Referring to the equation for earnings on a checking account (I = rB − sx − f), where, if r = 0.0095, B = $2,000.00, s = 0, x = 28, and f = $4.00, what are the customer’s earnings for the month if her minimum balance is $2,000.00?


$8.00


$21.00


$15.00


$7.00

2.1. Number sense refers to a person's intuitive understanding and flexibility with numbers.

2.2 Number sense is of utmost importance in elementary mathematics education as it serves as the foundation for more advanced mathematical concepts and skills.

2.1 It involves the ability to comprehend and manipulate numerical quantities, make reasonable estimates, recognize patterns and relationships, and use numbers in practical and meaningful ways. Number sense goes beyond mere memorization of numerical facts and procedures; it encompasses a deep understanding of the structure and properties of numbers.

2.2 Number sense is of utmost importance in elementary mathematics education as it serves as the foundation for more advanced mathematical concepts and skills.

In summary, number sense is vital in energizing mathematics because it fosters conceptual understanding, supports problem-solving abilities, enhances mathematical fluency, promotes mathematical reasoning, and facilitates real-world applications of mathematics.

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The previous year's total revenue for the small business was approximately $25,130.43.

The total revenue of the small business the previous year can be calculated by finding the value that is 15% more than the revenue of $28,900 this year.

To determine the previous year's revenue, we can set up the equation:

Previous Year's Revenue + 15% of Previous Year's Revenue = $28,900

Let's solve the equation to find the previous year's revenue:

Let x be the previous year's revenue.

x + 0.15x = $28,900

Combining like terms, we have:

1.15x = $28,900

Dividing both sides by 1.15, we get:

x = $28,900 / 1.15 ≈ $25,130.43

Therefore, the previous year's total revenue for the small business was approximately $25,130.43.

We set up the equation by adding 15% of the previous year's revenue to the previous year's revenue. This is done to find the total revenue that is 15% more than the previous year's revenue. By solving the equation, we find that the previous year's revenue was approximately $25,130.43.

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The correct answer is "Oy-axis" as it represents the line of reflection for triangle DEF to triangle D'EF.

To determine the line of reflection that maps triangle DEF to triangle D'EF, we can examine the coordinates of the corresponding vertices.

Given that E' is located at (10, 4) and the corresponding vertex E in triangle DEF is at (-10, 4), we can observe that the x-coordinate of E' is the negation of the x-coordinate of E.

This suggests that the line of reflection is the y-axis. A reflection across the y-axis results in a transformation where the x-coordinate of each point is negated while the y-coordinate remains the same.

Since "Oy-axis" indicates the line of reflection from triangle DEF to triangle D'EF, it is the appropriate response.

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Answer:

(-∞, -4]

Step-by-step explanation:

4x - 1 < -15

4x < -14

x < -14/4

x < -7/2

So the solution to the inequality is x < -7/2. This means that all integer values of x that make the inequality true are the integers less than -7/2. In interval notation, we can write this as:

(-∞, -4]

Answer: [-∞, -4]

Step-by-step explanation:

Given inequality

4x - 1 < -15

Add 1 on both sides

4x - 1 + 1 < -15 + 1

4x < -14

Divide 4 on both sides

4x / 4 < -14 / 4

x < -3.5

Since, -3.5 is not an integer and the interval needs to be less than -3.5.

The closest integer that is less than -3.5 is -4.

Therefore, all integers [-∞, -4] fulfill this inequality.

Hope this helps!! :)

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The equations solved by the graph are y = x + 3 and y = x - 3

From the question, we have the following parameters that can be used in our computation:

The graph of systems of equations

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

Using the points on the graph, we have

Line 1: y = mx + 3

Line 2: y = mx - 3

Using the common points, we have

Line 1: -m + 3 =  -4

Line 2: -m - 3 = -4

When evaluated, we have

Line 1: m = 1

Line 2: m = 1

So, we have

Line 1: y = x + 3

Line 2: y = x - 3

Hence, the equations solved by the graph are y = x + 3 and y = x - 3

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The solution to the color puzzle in decimal is 10.5

Blue:

8z - 15 = 17

Add 15 to both sides

8z = 17 + 15

8z = 32

divide both sides by 8

z = 32/8

z = 4

Purple:

22 = 4y - 2

22 + 2 = 4y

24 = 4y

divide both sides by 4

y = 24/4

y = 6

Green:

3(-7) + 25

= -21 + 25

= 4

Red:

16 - 6 ÷ 2

= 16 - 3

= 13

Hence,

Red + (purple ÷ blue) - green

= 13 + (6 ÷ 4) - 4

= 13 + 1.5 - 4

= 14.5 - 4

= 10.5

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Answer:

a) See below.

b) $911 billion

c) See below.

