if the odds on a bet are 41:1 against, what is the probability of winning? express your answer as a fraction.

1.  Exponential decay 2. Josh's function represents the situation correctly 3. V(x) = 1275(0.835)ˣ,  V(x) = 1275(1-0.165)ˣ

An exponential decay function is a mathematical function that describes the decrease in value of a quantity over time or through a series of events. It is often used to model natural phenomena such as radioactive decay or the spread of diseases.

In an exponential decay function, the value of the quantity decreases exponentially over time. This means that the rate of decrease is proportional to the value of the quantity at any given time.

The exponential decay function is characterized by a decreasing graph that approaches zero but never touches the x-axis. The rate of decay slows down over time, but the quantity never completely disappears. The function is used in various fields such as physics, chemistry, biology, finance, and economics, to name a few.

1. This situation represents exponential decay because the value of the computer decreases by 16.5% each year.

2. Josh's function represents the situation correctly because it involves the decay factor (0.835) which is less than 1, reflecting the decrease in value each year. Eve's function represents exponential growth which is not consistent with the situation where the value of the computer decreases each year.

3. V(x) = 1275(0.835)ˣ represents the function using the form V(x) = a(b)ˣ where a = 1275 and b = 0.835.

Alternatively, V(x) = 1275(1-0.165)ˣ represents the function using the form V(x) = a(1-r)ˣ where a = 1275 and r = 0.165.

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Using the stars and bars technique, Candice can distribute her 24 pieces of candy among her four siblings in 2,925 different ways. If she must give each sibling at least one of each type of candy, there are 67,200 ways to distribute the candy among the four siblings.

(A) To solve this problem, we can use the technique of stars and bars. We have a total of 24 pieces of candy to share among four children. We can represent this using 24 stars, with 3 bars to separate the stars into four groups, one for each child. For example, the following arrangement represents giving 6 pieces of candy to the first child, 10 pieces to the second child, 3 pieces to the third child, and 5 pieces to the fourth child:

*****|**********|***|****

The number of ways to arrange the stars and bars is equal to the number of ways to choose 3 positions out of the 27 possible positions for the stars and bars. Therefore, the number of different ways that Candice can share her candy with her three younger brothers is:

C(27, 3) = 27! / (3! * 24!) = 2925

(B) Now, we need to ensure that each child receives at least one Tootsie roll and one Twizzler. We can give each child one of each candy to start, and then distribute the remaining 13 Tootsie rolls and 7 Twizzlers using the stars and bars technique. We have 13 Tootsie rolls and 7 Twizzlers to distribute among four children, which can be represented using 13 stars and 3 bars for the Tootsie rolls, and 7 stars and 3 bars for the Twizzlers. The number of ways to arrange the stars and bars for each type of candy is:

C(16, 3) = 560 for the Tootsie rolls

C(10, 3) = 120 for the Twizzlers

To find the total number of ways to distribute the candy, we can multiply the number of ways for each type of candy:

560 * 120 = 67200

Therefore, there are 67,200 different ways for Candice to share her candy with her three younger brothers after her mother asks her to give at least one of each type of candies to each of her brothers.

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Complete question:

After a (not very successful) trick or treating round, Candice has 15 Tootsie rolls and 9 Twizzlers in her pillow case. Her mother asks her to share some of the loot with her three younger brothers.

(A) How many different ways can she do this?

(B) How many different ways can she do this after her Mother asks her to give at least one of each type of candies to each of her brothers?

The equation of the quadratic function that passes through these points is:

[tex]y = -3x^2 - 12x - 8.[/tex]

What is quadratic equation?

A quadratic equation is a polynomial equation of the second degree, which means it contains one variable with an exponent of 2. The general form of a quadratic equation is:

[tex]ax^2 + bx + c = 0[/tex]

Using polynomial interpolation with these 5 points, we can find a quadratic polynomial that passes through all the points. Let the equation of the polynomial be [tex]y = ax^2 + bx + c[/tex].

Using the point (0, -8), we get:

[tex]-8 = a(0)^2 + b(0) + c[/tex]

c = -8

Using the point (-1, 1), we get:

[tex]1 = a(-1)^2 + b(-1) - 8[/tex]

a - b = 9

Using the point (-3, 1), we get:

[tex]1 = a(-3)^2 + b(-3) - 8[/tex]

9a - 3b = 27

Using the point (-4, -8), we get:

[tex]-8 = a(-4)^2 + b(-4) - 8[/tex]

16a - 4b = 0

Using the point (-2, 4), we get:

[tex]4 = a(-2)^2 + b(-2) - 8[/tex]

4a - 2b = 12

Solving this system of equations, we get:

a = -3

b = -12

c = -8

Therefore, the equation of the quadratic function that passes through these points is:

[tex]y = -3x^2 - 12x - 8.[/tex]

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Mr. Kha Lipat should invest $5,000 today in order to receive $400.00 in interest one year from now at an 8% interest rate.

