4. What is the connection between exponential function and geometric sequence.

5. Define Moore's law. How Moore's law is associated with exponential function.

Answer: 4.5

Step-by-step explanation:

Answer:

.55b = 30

Step-by-step explanation:

55% is .55

You have .55 of b = 30

.55b=30

Sections taken through the narrow width of an entire building are known as transverse sections.

A building is an enclosed structure with a roof and walls standing more or less permanently in one place, such as a house or factory.

Given is a structural analysis blank statement as -

"Sections taken through the narrow width of an entire building are known as __________ sections.

Sections taken through the narrow width of an entire building are known as transverse sections. Those through the long dimension are known as longitudinal sections.

Therefore, Sections taken through the narrow width of an entire building are known as transverse sections.

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The conversion of 28 Fahrenheit to Celsius is -2.22.

To convert 28 degrees Fahrenheit (28°F) to Celsius (°C), you can use the formula:

°C = (°F - 32) x 5/9

Substituting 28 for °F in the formula, we get:

°C = (28 - 32) x 5/9

Simplifying the expression inside the parentheses and performing the arithmetic operations, we get:

°C = (-4) x 5/9

°C = -2.22

Therefore, 28°F is equal to -2.22°C (rounded to two decimal places).

Celsius and Fahrenheit are two scales used to measure temperature.

Celsius, also known as the centigrade scale, is a temperature scale where the freezing point of water is 0 degrees Celsius and the boiling point of water is 100 degrees Celsius at standard atmospheric pressure.

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Correct Question :

What is the conversion of 28 Fahrenheit to Celsius?

The average rate of change of candle height from time 45 minutes to time 109 minutes is -1 inch per 64 minutes.

The average rate of change is a measure of how quickly one quantity changes relative to another. It is calculated by dividing the difference between two values by the difference in time between those two values. It is a useful metric when trying to understand the speed at which a given quantity is changing over time.

For example, To calculate the average rate of change in the number of students enrolled in a particular school over the course of 5 years. In year 1, the school had 200 students enrolled and in year 5 it had 350 students enrolled. To calculate the average rate of change, one would divide the difference between the two values (150 students) by the difference in time between them (4 years):

Average rate of change = (350-200) / (5-1) = 150 / 4 = 37.5

This means that, on average, the school's enrollment increased by 37.5 students each year.

The table showing the height of a pyramid candle as it burns can be calculated by dividing the change in height (2 inches) by the change in time (64 minutes).

Change in height = 2 inches

Change in time = 64 minutes

Average rate of change = (2 inches) / (64 minutes) = -1 inch per 64 minutes

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The measurement of the LM will be 42.0

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Here given in the question that one side of the wall 5 feet

So as it is a rectangular bedroom it can be split into 2 right-angled triangles.

So the hypotenuse of the triangle is 13 feet

Now using the Pythagoras theorem we can find out the length of the other wall

b² = h² -p²

given KM = 52, NL = 33

So the triangle MLN

LM = √(33²+26²) = 42.0

Hence The measurement of the LM will be 42.0

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The conversion of 71kg to lbs is nearly equal to 156.53 lbs.

The kilogramme (symbol: kg)  is a SI unit of mass.

The pound (symbol: lb) is also the unit of mass.

One pound is nearly equal to 0.45359237 kilograms.

Here we want to convert 71 kilograms to pounds,

As we know that:

1 kilogram equal to 2.20462 pounds

So, for conversion of 71 kg into pound

Multiplying 71 by 2.20462

71 kilograms = 71 x 2.20462 pounds

After simplifying the calculation,

We get:

71 kilograms = 156.52802 lbs

Therefore,  the conversion of 71 kilograms is equal to nearly  156.52802 lbs (rounded to two decimal places).

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(i) An exponential function to model this situation, [tex]A=2500(1.035)^n[/tex].

(ii) The value of the investment after 20 years A =$ 4,974.47 .

When the input variable x appears as an exponent in the formula f(x) = ax, an exponential function is indicated. Both the exponential function and the value of x have an impact on the exponential curve.

An essential mathematical function is the exponential function, which has the following formula:

f(x) = ax

When a>0 and a=1 are not true.

x can be any real number.

The exponential function is given as :

[tex]A=P(1+r)^n[/tex]

Where :

A = amount

P = principal

r = rate %

n = number of years

the situation can be modelled using an exponential function by substituting.