Step-by-step explanation:

Linear regression is a statistical technique used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to the observed data.

It estimates the slope and y-intercept of a straight line that minimizes the overall distance between the observed data points and the predicted values. The linear regression equation is y = ax + b.

The association between year and amount of disposable income is indicated by the linear regression equation y = ax + b.

The value of a is the slope of the linear regression line, and represents the average rate of change in disposable income per year. As a = 14.0545, it means that the disposable income increases by approximately $14.0545 billion dollars each year.  

As the value of r (correlation coefficient) is very close to +1, it indicates a very strong positive linear correlation between the year and disposable income. This suggests that as the years progress, the disposable income tends to increase.

Linear regression equation:

[tex]\boxed{y=14.05454545x-27198}[/tex]

To predict the amount of disposable income for the year 2000, we can substitute x = 2000 into the linear regression equation:

[tex]y = 14.05454545 \cdot 2000 - 27198[/tex]

[tex]y=28109.0909...-27198[/tex]

[tex]y=911.0909...[/tex]

[tex]y=911[/tex]

Therefore, the predicted amount of disposable income for the year 2000 is approximately $911 billion.

The predicted value of $911 billion for the year 2000 is significantly lower than the actual value of $8128 billion. This implies that the model is not accurately capturing the increasing trend in disposable income over time, leading to an underestimation of the income level in 2000. This suggests that the model may have limitations or inaccuracies when extrapolating beyond the range of the provided data. It indicates the need for caution and further analysis when using the model to make predictions outside of the given timeframe.

The rectangular form of the complex number 12(cos(π) + isin(π)) is -12 + 0i.

To convert a complex number from polar form to rectangular form, we can use Euler's formula, which states that e^(ix) = cos(x) + isin(x). In this case, we have 12(cos(π) + isin(π)).

Since cos(π) = -1 and sin(π) = 0, we can substitute these values into the expression:

12(cos(π) + isin(π)) = 12(-1 + 0i) = -12 + 0i

In the rectangular form, a complex number is expressed as a combination of a real part (the coefficient of the real unit, represented as "a") and an imaginary part (the coefficient of the imaginary unit, represented as "bi").

In this case, the real part is -12 and the imaginary part is 0. The imaginary part is multiplied by the imaginary unit "i," which results in 0i. Therefore, the rectangular form of 12(cos(π) + isin(π)) is -12 + 0i.

In simpler terms, the rectangular form represents the complex number on the real number line (horizontal axis) and the imaginary number line (vertical axis). In this case, the complex number is purely real, as the imaginary part is 0, so it lies entirely on the real axis at -12.

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By calculating this average, we can approximate the slope of the tangent line to the curve at P (16, 7).

To find the slope of the secant line PQ, we need to calculate the difference in y-coordinates (change in y) divided by the difference in x-coordinates (change in x) between the points P and Q.

For x = 16.1:

Coordinates of Q: (16.1, √(16.1) + 3)

Slope of PQ = (y-coordinate of Q - y-coordinate of P) / (x-coordinate of Q - x-coordinate of P)

Slope of PQ = (√(16.1) + 3 - 7) / (16.1 - 16)

Slope of PQ = (√(16.1) - 4) / 0.1

Similarly, we can find the slope of PQ for the other given values of x:

For x = 16.01: Slope of PQ = (√(16.01) - 4) / 0.01

For x = 15.9: Slope of PQ = (√(15.9) - 4) / (-0.1)

For x = 15.99: Slope of PQ = (√(15.99) - 4) / (-0.01)

Based on the given values, we can observe that as x approaches 16, the values of the slopes of PQ get closer to a certain value. This suggests that the slope of the secant line PQ tends to converge to a specific value as x approaches 16.

Therefore, we can infer that the slope of the tangent line to the curve at P (16, 7) is the limit of the slopes of PQ as x approaches 16. To get an estimate of the slope of the tangent line, we can take the average of the slopes of PQ for x = 16.1 and x = 15.9:

Slope of the tangent line at P ≈ (slope of PQ for x = 16.1 + slope of PQ for x = 15.9) / 2.

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The distance travelled by the roller coaster to get on top is 415.8 ft.

The Distance travelled by the roller coaster on the downhill track is 212.6 ft.

