If $5000 is invested at 9% annual simple interest, how long does it take to be worth $7700 O a. 9 years Ob. 6 years c. 10 years O d. 5 years

Answer:

\(5mn^{2} (2+ 5m^{2} n)\)

Step-by-step explanation:

I assumed the polynomial is \(10mn^{2} +25m^{3}n^{2}\)

FIRST: Highlight the common factors{ 5 , m and\(n^{2}\))

\(5mn^{2} (2+ 5m^{2} n)\)

Answer: A (4, -7) B (9, -7)

Step-by-step explanation:

When it’s reflected over the x-axis, the y coordinates become negative but the x coordinates don’t change

x coordinates: 4, 9

y coordinates: 7, 7

Reflected over x-axis: (4, -7), (9, -7)

The volume of the solid obtained by rotating the region bounded by Y=5/x, X=5, X=10, and y=0 about the x-axis is approximately 119.87 cubic units.

To find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis, we can use the method of cylindrical shells.

First, we need to sketch the region and the axis of rotation to get a better understanding of the solid.

The region bounded by the curves Y=5/x, X=5, X=10, and y=0 is shown below:

     y |          

        |          

  5 _|________

       |\                |

       | \               |

       |   \             |

       |     \           |

       |        \        |

       |           \     |

       |             \   |

       |_______\|__

         5           10      x

We can see that the axis of rotation is the x-axis.

Next, we need to set up the integral that will give us the volume of the solid. To do this, we can use the formula:

V = ∫2πy * h * dx

where y is the radius of the cylindrical shell, h is the height of the cylindrical shell, and dx is the width of the cylindrical shell.

We can express y and h in terms of x as follows:

y = 5/x (since y = f(x) = 5/x)

h = x - 5 (since the height of the cylindrical shell is the difference between the upper and lower boundaries of the region)

Substituting these expressions into the formula, we get:

V = ∫2π(5/x)(x - 5)dx

V = 10π ∫(x - 5)/x dx (note that 2π is a constant that can be factored out of the integral)

V = 10π ∫(1 - 5/x) dx

V = 10π [x - 5ln|x|] from x=5 to x=10

V = 10π[(10 - 5ln(10)) - (5 - 5ln(5))]

V ≈ 119.87 cubic units

Therefore, the volume of the solid obtained by rotating the region bounded by Y=5/x, X=5, X=10, and y=0 about the x-axis is approximately 119.87 cubic units.

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Yes, the distance from (-2, 0) to (1, √7) is 4 units.

We know that the general form of equation of the circle is given by;

(x - h)² + (y - k)² = r²

where;

(h, k) is the coordinate of the center

r is the radius

From the attached image, the radius is equal to the distance between the center and the point (-2,4).  Thus, r = 4 and so we have;

(x + 2)² + (y - 0)² = 4²

(x + 2)² + y² = 16

If the distance between the center and the point is equal to the radius of the circle , then the point lies on the circle and the formula to calculate the distance between two points is;

d = √[(y₂ - y₁)² + (x₂ - x₁)²]

At A(-2, 0) and B(1, √7), we have;

d = √[(√7 - 0)² + (1 - (-2))²]

d = 4 units

Therefore we can conclude that  the distance from (-2, 0) to (1, √7) is 4 units.

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The system of inequalities did not have any solution, but after reversing the  sign we will get a solution of the system of inequalities.

The inequalities are : y > 2x + 2/3 and y < 2x + 1/3

There is no intersection and no solution to the system since the region above the line y = 2x + 2/3 and the region below the line y = 2x + 1/3, respectively, are the solutions to the inequality y > 2x + 2/3 and y <2x + 1/3, respectively.

Now when the signs are changed we get:

y < 2x + 2/3 and y > 2x + 1/3

The region below the line y = 2x + 2/3 is the solution of the inequality

y= 2x + 2/3, and the region above the line y = 2x + 1/3 is the solution of the inequality y > 2x + 1/3. This implies that the area between the two lines is where the system's solution lies.

Disclaimer: The complete question is :

How will the solution of the system y>2x+2/3 and y<2x+1/3 change if the inequality sign on both inequalities is reversed to y<2x+2/3 and y>2x+1/3?

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Answer:

There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions. 

Step-by-step explanation:

Sample answer

Answer:

i guess

Step-by-step explanation:

The correct terms for the segments on the circle are: chord for line CE and radius for line AB.

The following are the terms that best describes the segments CE and AB;

Chord: The segment AB is a circle chord, because it is a straight line segment that connects two points on the circumference of a circle.

Radius: AG is a radius because connects the center of a circle to any point on the circle's circumference.

