answer the gaps/questions attached

The area of the surface is  S = [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]

Now, According to the question:

The given equation is:

[tex]z = \frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2} )[/tex],

0 ≤ x ≤ 1 , 0 ≤ y ≤ 1

Let's know:

Surface Area:

To surface area of a solid E, defined by z = f(x , y) can be found by integrating[tex]\int\limits \int\limits_R \sqrt{(z_x)^2+(z_y)^2+1},dA[/tex] where R is the rectangular region

[0,1] × [0, 1] and [tex]z_x,z_y[/tex] corresponds to the partials of z w.r.t x and y.

Now,

[tex]\sqrt{(z_x)^2+(z_y)^2+1}[/tex] = [tex]\sqrt{1+(\sqrt{x} )^2+(\sqrt{y} )^2}[/tex] = [tex]\sqrt{1+x+y}[/tex]

S = [tex]\int\limits \int\limits_R \sqrt{(z_x)^2+(z_y)^2+1},dA[/tex]

  = [tex]\int\limits^1_0\int\limits^1_0 \sqrt{x+y+1}dy dx[/tex]

  [Integrate with respect to y ]

    =  [tex]\int\limits^1_0 (\frac{2}{3}(x + y + 1)^\frac{3}{2} )|^1_0 dx[/tex]                        

  = [tex]\int\limits^1_0 (\frac{2}{3}(x + (1) + 1)^\frac{3}{2}-\frac{2}{3}(x + (0) + 1)^\frac{3}{2} )dx[/tex]

 = [tex]\int\limits^1_0 ((\frac{2}{3}(x +2)^\frac{3}{2} ) - (\frac{2}{3}(x +1)^\frac{3}{2} ) , dx[/tex]

  =  [tex]\int\limits^1_0 (\frac{2}{3}((x +2)^\frac{3}{2} - (x +1)^\frac{3}{2} )) , dx[/tex]

  [Integrate with respect to x ]

   = [tex]\frac{2}{3} (\frac{2}{5}(x + 2)^\frac{5}{2} - \frac{2}{5}(x +1)^\frac{5}{2} )|^1_0[/tex]

    = [tex]\frac{2}{3}(\frac{2}{5}((1)+2 )^\frac{5}{2}-\frac{2}{5}((1)+1)^\frac{5}{2})-\frac{2}{3}(\frac{2}{5}((0)+2 )^\frac{5}{2} -\frac{2}{5}((0)+1)^\frac{5}{2}[/tex]

    = [tex]\frac{2}{3}(\frac{18\sqrt{3}}{5} -\frac{8\sqrt{2} }{5} )-\frac{2}{3} (\frac{8\sqrt{2} }{5} -\frac{2}{5} )[/tex]

     = [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]

Hence, The area of the surface is  S = [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]

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Answer:

600,000

Step-by-step explanation:

The mathematical concept demonstrated in this question is the process of exponential growth. Exponential growth demonstrates an increase in quantity by a percentage or factor over time. It is represented by the general formula [tex]f(x) = a(1+r)^{x}[/tex] where a is the initial amount, r is the growth rate, and x is the time interval expressed as an integer.

For this problem, we can see that the initial population of the town is 345,000, and it increases by a rate of 20% each year. We can determine that the growth rate is 20% because 1 + r = 1.2, so r must be equal to .20 (or 20%). We are given that t = 3, so we can plug that value in to the function given.

We calculate the population in 3 years to be 596,160. This can be approximated to 600,000.

The object will travel 639.36 yards in one minute.

Formula: Yards = Feet x 0.3333

The question is asking how many yards an object will travel in one minute when it is moving at a constant rate of 32 feet per second.

We can use the formula above to calculate the number of yards the object will travel in one minute. We know that the object is traveling at a rate of 32 feet per second.  To find the number of yards traveled in one minute, we need to multiply 10.6667 yards per second by 60 seconds in a minute. Therefore, in one minute (60 seconds), the object will travel 32 x 60 = 1920 feet. We can now use the formula to convert this to yards: Yards = 1920 x 0.3333 = 639.36 yards. Therefore, the object will travel 639.36 yards in one minute.