The Pythagorean Theorem describes the relationships between the sides of a right triangle. The square of the hypotenuse, the side opposite the right angle, is equal to the sum of the squares of the two sides.

The hypotenuse during uphill is;

Hypotenuse = √(360² + 208²)

Hypotenuse = 415.8 ft

The hypotenuse during downhill can be calculated as follows:

Hypotenuse = √(44² + 208²)

Hypotenuse = 212.6 ft

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Complete question is;

Suppose a roller coaster climbs 208 feet higher than its starting point, moving horizontally 360 feet. When it comes down, it moves horizontally 44 feet.

a. How far will it travel to get to the top of the ride?

b. How far will it travel on the downhill track?

The probability of exactly 15 out of 25 randomly selected adult smartphone users using their smartphones in meetings or classes is calculated using the binomial probability formula.

The formula is given by:

P(X = k) = (nCk) * [tex]p^k * (1 - p)^{(n - k)[/tex]

Where:

P(X = k) is the probability of exactly k successes,

n is the total number of trials or selections,

k is the number of successes,

p is the probability of success in a single trial,

(1 - p) is the probability of failure in a single trial,

nCk is the binomial coefficient, also known as "n choose k."

In this case, the values are:

n = 25 (total number of adult smartphone users selected)

k = 15 (number of smartphone users using their smartphones in meetings or classes)

p = 0.41 (probability of using smartphones in meetings or classes)

Using these values in the formula, we can calculate the probability:

P(X = 15) = (25C15) * 0.41^15 * (1 - [tex]0.41)^{(25 - 15)[/tex]

Calculating the binomial coefficient:

(25C15) = 25! / (15! * (25-15)!) = 3268760

Substituting the values:

P(X = 15) = 3268760 * 0.41^15 * (1 - 0.[tex]41)^{(25 - 15)[/tex]

Calculating this expression will give you the final probability.

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The 97% confidence interval for the mean amount of monthly mortgage payment for all homeowners in the area is between $1613.48 and $1536.52.

We shall use the following steps to find the 97% confidence interval:

First, we compute the margin of error using the formula:

Margin of error = Z * (σ / √n)

Where:

Z = the z-score

σ = standard deviation

n = sample size

Given:

Z = the z-score for a 97% confidence interval (which is 1.96 using the z-table).

σ = $215.

n = 120.

Putting the values:

Margin of error = 1.96 * (215 / √120)

= 1.96 * (215 / 10.95)

= 1.96 * 19.64

= $38.48

Next, we add and subtract the margin of error from the sample mean to find the confidence interval.

Confidence interval = $1575 +/- $38.48

= $1613.48 and $1536.52

Hence, the bank manager can be 97% confident that the average monthly mortgage payment for all homeowners in the area is between $1613.48 and $1536.52.

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Apart from division or a fraction, the symbol '/' can also represent a ratio or indicate a relationship between two quantities.

In addition to representing division or a fraction, the symbol '/' can have different meanings depending on the context in which it is used. Here are a few common interpretations of the '/' symbol:

Ratio: The '/' symbol can indicate a ratio between two quantities. For example, if we say the ratio of boys to girls is 3/2, it means there are three boys for every two girls.

Per: The '/' symbol can be used to express "per" or "each." For instance, when we see a speed limit sign that says "60 km/h," it means "60 kilometers per hour."

Similarly, in sports statistics, we might see "10 goals/season," which means an average of 10 goals per season.

Probability: In probability theory, the '/' symbol can represent the probability of an event.

For example, if we say the probability of rolling a six on a fair die is 1/6, it means there is a one in six chance of rolling a six.

Quotient: While '/' is commonly used to represent division, it specifically represents the quotient in mathematical expressions.

For instance, in the expression 6/3, '/' indicates that we are finding the quotient of 6 divided by 3, which is equal to 2.

Symbolic Representation: In certain cases, the '/' symbol can be used as a shorthand or symbol to represent a concept or operation in specific fields or contexts.

For instance, in computer programming, '/' is often used to indicate file path or directory structure.

It is important to consider the context in which '/' is used to determine its meaning, as it can vary across different disciplines and applications.

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By rearranging the equation M - q = (1/6)g, we can isolate the variable g and find that g = 6M - 6q.

To solve the equation M - q = (1/6)g for g, we can isolate the variable g by moving the terms involving g to one side of the equation.

