y by adding equation 1 to equation 2. It becomes

2x + 3x = 6 + 9

5x = 15

Dividing the left hand side and the right hand side of the equation by 5, it becomes

5x/5 = 15/5

x = 3

Substituting x = 3 into equation 1, it becomes

2 × 3 + 8y = 6

6 + 8y = 6

Subtracting 6 from the left hand side and the right hand side of the equation, it becomes

6 - 6 + 8y = 6 - 6

8y = 0

Dividing the left hand side and the right hand side of the equation by 8, it becomes

8y/8 = 0/8

y = 0

Answer:

a. 28

Step-by-step explanation:

Given:

[tex]155.78=2.95h+73.18[/tex]

We need to evaluate given expression to find the value of 'h'.

Solution:

[tex]155.78=2.95h+73.18[/tex]

Now first we will apply Subtraction property of equality and subtract both side by 73.18 we get;

[tex]155.78-73.18=2.95h+73.18-73.18\\\\82.6=2.95h[/tex]

Now we will use Division property of equality and divide both side by 2.95 we get;

[tex]\frac{82.6}{2.95}=\frac{2.95h}{2.95}\\\\h=28[/tex]

Hence After evaluating given expression we get the value of 'h' as 28.

Answer:Ashton used 390 centimeters of string for his project.

Step-by-step explanation:

The total length of the piece of string that Ashton has is 520 centimeters.

He cuts the string into 8 equal pieces. This means that the length of each string would be

520/8 = 65 centimeters.

If he 6 of the pieces for a project, it means that the number of centimeters of string that Ashton used for his project would be

65 × 6 = 390 centimeters

Answer:

The standard deviation of given data is 12.36  

Step-by-step explanation:

We are given the following data in the question:

40, 12, 17, 25, 9, 46, 13, 22, 16,7

Formula:

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.  

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{207}{10} = 20.7[/tex]

Sum of squares of differences =

372.49 + 75.69 + 13.69 + 18.49 + 136.89 + 640.09 + 59.29 + 1.69 + 22.09 + 187.69 = 1528.1

[tex]\sigma = \sqrt{\dfrac{1528.1}{10}} = 12.36[/tex]

Thus, the standard deviation of given data is 12.36

Final answer:

The standard deviation of the provided data set (number of merchandise returns on Mondays) is approximately 14.8.

Explanation:

To calculate the standard deviation of the provided data set (40, 12, 17, 25, 9, 46, 13, 22, 16, 7), we will follow these steps:

Let's apply these steps:

Therefore, the standard deviation is about 14.8.

Final answer:

The depth of the gutter that will maximize its cross-sectional area is 4 inches, and the maximum cross-sectional area that allows the greatest amount of water to flow is 32 square inches.

Explanation:

To determine the depth of the gutter that will maximize its cross-sectional area, we first need to assume that turning up the edges of the aluminum sheet at right angles will form a rectangular cross-section. If the width of the aluminum is 16 inches and 'x' represents the depth of the gutter (the height of the sides when bent), the width of the base of the gutter will be 16 - 2x (since both sides are turned up).

This means the cross-sectional area 'A' in square inches will be A = x(16 - 2x). This is a quadratic equation and can be expanded as A = -2x^2 + 16x. To find the maximum area, we need to find the vertex of this parabola, which occurs at x = -b/(2a), where 'a' is the coefficient of x^2 and 'b' is the coefficient of 'x'.

In our case, a = -2 and b = 16, so the depth that maximizes the area is x = -16/(2*(-2)) = 4 inches. Therefore, the maximum cross-sectional area is A = 4(16 - 2*4) = 4(8) = 32 square inches.

The depth of the gutter that will maximize its cross-sectional area is 16 inches, and the maximum cross-sectional area is[tex]\( 768 \)[/tex] square inches.

To solve this problem, we will use calculus to find the depth of the gutter that maximizes its cross-sectional area. We will start by defining the dimensions of the gutter and then use the derivative of the area function to find the critical points. Finally, we will determine which of these critical points gives the maximum area.

Let's denote the depth of the gutter as [tex]\( x \)[/tex]inches. Since the width of the aluminum sheets is 16 inches, the base of the gutter will also be 16 inches. When the edges are turned up to form right angles, the gutter will have a rectangular base and two rectangular sides.