[tex]A=2500(1+0.035)^n\\\\A=2500(1.035)^n[/tex]

(ii) when n = 20 , the Amount,

[tex]A=2500(1.035)^{20}[/tex]

A =$ 4,974.47

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Answer:a

Step-by-step explanation:

In the given scenario, the average is an example of a Parameter.

In statistics, a statistic is a numerical value or measure that is calculated from a sample of data. Statistics are used to summarize and describe the characteristics of a sample.

a variable is a symbol or letter that represents a quantity or value that can change or vary. Variables are used to describe relationships between quantities and to represent unknown values or values that can take on different values in different situations.

In statistics, a parameter is a characteristic of a population. A population refers to the entire group of individuals, objects, or events that we want to study. A parameter is a numerical value that describes some aspect of the population, such as its mean, variance, or proportion.

For example, if we want to study the average height of all students at a university, then the population is all the students at the university, and the parameter of interest is the population's mean height

A constant is a value that does not change. In mathematics, constants are often used to represent fixed values or quantities that do not depend on other variables or parameters.  

Here we have

A researcher record the individual change in weight for a small group of 25 freshmen from this college during their first semester.

Then, the researcher calculates the average change in weight during the first semester among these 25 students.  

By the given information,

In the given scenario, the average is an example of a Parameter.        

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The diameter of a circle is equal to twice the radius of the circle and is measured across the circle through its centre. The diameter of a circle can be calculated using either the radius or the circumference of the circle.

To calculate the diameter using the circumference, you can use the formula:

Diameter = Circumference / π

where π (pi) is a mathematical constant approximately equal to 3.14159.

For example, if the circumference of a circle is 31.4 cm, then the diameter can be calculated as follows:

Diameter = Circumference / π

Diameter = 31.4 cm / 3.14159

Diameter = 10 cm (rounded to the nearest tenth)

To calculate the diameter using the radius, simply multiply the radius by 2. The formula is:

Diameter = 2 x Radius

For example, if the radius of a circle is 5 cm, then the diameter can be calculated as follows:

Diameter = 2 x Radius

Diameter = 2 x 5 cm

Diameter = 10 cm

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The solution to the given system of linear equations is: x =3, y= -4

Here we have 2 linear equations

(1) y = -7/3x + 3

(2) y = 5/3x - 9

Firstly we need to convert these equations into their simplest forms:

(1) 7/3x - y = 3

(2) -5/3x - y = -9

to calculate the value of x, we need to subtract both equations:

7/3x + 5/3x = 3 +9

12/3x = 12

4x = 12

x = 12/4

x = 3

Now, to solve for y, we need to put the value of x in the first equation

y = -7/3 ( 3) +3

y= -7 + 3

y = -4

Therefore, the solution to the system of linear equations is:

(x,y) = ( 3, -4)

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An outlier is an extreme value that is significantly different from other values in a dataset.

A histogram is a graphical representation of the distribution of numerical data. It is a type of bar chart that displays the frequency of values in a dataset by dividing the range of values into intervals, or bins, and counting the number of values that fall into each bin. The bins are usually consecutive and non-overlapping intervals of a variable, such as time, temperature, weight, or height. To create a histogram, we first divide the range of values into a set of bins or intervals. Then, we count the number of data points that fall into each bin and plot a bar for each bin, where the height of the bar represents the frequency or count of data points in that bin. The bars in a histogram are typically drawn adjacent to each other, without gaps, to emphasize the continuity of the data.

Here,

It is typically defined as a value that is located far away from the other values, either above or below the typical range of values. Outliers can arise from various causes, such as measurement errors, data entry errors, or real differences in the underlying population.

Therefore, the correct options for this multiple select question are:

An extreme value that might have arisen from a different cause.

An extreme value that might have arisen from measurement error.

An extreme value that is located in the tail of the histogram.

The first option is correct because outliers may arise from different causes such as changes in the underlying population or errors in the data collection process.

The second option is also correct because outliers may arise due to errors in measurement, such as recording a value that is too high or too low, or a malfunctioning instrument.

The fourth option is not necessarily correct because an outlier may or may not be located in the tail of a histogram. A histogram is a graphical representation of the distribution of data, and outliers can appear anywhere in the distribution, not just in the tail.

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The home buyer saves $26,289 by choosing Loan A. The closest answer choice is $26,351.02.

