X= (3, 3², -2, 6) : F(x)= 2/3 x + 3

Answer:

4

Step-by-step explanation:

1/2 of 24=12

1/3 of 12=4

The Maclaurin polynomials of orders n=0, 1, 2, 3, and 4 for the function 5/(1+x) are P0(x) = 5, P1(x) = 5 - 5x, P2(x) = 5 - 5x + 5x^2, P3(x) = 5 - 5x + 5x^2 - 5x^3, and P4(x) = 5 - 5x + 5x^2 - 5x^3 + 5x^4, respectively.

The Maclaurin polynomials are a way to approximate a function using a polynomial expansion centered at x = 0. The Maclaurin polynomial of order n for a function f(x) is given by Pn(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + ... + (f^n(0)/n!)x^n, where f'(0), f''(0), f'''(0), ..., f^n(0) are the derivatives of f(x) evaluated at x = 0.

In this case, the given function is f(x) = 5/(1+x). To find the Maclaurin polynomials of orders n=0, 1, 2, 3, and 4, we evaluate the function and its derivatives at x = 0 and substitute them into the general formula for the Maclaurin polynomials.

For n=0, P0(x) = 5, as f(0) = 5.

For n=1, P1(x) = 5 - 5x, as f(0) = 5 and f'(0) = -5.

For n=2, P2(x) = 5 - 5x + 5x^2, as f(0) = 5, f'(0) = -5, and f''(0) = 10.

For n=3, P3(x) = 5 - 5x + 5x^2 - 5x^3, as f(0) = 5, f'(0) = -5, f''(0) = 10, and f'''(0) = -30.

For n=4, P4(x) = 5 - 5x + 5x^2 - 5x^3 + 5x^4, as f(0) = 5, f'(0) = -5, f''(0) = 10, f'''(0) = -30, and f^4(0) = 120.

These Maclaurin polynomials provide polynomial approximations of the given function 5/(1+x) for different orders. The higher the order (n), the more terms are included in the polynomial expansion, resulting in a more accurate approximation of the original function around x = 0.

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The average increase in spending per year from:

2000 to 2002 is $14.50.

2004 to 2006 is $27.50.

2000 to 2006 is $20.83.

The estimated instantaneous increase in spending in the year 2004 is $21.75.

The average increase per year = (spending in 2002 - spending in 2000) / (number of years)

= (142 - 113) / 2

= 14.5

The average increase per year = (spending in 2006 - spending in 2004) / (number of years)

= (238 - 183) / 2

= 27.5

To find the average increase in spending per year from the year 2000 to 2006, we first find the total increase in spending over the six-year period:

Total increase = spending in 2006 - spending in 2000

= 238 - 113

= 125

The average increase per year = total increase / (number of years)

= 125 / 6

= 20.83

To estimate the instantaneous increase in spending in the year 2004, we can take the average of the average rates of change between adjacent years:

Instantaneous increase in spending in 2004 = (average increase per year from 2002 to 2004 + average increase per year from 2004 to 2006) / 2

= ( (183-142)/2 + (238-183)/2 ) / 2

= 21.75

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Answer:

71 1/2 square feet

Step-by-step explanation:

We want to find the area of the wall that will be painted.

We need to find the area of the two windows and subtract it from the area of the wall.

Each window is 3 1 /2 ft by 4 1/2 ft. The area of each window is therefore:

A = L * B

A = 7/2 * 9/2 =  = 63/4 square feet = 15 3/4 square feet

The two windows therefore have an area of:

2 * 63/4 = 63/2 = 31 1/2 square feet.