 The area of the base of the gutter is [tex]\( 16x \)[/tex]. The area of each side is [tex]\( x^2 \),[/tex] and there are two sides, so the total area of the sides is[tex]\( 2x^2 \).[/tex] Therefore, the total cross-sectional area [tex]\( A \)[/tex]of the gutter is the sum of the area of the base and the areas of the two sides:

[tex]\[ A(x) = 16x + 2x^2 \][/tex]

To find the depth that maximizes the area, we need to take the derivative of [tex]\( A(x) \)[/tex] with respect to[tex]\( x \)[/tex]and set it equal to zero:

[tex]\[ A'(x) = \frac{d}{dx}(16x + 2x^2) = 16 + 4x \][/tex]

 Setting [tex]\( A'(x) \)[/tex] equal to zero gives us the critical points:

[tex]\[ 16 + 4x = 0 \][/tex]

[tex]\[ 4x = -16 \][/tex]

[tex]\[ x = -4 \][/tex]

Since the depth of the gutter cannot be negative, we discard[tex]\( x = -4 \)[/tex]and realize that we need to consider the physical constraints of the problem. The actual critical point occurs at the endpoint of the domain of [tex]\( x \),[/tex]which is[tex]\( x = 0 \)[/tex](no gutter) or[tex]\( x = 16 \)[/tex] (the gutter's width). Since[tex]\( x = 0 \)[/tex]gives a minimum area (no gutter at all), the maximum area must occur at [tex]( x = 16 \).[/tex]

 Now, we calculate the cross-sectional area at [tex]\( x = 16 \)[/tex]

[tex]\[ A(16) = 16(16) + 2(16)^2 \][/tex]

[tex]\[ A(16) = 256 + 2(256) \][/tex]

[tex]\[ A(16) = 256 + 512 \][/tex]

[tex]\[ A(16) = 768 \][/tex]

 Therefore, the maximum cross-sectional area of the gutter is[tex]\( 768 \)[/tex]square inches when the depth is equal to the width, which is 16 inches.

80 students gained more than 48 marks.

In the given box plot, we have the following information:

- The lowest test score is **10**, and the highest is **100**.

- The 25th percentile (Q1) is **30**, the median (Q2) is **48**, and the 75th percentile (Q3) is **70**.

- No student scored exactly **30**, **48**, or **70** marks.

- **120 students** scored less than **70** marks.

Let's analyze this:

1. The interquartile range (IQR) contains the middle **50%** of the data. Since the median (Q2) is **48**, we know that **50%** of the students scored more than **48** marks.

2. We are interested in how many students scored above **48**. Since **50%** scored more than **48**, the remaining **50%** scored less than or equal to **48**.

3. Given that **120 students** scored less than **70**, we can infer that **75%** of the students scored below **70** (since each region contains **25%** of the data).

4. Therefore, **25%** of the students scored between **48** and **70** (the region between Q2 and Q3).

5. To find out how many students scored more than **48**, we look at the region above Q2. Since there are **2 regions** above Q2, each containing **40 students** (since 120 students = 75%), the total number of students who scored more than **48** is:

[tex]\(2 \times 40 = 80\)[/tex]

Therefore, 80 students gained more than 48 marks.

The number of students who gained more than 48 marks is : 60

Using the information in the boxplot ;

The median represents 50% of the data .

The number above the median value can be calculated thus ;

Now we have :

50% × 120 = 60

Hence, the number of students who gained more than 48 marks is : 60

Answer: the number of multiple-choice questions in the math test is 35 and the number of open-ended questions in the math test is 3

Step-by-step explanation:

Let x represent the number of multiple-choice questions in the math test.

Let y represent the number of open-ended questions in the math test.

The math test has 38 questions. It means that

x + y = 38

This test consists of multiple-choice questions worth 4 points each and open-ended questions worth 20 points each. The total number of points is 200. It means that

4x + 20y = 200 - - - - - - - - - -1

Substituting x = 38 - y into equation 1, it becomes

4(38 - y) + 20y = 200

152 - 4y + 20y = 200

- 4y + 20y = 200 - 152

16y = 48

48/16

y = 3

Substituting y = 3 into x = 38 - y, it becomes

x = 38 - 3 = 35

Answer:

81.25%

Step-by-step explanation:

Given: There are 325 students who drive to school.

           There are 400 students that ride the bus to school.

Now, finding percentage of the number of student who drive to school over number of students who ride the bus to school.

Percentage of student who drive to school= [tex]\frac{325}{400} \times 100[/tex]

⇒ Percentage of student who drive to school= [tex]\frac{325}{4}[/tex]

⇒ Percentage of student who drive to school= [tex]81.25\%[/tex]

Hence, 81.25% is the percent of students who drive to school on the number of students who ride the bus to school.

Answer:

The answer is A on E2020!!

A) The linear model better represents the situation because the amount she owes is decreasing by about the same amount every 6 months.

Answer:

a was right

Step-by-step explanation:

Answer:32 cards

Step-by-step explanation:

just did it

Answer:

87.5%

Step-by-step explanation:

64:64-8

64:56

56/64 *100 = 87.5%

Answer:

Median = 5

Lower Quartile = 2.5

Upper Quartile = 8.5

Step-by-step explanation:

- First of all, you need to order the numbers from lowest to greatest: 2 2 3 4 4 6 6 8 9 9

- Then, you will find at the number that sits exactly at the middle of this set of numbers. Because this is a set of numbers that has 10 numbers, you will have to look at the two middle points (4 and 6) and divide them by 2 (essentialy finding the average).