To calculate how much money Mr. Kha Lipat should invest today to receive $400.00 one year from now at an 8% interest rate, we can use the formula for calculating simple interest though compound intrest:

I = P * r * t

where I is the interest earned, P is the principal (the initial amount invested), r is the interest rate (as a decimal), and t is the time period (in years).

We know that Mr. Kha Lipat wants to earn $400.00 in interest, the interest rate is 8% or 0.08 (as a decimal), and the time period is 1 year. We can plug these values into the formula and solve for P:

I = P * r * t

400 = P * 0.08 * 1

400 = 0.08P

P = 400 / 0.08

P = 5000

Therefore, Mr. Kha Lipat should invest $5,000 today in order to receive $400.00 in interest one year from now at an 8% interest rate.

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Therefore, approximately 68.26% of people are expected to score higher than 2.5 but lower than 3.5.

Based on the information provided, the mean (X) is 3.00 and the standard deviation (SD) is 0.50. To find the percentage of people expected to score higher than 2.5 but lower than 3.5, we will use the standard normal distribution (z-score) table.

First, we need to calculate the z-scores for both 2.5 and 3.5:
z1 =[tex] (2.5 - 3.00) / 0.50 = -1.0[/tex]
z2 = [tex](3.5 - 3.00) / 0.50 = 1.0[/tex]

Now, we can use the standard normal distribution table to find the probability of the z-scores. For z1 = -1.0, the probability is 0.1587 (15.87%). For z2 = 1.0, the probability is 0.8413 (84.13%).

To find the percentage of people expected to score between 2.5 and 3.5, subtract the probability of z1 from the probability of z2:

Percentage = [tex](0.8413 - 0.1587) x 100 = 68.26%[/tex]

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The correct answer to the question, "Which of the following is equivalent to the probability of getting less than 50% democrats in a random sample of size 100?" is: B. P( z < 50 — 55/ √55(45)/100).

To find the probability, we first calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value (50%), μ is the mean (55%), and σ is the standard deviation.

The standard deviation can be calculated as:

σ = √(np(1-p))

where n is the sample size (100) and p is the proportion of democrats (0.55).

Now, plug in the values into the z-score formula:

z = (50 - 55) / √(100 * 0.55 * 0.45)

The probability is then found as P(z < z-score), which is represented by the option B.

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We can claim that after answering the above question, the Therefore, the solution to the original equation is: [tex]q = 9^x\\[/tex]

In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" states that the sentence "2x Plus 3" equals the value "9". The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations 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 second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

given equation:

[tex]1/4xln(16q^8) - ln3 = ln24\\1/4xln(16q^8) = ln(24 * 3)\\1/4xln(16q^8) = ln72\\ln(16q^8)^(1/4x) = ln72\\16q^8^(1/4x) = 72\\16q^8 = 72^(4x)\\ln(16q^8) = ln(72^(4x))\\[/tex]

[tex]ln(16) + ln(q^8) = 4x ln(72)\\ln(q^8) = 4x ln(72) - ln(16)\\ln(q^8) = ln(72^(4x)) - ln(16^1)\\ln(q^8) = ln((72^(4x))/16)\\q^8 = e^(ln((72^(4x))/16))\\q^8 = (72^(4x))/16\\q^8 = 9^(8x)\\q = 9^x\\[/tex]

Therefore, the solution to the original equation is:

[tex]q = 9^x\\[/tex]

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After answering the prοvided questiοn, we can cοnclude that As a result, expressiοn the pizza place is abοut a mile away frοm the schοοl.

In mathematics, an expressiοn is a grοup οf representatiοns, digits, and cοnglοmerates that resemble a statistical cοrrelatiοn οr regimen. An expressiοn can be a real number, a mutable, οr a cοmbinatiοn οf the twο. Additiοn, subtractiοn, rapid spread, divisiοn, and expοnentiatiοn are examples οf mathematical οperatοrs.

Arithmetic, mathematics, and shape all make extensive use οf expressiοns. They are used in mathematical fοrmula representatiοn, equatiοn sοlutiοn, and mathematical relatiοnship simplificatiοn.  