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If sixteen teams compete, the winner will be decided after 15 games.

Since there are 16 teams and each team is playing with some of the other, there are 16/2 =8 pairs

Out of each pair only one team will move on.

So, there are 8 teams left after the first round.

These 8 teams pair up to have 8/2 =4 pairings

Continuing this process, we get the total number of games played to determine the winner is,

8+4+2+1=15

Each game's losing team gets eliminated from the tournament. If sixteen teams participate, the winner will be decided after 15 games.

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Answer: total cost of an international call with a duration of 10 minutes is 5.70 dollars.

Step-by-step explanation:

The expression 2.20 +0.35x represents the total cost of an international call in dollars, as a function of the duration x in minutes.

It is composed of two parts:

The first part, 2.20$, represents the fixed cost of making an international call. This cost does not change regardless of the duration of the call.

The second part, 0.35x$, represents the variable cost of the call, which is based on the duration of the call in minutes. This cost increases with the duration of the call.

When x=10, it means the duration of the call is 10 minutes, so the variable cost of the call would be 0.35*10 = 3.5$

Therefore, the total cost of the international call with a duration of 10 minutes is 2.20 + 3.5 = 5.7$

It's important to notice that this equation represents the total cost of the call not just the variable cost, but also the fixed cost.

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Answer:

isjsjdjejejrjebdkxn nsksksnenmdnxee nu pot snndnsnenenene

a) An inequality that can determine x the number of outfits Keiland can purchase while staying within her total budget of $660 is 529.59 + 37.26x ≤ 660.

b) The inequality solution shows that x cannot be more than 3.

An inequality is a mathematical statement that two or more mathematical expressions are unequal or not equivalent.

Inequalities are depicted as follows:

These inequality symbols are usually written between two numbers or algebraic expressions.

The total spending budget Keilantra has = $660

The cost of a new bicycle = $488.20

The cost of 2 reflectors = $22.34 ($11.17 x 2)

The cost of a pair of bike gloves = $19.05

The total costs for the above three items = $529.59

The unit cost of new biking outfits = $37.26

The number of outfits Keilantra can purchase = x

529.59 + 37.26x ≤ 660

37.26x ≤ 660 - 529.59

37.26x ≤ 130.41

x ≤ 3.5

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The probability is 8/33 is already in its simplest form as the numerator and denominator share no common factors.

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The probability is 8/33 is already in its simplest form as the numerator and denominator share no common factors.

Probability is a measure of the likelihood of an event occurring, represented as a decimal or fraction between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.

(Probability of choosing a green pen on the first draw) x (Probability of choosing a blue pen on the second draw, given that a green pen was chosen on the first draw)

= (4/12) * (8/11)

= (1/3) * (8/11)

= 8/33

So the probability is 8/33. This is already in its simplest form as the numerator and denominator share no common factors.

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The value of x is: x=88.

Here, given that, 36% of the letters in Pythagoras's alphabet soup are vowels.

33 1/3% of those vowels are "os."

To calculate the percentage of letters that are "os," we first need to find 33 1/3% of 36%.

33 1/3% is equivalent to 1/3. So, we can calculate the percentage of "os" as follows:

Percentage of "os" = (36% * 1/3) = 12%

Now, we know that 12% of the letters in the soup are "os."

Next, Pythagoras removes all the "os" from his soup.

This means that what remains are the non-"os" letters, which are the remaining vowels and consonants.

To calculate the percentage of the original letters that remain, we need to subtract the percentage of "os" from 100%:

Percentage of original letters remaining = 100% - Percentage of "os"

Percentage of original letters remaining = 100% - 12% = 88%

Therefore, x% of the original letters remain, and x is equal to 88.

Hence, The value of x is: x=88.

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John has 5 red balls and 8 blue balls. What is the ratio of red balls to blue balls? Answer: The ratio of red balls to blue balls is 5:8.

