5. What is the perimeter of polygon XYDB?

The exact acreage of wheat expansion during the first 5 years of the 1940s would require access to historical data .Land prices increased significantly due to the high demand for wheat and the increased production.

The Great Plains region includes parts of the United States and Canada, specifically the central and western portions of North America. In the United States, it includes parts of Montana, North Dakota, South Dakota, Nebraska, Kansas, Oklahoma, Texas, Colorado, Wyoming, and New Mexico. In Canada, it includes parts of Alberta, Saskatchewan, and Manitoba.

During the 1940s, the Great Plains region of the United States, which includes states such as Kansas, Nebraska, Oklahoma, and parts of other surrounding states, experienced a significant expansion in wheat production. This period is often referred to as the "wheat boom" era.

During the early 1940s, there was a high demand for wheat due to World War II, as wheat was a staple crop used to feed soldiers and provide food aid to war-torn regions. This resulted in increased wheat production in the Great Plains region. However, the exact acreage of wheat expansion during the first 5 years of the 1940s would require access to historical data .

As for the prices of land being sold during that time, it is also difficult to provide precise information without specific data. Land prices can vary depending on various factors such as location, quality of land, demand, and economic conditions. However, it is generally known that during the wheat boom era of the 1940s, land prices in the Great Plains region increased significantly due to the high demand for wheat and the increased production. The exact percentage of increase would require access to historical data and research.

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Answer:3) 50 feet and 10 feet

Step-by-step explanation: Multiply every single choice

Answer:

4)

Step-by-step explanation:

Let x1 = length; x2 = width

+) x1 × x2 = 500

+) 2(x1 + x2) = 90 => x1 + x2 = 45

=> x1 and x2 are the roots of equation: [tex]x^2-45x+500=0[/tex]

=> x1 = 25; x2 = 20

The weight of the diamonds in each lot was 1/10 of a pound, or 0.1 pound.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is found by adding 3 to the preceding term.

The nth term of an arithmetic sequence can be found using the formula:

an = a1 + (n-1)d.

The merchant received 7/10 of a pound of diamonds and divided them into 7 equal lots. To find the weight of each lot, we need to divide 7/10 by 7:

(7/10) ÷ 7 = (7/10) × (1/7) = 1/10

Therefore, the weight of the diamonds in each lot was 1/10 of a pound, or 0.1 pound.

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According to the question the volume of soil in Pedro's planter box is 56 cubic feet (ft³).

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is measured in units of cubic centimeters (cm3), cubic meters (m3) or liters. Volume is an important concept in many areas of mathematics, including geometry, calculus and physics. It is also a key concept in many other disciplines, including engineering, architecture and the sciences. Volume is an important property of a solid object, and it is often used to quantify the size or capacity of an object. Volume can be calculated by multiplying the length, width and height of an object. It can also be calculated using the formula for the volume of a cylinder, cone, sphere or other shapes.

To calculate this, we need to multiply the length of the planter box (7 ft) by the width (4 ft) by the height of the soil (2 ft). This gives us the following equation: 7 ft x 4 ft x 2 ft
= 56 ft³.

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Higher rates of depression and anxiety are one negative mental health outcome associated with social media use

The paragraph discusses the role of social media in modern life and its impact on mental health. It notes that social media has become a ubiquitous part of life that allows people to connect with others from around the world, including friends, family, and strangers.

However, the paragraph goes on to mention that social media use has been linked to negative mental health outcomes such as depression, anxiety, and stress.

These negative outcomes may be due to the pressure individuals feel to present a perfect image of themselves online, leading to feelings of inadequacy and self-doubt.

Despite these negative outcomes, the paragraph notes that social media can also be valuable for promoting social support and connection, especially among marginalized communities.

Furthermore, it can be a source of education and awareness, allowing people to learn about important social and political issues and engage with them.

Hence,

Higher rates of depression and anxiety are one negative mental health outcome associated with social media use

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The answers to both the subparts using the confidence interval are shown:
(A) His population's mean finishing time for the 100-meter event has a 99% confidence interval of (12.8081,15.5919).