The wall measures 12 7/8 ft by 8 ft. Therefore, the area of the wall is:

A = 103/8 * 8 = 103 square feet

The area of the wall that will be painted is therefore:

A = 103 - 31 1/2 = 71 1/2 square feet

Answer: 103

Step-by-step explanation:

Answer:

i think its 2

Step-by-step explanation:

Answer:

3,506

Step-by-step explanation:

Answer:

V = 88

Step-by-step explanation:

72/81 = V/99

72/81 x 99 = V

V = 88

Answer:

2.77

Step-by-step explanation:

The sample proportion is:

\(\hat{p}=\frac{x}{n}=\frac{184}{200}=0.92\)

Then, the standard score of the sample proportion is:

\(z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.92-0.85}{\sqrt{\frac{0.85(1-0.85)}{200}}}=2.77\)

Answer:

(g · f)(4) = 45

Step-by-step explanation:

f(x)=4x+1

g(x)=x² - 4x- 5

(g · f)(x) = 4(x² - 5) + 1

(g · f)(4) = 4(4² - 5) + 1

Following pemdas

(g · f)(4) = 4(16 - 5) + 1

(g · f)(4) = 4(11) + 1

(g · f)(4) = 44 + 1

(g · f)(4) = 45

Answer:

hello :

Step-by-step explanation:

x(x+3)(x+3)=0  means : x=0 or x+3=0 or x+3=0

x=0 or x=-3 or x=3

Answer:

frequency=speed/wavelength

f=250/50

f=50hz

Answer: 27.7 millimeters

Step-by-step explanation:

Let the missing leg be represented by x.

We will use Pythagoras formula to solve this. The measure of the missing leg will be:

x² = 37² - 24.5²

x² = 1369 - 600.25

x² = 768.75

x = ✓768.75

x = 27.7

The missing leg is 27.7 millimeter

Answer:

The correct answer is A: 10

Step-by-step explanation:

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The solution to |x| > |x + 2| is x < -2. This can be determined by looking at the two graphs on the grid, y = |x| and y = |x + 2|.

Inequality is the concept of representing a relationship between two values using a mathematical symbol. This can be used to express various forms of comparison such as greater than, less than, and not equal to. Inequality is an important concept for understanding and applying mathematical principles, such as in algebra and calculus.

The graph of y = |x| is a straight line at y = 0, and increases as x moves further away from 0. The graph of y = |x + 2| has a minimum at x = -2, and increases as x moves further away from -2. Therefore, at all locations where x is less than -2, the value of |x| is greater than the value of |x + 2|. These locations are all solutions to the inequality |x| > |x + 2|.

To visualize this solution, we can look at the graph of the two functions and see that the value of |x| is greater than the value of |x + 2| when x is less than -2. This can also be seen by looking at the numerical values of the two functions; for any x less than -2, the absolute value of x will be greater than the absolute value of x + 2.

In conclusion, the solution to the inequality |x| > |x + 2| is x < -2. This can be seen visually on the graph of the two functions, and can also be determined by looking at the numerical values of the two functions.

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Converting  the polar coordinates into rectangular coordinates (4,4π/3) is:  (-2, 2√3).

Using this formula to  convert from polar coordinates into  rectangular coordinates

x = r cos(θ)

y = r sin(θ)

Where:

r =  radius

θ = angle in radians

So,

(r, θ) = (4, 4π/3)

Substitute

x = 4 cos(4π/3)

x = 4 (-1/2)

x = -2

y = 4 sin(4π/3)

y = 4 (√3/2)

y = 2√3

Therefore the rectangular coordinates are (-2, 2√3).

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Trigonometry ratios are used to represent sine, cosine and tangent functions. The value of cos(30) ×tan(60) +sin(30)  is 2.

Trigonometry:

Trigonometry, a branch of mathematics concerned with the specific functions of angles and their use in calculations. There are six angular functions commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

According to the Question:

The trigonometry equation is given as:

cos(30) ×tan(60) +sin(30)  

In trigonometry,

cos(30) = √3/2

tan (60) = √3

and sin(30) = 1/2

Now, Putting the value:

cos(30) ×tan(60) +sin(30)  = √3/2 ×√3 + 1/2

Evaluate all products

cos(30) ×tan(60) +sin(30)  = √3/2 ×√3 + 1/2

Add roots

cos(30) ×tan(60) +sin(30)  = 3/2 + 1/2

⇒ cos(30) ×tan(60) +sin(30) = 4/2 = 2

Hence, the value of  cos(30) ×tan(60) +sin(30)  is 2.