We can solve this problem by using a ratio. Ratios are two values that are compared to each other. In this case, we need to compare the number of red balls to the number of blue balls. We are given that there are 5 red balls and 8 blue balls. To find the ratio, we need to write the numbers as a fraction. The fraction for red balls is 5/8 and the fraction for blue balls is 8/5. We can then simplify the fractions to get the ratio of 5:8. This means that there is a ratio of 5 red balls to 8 blue balls.

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Answer:

y = 3x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (1, 4) ← 2 points on the line

m = [tex]\frac{4-1}{1-0}[/tex] = [tex]\frac{3}{1}[/tex] = 3

the line crosses the y- axis at (0, 1 ) ⇒ c = 1

y = 3x + 1 ← equation of line

Null Hypothesis: The jeeps have an mpg rating of 34.9

Alternative Hypothesis: The jeeps have an mpg rating that is less than 34.9

Calculate the test statistic.

Test Statistic = (Sample Mean - Population Mean) / (Standard Deviation / √Sample Size)

Test Statistic = (34.6 - 34.9) / (2.0 / √16)

Test Statistic = -1.5 / 0.5

Test Statistic = -3

Calculate the critical value.

Critical Value = -2.960 Compare the test statistic with the critical value

Test Statistic = -3

Critical Value = -2.960

Since the test statistic is lower than the critical value, we reject the null hypothesis.

Make a conclusion The jeeps have an mpg rating that is less than 34.9

At the 0.025 level, there is enough proof to conclude that Jeeps do not get the claimed mpg.

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On solving the provided question, we can say that the value of the function is f(x) =  => f(x) = vf(x,y) = (x² + y²) = (x² + y²),

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here, the function is f(x) =

f(x) =

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The value of  zα for the following is :

(a)  α = 0.0089 is 2.37

(b) α = 0.09 is 1.34

(c)  α = 0.707 is -0.545

zα is the inverse function of the standard normal CDF.

(a) Central limit c= 1-α

for α = 0.0089 , c=1-0.0089

∴ c=0.9911

Hence confidence level in percentage= 99.5%

Now,  the value of zα will be calculated with the help of an excel sheet function normsinv(c).

∴zα = normsinv(c)

where c is central limit

zα = normsinv(0.9911)

zα =2.37

(b) Central limit c= 1-α

for α = 0.09 , c=1-0.09

∴ c=0.91

Hence confidence level in percentage= 91%

Now,  the value of zα will be calculated with the help of an excel sheet function normsinv(c).

∴zα = normsinv(c)

where c is central limit

zα = normsinv(0.91)

zα=1.34

(c) Central limit c= 1-α

for α = 0.707 , c=1-0.707

∴ c=0.293

Hence confidence level in percentage= 29.3%

Now,  the value of zα will be calculated with the help of an excel sheet function normsinv(c).

∴zα = normsinv(c)

where c is central limit

zα = normsinv(0.707)

zα= -0.545

Therefore zα value for 0.0089 is 2.37, for 0.09 is 1.34 and for 0.707 it is -0.545.

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The number of extra men required to erect 2 additional cottages is; 5 men

Let us use;

M = men

D = Days

C = Cottages

Thus;

5M * 21D = 2C

105MD = 2C

To erect 2 cottages in 21days, 5 men are required

To erect 2 more cottages or 4 cottages in 21 days;

(4 * 5)/2 = 10 men

Thus, we conclude that is the number of men required to erect 2 additional cottages which is 5 extra men

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Answer:

Step-by-step explanation:

none of these the corrct answer is 5

A = P(1+r/n)(nt), where P is the original principal, r is the annual interest rate, n is the number of times the interest is compounded annually, and t is the number of years the money has been held, is the formula for compound interest.

To calculate the final amount of money in the account:

 First, divide the 8% annual interest rate by 100 to get a decimal value: 0.08.

Find the number of times the interest is compounded annually. Since it is done quarterly, the answer is n = 4.

Put these values into the formula now, along with the $1200 principle sum and the number of years, 5, to complete it:

A = $1200(1+(0.08/4))^(4*5) = $2490.07

  to determine how long it will take for the initial sum to double to $2400.