(B) The right choice is Option B, which is Option II which is narrower.

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval.

Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.

The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

So, let X represent the amount of time (in seconds) needed to complete a 100-meter race with Tom.

His population's mean 100-meter race finishing time falls within a 99% confidence interval of 12.8081 and 15.5919.

x = 14.2

s²= 0.9867

s= 0.9933

t α2, n-1 = 3.7074

The margin of error= 1.3919

lower bound= 12.8081

upper bound= 15.5919

Therefore, the answers to both the subparts using the confidence interval are shown:
(A) His population's mean finishing time for the 100-meter event has a 99% confidence interval of (12.8081,15.5919).

(B) The right choice is Option B, which is Option II which is narrower.

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Correct question:

Tom is preparing for a 100 meters race competition. During his practice last week, a sample of seven 100

meters races is reviewed, and the finishing times (in seconds) were as below:

13.4

15.6

13.1

14.5

14.2

13.3

15.3

It is reasonable to assume his finishing times are normally distributed.

(a) Construct a 99% confidence interval estimate of his population mean finishing time of 100 meters race.

(b) If the confidence interval estimate of his population mean finishing time of 100 meters is constructed at 95% instead of 99%, would the new confidence interval be (I) wider, (II) narrower, or (III) the same as the interval constructed at part (a)? (Just state your answer, no calculation is needed in part (b))

a. The decision rule for this hypothesis test is: Reject H0 if the test statistic z is less than -1.645 or greater than 1.645. b. The test statistic for this hypothesis test is:  -2.05.

In statistics, a hypothesis is an assumption or claim about a population parameter that can be tested by collecting and analyzing sample data.

According to given information:

a. The decision rule for this hypothesis test is:

Reject H0 if the test statistic z is less than -1.645 or greater than 1.645.

b. The sample proportion of customers who prefer black teas is:

= 0.41

The population proportion under the null hypothesis is:

p = 0.51

The sample size is:

n = 158

The test statistic for this hypothesis test is:

[tex]z = ( - p) / \sqrt(p * (1 - p) / n)[/tex]

[tex]= (0.41 - 0.51) / \sqrt(0.51 * 0.49 / 158)[/tex]

[tex]= -2.05[/tex]

c. The test statistic z of -2.05 is less than the critical value of -1.645, so we can reject the null hypothesis H0. At the 0.10 significance level, there is enough evidence to suggest that the proportion of customers who prefer black teas is not 0.51, and the manager of Tea for Us should consider adjusting their stock orders accordingly.

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An image of polygon VWYZ has a line of reflection across the x-axis. So option A is correct.

In geometry, the line of reflection is the line over which a figure is reflected. When a point is reflected over a line, it moves the same distance on the opposite side of the line. The line of reflection is perpendicular to the figure at the point of reflection and is equidistant from the figure and its reflection.

A polygon is a closed two-dimensional shape with straight sides. The sides are line segments that intersect only at their endpoints, called vertices. Polygons can have any number of sides, but they must have at least three. Common examples of polygons include triangles, squares, rectangles, pentagons, hexagons, and octagons.

The formula for the line of reflection in a Cartesian coordinate system is:

x = a

where a is the equation of the line of reflection.

This formula represents a vertical line that passes through the point (a, 0) and reflects points across the line of reflection to their corresponding images on the other side.

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Answer:

reflection across x=2

Step-by-step explanation:

the picture should be able to explain itself! :)))

Answer:

9)

[tex]x = 16[/tex]

[tex]y = 8 \sqrt{3} [/tex]

10)

[tex]x = 8[/tex]

[tex]y = 8 \sqrt{2} [/tex]

The answer of the given question based on the fraction is ,  a value that is greater than 1/2.

A fraction is mathematical expression that represents part of  whole or ratio between the two numbers. It is expressed in the form of a ratio of two integers, with a numerator and a denominator separated by a horizontal or slanted line called a fraction bar.