4+6=10, 10/2 = 5 = Mean

- To find the upper and lower quartiles, you basically have to find the medians of the set of numbers that are below and above the central median

- So, for the lower quartile, the set of numebrs is: 2 2 3 4. The median sits between 2 and 3, so we have to find the average of those: 2+3=5, 5/2=2.5

- For the upper quartile, the set of numbers is 6 8 9 9. The median is the average of 8+9. So 8+9=17, 17/2 = 8.5

Lower Quartile (Q1) = 3 Median (Q2) = 5 Upper Quartile (Q3) = 8

First, arrange the data in ascending order:

2, 2, 3, 4, 4, 6, 6, 8, 9, 9

The median is the middle value of the sorted data set. Since there are 10 values (an even number), the median will be the average of the 5th and 6th values.

The 5th value is 4

The 6th value is 6

Median (Q2) = (4 + 6) / 2

= 5

The lower quartile is the median of the lower half of the data set (excluding the overall median). For this data set, the lower half is:

2, 2, 3, 4, 4

Since there are 5 values in this half, the lower quartile is the 3rd value.

Lower Quartile (Q1) = 3

The upper quartile is the median of the upper half of the data set (excluding the overall median). For this data set, the upper half is:

6, 6, 8, 9, 9

Since there are 5 values in this half, the upper quartile is the 3rd value.

Upper Quartile (Q3) = 8

Answer and Step-by-step explanation:

For general measurements, different people or organizations normally make slightly different measurements. Measurements are never a hundred percent accurate.

The published values are usually updated because in the modern world of discoveries, change is the only constant thing. As new discoveries roll in or not, it becomes necessary to update the current standards; no change in the updated value means the old standards hold, and any change is also updated in the published update.

For health standards/ranges, Different countries have different standards of health

And this requires regular updating because standards of health changes frim time to time.

Answer:

24.66

Step-by-step explanation:

You use the Pythagorean Theorem and do 27^2 -11^2= x            

Answer:

11x5=55

Step-by-step explanation:

The equation that best shows that 55 is a multiple of 11 is 11 × 5 = 55.

The equation that best shows that 55 is a multiple of 11 is Choice B: 11 × 5 = 55.

To determine if a number is a multiple of another number, we need to check if the first number can be divided evenly by the second number without any remainder. In this case, 55 can be divided evenly by 11 because 11 × 5 equals 55.

The other choices, A, C, and D, do not represent the relationship of 55 being a multiple of 11.

Answer:

$50

$30.45

Simple interest.

Step-by-step explanation:

If I invested $500 at 5% simple interest for 2 years, then the amount of interest that I will get will be calculated by the simple interest formula as

[tex]I = \frac{Prt}{100} = \frac{500 \times 5 \times 2}{100} = 50[/tex] dollars.

Now, if I invest $500 at 3% compounded monthly for 2 years, then the amount of compound interest will be calculated by the compound interest formula as

[tex]I = P(1 + \frac{r}{100})^{t} - P = 500(1 + \frac{3}{100})^{2} - 500 = 30.45[/tex] dollars.

So, I will prefer to invest in simple interest as the interest there is more. (Answer)

Mr. Sanchez expects to earn $54,806.25 this year.

To find the salary Mr. Sanchez expects to earn this year, we need to calculate 11% of his salary from last year and add it to his previous salary.

The 11% increase can be found by multiplying Mr. Sanchez's salary from last year by 0.11: $49,375 * 0.11 = $5,431.25

Adding this increase to his previous salary gives us the salary Mr. Sanchez expects to earn this year: $49,375 + $5,431.25 = $54,806.25

Answer:

[tex] a_{6} = - 11[/tex]

Final answer:

The 6th term in the recursive sequence with the first term 9 and each subsequent term decreasing by 4 from the previous term is -11.

Explanation:

To find the 6th term in the sequence described by the recursive formula given:

a1=9

an=an-1−4

We will apply the formula recursively to determine each term up to the 6th term.

First term (a1): 9

Second term (a2): a1 − 4 = 9 − 4 = 5

Third term (a3): a2 − 4 = 5 − 4 = 1

Fourth term (a4): a3 − 4 = 1 − 4 = -3

Fifth term (a5): a4 − 4 = -3 − 4 = -7

Sixth term (a6): a5 − 4 = -7 − 4 = -11

Therefore, the 6th term in the sequence is -11.

Answer:

313 ft

Step-by-step explanation:

If 12in = 12 ft

313in = x

= 313 ft

To find the actual length of the room, use the scale to set up a proportion and solve for the actual length.

