Find f(2) if f(x) = (x + 1)2. 9 6 5



I'll give brainiest if right

a)The standard error of the mean is 0.85.b) the margin of error is 1.67 at 95% confidence level.

a) To calculate the standard error of the mean, the formula is given by:σx = σ / √nWhere,σ is the population standard deviation, n is the sample size√n = √50 = 7.071σx = σ / √n= 6 / 7.071σx = 0.85 (rounded to two decimal places)

b) At 95% confidence level, the margin of error is calculated by using the following formula:

ME = z* σxWhere,z* is the z-value for 95% confidence level and σx is the standard error of the mean.

The z-value for 95% confidence level is 1.96

ME = z* σx = 1.96 x 0.85

ME = 1.67 (rounded to two decimal places)

Therefore, the margin of error is 1.67 at 95% confidence level.

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The system of equations 5x - 3y = -26 and x + 2y + 1 = 2 can be solved using the substitution method. The solution of the system of equations is x = -8.2 and y = -5.

An equation is a mathematical statement that expresses two expressions as equal. It consists of two expressions separated by an equals sign (=). Equations are used to describe relationships between different quantities, and to solve problems involving those quantities. Equations may be written in words, symbols, or both. They can be used to solve problems in science, engineering, economics, and other fields.

The system of equations can be solved using substitution method or addition method. In this solution, we will use the substitution method.

Substitution Method:

Step 1: Solve one of the equations for either x or y.

Let us solve the first equation for x.

5x - 3y = -26

5x = -3y - 26

x = (-3y - 26)/5

Step 2: Substitute the expression for x in the second equation.

x + 2y + 1 = 2

(-3y - 26)/5 + 2y + 1 = 2

Step 3: Solve the equation for y.

(-3y - 26)/5 + 2y + 1 = 2

-3y/5 - 26/5 + 2y + 1 = 2

2y - 3y/5 - 26/5 + 1 = 2

-y/5 - 26/5 + 1 = 2

y/5 + 26/5 - 1 = -2

y/5 + 25/5 = -1

y = -5

Step 4: Substitute the value of y in either of the equations to calculate the value of x.

5x - 3(-5) = -26

5x + 15 = -26

5x = -41

x = -41/5

x = -8.2

Therefore, the solution of the system of equations is x = -8.2 and y = -5.

Conclusion:

The system of equations 5x - 3y = -26 and x + 2y + 1 = 2 can be solved using the substitution method. The solution of the system of equations is x = -8.2 and y = -5.

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Square and rhombus have

4 equivalent sides

4 angles

2 pair of congruent sides

2 pair of parallel sides

Answer:

A data type is an attribute associated with a piece of data that tells a computer system how to interpret its value

Step-by-step explanation:

Data types categorize data and specify its nature, amount characteristics, and behavior. It decides how data is handled within a computer system in terms of storage and manipulation.

Data types categorize data and specify its nature, characteristics, and behavior. It is a crucial part of every data structure and computer language. Primitive data types and complex data types are the two basic divisions of data types. Basic types like numbers, characters, booleans, and strings are examples of primitive data types. Arrays, objects, and records are examples of sophisticated data types that are more complex. Data types specify how information is handled and stored by computer systems. Size, precision, and range are a few examples of the unique qualities that each data type possesses. The arithmetic, comparison, and logic operations that can be carried out on the data are also determined by the data types.

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Answer:

D (-1,-3)

Step-by-step explanation:

If h(x)=-3x-6, plug in for x

-3 =-3(-1)-6

-3=3-6

-3=-3

so two negatives cancel out and get you the positive three minus six, resulting in negative 3, which is also the h(x) value.

Answer:

D

Step-by-step explanation:

Plug it in

Y=3x-6

-3=-3(-1)-6

-3=-3

Answer:

It would take 200 minutes

Step-by-step explanation:

Step-by-step explanation:

To simplify the given radical expression, we can first break down 2401 into its prime factors, which gives us:

2401 = 7^4

We can then simplify the given expression as follows:

^4 sqrt (2401x^12y^16) = ^4 sqrt (7^4 * x^12 * y^16)

= ^4 sqrt (7^4) * ^4 sqrt (x^12) * ^4 sqrt (y^16)

= 7 * x^3 * y^4

Therefore, the simplified form of the given expression is 7x^3y^4.