In conclusion, the best terms for the segments on the circle are: chord for line CE and radius for line AB.

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Answer:

x=4

Step-by-step explanation:

To solve for x, we need to isolate it.

Start by adding 16 to each side to cancel out the -16:

-x=-4

-x is essentially -1 * x which can be written as -1x

-1x=-4

Divide both sides by -1 to isolate x

x=4

We can also plug this back into the equation to check:

-16-x=-20

-16-4=-20

-20=-20 --> correct!

All six trigonometric functions of θ if the given point is on the terminal side of θ are sin θ = 0, cos θ = 1, tan θ = 0, cot θ = not defined, csc θ = not defined, and sec θ = 1.

Given that the point is on the terminal side of θ, i.e. (1,0). We need to find all the six trigonometric functions of θ. Using the Pythagorean Theorem, we can find the hypotenuse of the triangle formed by the point and the origin.

Let x be the adjacent side of the right-angled triangle formed by the point (1, 0), y be the opposite side, and r be the radius/hypotenuse. Using the Pythagorean Theorem, we can write: r² = x² + y².

Since the given point is (1,0), we have x = 1 and y = 0.

r² = 1² + 0² = 1

r = 1

Therefore, we have: r = 1

We can now find the trigonometric functions of θ: sin θ = y/r = 0/1 = 0, cos θ = x/r = 1/1 = 1, tan θ = y/x = 0/1 = 0, cot θ = x/y = 1/0 = not defined, csc θ = r/y = 1/0 = not defined and sec θ = r/x = 1/1 = 1. Thus, the six trigonometric functions of θ for the given point (1,0) are as follows: sin θ = 0, cos θ = 1, tan θ = 0, cot θ = not defined, csc θ = not defined and sec θ = 1.

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Answer:The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.

Step-by-step explanation:

Answer:

x=4.6

Step-by-step explanation:

Because we are finding C, first use the distributive property.

33-(2c+4)=2(c+7)+c can turn into:

33-2c+4=2c+14+c

Now, combine like terms.

33+4=37

2c+c=3c

Now you are left with:

37-2c=3c+14

Now, add 2c on both sides.

37=5x+14

Next, subtract 14 on both sides.

37-14=23

23=5x

Finally, divide by 5 on both sides

x=4.6

Answer:

let the first term of an A.P. is 'a' and common difference 'd'

∴ 8th term = sum of the first 8 terms

a8 = S

a + 7d = 8/2(2a + (8 - 1)d)

a + 7d = 8/2(2a + 7d)

2a + 14d = 16a + 56d

16a + 56d - (2a + 14d) = 0

14a + 52d = 0

divide eq. by 14 we get  ,

a + 3d = 0

and a + 3d = a4  = 0

the eigenvalues for the given boundary value problem are λ = 0 and λ = 1, and the corresponding eigenfunctions are y₁(x) = 1 and y₂(x) = \(x^{(1-\lambda)\).

To find the eigenvalues and eigenfunctions for the given boundary value problem, we can solve the differential equation and apply the boundary conditions.

First, let's rewrite the differential equation in standard form by dividing through by x²:

y'' + (1/x) y' + (λ/x²) y = 0

Now, let's assume the solution has the form y(x) = \(x^r\), where r is a constant to be determined. Substituting this into the differential equation:

\(x^r\) (r(r-1) + r + λ/x) = 0

Rearranging and simplifying:

r² + (λ - 1) r = 0

This is a quadratic equation for r. The solutions for r are:

r₁ = 0

r₂ = 1 - λ

These are the eigenvalues.

Next, we find the corresponding eigenfunctions for each eigenvalue by substituting the values of r back into the assumed form of the solution.

For r₁ = 0, the corresponding eigenfunction is y₁(x) = x⁰ = 1.

For r₂ = 1 - λ, the corresponding eigenfunction is y₂(x) = \(x^{(1-\lambda)\).

Therefore, the eigenvalues for the given boundary value problem are λ = 0 and λ = 1, and the corresponding eigenfunctions are y₁(x) = 1 and y₂(x) = \(x^{(1-\lambda)\).

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Answer:

Using the given information from the graph, the x-intercept of the line is -1 and the y-intercept of the line is -4.

Step-by-step explanation:

For this problem, we are asked to find the x-intercept and the y-intercept of the line. The x-intercept represents the point where the line hits the x-axis. The y-intercept represents the point where the line hits the y-axis.

So, knowing this, we have the find the points where the line hits the x-axis and the point where the line hits the y-axis.

The line hits the x-axis at (-1,0). The line hits the y-axis at (0,-4)

So, the x-intercept of the line is -1 and the y-intercept of the line is -4.