Let's rearrange the equation step by step:

Start with the given equation: M - q = (1/6)g

To isolate the term involving g, we can add q to both sides of the equation: M - q + q = (1/6)g + q

Simplify the equation: M = (1/6)g + q

Next, we can subtract q from both sides of the equation: M - q = (1/6)g + q - q

Simplify further: M - q = (1/6)g

To isolate g, we can multiply both sides of the equation by 6: 6(M - q) = 6(1/6)g

Simplify the equation: 6M - 6q = g

Therefore, the solution for g is g = 6M - 6q.

In summary, by following the steps outlined above, we have solved the equation M - q = (1/6)g for g, and the solution is g = 6M - 6q.

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The ratio given can be written in the lowest simplified form as 14:11

Given the ratio

To write in the form 1 : n, we need to divide to its simplest term, To do this we divide by 2.

Hence, we have :

Looking at the ratio we have, it can no longer be divided further by a cook factor.

Hence, the ratio would be written as 14:11

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The width of the walkway around the community garden is 19.5 feet.

To find the width of the walkway around the community garden, we can subtract the area of the garden from the total area of the garden and walkway combined.

Let's denote the width of the walkway as 'w'.

The area of the garden is given as 12 feet wide by 15 feet long, so its area is:

Area of the garden = 12 feet * 15 feet = 180 square feet

The total area of the garden and walkway combined is given as 648 square feet.

Area of the garden and walkway = 648 square feet

Now, we can set up an equation to find the area of the walkway:

Area of the walkway = Area of the garden and walkway - Area of the garden

Area of the walkway = 648 square feet - 180 square feet

Area of the walkway = 468 square feet

Since the walkway surrounds the garden on all sides, we can calculate its width by dividing the area of the walkway by the length of the garden plus twice the width of the walkway:

Width of the walkway = Area of the walkway / (Length of the garden + 2 * Width of the walkway)

Width of the walkway = 468 square feet / (15 feet + 2w)

Now we can substitute the given values and solve for 'w':

468 square feet / (15 feet + 2w) = w

Multiply both sides by (15 feet + 2w):

468 square feet = w(15 feet + 2w)

Rearrange the equation:

2w^2 + 15w - 468 = 0

Now, we can solve this quadratic equation for 'w' using factoring, completing the square, or the quadratic formula.

In this case, factoring is the most convenient method:

(2w - 39)(w + 12) = 0

Setting each factor to zero gives us two possible solutions:

2w - 39 = 0 or w + 12 = 0

Solving each equation for 'w' gives us:

2w = 39 or w = -12

w = 39/2 = 19.5

Since the width cannot be negative, the width of the walkway is 19.5 feet.

Therefore, the width of the walkway around the community garden is 19.5 feet.

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Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

The best use for a sign chart when graphing rational functions is Option D: To check whether F(x) is positive or negative for values of x.

A sign chart, also known as an interval chart, is a tool used to determine the sign (positive or negative) of a function over different intervals. When graphing rational functions, it is essential to identify the intervals where the function is positive or negative.

By constructing a sign chart for the rational function, you can analyze the behavior of the function and determine its sign over different intervals. This information is crucial for sketching an accurate graph of the rational function.

The sign chart helps identify intervals where the function is positive (above the x-axis) or negative (below the x-axis), which directly impacts the shape and position of the graph. It provides information about the regions where the function is increasing or decreasing.

The best use for a sign chart when graphing rational functions is Option D: To check whether F(x) is positive or negative for values of x. Options A, B, and C are not the best uses for a sign chart when graphing rational functions. Checking whether the function is a straight or curved line (Option A), the slope (Option B).

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The inequality is x < -1

An inequality is a mathematical statement that represents the relation between two expressions that are not equal.

Symbol used to denote inequalities are signs such as

≠ ‘not equal to’,

> ‘greater than’,

< ‘less than’

≥ ‘greater than or equal to’

≤ ‘lesser than or equal to’

From the given diagram, the circle is resting at -1 but the circle is not shaded. This means that -1 is not included in the inequality.

Furthermore, the arrow is pointing towards the left side of the number line which means only numbers lesser than -1 (towards the left of -1) are included. Therefore, the inequality is

x < -1

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The amount of money increases by $125,000 due to the decrease in the reserve rate. The correct answer is B. It increases the amount by $125,000.

When the Federal Reserve decreases the reserve rate, it allows banks to hold a smaller portion of their deposits as reserves and lend out a larger portion. This change stimulates lending and increases the money supply in the economy through the process of fractional-reserve banking.