The polynomial function is V(x) = (30-2x)(20-2x)x and the volume of the pan is 864 cm^3.

The polynomial function

To find the volume of the pan, we first need to determine the dimensions of the base and height.

If we cut equal squares with sides of length x from the corners of a 30 cm by 20 cm piece of aluminum, then

Thus, the volume of the pan can be expressed as:

V(x) = (30-2x)(20-2x)x

The volume

Using the remainder theorem, we have

V(6) = (30 - 2 * 6)(20 - 2 * 6) * 6

Evaluate

V(6) = 864

Thus, when x = 6, the volume of the pan is:

V(6) = 864 cm^3.

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Answer:

1, 2, 5, and 10

Step-by-step explanation:

Factors for 20 are:

1, 2, 4, 5, 10, 20

Factors for 30 are:

1, 2, 3, 5, 6, 10, 15, 30

Answer: 7.12

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Sebastian ran 11 kilometers before school on weekdays. To find out how many kilometers he ran before school on weekdays, we need to subtract the distances he ran on weekend from the total distance he ran in a week.

We know that Sebastian ran a total of 22.7 kilometers in 1 week. This includes the distances he ran on Saturday, Sunday, and the weekdays before school.

On Saturday, he ran 8 kilometers, and on Sunday, he ran 3.7 kilometers. These two distances combined account for 8 + 3.7 = 11.7 kilometers of his total distance.

To determine the distance he ran before school on weekdays, we need to subtract the distance covered on Saturday and Sunday from the total distance. This can be calculated as follows:

Total distance before school on weekdays = Total distance - Distance on Saturday - Distance on Sunday

= 22.7 kilometers - 8 kilometers - 3.7 kilometers

= 11 kilometers

Therefore, Sebastian ran 11 kilometers before school on weekdays.

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The code implementation of shell sort in C++ using the provided `city.h` header file and `cityArray[]`:

```cpp

#include "city.h"

City cityArray[] = {

   {"Tokyo", 38.98}, {"Delhi", 28.5}, {"Shanghai", 25.58}, {"São Paulo", 21.65},

   {"Mumbai", 21.04}, {"Mexico City", 20.99}, {"Beijing", 20.38}, {"Osaka", 19.28},

   {"Cairo", 18.77}, {"New York City", 18.6}, {"Dhaka", 18.24}, {"Karachi", 18},

   {"Buenos Aires", 15.59}, {"Istanbul", 15.29}, {"Kolkata", 14.85}, {"Manila", 14.7},

   {"Lagos", 14.37}, {"Rio de Janeiro", 14.31}, {"Tianjin", 13.4}, {"Kinshasa", 13.31},

   {"Guangzhou", 13.08}, {"Los Angeles", 12.82}, {"Moscow", 12.54}, {"Shenzhen", 12.44},

   {"Lahore", 11.13}

};

void shellSort(City arr[], int n) {

   for (int gap = n / 2; gap > 0; gap /= 2) {

       for (int i = gap; i < n; i += 1) {

           City temp = arr[i];

           int j;

           for (j = i; j >= gap && arr[j - gap].getPopulation() > temp.getPopulation(); j -= gap) {

               arr[j] = arr[j - gap];

           }

           arr[j] = temp;

       }

   }

}

int main() {

   int n = sizeof(cityArray) / sizeof(cityArray[0]);

   shellSort(cityArray, n);

   for (int i = 0; i < n; i++) {

       cityArray[i].print();

   }

   return 0;

}

```

Explanation:

The provided code demonstrates the implementation of the shell sort algorithm in C++. The `shellSort` function takes an array of `City` objects `arr[]` and its size `n` as parameters.

The outer `for` loop initializes the `gap` variable to `n/2`, representing the initial gap size for the first pass of shell sort. In each pass, the elements that are `gap` distance apart from each other are sorted. After each pass, the gap size is reduced by half until it reaches 0, indicating that the array is completely sorted.

The inner `for` loop iterates through the unsorted portion of the array, starting from the `gap` index and incrementing by 1. It performs an insertion sort on the sub-array by comparing and shifting elements that are greater than the key element (`temp`) to the right by `gap` distance. Finally, it inserts the key element into the correct position in the sub-array.