If the pizza place is 7 miles frοm yοur friend's hοuse and her hοuse is 8 miles frοm schοοl, the distance between the twο can be calculated as fοllοws:

distance frοm pizza shοp tο schοοl = distance frοm friend's hοuse tο schοοl - distance frοm friend's hοuse tο pizza shοp

8 miles minus 7 miles = distance frοm pizza place tο schοοl

1 mile frοm the pizza place tο the schοοl

As a result, the pizza place is abοut a mile away frοm the schοοl.

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We can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.

The matrix product of two matrices, A and B, is defined as the matrix C, where C = AB. To calculate the product of two matrices, we must take the dot product of each row of A and each column of B. If we are given a matrix product A1B, then we can calculate B1A without necessarily knowing what A and B are.

To do so, we must first invert the matrix A1B. We can do this by solving a system of equations. We can set up this system of equations by treating the entries of A1B as the coefficients in a system of equations, and solving for the entries of B1A. Once we have found the inverse, we can calculate the matrix B1A.

Finally, once we have the matrix B1A, we can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.

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Answer:

The answer is

-7/8 + 3/10

Step-by-step explanation:

See the picture

Hope you understand :)

The probability of randomly chosen, a 50-year-old or older voter from the winning party is 45.84%

Given the table of values

From the table of values, we have the winning party to be

New Democratic

From the column of New Democratic, we have

Total = 9422

50-year-old or older voter = 4319

So, the required probability is

Probbaility = 4319/9422

Evaluate

Probbaility = 0.45839524517

This gives

Probbaility = 45.839524517%

Approximate

Probbaility = 45.84%

Hence, the probability is 45.84%

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The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

To calculate this probability, we need to consider the following components:

1. The total number of customers purchasing cooking and BobVilla books: This is the denominator of our equation, and it represents the total number of customers who purchased the two books.

2. The number of customers purchasing the biography book: This is the numerator of our equation, and it represents the number of customers who purchased the biography book.

3. The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books: This is the fraction of customers who purchased the biography book over the total number of customers who purchased the two books.

To calculate the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books, we need to divide the numerator (the number of customers purchasing the biography book) by the denominator (the total number of customers purchasing the two books).

This probability can be expressed as a decimal, which is 0.08. This value can also be rounded to two decimal places, which is 0.08.

In conclusion, the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

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Answer:

1. 1/2

2. -4/1

3. 1/1

Step-by-step explanation:

Answer:

1 y=2/1+2

2 y=.25x+3

3 y=x-2

Step-by-step explanation:

Step-by-step

y=mx+b

1. 2

2. .25

3. 1

The margin of error of the 98.4% confidence interval for snapdragons  is 3.71.

The midpoint of the range is calculated by adding the upper and lower bounds and then dividing by two. So, the sample mean is `(20.91 + 38.43) / 2 = 29.67`.

The margin of error is calculated by multiplying the critical value of z* (1.96 for a 98.4% confidence level) by the standard error of the mean. The formula for calculating the margin of error is:

`Margin of error z*(standard deviation/√n`).

The formula is `range/4 = 1.96 * standard deviation/√n`.Now, solve for the standard deviation:

`standard deviation = (range/4) * √n / 1.96`

Substituting the values: `(38.43 - 20.91)/4 = 1.96 * standard deviation/√n`

Simplifying the equation: `4.26 = (1.96*standard deviation)/√n`

Squaring both sides: `4.26^2 = 3.8416 = (1.96^2 * standard deviation^2)/n`

Substituting the value of the standard deviation: `3.8416 = (1.96^2 * ((38.43 - 20.91)/4)^2) / n`

Solving for n: `n = ((1.96^2 * ((38.43 - 20.91)/4)^2) / 3.8416) = 31.54`

Now that we know the sample size, we can calculate the standard error of the mean:

`standard error = standard deviation/√n = ((38.43 - 20.91)/4)/√31.54 = 1.89`.

The margin of error is `1.96 * 1.89 = 3.71`.

The 98.4% confidence interval for snapdragons grown in compost is (20.91, 38.43). The margin of error of this confidence interval is 3.71.

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A) 35. 8 million; thirty-five million eight hundred thousand, or thirty-five million eight hundred thousand dollars ,(b)115. 2 thousand; one hundred and fifteen thousand two hundred.(c) 97.8 million eight hundred thousand; 97.8 million eight hundred thousand. or 978 million.

What significance do numbers have?