In this scenario, the initial deposit of $15,000 can be multiplied by the money multiplier, which is the reciprocal of the reserve rate. Initially, with a reserve rate of 6%, the money multiplier is 1/0.06 = 16.67. Therefore, the initial deposit can lead to a maximum increase in the money supply of $15,000 x 16.67 = $250,050.

When the reserve rate is decreased to 4%, the money multiplier becomes 1/0.04 = 25. Therefore, the same initial deposit of $15,000 can now result in a maximum increase in the money supply of $15,000 x 25 = $375,000.

The difference between the two scenarios is $375,000 - $250,050 = $124,950, which is approximately $125,000. Hence, the amount of money increases by $125,000 due to the decrease in the reserve rate.

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z1 = 3 + 3i and z2 = 7(cos(5π/9) + i sin(5π/9)). z1z2, we first need to convert z2 into Rectangular form using the trigonometric form of complex numbers.z1z2 = 42 √2 cos(13π/36) + i 42 √2 sin(13π/36).Thus, the answer is z1z2 = 42 √2 cos(13π/36) + i 42 √2 sin(13π/36).

Given that, z1 = 3 + 3i and z2 = 7(cos(5π/9) + i sin(5π/9)).To find z1z2, we first need to convert z2 into rectangular form using the trigonometric form of complex numbers.

As we know, cosθ = Re^(iθ), where Re is the real part and i is the imaginary part.

Therefore, cos(5π/9) = Re^(i5π/9) = Re^(iπ/9) * Re^(i2π/3) = cos(π/9) + i sin(π/9) * (-1/2 + i √3/2) = (7/2) cos(π/9) - (7/2) sin(π/9) i √3 and sinθ = Im^(iθ),

where Im is the imaginary part and i is the imaginary unit.

Therefore, sin(5π/9) = Im^(i5π/9) = Im^(iπ/9) * Im^(i2π/3) = sin(π/9) + i cos(π/9) * (-1/2 + i √3/2) = (7/2) sin(π/9) + (7/2) cos(π/9) i √3So, z2 = 7(cos(5π/9) + i sin(5π/9)) = 7[(7/2) cos(π/9) - (7/2) sin(π/9) i √3 + (7/2) sin(π/9) + (7/2) cos(π/9) i √3]= 7(2 cos(π/9) + i 2 sin(π/9))= 14 cos(π/9) + i 14 sin(π/9)Now, z1z2= (3 + 3i)(14 cos(π/9) + i 14 sin(π/9))= 42 cos(π/9) + i 42 sin(π/9) + 42i cos(π/9) - 42 sin(π/9)= 42(cos(π/9) + i sin(π/9)) (1 + i)= 42(cos(π/9) + i sin(π/9)) √2 cis(π/4)= 42 √2 cos(π/9 + π/4) + i 42 √2 sin(π/9 + π/4)

Therefore, z1z2 = 42 √2 cos(13π/36) + i 42 √2 sin(13π/36).Thus, the answer is z1z2 = 42 √2 cos(13π/36) + i 42 √2 sin(13π/36).

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Answer:

[tex]21\sqrt{2} (cos\frac{29\pi }{36} +i sin\frac{29\pi }{36} )[/tex]

Step-by-step explanation:

Convert z1 to trig form, multiply the modulus and add the angles together with a common denominator of 36

The surface area of the square pyramid with height of 12 cm, side of 10 cm, and slanting height of 13 cm is 360 cm².

A square pyramid has a square base, so to find the surface area of the pyramid, we need to find the area of each face and add them together. The pyramid has four triangular faces and a square base, so:

Surface area = area of base + sum of areas of all faces

The base of the pyramid is a square with side length of 10 cm, so its area is:

Area of base = side length^2 = 10 cm x 10 cm = 100 cm^2

To find the area of each triangular face, we can use the formula for the area of a triangle:

Area of triangular face = (1/2) x base x height

where the base is equal to the side length of the square base and the height is equal to the slanting height of the pyramid.

So, we have:

Area of triangular face = (1/2) x 10 cm x 13 cm = 65 cm^2

Therefore, the total area of all four triangular faces is:

Total area of triangular faces = 4 x Area of one triangular face

= 4 x 65 cm^2

= 260 cm^2

Now we can add the area of the base and the total area of the four triangular faces to get the total surface area of the pyramid:

Surface area = Area of base + Total area of triangular faces

= 100 cm^2 + 260 cm^2

= 360 cm^2

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The probability that it will rain on exactly three of the six days they are there is 0.242.

The given information can be represented as follows:P(Rain on any given day) = 4/9

The hiking club is camping for 6 days and the probability of rain on any given day is given as 4/9.