In the `main` function, the `shellSort` function is called to sort the `cityArray` based on the population of each city. After sorting, the sorted `cityArray` is printed using the `print` function defined in the `City` class.

This implementation demonstrates the shell sort algorithm's ability to sort the given array of `City` objects based on population in ascending order.

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After evaluating the given integral we get:

1. ∫\(sin^3(x)cos^2(x)dx\) = \(sin^4(x)/4\) \(-sin^6(x)/6 + C\)

2. ∫\(sin^3(9x)dx = -(1/9)cos(9x)sin^2(9x) + (2/27)sin^3(9x) + C\)

3. ∫\(cos^6(8-x)sin(8-x)dx = (1/7)cos^7(8-x) + C\)

1. Here we have to evaluate the integral ∫\(sin^3(x)cos^2(x)dx\),

By substitution u = sin(x), du = cos(x)dx.

Then the integral becomes:

∫\(sin^3(x)cos^2(x)dx\) = ∫\(u^3(1-u^2)du\)

By integrating and expanding the integrand term by term, we arrive at:

∫\(u^3(1-u^2)du\) = ∫\(u^3\)du - ∫\(u^5\)du

= \(u^4/4 - u^6/6 + C\)

By substituting back u = sin(x), we get the final answer:

∫\(sin^3(x)cos^2(x)dx\) = \(sin^4(x)/4\) \(-sin^6(x)/6 + C\)

2. Using the substitution u = 9x, we have du = 9 dx. Thus, we can rewrite the integral as:

∫\(sin^3(9x)dx = (1/9)\)∫\(sin^3(u)du\)

Using the power reduction formula for sine, we have:

(1/9)∫\(sin^3(u)du = -(1/9)cos(u)sin^2(u) + (2/27)sin^3(u) + C\)

Substituting back u = 9x and simplifying, we have:

∫\(sin^3(9x)dx = -(1/9)cos(9x)sin^2(9x) + (2/27)sin^3(9x) + C\)

Therefore, the answer is:

∫\(sin^3(9x)dx = -(1/9)cos(9x)sin^2(9x) + (2/27)sin^3(9x) + C\)

3. Using the substitution u = 8 - x, we have du = -dx.

Thus, we can rewrite the integral as:

∫\(cos^6(8-x)sin(8-x)dx = -\)∫\(cos^6(u)sin(u)du\)

Using the substitution v = cos(u), we have dv = -sin(u)du. Thus, we can rewrite the integral as:

-∫\(cos^6(u)sin(u)du =\) ∫\(v^6dv\)

Using the power rule, we have:

∫\(v^6dv = (1/7)v^7 + C\)

Substituting back v = cos(u) and then u = 8 - x, we have:

∫\(cos^6(8-x)sin(8-x)dx = (1/7)cos^7(8-x) + C\)

Therefore, the answer is:

∫\(cos^6(8-x)sin(8-x)dx = (1/7)cos^7(8-x) + C\)

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Answer:

The Median is 15

The Mean is 22

a) The binomial expansion of (1+12x)^1/2 is given by:

(1+12x)^1/2 = 1^1/2 + (1/2)(1^-1/2)(12x) + (1/2)(1^-1/2)(-1/2)*(12x)^2 + ...

Binomial expression: what is it?

A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.

The first four terms, in ascending powers of x, are:

1, (1/2)(12x), (1/8)(12x)^2, (1/16)*(12x)^3

b) To use x=1/36 in the expansion, you would substitute x=1/36 into the expansion, and keep only the terms up to x^3 (the fourth term in the expansion). This will give an approximation of the value of (1+12x)^1/2 when x=1/36.

This will be an approximation of √12 because x=1/36 corresponds to 12x = 1 and the initial value of the expansion is 1 + 12x .

We can use this approximation to approximate square root of 12 and also for other square roots by using appropriate x values.