 Divide the final sum by the starting sum: 2400/1200 = 2

 Take the natural logarithm of 2: ln(2) = 0.693

Decimalize the result and divide it by the interest rate: 0.693 / 0.08 = 8.66 years

 Therefore, the time it will take for the initial sum of money to double to $2400 is 8.66 years.

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Emma has been saving up to go on a big summer trip, visiting the United States and Russia. Emma should spend $2951.46 while in the United States.

Generally, To maximize the amount of cash Emma has in Russia, she should spend all of her money in the United States before entering Russia. First, we convert the Ruble limit to USD:

32,285 Rubles / 129.35 =249.594 USD.

Next, we convert Emma's savings from pounds to USD:

£2500 x 1.28 = $3200.

Finally, we subtract the Ruble limit from Emma's total savings in USD: $3200 - $248.54 = $2951.46.

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Nonvisual language is used to describe the visual world verbally. It can lead people around a museum, help an audience member find their way around an artwork, or provide them access to the visual elements of a performance.

It was in 1981 when Dr. Margaret Pfanstiehl, founder and president of The Metropolitan Washington Ear Inc., and her husband Cody perfected the art and practice of verbal description.

Standard information found on a label, such as an artist's name, nationality, the title of the artwork, date, dimensions or size of the piece, media, and method, can be found in a spoken description as well. In addition, a vocal description can offer a broad overview of the work's subject matter and structural elements.

1. Lines

2. Planes

3. Hyperboloids

4. Lines

5. Spheres

6. Ellipsoids

7. Paraboloids

8. Hyperbolas

9. Ellipses

10. Hyperbolas

11. Circles

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The new store will have a profit of $3400 after its third month in business.

The correct option is D.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

George has opened a new store, and he is monitoring its success closely.

He has found that this store’s revenue each month can be modeled by r(x)=x²+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars.

He has also found that his expenses each month can be modeled by c(x)=x²−3x+4 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars.

(r−c)(x) = x²+5x+14 -x²+3x-4

(r−c)(x) = 8x+10

(r−c)(3) = 24+10 = 34 in hundreds of dollars.

Therefore, the new store has profit of $3400.

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System components in mathematics involves the study of equations and their solutions, shapes and their properties, rate of change and area under a curve, angles and their relationships, and the properties of numbers.

1. Algebra: This is the study of equations and their solutions, as well as the manipulation of symbols and operations.

2. geometry: This involves the study of shapes and the properties of space, such as angles and distances.

3. Calculus: This involves understanding the rate of change of a function and the area under a curve.

4. Trigonometry: This involves the study of angles and their relationships to one another and to other types of measurements.

5. Number Theory: This involves the study of the properties of numbers, such as divisibility, primes, and multiplicative functions.

System components in mathematics involves the study of equations and their solutions, shapes and their properties, rate of change and area under a curve, angles and their relationships, and the properties of numbers.

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quadratic model; y = 0.13x2 – 2.38x + 12.27 is the best to fit the regression model for the data.

ax2+bx+c=0, with a not, equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

For the given Dataset

Sum of X = 27

Sum of Y = 22

Mean X = 5.4

Mean Y = 4.4

Sum of squares (SSX) = 45.2

Sum of products (SP) = -42.3

Regression Equation = ŷ = bX + a

b = SP/SSX = -42.3/45.2 = -0.93584

a = MY - bMX = 4.4 - (-0.94*5.4) = 9.45354

ŷ = -0.93584X + 9.45354

Thus Given linear Equation is not the best fit

Since the graph is decreasing Option b and c are also not possible

Therefore, the best to fit the regression model for the data is the quadratic model; y = 0.13x2 – 2.38x + 12.27.

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Random mean assignment involves randomly assigning participants to different groups, so that each group is similar in terms of characteristics such as age, gender, race, etc. This ensures that the groups are as similar as possible, reducing the chance of bias in the experiment.