Although increasing the sample size can improve the accuracy of the estimate, there are some problems that may arise with very large samples.

The following are the problems that can occur:

Difficulty in obtaining a very large sample: It may be difficult to obtain a large sample that is representative of the population and has a low bias.

Cost of sampling: Collecting data from a very large sample can be time-consuming and expensive.

None of these: This is not a problem that can arise with very large samples.

Increase in standard error: As the sample size increases, the standard error of the estimate tends to decrease, but after a certain point, increasing the sample size further may not lead to a significant reduction in the standard error, and may even increase it due to other factors such as measurement errors or non-random sampling. This is called the "law of diminishing returns".

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The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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The outliers of the given data set are 2 and 12.

The given data set is 2, 4, 6, 8, 10 and 12.

Outliers are extreme values that stand out greatly from the overall pattern of values in a dataset or graph

A value that "lies outside" (is much smaller or larger than) most of the other values in a set of data. For example in the scores 25,29,3,32,85,33,27,28 both 3 and 85 are "outliers".

In the given data set 2, 4, 6, 8, 10 and 12.

2 is the lowest observation and 12 is the highest observation.

So, 2 and 12 are two extreme values and these two are outliers.

Therefore, the outliers of the given data set are 2 and 12.

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The equation given, 5x + 10y, does not represent the total amount of fiber in a package containing x apples and y oranges.

To calculate the total amount of fiber in a package containing x apples and y oranges, you would need to know the amount of fiber in each apple and orange and the number of apples and oranges in the package.

For example, if each apple contains 3 grams of fiber and each orange contains 2 grams of fiber, and there are x apples and y oranges in the package, the total amount of fiber in the package would be:

Total fiber = (3 grams of fiber per apple)(x apples) + (2 grams of fiber per orange)(y oranges)

Total fiber = 3x + 2y grams

what is number?

A number is a mathematical concept used to represent quantity or magnitude. Numbers can be used to count objects, measure distances or sizes, perform calculations, and describe various other mathematical concepts. The most basic types of numbers are the natural numbers, which include all positive integers (1, 2, 3, ...), and sometimes zero (0) as well. Other types of numbers include fractions, decimals, negative numbers, complex numbers, irrational numbers, and more. Numbers are a fundamental concept in mathematics and are used extensively in many fields, including science, engineering, economics, and finance.

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Answer:

y = 2x + 7

Step-by-step explanation:

The square with the side length 26 is the Square C.

The square with the side length 11 is the Square B.

The square with the side length 4.2 is the Square A.

As,

4.2<11<26

Answer:

$32.52

Step-by-step explanation:

Hope it helps! =D

Answer:

Its D

Step-by-step explanation:

Answer:

1. b

2. d

3. c

4. a

5. f

6. e

Step-by-step explanation:

Answer:

57 hours

Step-by-step explanation:

substitute the value 12.5 as x and solve

4(12.5)+7

50+7

57

so she works 57 hours

Answer:

choice 1) 2x+4

Step-by-step explanation:

(6x²+12x)/3x = 2x+4

Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

such as a day or a week. Number of Failed Parts: The number of parts that have failed over a given period of time, such as a day or a week. Hours of Operation: The amount of time that a machine or system was operational during a given period of time, such as a day or a week. Maintenance Time: The amount of time that was spent maintaining a machine or system during a given period of time, such as a day or a week.

Mark for Follow-Up: An indication of which issues need to be addressed or followed up on to prevent future failures or improve performance. Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

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In the given equation r = 2/5 t "r" is the dependent variable.

In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.

An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.

A dependent variable is a variable whose value depends on the value of one or more other variables in the equation

Here we have

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups.

She writes the equation r = 2/5 t to describe the relationship.

In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.

Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.

The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.

Therefore,

In the given equation r = 2/5 t "r" is the dependent variable.

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Complete Question:

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.

To write a program that prompts the user for a list of values, stores them in an array using dynamic memory allocation, and computes the average value, you can follow these steps:

Declare necessary variables, such as the size of the array, a pointer to the dynamically allocated array, and a variable to store the sum of values.

Prompt the user to enter the size of the array and read the input.

Allocate memory for the array dynamically using the size entered by the user.

Prompt the user to enter values for each element of the array and store them.

Calculate the sum of all values entered.

Compute the average value by dividing the sum by the size of the array.

Output the list of values entered by iterating over the array.

Display the calculated average value as an integer.

By following these steps, you can create a program that interacts with the user, dynamically allocates memory for the array, stores the entered values, calculates the average, and outputs the results. It's important to properly manage memory allocation and deallocation to avoid memory leaks and ensure efficient memory usage.

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