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Answer:

125 questions

Answer:

125 questions

Step-by-step explanation:

Answer:

50 students from each grade

Step-by-step explanation:

If we get the similar amount of people from each and every grade so this would represent the percentage occur from each grade this determine the number of people who vote per grade and represent that how much would the vote for student comes

Also 50 is easily divisible by 750

Therefore the above represent the answer

The derivative of the function y = (x^3 + 2)^2(x^4 + 4)^4 using logarithmic differentiation is: y' = 2(x^3 + 2)(x^4 + 4)^3[3x^2(x^4 + 4) + 8x(x^3 + 2)^2]

To use logarithmic differentiation, we take the natural logarithm of both sides of the equation and then differentiate with respect to x using the rules of logarithmic differentiation.

ln(y) = ln[(x^3 + 2)^2(x^4 + 4)^4]

Now, we use the product rule and chain rule to differentiate ln(y):

d/dx [ln(y)] = d/dx [2ln(x^3 + 2) + 4ln(x^4 + 4)]

Using the chain rule, we get:

d/dx [ln(y)] = 2(1/(x^3 + 2))(3x^2) + 4(1/(x^4 + 4))(4x^3)

Simplifying this expression, we get:

d/dx [ln(y)] = 6x^2/(x^3 + 2) + 16x^3/(x^4 + 4)

Finally, we use the fact that d/dx [ln(y)] = y'/y to solve for y':

y' = y(d/dx [ln(y)])

Substituting in the expression for d/dx [ln(y)], we get:

y' = (x^3 + 2)^2(x^4 + 4)^4 [6x^2/(x^3 + 2) + 16x^3/(x^4 + 4)]

Simplifying this expression, we get:

y' = 2(x^3 + 2)(x^4 + 4)^3[3x^2(x^4 + 4) + 8x(x^3 + 2)^2]

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1) Cada uno de los cuatro compañeros tiene correspondido \(\frac{1}{8}\) litros de pintura verde.

2) Cada uno de los tres compañeros tiene correspondido \(\frac{1}{4}\) litros de pintura roja.

3) Cada uno de los cuatro compañeros tiene correspondido \(\frac{1}{6}\) litros de pintura azul.

En este problema debemos calcular la cantidad y los tipos de pintura correspondiente a cada compañero, el cual se calcula la cantidad dividida por la cantidad de compañeros:

Pintura verde

\(v = \frac{\frac{1}{2}\,L }{4}\)

\(v = \frac{1}{8}\,L\)

Pintura roja

\(r = \frac{\frac{3}{4}\,L }{3}\)

\(r = \frac{1}{4}\,L\)

Pintura azul

\(a = \frac{\frac{2}{3}\,L }{4}\)

\(a = \frac{1}{6}\,L\)

Las cantidades correspondientes a cada compañero son las siguientes:

1) Cada uno de los cuatro compañeros tiene correspondido \(\frac{1}{8}\) litros de pintura verde.

2) Cada uno de los tres compañeros tiene correspondido \(\frac{1}{4}\) litros de pintura roja.

3) Cada uno de los cuatro compañeros tiene correspondido \(\frac{1}{6}\) litros de pintura azul.

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A vector field is conservative if its curl is zero. The curl of the vector field F is zero, so F is conservative. The scalar potential of F is given by: f(x, y, z) = x^3 + 2xyz + z^4/4 + C. The work done in moving an object in this field from (1, -2, 1) to (3, 1, 4) is: W = f(3, 1, 4) - f(1, -2, 1) = 70

A vector field is conservative if its curl is zero. The curl of a vector field is a vector that describes how the vector field rotates. If the curl of a vector field is zero, then the vector field does not rotate, and it is said to be conservative.

The curl of the vector field F is given by: curl(F) = (3z^2 - 2y)i + (2x - 3z)j

The curl of F is zero, so F is conservative.

The scalar potential of a conservative vector field is a scalar function that has the property that its gradient is equal to the vector field. In other words, F = ∇f.

The scalar potential of F is given by:

f(x, y, z) = x^3 + 2xyz + z^4/4 + C

The work done in moving an object in a conservative field from one point to another is equal to the change in the scalar potential between the two points. In this case, the work done in moving an object from (1, -2, 1) to (3, 1, 4) is:

W = f(3, 1, 4) - f(1, -2, 1) = 70

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Answer:

the perimeter of this trapzoid is 26.5.

Sorry if I am wrong and please do correct me if I am wrong.

Step-by-step explanation:

At the moment when the radius is 12 inches, the balloon is inflating at a rate of 20 cubic inches per second.

To determine the rate at which the radius is changing, we can use the formula for the volume of a sphere, which is given by \(V = \left(\frac{4}{3}\right)\pi r^3\), where V is the volume and r is the radius.