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Answer:

5

Step-by-step explanation:

In the case when we multiplied 0.014 by 100,000 so it comes

= 0.014 × 100,000

= 1,400

Since The value 0.014 were times by 5 zeros.

Therefore the decimal point would move 5 places to the right

The metal that was used to construct the small rectangular pyramid-shaped metal object found in the archaeological dig is B. Lead of density \(11.34 grams/cm^{3}\)

Given :

The weight of the object is 612.4 grams.

The Height of the object = 9cm

The Breadth of the rectangular base = 3cm

The Length of the rectangular base = 6cm

Area of the rectangular base = Length*Breadth = 3*6 sq. cm = 18 sq. cm

Calculating the volume of the Object,

Volume = \(\frac{Length*Width*Height}{3}\)

Volume = \(\frac{6*3*9}{3} = 54 cm^{3}\)

Now, Calculating density,

\(Density = \frac{Mass}{Volume }\\\\\)

Putting the values of mass and volume, we have \(Density =\frac{612.4}{54} = 11.34 grams/cm^{3}\)

Hence, the density of the material is \(11.34 grams/cm^{3}\)

The density matches the density of LEAD.

Hence, the metal that was used to construct the small rectangular pyramid-shaped metal object found in the archaeological dig was B. Lead

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Answer:

470 g

Step-by-step explanation:

1 cm^3 = 1 gram

210 grams + 260 grams = 470 grams

The world population in 2030 will be of 9.0062 billion.

The exponential formula for population growth is given below:

P(t) = P (0)e^rt

Here, P(t) is the population in t years from now P (0) is the population in the current year and r(decimal) is the growth rate, e=2.7 is the Eular number.

If the world population is 7.0 billion in 2012.

2012 is the initial year, P (0) =7

P(t) will be measured in billions of people.

The growth rate is constant at 1 .4%.

So that, r = 0.014

Now, the population in 2030 will be :

2030-2012=18 years after 2012, so this is P(18).

P(t)= 7e^rt

P(18) = 7e^0.0014*18

       = 9.0062

So, the world population in 2030 will be of 9.0062 billion.

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The world population will be 9.0062 billion in 2030.

The population growth exponential formula is as follows:

P(0)ert = P(t)

P(t) denotes the population in t years. P (0) is the current year's population, r(decimal) is the growth rate, and e=2.7 is the Euler number.

If the world population in 2012 is 7.0 billion.

The first year is 2012, and P (0) = 7.

The magnitude of P(t) will be measured in billions of people.

The rate of growth remains constant at 1.4%.

As a result, r = 0.014.

Now, in 2030, the population will be:

2030-2012 = 18 years after 2012, so P (18).

P(t)= 7e^rt

P(18) = 7e^0.0014*18

= 9.0062

As a result, the world population in 2030 will be 9.0062 billion people.

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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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Answer:

Yes

Step-by-step explanation:

Substitute:

Calculate the product or quotient:

Calculate the sum or difference:

Obtain a simplified relation:

Determine true or false: True

Answer: True

Answer:

The height of the window is 150 centimeters.

Step-by-step explanation:

Use ratio and proportion to find the height of the window.

\(\frac{h}{60cm} = \frac{210cm}{84cm}\)

Cross multiply

\(h = \frac{210cm(60cm)}{84cm} \\h = \frac{12600cm^2}{84cm} \\h = 150 cm\)

Liberal arts colleges have a higher median SAT score and a lower acceptance rate compared to research universities, while research universities have a higher expenditure per student and a higher percentage of top 10% high school graduates.

Descriptive statistics were calculated for liberal arts colleges and research universities based on the data given in the Excel file. The summary of descriptive statistics for each variable by school type is as  shown in the table.

Based on the results, it appears that liberal arts colleges have higher median SAT scores, lower acceptance rates, and lower expenditures per student than research universities. On the other hand, research universities have higher mean expenditures per student and higher median percentages of top 10% high school graduates than liberal arts colleges. Overall, there are differences in the characteristics of these two types of colleges.

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--The complete question is, Compute descriptive statistics for liberal arts colleges and research universities in the Excel file Colleges and Universities. Compare the two types of colleges. What can you conclude?

Colleges and Universities

School Type Med SAT Accept Rate Exp./Student Top 10% HS Grad %

Amherst Lib Arts 1315 22% $26,636 85 93

Barnard Lib Arts 1220 53% $17,653 69 80

Bates Lib Arts 1240 36% $17,554 58 88

Berkeley Univ 1176 37% $23,665 95 68

Bowdoin Lib Arts 1300 24% $25,703 78 90

Brown Univ 1281 24% $24,201 80 90

Bryn MawrLib Arts1255 56% $18,847 70 84

Cal Tech Univ 1400 31% $102,262 98 75

Carleton Lib Arts 1300 40% $15,904 75 80

Carnegie University1225 64% $33,607 52 77

Claremont Lib Arts1260 36% $20,377 68 74

Colby Lib Arts 1200 46% $18,872 52 84

Colgate Lib Arts 1258 38% $17,520 61 85

ColumbiaUniversity1268 29% $45,879 78 90

Cornell University1280 30% $37,137 85 83

DavisdsonLib Arts 1230 36% $17,721 77 89

Duke University 1310 25% $39,504 91 91

GeorgetownUniv 1278 24% $23,115 79 89

Grinnell Lib Arts 1244 67% $22,301 65 73

HamiltonLib Arts 1215 38% $20,722 51 85

Harvard Univ 1370 18% $46,918 90 90

HaverfordLib Arts 1285 35% $19,418 71 87

Johns Hop. Univ 1290 48% $45,460 69 86

MiddleburyLib Arts 1255 25% $24,718 65 92

MIT University 1357 30% $56,766 95 86

Mount Lib Arts 1200 61% $23,358 47 83

NWrn University 1230 47% $28,851 77 82

Oberlin Lib Arts 1247 54% $23,591 64 77

Occidental Lib Arts 1170 49% $20,192 54 72

Pomona Lib Arts 1320 33% $26,668 79 80

Princeton University 1340 17% $48,123 89 93

Rice University 1327 24% $26,730 85 88

Smith Lib Arts 1195 57% $25,271 65 87

Stanford University 1370 18% $61,921 92 88

Swarthnore Lib Arts 1310 24% $27,487 78 88

U of MI University 1195 60% $21,853 71 77

U of Chi University 1300 45% $38,937 74 73

U of Roc University 1155 56% $38,597 52 73

U PA University 1280 41% $30,882 87 86

U Va University 1218 37% $19,365 77 88

UCLA University 1142 43% $26,859 96 61

UNC University 1109 32% $19,684 82 73

Vassar Lib Arts 1287 43% $20,179 53 84

Wash U University 1225 54% $39,883 71 76

Wash & Lee Lib Arts 1234 29% $17,998 61 78

Wellesley Lib Arts 1250 49% $27,879 76 86

Wesleyan Lib Arts 1290 35% $19,948 73 91

Williams Lib Arts 1336 28% $23,772 86 93

Yale University 1350 19% $52,468 90 93--

Answer:

216 units

Step-by-step explanation:

lenght x width x height

Answer:

up

Step-by-step explanation:

a is positive

Answer:

me kown it

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Step 1: Write out equation

-12 + n = -15

Step 2: Add 12 on both sides

n = -3

So our answer is -3 and not 3.

Answer: \(False\)

The answer to this problem is \(n=-3\)

To get -3 here is the work shown

Simplify both sides of the equation

\(n-12=-15\)

Add 12 to both sides

\(n-12+12=-15+12\\n=-3\)

The dot product is a scalar quantity that represents the projection of one vector onto another, and can be used to calculate the angle between two vectors.

The cross product is a vector quantity that represents the magnitude and direction of the orthogonal projection of one vector onto another. Orthogonality is related to both results in that the dot product of two orthogonal vectors is zero, while the cross product of two parallel vectors is also zero. In addition to that, the cross product of two non-zero vectors results in a third vector that is orthogonal to both.

The dot product is a scalar product that calculates the projection of one vector onto another. The cross product is a vector product that calculates the orthogonal component of one vector with respect to another.

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