We are to find the probability that it will rain exactly three days out of the six days they are camping.

The number of ways that it can rain exactly three days out of the six days is given by:C(6,3) = 6!/(3!3!) = 20The probability of rain for any one of the 20 ways of getting exactly three days of rain is:

P(Rain on three days and no rain on three days) = (4/9)³(5/9)³

The probability of getting exactly three days of rain out of six is given by: P(exactly three days of rain) = 20(4/9)³(5/9)³ = 0.242, rounded to the nearest thousandth.

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When a process is in control but does not meet specification, it is referred to as a Type II error, also known as a producer's risk or a beta error.

In statistical process control, a process is considered to be in control when it is stable, predictable, and the variation is within acceptable limits. However, even when the process is in control, there is still a possibility that it may produce outputs that do not meet the desired specifications or requirements.

A Type II error occurs when the process fails to detect and identify these non-conforming outputs, leading to the acceptance of defective products or services. In other words, it means that the process is not sensitive enough to identify deviations from the specification, resulting in the production of items that do not meet the desired quality standards.

Type II errors can have various consequences depending on the context. It can lead to increased costs due to rework, scrap, or customer dissatisfaction. It can also have implications for safety, reliability, or performance in critical applications.

To minimize Type II errors, it is important to continually monitor and improve the process, enhance the sensitivity of quality control measures, and ensure that appropriate inspection and testing methods are in place to detect deviations from specifications.

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We can conclude that point A is located at the origin (0, 0).

There is only one possible location for point A is at the origin.

Let's revisit the given information to determine the possible location of point A.

Point C has the same y-coordinate as point B.

This means that the y-coordinate of point C is equal to the y-coordinate of point B.

The distance between point B and point C is equal to the distance between point C and the y-axis.

Let's assume the distance between point B and point C is represented by "d".

According to the information given, the distance between point C and the y-axis is also "d".

Point A has the same x-coordinate as point C.

This implies that the x-coordinate of point A is equal to the x-coordinate of point C.

The distance between point A and point C is twice the distance between point B and point C.

Let's assume the distance between point B and point C is represented by "d".

According to the information given, the distance between point A and point C is 2d.

Based on this information, we can analyze the relationships between the points:

Since the distance between point B and point C is equal to the distance between point C and the y-axis, we can infer that point B lies on the y-axis.

The x-coordinate of point B is 0.

As point C has the same y-coordinate as point B, the y-coordinate of point C is also determined to be the same as the y-coordinate of point B.

Since point A has the same x-coordinate as point C, the x-coordinate of point A will also be 0.

The distance between point A and point C is twice the distance between point B and point C.

As the distance between point B and point C is "d", the distance between point A and point C is 2d.

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To change fractions with a denominator of 2 to whole numbers, multiply each fraction by 2, because multiplying both the numerator and denominator by the same number results in an equivalent fraction with a denominator of 1, effectively converting it to a whole number.

To change a list of inputs that are fractions with a denominator of 2 to whole numbers, we can apply the rule of multiplying each fraction by 2. The reason for this is based on the fundamental concept of equivalent fractions.

When we multiply a fraction by a certain number, we are essentially multiplying both the numerator and denominator by that number. In this case, since we want to convert fractions with a denominator of 2 to whole numbers, we need to find a number that, when multiplied by 2, results in a denominator of 1.

By multiplying each fraction in the list by 2, the denominator will become 1 (2 multiplied by 2 is 4, which simplifies to 1).

Since any number divided by 1 is equal to that number itself, the fractions will be converted to whole numbers.

For example, let's consider the fraction 3/2.

When we multiply it by 2, we get (3/2) [tex]\times[/tex] 2 = (32)/(22) = 6/4.

Simplifying 6/4 gives us 3/2 again, but now the denominator is 1.

Therefore, by applying the rule of multiplying each fraction by 2, we can convert a list of fractions with a denominator of 2 to whole numbers.

This rule works because it effectively cancels out the denominator of 2, resulting in equivalent fractions with a denominator of 1, which are whole numbers.

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/ mean do or does when a 3rd person is present

Answer:

Step-by-step explanation:

They are wanting to find out what the size of the state is.  I look at the units.

Population density is in People/mi²

Population is people

and they are looking for _____ mi²

Population density = population / size of state

Let's rework that equation so we can solve for size of state

size of state = population/population density

size of Texas = (29145505 people) / (108.51 people/mi²)

size of Texas = 268597 mi²