Taking the derivative of both sides with respect to time t, we get \(\frac{dV}{dt} = 4\pi r^2\left(\frac{dr}{dt}\right)\), where \(\frac{dV}{dt}\) represents the rate of change of volume with respect to time and \(\frac{dr}{dt}\) represents the rate of change of radius with respect to time.

Given that \(\frac{dV}{dt} = 20\) cubic inches per second, we can substitute this value into the equation and solve for \(\frac{dr}{dt}\) when r = 12 inches:

\(20 = 4\pi (12)^2 \left(\frac{dr}{dt}\right)\)

Simplifying the equation:

\(20 = 576\pi \left(\frac{dr}{dt}\right)\)

Dividing both sides by 576π:

\(\left(\frac{dr}{dt}\right) = \frac{20}{576\pi}\)

Therefore, the rate at which the radius is changing when the radius is 12 inches is approximately \(\frac{20}{576\pi}\) inches per second.

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Answer:

6/25 of the fish are red guppies.

Step-by-step explanation:

2/5 of the fish in Gary's fish tank are guppies.

Out of 2/5 the  of the fish in Gary's fish tank  3/5 of the guppies are red.

So, The fraction of fish in Gary's tank are red guppies = 3/5 x 2/5

=6/25

Hope this helps!

Answer:

0.5 g/cm³

Step-by-step explanation:

Density is the amount of substance per unit volume, and can be found using the formula below.

\(\boxed{Density= \frac{mass}{volume} }\)

Find the volume of the cube:

Volume of cube

= side³

= 2³

= 8 cm³

Divide the mass of the cube by its volume:

Density of cube

= 4 ÷8

= 0.5 g/cm³

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You can make your life as a good day for your response and best you have been doing it well ☺I know you don't

Answer

The answer is A.

Step-by-step explanation:

i have big iq

Answer:

The correct answers are:

Part A: For State A, the median is 36; Q1 is 35; Q3 is 37; the lowest value is 34; and the highest value is 38. For State B, the median is 25; Q1 is 23; Q3 is 38; the lowest value is 26; and the highest value is 65.

Part B: State A has a symmetric box plot; State B does not.

Explanation:

To find the five number summary for each set, we must first order the numbers from least to greatest:

State A: 34, 35, 35, 35, 36, 36, 36, 38, 38

The median is the middle value. We can see this is 36. Q1 is the value halfway between the median and the lowest value (do not include the median in this list); this is between 35 and 35, which is 35. Q3 is the value halfway between the median and the highest value (do not include the median in this list); this is between 36 and 38, which is 37. The lowest value is 34, and the highest value is 38. This is a symmetric plot, since there is 1 unit between the lowest value and Q1; 1 unit between Q1 and the median; 1 unit between the median and Q3; and 1 unit between Q3 and the highest value.

For State B: 20, 22, 24, 24, 25, 25, 26, 50, 65

The median, or middle value, is 25. Q1, halfway between the median and the lowest value, is 23 (between 22 and 24). Q3, halfway between the median and the highest value, is 38 ((26+50)/2 = 76/2 = 38). The highest value is 65 and the lowest value is 20. This box plot is not symmetric; this is because there are 3 units from the lowest value to Q1, 2 units from Q1 to the median, 13 units from the median to Q3, and 27 units from Q3 to the highest value.

Step-by-step explanation:

Answer:

(0, 0 )

Step-by-step explanation:

y = 4x is the equation of a line passing through the origin.

Then its y- intercept is 0 or (9, 0 )

The angular velocity of the circle is approximately 19 m/s.

In order to find the missing quantity, we can use the relationship between linear velocity and angular velocity in a circle. The linear velocity of a point on the edge of a circle is the product of the radius and the angular velocity. This can be expressed as:

v = r * w

where v is the linear velocity, r is the radius, and w is the angular velocity.

To find the value of w, we can rearrange this equation to solve for w:

w = v / r

Substituting the given values of v and r, we get:

w = 1235 m/min / 65 m

w = 19 m/s

It's important to note that units must be consistent when using formulas to solve problems. In this case, we converted the given linear velocity from m/min to m/s before plugging it into the formula. Also, we rounded the answer to the nearest tenth, as instructed, since the given values were rounded to the nearest unit.

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