Random mean assignment is an important procedure used in experiments to reduce experimenter and participant bias. This involves randomly assigning participants to different groups in the experiment, so that the groups are as similar as possible in terms of characteristics such as age, gender, race, etc. This ensures that any differences observed in the results are due to the experimental variables, rather than any pre-existing differences between the groups. Random assignment also ensures that any experimenter bias is minimized, as the experimenter is not able to select which participants go into which group. Random assignment is therefore a key procedure used to reduce the chance of bias in experiments, and ensure that the results are more reliable and valid.

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Therefore , the solution of the given problem of speed comes out to be

he needs to drive at 77.77 mph.

How quickly something is traveling is determined by its speed from a distance. How far an object moves in a certain length of time depends on its speed. Speed is calculated as follows: velocity = range x time. The most used units for expressing speed are meters per second (m/s), kilometers per hour (km/h), and kilometers per second (mph) (mph).

Here,

70 + 50 = 120 miles is indeed the total distance.

You would need 2.4 hours to travel the 120 miles at such an approximate speed of 50 mph.

However, you are already on the road for 1.5 hours, so you must finish the trip in 0.9 hours.

You need to travel at a speed of 77.77 mph to complete the final 70 miles approximately 0.9 hours.

Therefore , the solution of the given problem of speed comes out to be

he needs to drive at 77.77 mph.

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The area of trapezoid ABCD is 98 square units.

Based on the data given, The area of  ΔDBA  = area of  ΔADE  + area of ΔABE  = 20 + 50  = 70. So  

area of Δ DBA  = 0.5 sin DBA (AB x DB)  = 70

sin DBA = 140 / ( AB x DB)

sin DBA = sin CDB

The area of  ΔCDB  would be 0.5 sin (DBA) (DB x DC)  

The area of  ΔCDB = 0.5 (140 / [(AB x DB] ) (DB x DC)

The area of  ΔCDB = 70 (DC/AB)  = 70 ( DE /BE)

The area of ΔAEB  would be 0.5 sin AEB ( AE * BE)

The area of ΔAEB = 50  (1)

Area Δ ADE  would be 0.5 sin DEA (AE * DE)  

Area Δ ADE  = 20  (2)

Because of  angle AEB  is  supplemental to angle DEA, their sines are equal. So  

sin AEB  = sin DEA

Let rearranging (1), (2). So we will have

sin AEB  =   sin DEA

100 / [ AE * BE] = 40 / [ AE * DE ]

DE / BE  = 40/100  = 2/5

Since area of ΔCDB  equal to  70 (DE / BE) then

ΔCDB = 70 (2/5)  =  28

So...area of trapezoid ABCD  = area of ΔDBA  + area of ΔCDB  

area of trapezoid ABCD =  70 + 28 = 98  

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Answer:

1. Pt. A: -6               3. Pt. C: 3               5. Pt. E: 0

2. Pt. B: -2              4. Pt. D: 5

Step-by-step explanation:

By looking at the number line, you can see that a few points are labled from letter A to letter E.

In order to know the value of each point, you just have to look at their placement in the number line. For example, we can see that Point B is plotted at -2 on the number line, this means that the value of Point B is -2.

I hope this helps! :)

Answer:

y = 4/3x - 1

Step-by-step explanation:

(3, 3) and (0, -1)

m = -1-3 / 0-3

m = -4/-3

m = 4/3

y = 4/3x + b

-1 = 4/3(0) + b

-1 = 0 + b

b = -1

y = 4/3x - 1

The first equation, 3^x = 12, is an exponential equation. To solve for x, we would take the logarithm of both sides with base 3:

x = log3(12)

The second equation, x^3 = 12, is a polynomial equation of degree 3. To solve for x, we would take the cube root of both sides:

x = ∛12

The similarity between these two equations is that both are equations with one variable and are looking for the value of that variable.

The main difference between these two equations is the type of function they represent. The first equation is an exponential function, represented by 3^x, while the second equation is a polynomial function, represented by x^3.

As a result, the methods used to solve these equations are also different. The first equation is solved by taking the logarithm of both sides and the second equation is solved by taking the cube root of both sides.

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