Fractions that are closer to 1 than to 0 have a value that is greater than 1/2. This is because 1/2 is exactly halfway between 0 and 1 on the number line.

So, any fraction that has a numerator greater than its denominator is closer to 1 than to 0. For example:

2/3 is closer to 1 than to 0 because it is greater than 1/2

7/8 is closer to 1 than to 0 because it is greater than 1/2

3/4 is closer to 1 than to 0 because it is greater than 1/2

On the other hand, fractions that have a value less than 1/2 are closer to 0 than to 1. For example:

1/4 is closer to 0 than to 1 because it is less than 1/2

3/10 is closer to 0 than to 1 because it is less than 1/2

2/5 is closer to 0 than to 1 because it is less than 1/2

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Answer:

the value of $s$ is 13.

Step-by-step explanation:

We are given that $r=9$ and $4r+3s=75$. We can use the value of $r$ to find $s$.

Substituting $r=9$ into the second equation, we get:

$4(9) + 3s = 75$

Simplifying the left-hand side, we get:

$36 + 3s = 75$

Subtracting 36 from both sides, we get:

$3s = 39$

Dividing both sides by 3, we get:

$s = 13$

Therefore, the value of $s$ is 13.

Jackson's total cost after the discount and before tax would be $24.67.

When a store offers a discount, it reduces the price of the item by a certain percentage. In this case, Jackson has a loyalty card that gives him a 10% discount on his purchase.

To calculate the price after the discount, we multiply the original price by 1 minus the discount percentage (in decimal form).

Here we have

Jackson has a 10% discount at his local hardware store.

Let 'x' be the cost before tax

After a 10% discount,

The amount that Jackson could pay 90% of the cost

Given that he wants to buy $ 27.40  

The cost of items after discount = 90% of 27.40

= [ 90/100 ] × 27.40

= [ 0.9 ] × 27.40

= 24.66

Therefore,

Jackson's total cost after the discount and before tax would be $24.67.

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Answer: $18.6

Step-by-step explanation: If we take a look at the sale off the shoes cost which is $43.4 and look at the sale amount (30%) which is 18 dollars and 60 cents the answer is: 18.6 or $18.6 off

Answer:

In order to determine whether 387 is a term of a sequence, we need to know the rule or formula for generating the sequence. Without this information, it is not possible to determine whether 387 is a term of the sequence or not.

If we assume that the sequence is an arithmetic sequence, where each term is obtained by adding a fixed constant to the previous term, we can use the following formula to determine whether 387 is a term of the sequence:

an = a1 + (n-1)d

where a1 is the first term of the sequence, d is the common difference between consecutive terms, and n is the term we are trying to find.

If we substitute the values for the first few terms of the sequence, we can check whether 387 is a term or not. For example, if the first few terms of the sequence are:

a1 = 3

a2 = 8

a3 = 13

a4 = 18

and so on, with a common difference of 5 between consecutive terms, we can use the formula to find the value of the 129th term of the sequence:

a129 = a1 + (129-1)d

a129 = 3 + 128(5)

a129 = 643

Since 387 is not equal to 643, it is not a term of this sequence. However, without knowing the rule or formula for generating the sequence, it is impossible to say for certain whether 387 is a term or not.

Therefore, Fatima's monthly payment would be $460.23.

Interest is the amount of money that is charged by a lender to a borrower for the use of money or a loan. It is usually calculated as a percentage of the principal amount (the amount of money borrowed) and can be either simple or compound, depending on the type of loan. Interest is typically paid by the borrower to the lender over a set period of time, such as monthly, quarterly, or annually. The interest rate can be fixed or variable, and is determined by a variety of factors including the borrower's creditworthiness, the amount of the loan, and the length of the repayment period.

Here,

To calculate the monthly payment for a car loan, we need to use the formula:

M = P [ i(1 + i)ⁿ] / [ (1 + i)ⁿ – 1]

Where:

M = monthly payment

P = principal (the amount of the loan)

i = monthly interest rate (annual interest rate divided by 12)

n = number of months

First, we need to calculate the monthly interest rate:

i = 4.7% / 12

= 0.003917

Next, we need to calculate the number of months:

n = 5 years x 12 months/year

= 60 months

Now, we can plug in the values and solve for M:

M = 25,000 [ 0.003917(1 + 0.003917)⁶⁰ ] / [ (1 + 0.003917)⁶⁰ – 1]

M = $460.23 (rounded to the nearest cent)

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Using factorization and simplifying the equations, the points of intersections are (-2, 0), ( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 ) and ( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )

We are given two equations:

y = 4x² - 3x + 3

y = x³ + 7x² - 3x + d

and we know that they intersect at x = -4, so we can substitute -4 for x in both equations:

y = 4(-4)² - 3(-4) + 3 = 49

y = (-4)³ + 7(-4)² - 3(-4) + d = -64 + 112 + 12 + d = 60 + d

So, at x = -4, we have y = 49 and y = 60 + d. Since the graphs intersect, these two equations must be equal:

49 = 60 + d

Solving for d, we get:

d = -11

Therefore, the two equations become:

y = 4x² - 3x + 3

y = x³ + 7x² - 3x - 11

We can now set them equal to each other:

4x² - 3x + 3 = x³ + 7x² - 3x - 11

Simplifying and rearranging, we get:

x³ + 3x² - 8x - 14 = 0

We can try to factor this expression by testing possible roots. One possible root is x = 2, because if we substitute 2 for x, we get:

2³ + 3(2)² - 8(2) - 14 = 8 + 12 - 16 - 14 = -10

Since this expression evaluates to a non-zero value, x = 2 is not a root. Similarly, we can test x = -1:

(-1)³ + 3(-1)² - 8(-1) - 14 = -1 + 3 + 8 - 14 = -4

This expression also evaluates to a non-zero value, so x = -1 is not a root. Finally, we can test x = -2:

(-2)³ + 3(-2)² - 8(-2) - 14 = -8 + 12 + 16 - 14 = 6

This expression evaluates to zero, so x = -2 is a root. Using long division or synthetic division, we can divide the cubic polynomial by x + 2 to get:

x³ + 3x² - 8x - 14 = (x + 2)(x² + x - 7)

The quadratic factor x² + x - 7 can be factored using the quadratic formula, giving us:

x² + x - 7 = [ -1 ± √(1 + 4*7) ] / 2

= [ -1 ± 3√(7) ] / 2

Therefore, the three intersection points are:

(-2, 0)

( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 )

( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )

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We can classify the polynomial as a "trinomial" with a degree of 3.

The given polynomial is:

9x^3 + 4x^2 - 7

The degree of a polynomial is the highest power of the variable present in the polynomial. In this case, the degree of the polynomial is 3, because the highest power of x in the polynomial is 3.

The number of terms in a polynomial is the number of individual expressions added or subtracted together. In this case, the polynomial has three terms: 9x^3, 4x^2, and -7.

Therefore, we can classify the polynomial as a "trinomial" with a degree of 3.

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The median of the data set is: 95.5

What is median?

median is the number at the middle of the given data.

To find the median of the data set {102, 74, 86, 74, 96, 95, 103, 102}, we first need to arrange the values in order from lowest to highest:

74, 74, 86, 95, 96, 102, 102, 103

Since the data set has an even number of values, the median is the mean of the two middle values. In this case, the two middle values are 95 and 96.

Therefore, the median of the data set is: (95 + 96) / 2 = 95.5

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The equation that shows how to find a percentage is:

part/whole = percent/100

This equation can be used to solve for any of the three variables, given the values of the other two.

One expression that has a value between -4 and -3 is (-7/2) - 3.

Expression in math is a combination of numbers, symbols, and operations that represent a value, quantity, or an idea. Expressions can be used to represent equations, relationships between quantities, solutions to problems, and more. They can also be used to represent functions, which are a special type of expression that assign a unique output to a given input.

This expression can be simplified to (-1/2) - 3, which evaluates to -3.5. This value is between -4 and -3, as desired.

To confirm this, we can plug -3.5 into the original expression and see that it evaluates to -3.5: (-7/2) - 3 = -7/2 - 3 = -7/2 + (-3) = -7/2 - 3(-1/2) = -7/2 - (-3/2) = -7/2 + 3/2 = -7 + 3/2 = -7/2 + 3 = -4 + 3 = -1/2 = -3.5.

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Answer: 34

Step-by-step explanation:

To find 8% of 425 coins, multiply 425 by 0.08 (which is the decimal equivalent of 8%).

425 * 0.08 = 34

So, 8% of 425 coins is 34 coins.

Answer:

7 and 31 it asks

the 3rd and 6th is

The 1st and 2nd terms of this Fibonacci sequence, given the 3rd and 6th terms would be 2 and 5.

Let's denote the first and second terms of the Fibonacci sequence as F1 and F2. The Fibonacci sequence is defined by the recurrence relation:

F(n) = F(n-1) + F(n-2)

We are given that the 3rd term (F3) is 7 and the 6th term (F6) is 31. We can use this information to set up the following equations:

F3 = F2 + F1 = 7

F6 = F5 + F4 = 31

We can also express F4 and F5 in terms of F1 and F2:

F4 = F3 + F2 = (F2 + F1) + F2 = F1 + 2F2

F5 = F4 + F3 = (F1 + 2F2) + (F2 + F1) = 2F1 + 3F2

Now, let's substitute equation (4) into equation (2):

F6 = 2F1 + 3F2 + F1 + 2F2 = 31

3F1 + 5F2 = 31

By trial and error, we can find the possible values for F1 and F2 that satisfy this equation:

F1 = 1, F2 = 6: 3(1) + 5(6) = 3 + 30 = 33 (not a solution)

F1 = 2, F2 = 5: 3(2) + 5(5) = 6 + 25 = 31 (solution)

The solution is F1 = 2 and F2 = 5, so the first two terms of the Fibonacci sequence are 2 and 5.

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The three statements that are true about the lines are: Line WZ has the same slope as line XY. Line YX has a greater slope than line ZY, and Line XW has a lesser slope than line YZ.

A linear equation has the form y = mx + b, where m is the slope of the line and b is the y-intercept, or the y-coordinate of the line's intersection with the y-axis. The slope measures how steep a line is, or how quickly the y-coordinate changes for every unit change in the x-coordinate. A line has a positive slope if it is moving upward from left to right, and a negative slope if it is moving downward. The line's intersection point with the y-axis, or the value of y when x is equal to 0, is known as the y-intercept.

Because both lines travel through the same point (0, -3) and have a slope of 1/3, line WZ and line XY have the same slope.

Given that both lines pass through the same point (3, 0), line YX has a bigger slope than line ZY.

Because line XW passes through points (-4, 1) and (3, 3), which have a little change in y over a large change in x, as opposed to line YZ, which passes through points (0, -3) and (3, 0), which have a large change in y over a small change in x, line XW has a lower slope than line YZ.

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Answer:

A. B. C.

Step-by-step explanation:

Answer: $9.66

Step-by-step explanation: perimeter = 345mm + 345mm + 345mm + 345mm = 1380

We need 1380 millimeters which is equivalent to 1.38 meters.

We can multiply the number of meters by the cost of meters to find the total

We have to find the Taylor Polynomial of $f(x)=e^x$ up to the third degree, centered at $x=0$.

The Taylor Polynomial is given by:

(x)=∑

k=0

n

​k!

f

(k)

(a)

​(x−a)

k

where $f^{(k)}(a)$ is the $k$th derivative of $f(x)$ evaluated at $a$.

Using this formula, we can find the Taylor Polynomial as follows:

\begin{align*}

f(x) &= e^x \

f'(x) &= e^x \

f''(x) &= e^x \

f'''(x) &= e^x \

\end{align*}

Evaluating each derivative at $x=0$, we get:

\begin{align*}

f(0) &= e^0 = 1 \

f'(0) &= e^0 = 1 \

f''(0) &= e^0 = 1 \

f'''(0) &= e^0 = 1 \

\end{align*}

Substituting these values into the formula for the Taylor Polynomial, we get:

\begin{align*}

P_3(x) &= \frac{f(0)}{0!}(x-0)^0 + \frac{f'(0)}{1!}(x-0)^1 + \frac{f''(0)}{2!}(x-0)^2 + \frac{f'''(0)}{3!}(x-0)^3 \

&= 1 + x + \frac{x^2}{2} + \frac{x^3}{6}

\end{align*}

Therefore, the Taylor Polynomial of $f(x)=e^x$ up to the third degree, centered at $x=0$, is $P_3(x) = 1 + x + \frac{x^2}{2} + \frac{x^3}{6}$.

Answer:

[tex]5x^4(2x+1)^4(4x+1)[/tex]

Step-by-step explanation:

Okay so we have to use the product rule for this i.e.

d/dx[uv] = u'v + uv'

d/dx[x^5(2x+1)^5] =

[tex]5x^4(2x+1)^5 + x^5 * 2 * 5(2x+1)^4\\\\= 5x^4(2x+1)^5 + 10x^5(2x+1)^4\\\\= (2x+1)^4[5x^4(2x+1) + 10x^5]\\\\= (2x+1)^4[10x^5 + 5x^4 + 10x^5]\\\\= (2x+1)^4(20x^5+5x^4)\\\\=5x^4(2x+1)^4(4x+1)[/tex]

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Answer:

6 years = $22,536.50

12 years = $25,394.69

18 years = $28,615.38

Step-by-step explanation:

The find the value of the investment after the given number of years, first create an equation for A in terms of t using the compound interest formula.

[tex]\boxed{\sf A=P\left(1+\frac{r}{n}\right)^{nt}}[/tex]

where:

Given values:

Substitute the given values into the formula to create an equation for the value of the investment, A, in terms of time in years, t:

[tex]\implies \sf A=20000\left(1+\dfrac{0.02}{2}\right)^{2t}[/tex]

[tex]\implies \sf A=20000\left(1+0.01\right)^{2t}[/tex]

[tex]\implies \sf A=20000\left(1.01\right)^{2t}[/tex]

[tex]\hrulefill[/tex]

To find the value of the investment after 6 years, substitute t = 6 into the equation:

[tex]\implies \sf A=20000\left(1.01\right)^{2\cdot 6}[/tex]

[tex]\implies \sf A=20000\left(1.01\right)^{12}[/tex]

[tex]\implies \sf A=20000(1.12682503...)[/tex]

[tex]\implies \sf A=22536.5006026...[/tex]

Therefore, the value of the investment after 6 years is $22,536.50 rounded to the nearest cent.

[tex]\hrulefill[/tex]

To find the value of the investment after 12 years, substitute t = 12 into the equation:

[tex]\implies \sf A=20000\left(1.01\right)^{2 \cdot 12}[/tex]

[tex]\implies \sf A=20000\left(1.01\right)^{24}[/tex]

[tex]\implies \sf A=20000\left(1.2697346...\right)[/tex]

[tex]\implies \sf A=25394.69297...[/tex]

Therefore, the value of the investment after 12 years is $25,394.69 rounded to the nearest cent.

[tex]\hrulefill[/tex]

To find the value of the investment after 18 years, substitute t = 18 into the equation:

[tex]\implies \sf A=20000\left(1.01\right)^{2\cdot 18}[/tex]

[tex]\implies \sf A=20000\left(1.01\right)^{36}[/tex]

[tex]\implies \sf A=20000\left(1.43076878...\right)[/tex]

[tex]\implies \sf A=28615.37567...[/tex]

Therefore, the value of the investment after 18 years is $28,615.38 rounded to the nearest cent.