From the question, we are to determine the amount the home buyer saves in total by choosing loan A

To calculate the savings, we need to find the total amount paid for both loans and then subtract the total paid for Loan A from the total paid for Loan B.

For Loan A:

M = $3,509.71

Total amount paid = 15 years x 12 months/year x $3,509.71/month = $631,748.20

For Loan B:

M = $3,659.86

Total amount paid = 15 years x 12 months/year x $3,659.86/month = $658,037.20

The difference between the two is:

$658,037.20 - $631,748.20 = $26,289.00

Hence, the amount the home buyer saves is $26,289

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Answer:

B. 11,427.00

Step-by-step explanation:

got it right on test

Molar mass, or the mass of one mole of a material, is used to convert grams to moles.

It is possible to translate between grams into moles of material using molar mass, which is commonly given in grams per mole.

Divide the substance's mass in grams by its molar mass in grams per mole to convert grams to moles. This provides you with the substance's molecular weight.

For instance, you must first establish the molar mass of sodium chloride (NaCl), which is roughly 58.44 grams per mole, in order to convert 50 grams of NaCl to moles. Thereafter, you may apply the subsequent equation:

gram mass divided by molar mass equals one mole (in grams per mole)

Mole = 50 g / 58.44 g/mol = 0.856 mol 

Hence, 0.856 moles of sodium chloride are equal to 50 grams of sodium chloride. Applications for this conversion may be found in chemistry, physics, and engineering.

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The correct answer is D. Both A and B are correct, to make predictions about values of y for given x value and to determine the strength of linear association between variables.

The regression line is a statistical tool that allows us to model the relationship between two variables, usually called X (the independent variable) and Y (the dependent variable), assuming a linear relationship between them. Once the regression line has been fitted to the data, it can be used for two main purposes:

A. To make predictions about the values of Y for a given X-value: Once the regression line has been fitted, we can use it to predict the value of Y for any given X-value. This is done by plugging in the X-value into the equation of the regression line, which will give us an estimated value of Y.

B. To determine the strength of a linear association between two variables: The regression line is also a measure of the strength of the linear relationship between X and Y. Specifically, the slope of the regression line (which represents the change in Y for a unit change in X) is a measure of how much Y changes for a given change in X. The closer the slope is to zero, the weaker the linear relationship between X and Y; the farther the slope is from zero, the stronger the linear relationship between X and Y.

Therefore, both A and B are correct uses of the regression line.

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The statements that are true about object-oriented analysis are: b) Control classes receive or handle system events, c) encapsulate behavior of use case, d) implement the controller pattern.

Object-oriented analysis and design (OOAD) is a technical method for analyzing and planning an application, system, or business using object-oriented programming and visual modeling to direct stakeholder communication and product quality throughout the software development process.

Modern software engineering practices typically involve iterative, incremental OOAD. Analysis models for OOA and design models for OOD are the byproducts of OOAD activities, respectively. The goal is for these to continuously improve and change, guided by important factors like risks and business value.

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Note that the full question is:

Which statements are true about control classes in object-oriented analysis? Select all that apply.

a) Control classes manage data structures.

b) Control classes receive or handle system events.

c) Control classes encapsulate behavior of use case.

d) Control classes implement the controller pattern.

Answer:

The solutions to the equation f(x) = g(x) to the nearest hundredth are x ≈ 1.76 and x ≈ 7.85.

Step-by-step explanation:

f(x) = 0.15x³ - 2x² + 7x - 3.3

g(x) = 1.5|x - 7.3|

To solve the equation, we can set the two functions equal to each other and then solve for x:

0.15x³ - 2x² + 7x - 3.3 = 1.5|x - 7.3|

We can split this equation into two cases, depending on the sign of x - 7.3:

Case 1: x - 7.3 ≥ 0

In this case, we have:

0.15x³ - 2x² + 7x - 3.3 = 1.5(x - 7.3)

0.15x³ - 2x² + 7x - 3.3 = 1.5x - 10.95

0.15x³ - 2x² + 5.5x + 7.65 = 0

We can solve this cubic equation by using numerical methods, such as the Newton-Raphson method or the bisection method. One solution to this equation is x ≈ 1.76.