To find the actual length of the room, we can use the scale provided. According to the scale, 12 inches on the drawing corresponds to 12 feet in the actual room. Since the length of the room in the drawing is 313 inches, we can set up a proportion to find the actual length:
12 inches on the drawing / 313 inches on the drawing = 12 feet in the actual room / actual length of the room
Cross-multiplying, we get:
12 inches x actual length of the room = 313 inches x 12 feet
Dividing both sides by 12 inches, we find:
Actual length of the room = (313 inches x 12 feet) / 12 inches
Calculating this, we get:
Actual length of the room = 313 feet

https://brainly.com/question/31567993

#SPJ3

Answer:

The second choice:

          [tex]\large\boxed{\large\boxed{1/x\cdot x=1}}[/tex]

Explanation:

The closure property on an operation means that the operation between two elements of a set produce one element of the same set.

In this case, the operation is multiplication and the set is the polynomials.

Then, the closrue property is that the multiplication of two polynomials will always produce a polynomial.

Since, [tex]1/x[/tex] is not a polynomial, the equation [tex]1/x\cdot x=1[/tex] does not support the fact that polynomials are closed under multiplication.

Answer:

  52.2 ft

Step-by-step explanation:

Triangle JSV is similar to triangle HTV so you have the proportion ...

  JS/SV = HT/TV

  JS/(36 ft) = (5.8 ft)/(4 ft) . . . . . . . fill in the given values

  JS = (36 ft)(5.8/4) = 52.2 ft . . . . multiply by 36 ft

The height of the wall is 52.2 ft.

We know that m<HVT = m<JVS because the mirror projects equal angles. We can claim this about the angle theta.

tan(θ) = 5.8/4

θ = [tex]tan^{-1}(5.8/4)=55.4[/tex] degrees approx.

So, we want sin theta in the other triangle. Luckily, we also know that...

cos(55.4°) x hypotenuse = 36

hypotenuse = 63.4 ft approx.

So we can find the height by evaluating...

sin(55.4°) x 63.4 = 52.2 ft

answer: 52.2 ft

Answer:

The quadratic mean of 2 real positive numbers is greater than or equal to the arithmetic mean.

Step-by-step explanation:

x and y      Quadratic Mean       Arithmetic mean

3 and 3                    3                                    3

2 and 3                   2.55                               2.5

3 and  6                  4.74                                4.5

2 and 5                   3.8                                  3.5

2 and 17                 12.1                                   9.5

18 and 28              23.5                                  23

10 and  48             34.7                                  29

The quadratic mean is always greater than the arithmetic mean except when  x and y are the same.

When the difference between the pairs is  small the difference in the means is also small. As that difference increases the difference in the means also increases.

So we conjecture that the quadratic mean is always greater than or equal to the arithmetic mean.

Proof.

Suppose it is true then:

√(x^2 + y^2) / 2) ≥ (x + y)/2       Squaring  both sides:

(x ^2 + y^2) / 2 ≥ (x + y)^2 / 4    Multiply through by 4:

2x^2 +2y^2  ≥  (x + y)^2

2x^2 +2y^2 >=  x^2 + 2xy + y^2

x^2 + y^2 >= 2xy.

x^2 - 2xy + y^2 ≥ 0

(x - y)^2 ≥ 0

This is true  because the square of any real number is positive so the original inequality must also be true.

The quadratic mean of two real numbers, x and y, is given by the formula sqrt((x^2 + y^2)/2). A conjecture can be made that the quadratic mean is greater than or equal to the arithmetic mean for positive real numbers. This conjecture can be proved using the AM-QM inequality and algebraic manipulations.

The quadratic mean of two real numbers, x and y, is given by the formula:

Q(x, y) = sqrt((x^2 + y^2)/2)

To formulate a conjecture about the relative sizes of the arithmetic and quadratic means of different pairs of positive real numbers, we can compare the two means for various pairs of numbers. Based on observations, it can be conjectured that the quadratic mean is always greater than or equal to the arithmetic mean for positive real numbers.

To prove the conjecture, we can use the AM-QM inequality, which states that the quadratic mean is greater than or equal to the arithmetic mean:

Q(x, y) >= A(x, y)

Where Q(x, y) is the quadratic mean and A(x, y) is the arithmetic mean.

Let's consider two positive real numbers, a and b:

Q(a, b) = sqrt((a^2 + b^2)/2)

A(a, b) = (a + b)/2

Now, we need to prove that Q(a, b) >= A(a, b):

(a^2 + b^2)/2 >= (a + b)/2

a^2 - a + b^2 - b >= 0

(a^2 - a) + (b^2 - b) >= 0

a(a - 1) + b(b - 1) >= 0

a(a - 1) >= 0

Therefore, Q(a, b) >= A(a, b), which confirms the conjecture that the quadratic mean is always greater than or equal to the arithmetic mean for positive real numbers.

https://brainly.com/question/35432156

#SPJ3