We need good numeracy skills as parents to assist our children to develop, as patients to grasp healthcare information, and so as politicians to make sense of numbers and economic news. Selections in life were frequently based upon numerical data; in order to arrive at optimal decisions, we must be good at maths.

How are numbers used in everyday life?

Numbers are utilized in a variety of mathematical operations such as summation, subtraction, multiplication, division, percentage, and so on, that we employ in the everyday companies and exchanges. Quantities are numerical symbols representing integers that may be used for numbering, estimating, and doing other arithmetic operations.

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Answer: multiplied by 5 or squared

Step-by-step explanation:

If the number 5 goes in and 25 is the result, the rule could be multiplying by 5 or squaring the number that goes in (input).

5 x 5 = 25

5^2 = 25.

To measure central tendencies in the data collected from the Consumer Price Index (CPI), the dental director should use measures of central tendency, such as the mean, median, and mode.

The mean is the average of a set of numbers and is calculated by adding all the numbers together and then dividing by the total number of numbers. The median is the middle number when the numbers are placed in order from least to greatest. The mode is the number that appears most often in a set of numbers.

Using these measures of central tendency will allow the dental director to gain a better understanding of the CPI data, as they will be able to identify the center point of the data and also see how frequently particular values appear. This can help in making informed decisions about policies and other changes.

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The probability of winning is 1/17, which can also be expressed as a decimal (approximately 0.059) or as a percentage (approximately 5.9%).

The odds on a bet represent the ratio of the probability of winning to the probability of losing. In this case, the odds are 16:1 against winning, which means that the probability of winning is 1 out of 16.

To express this probability as a fraction, we can use the formula:

Probability of winning = 1 / (odds + 1)

Plugging in the given odds, we get:

Probability of winning = 1 / (16 + 1)

Probability of winning = 1/17

In this case, the odds of 16:1 against winning correspond to a probability of 1/17, which represents the chance of winning the bet.

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The child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.

The given problem requires us to determine the number of milliliters of a liquid medicine that a child should receive in order to obtain a specific dosage of the active ingredient. We are given that the medicine contains 100 mg of the active ingredient in 5 ml.

The child needs to receive 300 mg of the active ingredient, and there are 100 mg of the active ingredient in 5 ml of the medicine. Therefore, the child should be given:

[tex]\frac{300 mg}{100mg/5ml} = \frac{300\text{ mg} \times 5\text{ ml}}{100\text{ mg}} = 15\text{ ml}$$[/tex]

So the child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.

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Thus, 4.0 moles of NH3 would be produced when 6.0 moles of H2 react with sufficient N2.

Suppose 6.0 mol of H2 reacts with sufficient N2 to produce ammonia, NH3. We can determine the number of moles of NH3 produced using stoichiometry.The balanced chemical equation for the reaction is:[tex]3H2(g) + N2(g) → 2NH3(g)[/tex]

From the equation, we can see that 3 moles of H2 react with 1 mole of N2 to produce 2 moles of NH3.

Therefore, using the mole ratio from the balanced equation, we can calculate the number of moles of NH3 that would be produced when 6.0 mol of H2 reacts with [tex]N2:6.0 mol H2 × (2 mol NH3/3 mol H2) = 4.0 mol NH3[/tex]

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If 10 friends are going to occupy 10 seats in a shuttle on the way to the airport, then they can arrange themselves in the shuttle in 10! or 3,628,800 ways.

Step-by-step explanation: There are 10 friends and 10 seats to be occupied in a shuttle.

Therefore, the number of ways to arrange the 10 friends in 10 seats is given by 10! (10 factorial), which is calculated as follows: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 3,628,800

Therefore, 10 friends can arrange themselves in the shuttle in 3,628,800 ways.

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Answer: 3 5/8 pizzas were there at the start of the party.

Step-by-step explanation:

At the party let number of pizzas were = x Aisha and her friends ate 2 1/2 pizzas after which 1 1/8 pizzas were left.

Therefore the equation formed will be

x- 2 1/2= 1 1/8

x-(5/2)= 9/8

x= 9/8 + 5/2

x= 29/8= 3 5/8

Therefore 3 5/8 pizzas were there at the start of the party.

In the figure of circle provided. the value of x is

In a circle, equal chords subtends equal arc length.

In the problem it was given that:

chord SU is equal to chord ST hence we have that

x + x + 38 = 360 (angle in a circle)

collecting like terms

2x + 38 = 360

2x = 360 - 38

2x = 322

Isolating x by dividing both sides by 2

2x / 2 = 322 / 2

x = 161

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Answer:

x= 2

Step-by-step explanation:

² means times the number itself 2 times.

2×2=4

In this particular question, the following statements can be used to complete each sentence with either "increases" or "decreases":

- Phytic acid decreases the absorption of zinc from grains.

Oxalic acid decreases the absorption of calcium from spinach.

- Refinement of grains decreases the mineral content of grain products.-

Vitamin C increases the absorption of iron from foods.-

Vitamin D increases the absorption of calcium from foods.

Explanation:

Bioavailability refers to the proportion of a nutrient that is absorbed from food and made available for use in the body. Factors that alter bioavailability of minerals from foods include phytic acid, oxalic acid, refinement of grains, and vitamins C and D. Phytic acid, for instance, decreases the absorption of zinc from grains while oxalic acid decreases the absorption of calcium from spinach.

           Refinement of grains, on the other hand, decreases the mineral content of grain products. Conversely, vitamin C increases the absorption of iron from foods while vitamin D increases the absorption of calcium from foods.

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To increase £88 by 14%, we can use the multiplication method, which involves multiplying the original amount by the decimal equivalent of the percentage increase.

The multiplication method is a mathematical technique used to solve problems involving multiplication. It involves breaking down numbers into their constituent parts and then multiplying those parts together to arrive at the final answer.

To find the decimal equivalent of 14%, we divide the percentage by 100:

14% ÷ 100 = 0.14

This tells us that a 14% increase is equivalent to multiplying the original amount by 1.14 (1 + 0.14).

To increase £88 by 14%, we can multiply it by 1.14:

£88 x 1.14 = £100.32

Therefore, the increased amount is £100.32.

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Answer:

Step-by-step explanation:

nothing makes it true

The answer of the given question based on the  linear regression  is , the predicted distance the person will travel after 10 hours of driving is approximately 252.05 miles.

Distance is measurement of length between the two points or objects. It is a scalar quantity that only has a magnitude and no direction. In mathematics, distance can be measured in various units such as meters, kilometers, miles, or feet, depending on the context.

Distance can be calculated using the distance formula, which is based on the Pythagorean theorem in two or three dimensions.

Assuming the equation you meant to write is y = 34.38x - 91.75, where y is the predicted distance traveled in miles and x is the number of hours driven, we can use this equation to predict how far the person will travel after 10 hours of driving:

y = 34.38x - 91.75

y = 34.38(10) - 91.75

y = 343.8 - 91.75

y = 252.05

Therefore, the predicted distance the person will travel after 10 hours of driving is approximately 252.05 miles.

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During 10 hours of driving, the projected distance according to linear regression is roughly 252.05 miles.

The term "distance" refers to the length between two points or objects. Having merely a magnitude and no direction, it is a scalar quantity. Depending on the situation, distance in mathematics can be expressed in a variety of ways, including meters, kilometers, miles, or feet.

The distance formula, which depends on the Pythagorean theorem in either two or three dimensions, can be used to compute distance.We may use this equation to forecast how far the individual would go after 10 hours of driving, assuming the equation you meant to write is

y = 34.38x - 91.75, where y is the expected distance travelled in miles and x is the number of hours driven:

y = 34.38x - 91.75

y = 34.38(10) - 91.75

y = 343.8 - 91.75

y = 252.05

The estimated distance that the driver will cover after 10 hours on the road is 252.05 miles.

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The complete question is,

The equation for linear regression is = 34.38x - 91.75. Calculate this person's estimated distance after 10 hours of driving using the equation: 4.38x-91-75.

the missing dimension of the triangle is the base, which has a length of 21 feet. To find the missing dimension of the triangle, we will use the formula for the area of a triangle, which is:

Area = 1/2 x base x height

We know that the area of the triangle is 14 ft squared and the height is 6 ft. We can substitute these values into the formula and solve for the base:

14 = 1/2 x base x 6

Multiplying both sides by 2/6 (or simplifying to 1/3) gives:

14 x 3/2 = base

21 = base

Therefore, the missing dimension of the triangle is the base, which has a length of 21 feet.

This means that the triangle has a height of 6 feet and a base of 21 feet, and its area is 14 square feet. The height of a triangle is the perpendicular distance from the base to the opposite vertex, and in this case, it is given as 6 feet. The base of a triangle is the side opposite the height, and we have found that it has a length of 21 feet.

In summary, we can find the missing dimension of a triangle by using the formula for the area of a triangle and the given dimensions. In this case, we found that the missing dimension is the base, which has a length of 21 feet, and we know that the height is 6 feet.

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