Case 2: x - 7.3 < 0

In this case, we have:

0.15x³ - 2x² + 7x - 3.3 = -1.5(x - 7.3)

0.15x³ - 2x² + 7x - 3.3 = -1.5x + 10.95

0.15x³ - 2x² + 8.5x - 14.25 = 0

Again, we can solve this cubic equation by using numerical methods. One solution to this equation is x ≈ 7.85. Therefore, the solutions to the equation f(x) = g(x) to the nearest hundredth are x ≈ 1.76 and x ≈ 7.85.

Answer:

x = -4.05, x = 2.15, and x = 4.96.

Step-by-step explanation:

To find the solutions to the equation f(x) = g(x), we need to substitute the expressions for f(x) and g(x) and solve for x.

0.15x³ - 2x² + 7x - 3.3 = 1.5x - 7.3

0.15x³ - 2x² + 5.5x + 3 = 0

We can solve this equation using numerical methods, such as graphing or using a calculator, to find the solutions to two decimal places. One possible method is to use a graphing calculator and graph the function y = 0.15x³ - 2x² + 5.5x + 3, and then use the intersect function to find the x-values where the function intersects the line y = 1.5x - 7.3.

Using this method, we find that there are three solutions to the equation, to the nearest hundredth: x = -4.05, x = 2.15, and x = 4.96.

Therefore, the solutions to the equation f(x) = g(x) to the nearest hundredth are x = -4.05, x = 2.15, and x = 4.96.

Answer: 96

Step-by-step explanation:

Answer:

You are correct! The actual distance, in miles, between Zionsville and Lafayette is 96 miles. This is calculated by multiplying 8 inches (the distance on the map) by 12 miles (the scale of the map), which results in 96 miles.

We can see here that determining which polygons are being described below, we have:

1. A parallelogram with congruent sides - rhombus

2. A polygon with equal sides and equal angles - equilateral polygon.

3. A quadrilateral with 1 pair of acute angles and 1 pair of obtuse angles - kite.

4. Can be classified as a parallelogram and a rhombus - rhombus.

A quadrilateral is a geometric shape that has four sides, four vertices (corners), and four angles. The sum of the angles in a quadrilateral is always 360 degrees. Some common examples of quadrilaterals include rectangles, squares, trapezoids, parallelograms, rhombuses, and kites.

5. Can be classified as a quadrilateral and a parallelogram - parallelogram.

6. Has 4 sides, 2 pairs of parallel sides, and 2 sets of congruent sides - rectangle.

7. Has only one set of parallel sides - trapezoid

8. A polygon with 3 equal sides and 3 acute angles - equilateral triangle.

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The number of adults and the number of children who used the swimming pool is 102 and 304 respectively.

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations which on solving gives the intersecting point of all the solutions.

Let x be the number of adults and y be the number of children who swam on that day.

Total of 406 people swam in the swimming pool that day.

Number of adults + number of children = 406

x + y = 406

Assuming the receipts for admission totaled $609.5.

Cost per child is $1.25 and cost per adult is $2.25.

Cost for x adults and y children is $609.5.

2.25x + 1.25y = 609.5

We have to solve,

x + y = 406

2.25x + 1.25y = 609.5

Multiplying the first equation with 2.25,

2.25x + 2.25y = 913.5

Subtracting 2.25x + 1.25y = 609.5 from 2.25x + 2.25y = 913.5,

y = 304

x = 406 - 304 = 102

Hence the number of adults are 102 and the number of children are 304.

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The total distance that she sprint on day 21 is option (c) 180 yards

To solve the problem, we need to use the explicit formula for an arithmetic sequence, which is:

an = a1 + (n - 1) × d

where:

an is the nth term of the sequence

a1 is the first term of the sequence

n is the number of the term we want to find

d is the common difference between consecutive terms

To find out how far Marika sprints on day 21, we can substitute n = 21 into the explicit formula:

an = 100 + (n - 1) × 4

a21 = 100 + (21 - 1) × 4

a21 = 100 + 20 × 4

a21 = 100 + 80

a21 = 180 yards

Therefore, the correction option is (c) 180 yards

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The volume of the empty portion of Container B is approximately 47.1 cubic feet, to the nearest tenth of a cubic foot.

The formula V = r2h, where r is the cylinder's radius and h is its height, can be used to determine a cylinder's volume.

Water in Container A has a volume of:

V A is equal to (3 ft)2(5 ft) 141.37 ft3.

This amount of water will be moved to Container B, which has a 15-foot height and a 2-foot radius. Container B contains a total of:

V B = (1.5 x 2 x 15) x 188.5 ft 3

The volume of the empty space in Container B after the water has been pumped from Container A to Container B can be estimated by deducting the volume of the water from the overall volume of Container B:

47.1 ft3 = V empty = V B - V A

As a result, to the nearest tenth of a cubic foot, the volume of Container B's empty space is roughly 47.1 cubic feet.

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The product of 2.43 and 13, which is the result of the multiplication operation, is 31.59.

The product of two or more numbers is the result of the multiplication operation performed on the numbers.

Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.

The multiplication operation involves the multiplicand, the multiplier, the multiplication operand (x), the equal symbol (=), and the result, known as the product.

2.43 x 13 = 31.59

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The correct statements are (a) and (d). which are the graph is reflected over the x - axis and the the graph is shifted down 1 unit.

a. The graph is reflected over the x-axis.

This statement is true. The negative sign in front of the sine function reflects the graph of the parent function over the x-axis.

b. The frequency decreases by a factor of 1/4.

This statement is false. The coefficient in front of the x in the sine function determines the frequency of the wave. Since there is no coefficient in front of x in this case, the frequency of the wave remains the same.

c. The phase shift is 1/4 unit to the right.

This statement is false. The phase shift determines how the graph is horizontally shifted left or right. However, there is no horizontal shift in this case, so the phase shift is 0.

d. The graph is shifted down 1 unit.

This statement is true. The negative sign in front of the sine function also shifts the graph down by 1 unit.

e. The graph is reflected over the y-axis.

This statement is false. A reflection over the y-axis would require a negative sign in front of x, not in front of the sine function.

f. The frequency increases by a factor of 4.

This statement is false. As mentioned in (b), there is no change in frequency in this case.

Therefore, the correct statements are (a) and (d).

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Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

The angle measures of the triangle are  45°,45°, and 90°.

What is the angle measure?

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Here, we have

Given, the triangle is a right-angle triangle.

And the sides are 7√3, 14√3, 21.

Sides are a multiple of 7.

So, divide each side by 7.

We get the sides  √3, 2√3, 3.

In a 45°−45°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

Hence, the angle measures of the triangle are 45°, 45° and 90°

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Answer:

80 degrees

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360 degrees. Adding up the known measures gives you 95 + 123 + 62 = 280. Then you can subtract that from 360. 360 - 280 = 80. So x has to be 80 degrees.

The absolute value inequality for the graph is given as follows:

|x| < 3.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

|x| = x, x ≥ 0.

|x| = -x, x < 0.

It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.

From the graph, the shaded region is less than 3 units from the origin, as |-3| = |3| = 3, hence the inequality is defined as follows:

|x| < 3.

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Sure! A table of values for f(x) = log base 8 of x is shown below:

x) f(x)

1) 0

2) 1/3

3) 0.54

4) 0.67

5)0.79

6)0.89

7) 0.97

8) 1

9) 1.10

10) 1.18

A logarithmic function is a type of mathematical function that involves the use of logarithms. Logarithms are a way of expressing numbers in terms of exponents, and logarithmic functions are functions that involve the logarithm of one or more variables.

The general form of a logarithmic function is:

f(x) = log_b(x)

where b is the base of the logarithm, and x is the argument of the logarithm.

Logarithmic functions have several important properties. One of the main properties is that they can be used to convert between exponential and logarithmic forms of equations. For example, the equation[tex]2^3[/tex] = 8 can be written in a logarithmic form as log_2(8) = 3.

Logarithmic functions are also used in many applications in science, engineering, and finance. In science, logarithmic functions are used to describe the behavior of phenomena that exhibit exponential growth or decay, such as radioactive decay or population growth. In finance, logarithmic functions are used to calculate compound interest and to model the growth of investments over time.

The graph of a logarithmic function is a curve that approaches but never touches the x-axis as the x approaches zero. The shape of the curve depends on the base of the logarithm, and it becomes steeper as the base gets larger. The inverse function of a logarithmic function is an exponential function.

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The solution of the given equation is 1/4

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Given equation can be rewritten as:

(1/8 -x)^(1/3) = -1/2

raising the power 3 on both the sides, we get

(1/8 -x) = (-1/2)³

(1/8 -x) = -1/8

=> x= 1/8 + 1/8 = 2/8 = 1/4

The solution of the given equation is 1/4

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Answer:

I would assume that 100 would be 100 minutes in the air, if -100 represents 100 minutes before take-off.

Step-by-step explanation: