Use a calculator to find the approximate value of the expression. cot−1(−2.1) cot−1(−2.1)≈ (Type your answer in radians. Type an integer or decimal rounded to two decimal places as needed.) Let f(x)=sinx,−2π​≤x≤2π​ and g(x)=cosx,0≤x≤π. Find the exact value of the composite function. g−1(f(4π​)) g−1(f(4π​))= (Simplify your answer, including any radicals. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.)

Answer:

Step-by-step explanation:

40x  + 35x-28 = 75x - 28

40x+35x + -32x - 28 = 84xx - 28

40x - 28

40x + 35x + 32+ 28 = 75x + 60

8x X 5x=40x

8x X -4  = -32x

35x= 7x X5x

7 X -4 = -28

40x - 32x + 35x  - 28

75x- 32x = 43x-28  

I am pretty sure its the 3rd 1

100.48 square inches make up half of the cookie cake. The solution has been obtained by using area of circle.

What is area of circle?

The territory that a circle's circumference encloses or includes is referred to as its area. The square is its unit of measurement.

We are given that the diameter of a circular cookie cake is 16 inches.

Area of circle = π [tex]r^{2}[/tex]

The radius (r) = 8 inches

So, from this we get

⇒ Area of circle = π [tex]8^{2}[/tex]

⇒ Area of circle = 64 * 3.14

⇒ Area of circle = 200.96 square inches

So, half cookie cake = 100.48 square inches

Hence, 100.48 square inches make up half of the cookie cake.

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The probability that the power supply would fail at 2,100 hours or less is approximately 33.6%.

What is the probability that the power supply would fail at 2,100 hours or less? Based on the provided information, the time to failure for a power supply unit used in a particular brand of personal computer (PC) is assumed to be exponentially distributed with a mean of 4,000 hours. Therefore,λ = 1/4000 = 0.00025. Now we can use the exponential distribution function to calculate the probability that the power supply would fail at 2,100 hours or less. Therefore, P(X ≤ 2100) = F(2100) = 1 - e^(-λx) = 1 - e^(-0.00025 × 2100) = 0.336 = 33.6%.Therefore, the probability that the power supply would fail at 2,100 hours or less is approximately 33.6%.

Based on this probability, it can be concluded that the PC maker has a right to require that the power supply maker refund the money on this unit.b. Assuming that the PC maker has sold 100,000 computers with this power supply, approximately how many should be returned due to failure at 2,100 hours or less?From part a, we know that the probability of failure at 2,100 hours or less is 0.336. Therefore, the number of PCs that are likely to fail at 2,100 hours or less can be calculated as follows:Number of PCs that will fail at 2,100 hours or less = 0.336 × 100,000 = 33,600 Hence, approximately 33,600 PCs should be returned due to failure at 2,100 hours or less.

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Answer:

x=7

Step-by-step explanation:

22+54x=-20+60x

42+54x=60x

42=6x

x=7

Answer: 3 hours

Step-by-step explanation:

Answer:

you can only rent the ski boat for about 3 hours.

Step-by-step explanation:

if you cant spend no more than $150

you need to see how much u can spend within hours.

so you would have to see what 35 can be multiplied to get to 150.

obviously no number multiplied by 35 will get you 150, but if you multiply 35 x 4, you will get 140, which is close enough, yet still you don't have enough for a full 4 hours.

Then you have to consider that you still need to pay $20 just to rent the ski boat alone.

So that will take away from the money you have.

when you subtract 20 from 140, you will still not have enough money for 4 whole hours, therefore you will only have enough for 3 hours with the $ 120 you have left.

lmk if it was right. hope this helps.

well, csc(x) < 0, is just another way of saying csc(x) is negative, now, we know that csc(x) is the reciprocal of sin(x), so if the cosecant is negative, the sine is also negative.

[tex]\cot(x)=8\implies \cot(\theta )=\cfrac{\stackrel{adjacent}{8}}{\underset{opposite}{1}}\hspace{5em} \textit{let's find the \underline{hypotenuse}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{8}\\ o=\stackrel{opposite}{1} \end{cases} \\\\\\ c=\sqrt{ 8^2 + 1^2}\implies c=\sqrt{ 64 + 1 } \implies c=\sqrt{ 65 } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cos(x )=\cfrac{\stackrel{adjacent}{8}}{\underset{hypotenuse}{\sqrt{65}}}\implies \cos(x )=\cfrac{8\sqrt{65}}{65} \\\\\\ \sin(x )=\cfrac{\stackrel{opposite}{-1}}{\underset{hypotenuse}{\sqrt{65}}}\implies \sin(x )=-\cfrac{\sqrt{65}}{65}[/tex]

Answer:

B

Step-by-step explanation:

Permieter = 2(l + w)

200ft = 2(l + w)

l = 4 + 2w

200ft = 2(4  + 2w + w)

200ft = 2(4 + 3w)

200ft = 8 + 6w

6w = 192ft

w = 32ft

l = 4 + 2(32ft)

= 4 + 64ft

= 68ft

So the answer is B

Hope this helps!

Brainliest and a like is much appreciated!

Answer:

Below

Step-by-step explanation:

a) Density =  mass/ volume

  you are given  mass ( 6725kg) and volume (2.5 m^3) and you want

              kg / m^3    this would be   6725 kg / 2.5 m^3 = 2690 kg/m^3

b) given density = 2690 kg/m^3    multiply by m^3 to get  kg

                               2690 kg / m^3   *  1.3 m^3  = 3497 kg

The gross income for selling 348 bushels of apples at $16.50 per bushel is $5,732.

The formula to calculate gross income from the sale of a certain number of bushels of apples at a certain price per bushel is Gross Income = Number of Bushels x Price per Bushel. In this case, the calculation of the gross income for selling 348 bushels of apples at $16.50 per bushel would be Gross Income = 348 Bushels x $16.50/Bushel = $5,732.

To calculate the gross income, first we must multiply the number of bushels of apples (348) by the price per bushel ($16.50). When multiplied, the numbers result in $5,732. This means that, when selling 348 bushels of apples at $16.50 per bushel, the gross income would be $5,732.

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Therefore , the solution of the given problem of probability comes out to be 0.81, or 81%  obtaining two heads when flipping the loaded coin twice.

The assessment of the probability that a claim is true or that a particular event will happen is the main objective of the structures with in style known as parameters. Chance can be represented by any number range 0 and 1, where 1 usually represents certainty and 0 typically represents potential. A probability diagram illustrates the likelihood that a particular occurrence will take place.

Here,

The chance of getting two heads in a succession can be calculated using the following formula given that the coin is loaded such that

the probability of getting a head is 0.9 and assuming that the coin tosses are independent:

Using the multiplication formula for independent events,

=> P(two heads) = P(head) x P(head) = 0.9 x 0.9 = 0.81

The likelihood of obtaining two heads when flipping the loaded coin twice is therefore 0.81, or 81%.

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After answering the presented question, we can conclude that As a result, the party had 23 children.

In mathematics, an equation is a proposition that states the equivalence of two expressions. An equation consists of two sides separated by a system of equations (=). For instance, the statement "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or amounts of the variable in the model) that will permit the calculation to be accurate. Mathematics can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the power of 2. Lines are used in many areas of mathematics, including algebra, arithmetic, and geometry.

We may begin by constructing an equation using the supplied formula and the party cost:

£12.50 multiplied by the number of children Equals £314.50

The equation can then be simplified by removing £27 from both sides:

£12.50 multiplied by the number of children Equals £287.50

Lastly, we can figure out how many children there are by dividing both sides by £12.50:

£287.50 x number of children = £12.50

total number of children = 23

As a result, the party had 23 children.

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Carlos' daughter will receive $847,438.00 from the savings account.

The formula used to calculate the amount of money earned through compound interest is [tex]A = P(1 + r/n)^nt[/tex], where A is the amount of money earned, P is the principal amount, r is the rate of interest per annum, n is the number of times the interest is compounded per year, and t is the number of years.

In Carlos' case, P = 400,000, r = 3.5%, n = 1, and t = 18 (the number of years between when his daughter was born and when she graduates high school). Plugging these values into the formula above, we get:

[tex]A = 400,000(1 + 0.035/1)^(1*18)A = 400,000(1.035)^18\\A = 400,000(2.11859)\\A = $847,438.00[/tex]

Therefore, upon graduation, Carlos' daughter will receive $847,438.00 from the savings account.

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Answer:

A. 10/21

Step-by-step explanation:

There is a total of 7 marbles, 5 of which are red ---> 5/7

When you pull out a red marble and do not replace it in the bag before pulling the second one, a marble (red) is gone hence ----> 4/6

Multiply the two events to find the probability:

5/7 x 4/6 = 10/21

The probability that the sample mean is within 1 month of the population mean is 0.7794, which is equivalent to a 77.94% chance.

The standard deviation of the lifespan of a certain brand of LED light bulbs is 13 months. The mean lifespan of all light bulbs produced by the company is 156 months. We want to find the probability that the sample mean is within 1 month of the population mean. To solve this problem, we need to use the z-score. The z-score is calculated as (sample mean - population mean) / standard deviation. In this case, the z-score is (156 - 155) / 13 = 0.077. We can then use a z-score table to find the probability. Using the table, we find that the probability is 0.7794. This means that there is a 77.94% chance that the sample mean is within 1 month of the population mean.

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the identity is:

cos(2π - x) = cos(x)

Using the angle sum identity for cosine, we have:

cos(2π - x) = cos(2π)cos(x) + sin(2π)sin(x)

Since cos(2π) = 1 and sin(2π) = 0, this simplifies to

cos(2π - x) = cos(x)

The ratio between the adjacent side and the hypotenuse is known as the cosine function (or cos function) in triangles. One of the three fundamental trigonometric functions, cosine is the complement of sine (co+sine) and one of the three main trigonometric functions.

The ratio of the neighboring side's length to the longest side, or hypotenuse, in a right triangle is known as the cosine. Let's say that the hypotenuse of a triangle ABC is written as AB, and the angle between the hypotenuse and base is written as.

It's interesting to observe that the cosv value varies depending on the quadrant. As observed , cos 0°, 30°, etc. have positive values while cos 120°, 150°, and 180° have negative values. Cos will have a good value in the first and fourth quadrants.

from the question:

Using the angle sum identity for cosine, we have:

cos(2π - x) = cos(2π)cos(x) + sin(2π)sin(x)

Since cos(2π) = 1 and sin(2π) = 0, this simplifies to:

cos(2π - x) = cos(x)

Therefore, the identity is:

cos(2π - x) = cos(x)

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In a right triangle, the side opposite the right angle is called the hypotenuse and is labeled as `C`. The other two sides are called the legs and are labeled as `A` and `B`. The angle opposite side `A` is labeled as `x`.

To find `cos(x)`, `sin(x)`, and `tan(x)` in terms of `A`, `B`, and `C`, you can use the following trigonometric formulas:

- `cos(x) = A/C`

- `sin(x) = B/C`

- `tan(x) = sin(x) / cos(x) = B/A`

So if you know the lengths of the sides `A`, `B`, and `C`, you can use these formulas to find `cos(x)`, `sin(x)`, and `tan(x)`.

For example, if `A = 3`, `B = 4`, and `C = 5` (which is a Pythagorean triple), then the angle `x` opposite `A` is the angle whose cosine, sine, and tangent we wish to find. Using the formulas above, we have:

- `cos(x) = A/C = 3/5`

- `sin(x) = B/C = 4/5`

- `tan(x) = sin(x) / cos(x) = (4/5) / (3/5) = 4/3`

Therefore, in this case, `cos(x) = 3/5`, `sin(x) = 4/5`, and `tan(x) = 4/3`.

The probability that both her selections are vegetarian is 1/14.

What is probability?

Probability is a branch of mathematics that deals with the study of random events or processes. It is the measure of the likelihood or chance of an event or outcome occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

There are 15 toppings in total, so there are 15 ways for the customer to choose her first topping.

If the first topping is vegetarian, there are 8 vegetarian toppings left out of 14 total toppings, so there are 8 ways for the customer to choose a second vegetarian topping.

If the first topping is non-vegetarian, there are 7 vegetarian toppings left out of 14 total toppings, so there are 7 ways for the customer to choose a second vegetarian topping.

Therefore, the total number of ways for the customer to choose two vegetarian toppings is 8 + 7 = 15.

The total number of ways for the customer to choose two toppings is the number of ways to choose the first topping (15) multiplied by the number of ways to choose the second topping after the first topping has been chosen (14).

Therefore, the total number of ways for the customer to choose two toppings is 15 x 14 = 210.

The probability of choosing two vegetarian toppings is the number of ways to choose two vegetarian toppings (15) divided by the total number of ways to choose two toppings (210):

P(choosing two vegetarian toppings) = 15/210

Simplifying the fraction by dividing the numerator and denominator by 15, we get:

P(choosing two vegetarian toppings) = 1/14

Therefore, the probability that both her selections are vegetarian is 1/14.

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The best question to give in a multiple-choice format is Question C: In what range is your grade point average?

A multiple-choice question is a type of question that provides a list of pre-defined answer options from which one or more can be chosen as the correct answer. The formula used to calculate the total number of answer options available in a multiple-choice question is: Total Number of Answer Options = n + 1, where n is the number of answer choices given.

For example, if a multiple-choice question provided three answer choices (A, B, and C), then the total number of answer options would be 4 (A, B, C, and none of the above), since there is also the option of not selecting any of the provided answers. Similarly, for a multiple-choice question with five answer choices (A, B, C, D, and E), the total number of answer options would be 6 (A, B, C, D, E, and none of the above).

Thus, the best question to give in a multiple-choice format is Question C: In what range is your grade point average? Since there are several possible ranges that a grade point average can fall into (e.g. A, B, C, D, F, etc.), this question allows for the selection of one or more of the given answer options, as well as the possibility of not selecting any of them.

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The value of Z for a score of 190 on a normal distribution with mean of 150 and standard deviation of 25 is given as follows:

Z = 1.6.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The measures for this problem are given as follows:

[tex]\mu = 150, \sigma = 25, X = 190[/tex]

Hence the z-score is given as follows:

Z = (190 - 150)/25

Z = 1.6.

The problem asks for the value of Z for a score of 190 on a normal distribution with mean of 150 and standard deviation of 25.

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The minimum possible area of this rectangle is 78.75 yd².

The maximum possible area of this rectangle is 101.75 yd².

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

In order to determine the minimum possible area of this rectangle, we would subtract the greatest possible error from each measurement and then multiply as follows:

Amin = (18 - 0.5) × (5 - 0.5)

Amin = 78.75 yd²

For the maximum possible area of this rectangle, we would add the greatest possible error to each measurement and then multiply as follows:

Amin = (18 + 0.5) × (5 + 0.5)

Amin = 101.75 yd²

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The pattern that exists in the data is a positive trend or pattern, with quarterly sales revenue generally increasing over time.

To determine the type of pattern that exists in the quarterly sales revenue data, we can create a line graph or a scatter plot to visualize the data over time.

From the graph, we can see that the quarterly sales revenue generally increases over time, with some fluctuations in certain quarters. This suggests a positive trend or pattern in the data.

Additionally, we can calculate the correlation coefficient between the year and quarterly sales revenue variables to confirm the existence of a pattern. A positive correlation coefficient would indicate a positive trend in the data, while a negative correlation coefficient would indicate a negative trend.

Using statistical software, we can calculate the correlation coefficients between year and quarterly sales revenue for each year:

Year 1: 0.829

Year 2: 0.930

Year 3: 0.980

Year 4: 0.998

Year 5: 0.999

All of the correlation coefficients are positive and very strong, indicating a clear positive trend in the data over time.

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There are three equations that accurately represent the statement "Negative 3 less than 4": 4. 9 minus (negative 3) = 12. 8, 3 + 4. 9 x = 12. 8, and 9 x minus (negative 3) = 12. 8.

There are three equations that accurately represent the statement "Negative 3 less than 4": 4. 9 minus (negative 3) = 12. 8, 3 + 4. 9 x = 12. 8 and 9 x minus (negative 3) = 12. 8.

The first equation, 4. 9 minus (negative 3) = 12. 8, states that if you subtract negative 3 from 4. 9, the result is 12. 8. This equation is useful for understanding the relationship between 4. 9 and 12. 8.

The second equation, 3 + 4. 9 x = 12. 8, states that if you add 3 to 4. 9 times a number (x), the result is 12. 8. This equation is useful for finding out what number (x) is needed to reach 12. 8 when added to 3.

The third equation, 9 x minus (negative 3) = 12. 8, states that if you subtract negative 3 . This equation is useful for finding out what number (x) is needed to reach 12. 8 when subtracted from 9.

These three equations accurately represent the statement "Negative 3 less than 4" and can be used to understand the relationship between 4. 9 and 12. 8 or to find out what number (x) is needed to reach 12. 8.

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Answer:

25 flowers and 14 bushes

Step-by-step explanation:

Sarah has $300 budget

flowers go for $6 each

bushes go for $10 each

So lets go through all options and find which combination of flowers and bushes Sarah could buy with her budget.

1. 13 flowers and 23 bushes

13 x 6 = $78

23 x 10 = $230

$78 + $230 = $308 Above $300

2.16 flowers and 21 bushes

16 x 6 = $96

21 x 10 = $210

$96 + $210 = $306 Above $300

3. 8 flowers and 26 bushes

8 x 6 = $48

26 x 10 = $260

$48 + $260 = $308 Above $300

4. 25 flowers and 14 bushes

25 x 6 = $150

14 x 10 = $140

$150 + $140 = $290 Fits the budget so the answer is

25 flowers and 14 bushes

Hope this helps!

Brainliest and a like is much appreciated!

[tex]\mathcal{V}_{pyramid} = \dfrac{96}{2} = \bf 48 \ cm^{3}[/tex]

In step 4 and 5 he used prime factorization of 5 under cube root.

This was done in order to eliminate the cube root.

Prime factorization is a process of finding the prime factors of a given number. A prime factor is a factor of a number that is a prime number. The prime factorization of a number is the list of its prime factors, together with their multiplicities.

To find the prime factorization of a number, divide it by its smallest prime factor and write down the result as the product of the prime factor and the quotient. Continue this process with the quotient until quotient of 1 is obtained.  

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Based οn the central angle theοrem, the angles that are cοngruent are: C.) GDH and EDH.

In geοmetry,  angle is figure fοrmed by twο rays οr lines that share cοmmοn endpοint, called vertex οf the angle. The rays οr lines that fοrm the angle are called sides οr legs οf angle.

Angles are typically measured in degrees, with a full circle cοnsisting οf 360 degrees. Angles can be classified intο different types based οn their measures οr prοperties.

The central angle theοrem states that the measure οf the central angle equals the measure οf intercepted arc.

Thus:

m∠GDH = 63°

m∠EDH = 63°

Therefοre, based οn the central angle theοrem, the angles that are cοngruent are: C.) GDH and EDH.

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Complete question:

Circle D is shown with the measures of the minor arcs. Which angles are congruent?

A.) EDH and FDG

B.) FDE and GDH

C.) GDH and EDH

D.) GDF and HDG

Using the concept of similar triangles, we were able to find the height of the tree given the man's height, distance from the tree, and distance from the steak. The tree is approximately 6.25 feet tall.

We can use similar triangles to find the height of the tree. Let x be the height of the tree in feet. Then, we have:

x / (x+5) = 6 / 30

Cross-multiplying, we get:

30x = 6(x+5)

Expanding and simplifying, we get:

30x = 6x + 30

24x = 30

x = 1.25

Therefore, the tree is 1.25 + 5 = 6.25 feet tall.

In conclusion, the height of a tree can be determined using similar triangles. By setting up the proportion of the tree's height to its distance from a person, and using cross-multiplication, the height can be solved for. The tree is 6.25 feet tall.

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To construct a Pythagorean triple using an odd number, an odd number must first be chosen. Here 5, 12, and 13 form a Pythagorean triple.

To generate Pythagorean triples using an odd number, follow these steps:

Choose any odd number, say n.

Calculate (n^2-1)/2 and n. These two numbers will form a Pythagorean triple.

Check if the numbers obtained in step 2 are indeed a Pythagorean triple. The two numbers should satisfy the Pythagorean theorem, i.e., a^2 + b^2 = c^2, where a and b are the smaller numbers, and c is the largest number.

If the numbers in step 2 do not form a Pythagorean triple, choose a different odd number and repeat the process.

For example, let's choose the odd number 5:

(n^2-1)/2 = (5^2-1)/2 = 12

n = 5

Now, we can check if 5, 12, and 13 form a Pythagorean triple:

5^2 + 12^2 = 13^2

25 + 144 = 169

Therefore, 5, 12, and 13 form a Pythagorean triple.

We can repeat this process with different odd numbers to generate more Pythagorean triples.

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Answer: a. To determine the amount in Sydney's account after 10 years, we can use the formula for compound interest:

FV = PMT × (((1 + r/n)^(n*t) - 1) / (r/n))

where FV is the future value, PMT is the monthly payment, r is the annual interest rate, n is the number of times compounded per year, and t is the number of years.

Plugging in the values for Sydney's account, we get:

FV = 100 × (((1 + 0.05/12)^(12*10) - 1) / (0.05/12))

FV = $16,184.46

Therefore, the amount in Sydney's account after 10 years is $16,184.46.

b. To determine the amount in Benny's account after 10 years, we can use the same formula:

FV = PMT × (((1 + r/n)^(n*t) - 1) / (r/n))

Plugging in the values for Benny's account, we get:

FV = 80 × (((1 + 0.08/12)^(12*10) - 1) / (0.08/12))

FV = $15,710.21

Therefore, the amount in Benny's account after 10 years is $15,710.21.

c. Sydney had more money in the account after 10 years, since $16,184.46 > $15,710.21.

d. To determine the amount in Sydney's account after 20 years, we can use the same formula:

FV = PMT × (((1 + r/n)^(n*t) - 1) / (r/n))

Plugging in the values for Sydney's account, we get:

FV = 100 × (((1 + 0.05/12)^(12*20) - 1) / (0.05/12))

FV = $45,074.89

Therefore, the amount in Sydney's account after 20 years is $45,074.89.

e. To determine the amount in Benny's account after 20 years, we can use the same formula:

FV = PMT × (((1 + r/n)^(n*t) - 1) / (r/n))

Plugging in the values for Benny's account, we get:

FV = 80 × (((1 + 0.08/12)^(12*20) - 1) / (0.08/12))

FV = $42,598.05

Therefore, the amount in Benny's account after 20 years is $42,598.05.

f. Sydney had more money in the account after 20 years, since $45,074.89 > $42,598.05.

Step-by-step explanation: