how to factor a trinomial when a is greater than 1

There are a total of 32 different possible footwear choices that we can make.

Given, The number of pairs of socks = 4

The number of pairs of shoes = 4

We are to find out the number of possible footwear choices we can make if we can wear any combination of socks and shoes, including mismatched pairs.

So, We can wear any pair of socks with any pair of shoes including a mismatch.

Thus, for each pair of socks, there are 4 possible pairs of shoes.

And for each pair of shoes, there are 4 possible pairs of socks.

Therefore, we can form,

Total number of possible footwear choices = 4 pairs of socks * 4 pairs of shoes * 2 (considering the case of mismatched pairs) = 32 pairs.

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Answer:

3.6 miles

Step-by-step explanation:

hope this helps!

Answer:

40 and 45

Step-by-step explanation:

let the 2 numbers be x and y with y the larger of the two, then

x + y = 85 → (1)

x = y + 5 → (2)

substitute x = y + 5 into (1)

y + 5 + y = 85

2y + 5 = 85 ( subtract 5 from both sides )

2y = 80 ( divide both sides by 2 )

y = 40

substitute y = 40 into (2)

x = 40 + 5 = 45

the two numbers are 40 and 45

Thus, total garden area calculated in square meters is found to be 40  sq. m.

If the degree n in the equation is equal to 1, then a linear equation only contains ONE variable. The highest exponent a single variable can have is referred to as the equation's degree. Any arbitrary variable, such as x, y, or z, may be used as long as the linear equation is homogeneous.

Given data:

Let x be the total area of land.

Area of planted flowers : 2/5 x

Remaining area = 24 sq. m.

Thus,

Total area = Area of planted flowers + Remaining area

x = 2/5 x + 24

x - 2/5 x = 24

(5 -2)/5 x = 24

3x/5 = 24

x = 24*5 / 3

x = 8*5

x = 40

Thus, total area of the garden calculated in square meters is found to be 40  sq. m.

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Born: 582 BCE

Died: 497 BCE

582-497= 85

Answer: 85 years old

The population of a district in 2005 was 35,700 with a continuous annual growth rate of approximately 4%. the population in 2030 will be approximately 97,209 according to the exponential growth function.

The formula for the continuous exponential growth is given by the formula:

P = Pe^(rt)

where,P is the population in the future.

P0 is the initial population.

t is the time.

r is the continuous interest rate expressed as a decimal.

e is a constant equal to approximately 2.71828.In this problem, the initial population P0 is 35,700. The rate r is 4% or 0.04 expressed as a decimal. We want to find the population in 2030, which is 25 years after 2005.

Therefore, t = 25.We will now use the formula:

P = Pe^(rt)P = 35,700e^(0.04 × 25)P = 35,700e^(1)P = 35,700 × 2.71828P = 97,209.09.

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Answer: I got 97,042.7

Step-by-step explanation:

Answer:r=25

Step-by-step explanation: he spends 96$ on 12 pairs of gloves and 25 dollars per 1 rake.  thus r equals 25

Answer:

See below answer of each.

Step-by-step explanation:

Let's assume the cost of one small popcorn to be 'x'.

Each friend bought one ticket and one small popcorn, so the cost of one ticket and one small popcorn is $7.50 + x.

The total amount spent by 8 friends is $83.60.

Therefore, we can set up the following equation:

8(7.50 + x) = 83.60

Simplifying the equation, we get:

60 + 8x = 83.60

8x = 23.60

x = 2.95

Therefore, the cost of one small popcorn is $2.95.

The equation to represent the situation is:

Total cost = Initial cost + (Cost per mile x Number of miles)

$24.25 = $3.00 + ($2.50 x m)

where m represents the number of miles to Jeremiah's house.

Let's start by setting up the equation for the total cost of the gloves:

12 pairs of gloves x $8 per pair = $96

We know that the gardener spent a total of $300 on both rakes and gloves, so we can set up an equation:

12r + $96 = $300

Now we can solve for r:

12r = $204

r = $17

Therefore, the cost of 1 rake is $17.

The equation that models the situation is:

12($17) + $96 = $300

The two figures shown are made of unit squares. The positive difference of the perimeters, in units, is 8.

Perimeter is the total distance around the boundary of the shape. Since each square has a side length of 1 unit, the perimeter is equal to the number of sides.

1. Figure A: Counting the number of unit squares on the boundary of the shape, the perimeter of the first shape is:   8+4+4+4+4=24 units.

2. Figure B:Counting the number of unit squares on the boundary of the shape, the perimeter of the second shape is: 10+2+10+2=24 units.

The positive difference of the perimeters in units = |24 - 24| = 0 units. Therefore, the positive difference of the perimeters, in units is 0.

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After solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, the cost of each blouse and skirt:

x be the price of one blouse and y is the price of one skirt.

For a total of $215, Carol purchased 3 skirts and 5 blouses.

5x + 3y = 215

For a total of $135, Ellen purchased 2 skirts and 3 blouses.

3x + 2y = 135

By resolving the equations in the system:

5x + 3y = 215

3x + 2y = 135

We will obtain:
x = $25

y = $30

Therefore, after solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.

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Correct question:

Carol bought 5 blouses and 3 skirts for a total of $215. At the same time, her sister Ellen bought 3 blouses and 2 skirts for a total of $135. What was the price of each blouse and each skirt?

Answer:

To add these fractions, we need to find a common denominator. The least common multiple of 3, 5, and 6 is 30, so we can convert each fraction to an equivalent fraction with a denominator of 30:

7/3 = 70/30

21/5 = 126/30

7/6 = 35/30

Now we can add the fractions:

7/3 + 21/5 + 7/6 = 70/30 + 126/30 + 35/30

Combining the numerators, we get:

= (70 + 126 + 35) / 30

= 231 / 30

Simplifying this fraction by dividing the numerator and denominator by their greatest common factor, which is 3, we get:

= 77 / 10

Therefore, the sum of the fractions 7/3, 21/5, and 7/6 is equal to 77/10.

A graph that shows the line that passes through (-8, 1) and is parallel to a line with a slope of 1/2 is: B. graph B.

In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-8, 1), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = 1/2(x - (-8))

y - 1 = 1/2(x + 8)

y - 1 = x/2 + 4

y = x/2 + 5

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The relative frequency for the event "spin a 2" is 1/5.

Relative frequency measures how often a value appears relative to the sum of the total values.

In order to determine the relative frequency of spinning a 2, divide the frequency of spinning a two by the total number of trials.

Division is the process of determining the quotient of two or more numbers. It entails grouping a number into equal parts using another number. The sign that is used to represent division is ÷.

Relative frequency = number of times a two was spun / total number of trials

= 10 / 50 = 1/5

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Answer:

Step-by-step explanation:

i don't see a statement but use 7 i guess

Total longer distance is [tex]3\frac{2}{21} miles[/tex], that kiki run during the second week of track practice than the first week of track practice.

We have, a runner Kiki and she runs on track for practice. In first week,

Distance runs by Kiki on track practic = [tex]4 \frac{3}{7} miles[/tex]

which is a mixed fraction so, simplify it into simple fraction that is 25/7 miles. In second week,

Distance runs by Kiki on track practice = [tex]6 \frac{2}{3} miles[/tex]

After simplification, it is equals to 20/3 miles. We have to calculate the longer distance that kiki run during the second week of track practice than the first week of track practice. Let the distance run during second week be longer by 'x miles' from distance run during first week. The required distance can be calculated by difference between the distance that kiki run during the second week of track practice and the first week of track practice. So, [tex]x = \frac{20}{3} - \frac{25}{7 }[/tex].

taking least common multiple of (3,7)= 21

=> [tex] x = \frac{20× 7 - 3× 25}{21} [/tex]

[tex] =>x = \frac{ 140 - 75}{21} = \frac{65}{21 }[/tex].

Hence, required distance value is

[tex]3\frac{2}{21} [/tex].

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Therefore, the pilot should turn by approximately 41.8 degrees to fly directly to the airport.

Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It has applications in various fields, such as engineering, physics, architecture, and astronomy. Trigonometry is based on the use of six fundamental trigonometric functions, which are sine, cosine, tangent, cosecant, secant, and cotangent. These functions are defined in terms of the ratios of the sides of a right triangle. In a right triangle, one angle is a right angle, which measures 90 degrees, and the other two angles are acute angles, which are less than 90 degrees. The three sides of a right triangle are called the hypotenuse, the adjacent side, and the opposite side. The hypotenuse is the longest side, and it is always opposite to the right angle. The adjacent side is the side that is adjacent to the angle of interest, and the opposite side is the side that is opposite to the angle of interest.

Here,

We can use trigonometry to find the angle x that the pilot should turn in order to fly directly to the airport.

First, let's draw a diagram of the situation:

A(airport)

|\

| \

|  \

|   \

|    \

|     \

|      \

|       \

|        \

|         \

|          \

P         x mi

In the diagram, P represents the position of the plane, which is 148 miles north and 167 miles east of the airport A. The line labeled "x mi" represents the distance that the plane needs to fly in order to reach the airport, and the angle x is the angle between the line x mi and the line representing the eastward direction.

To find x, we can use the trigonometric ratio for tangent (tan):

tan(x) = opposite/adjacent

In this case, the opposite side is 148 miles (the distance north of the airport) and the adjacent side is 167 miles (the distance east of the airport). Therefore:

tan(x) = 148/167

Using a calculator, we can find that:

tan(x) ≈ 0.8868

To find x, we need to take the arctangent (tan⁻¹) of both sides:

x = tan⁻¹(0.8868)

Using a calculator, we find that:

x ≈ 41.8°

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Consequently, in this rhombus-shaped skating rink, the longest distance that may be covered without changing directions is 40 metres.

The total distance encircling a two-dimensional shape's perimeter is known as its perimeter. It represents the total length of the shape's sides. The perimeter of a rectangle, for instance, can be determined by combining the lengths of its four sides: A rectangle's perimeter equals 2 x (length + width). Other shapes, such triangles, circles, and polygons, can have their perimeters determined using the appropriate formulas.

given

The formula for the perimeter of a rhombus, which is the sum of the lengths of its four sides, can be used to determine the greatest distance that can be covered in a rhombus-shaped skating rink without changing direction.

Given that the sides are each 26 metres long, the rhombus's perimeter would be:

Perimeter: (4 x 26) = 104 metres

But, we must consider that the smaller diagonal of the skating rink measures 40 metres in order to determine the most distance that may be traversed without changing directions. This means that the skater is limited to a 40-meter radius before having to change directions.

Consequently, in this rhombus-shaped skating rink, the longest distance that may be covered without changing directions is 40 metres.

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The complete question is:- 3.- What is the maximum distance that can be traveled without changing direction in a rhombus-shaped skating rink, if each side measures 26 meters and the smaller diagonal is 40 meters?

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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The experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is approximately 0.263

The experimental probability is found by dividing the number of times the desired outcome occurred by the total number of trials. In this case, the desired outcome is selling a slice of pepperoni pizza as the first slice tomorrow.

Since we only know the number of slices sold today, we don't have any specific information about the number of slices that will be sold tomorrow. However, we can assume that the same types of pizzas will be sold tomorrow, and the probability of selling a slice of pepperoni pizza tomorrow will be the same as the proportion of pepperoni slices sold today.

So, the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is

Experimental probability = Number of pepperoni slices sold today / Total number of slices sold today

Experimental probability = 20 / 76

Experimental probability = 0.263

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The price of 1 liter of petrol at the cheaper petrol station is £0.68.

What is the conversion rate?

Just dividing the number of conversions by the total number of ad interactions that can be linked to a conversion within the same time period yields the conversion rate. Your conversion rate would be 5%, for instance, if you had 50 conversions out of 1,000 interactions, as 50 divided by 1,000 equals 5%.

Here, we have

Given: The prices of petrol in a British and an American petrol station are shown below. The conversion rate is $1 = £0.80.

We have to find the price of 1 liter of petrol in the cheaper petrol station.

$1 = £0.80

= £13.20×($1/£0.80)

= $16.5

For British petrol station

12 liter of petrol = $16.5

1 liter = $16.5/12

1 liter = $1.375

For American petrol station

20 liters of petrol = $17

1 liter = $17/20

1 liter = $0.85

The price of cheaper petrol from American petrol stations = $0.85× (£0.80/$1)

= £0.68

Hence, the price of 1 liter of petrol at the cheaper petrol station is £0.68.

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x is the base of given right angled triangle, which is calculated as 7 using the Pythagoras theorem.

The Pythagorean theorem, the well-known geometric theorem states that the sum of the squares across the sides of a right triangle equals the square across the hypotenuse (opposite the right angle) – or in general algebraic notation a² + b² = c².

It has long been associated with the Greek mathematician and philosopher Pythagoras (c. 570-500/490 BC), but is actually much older. His four clay tablets in Babylonia, circa 1900 BC to his 1600. Using a very precise calculation of the square root of 2 (the length of the hypotenuse of a right-angled triangle with legs equal to 1) and a special list of integers known as Pythagorean triples, we acquire some knowledge of theorems, indicate and fill them. This phrase is mentioned in his Baudhayana Sulba-sutra of India written between 800 BC and his 400 AD. written.

Given,

DF = 24

DE = 25

Using Pythagoras theorem:

Hypotenuse² = Base² + Perpendicular²

25² = x² + 24²

x² = 25² - 24²

x² = 625 - 576

x² = 49

x = √49

x = 7

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The type of average that can be found is the median. The median is the middle value of the data set when the values are arranged in order. In this case, the median is 11, as shown by the line inside the box.

Value is the relative worth, merit, or importance of something. It is subjective and can be determined by a variety of factors, including personal preferences, beliefs, and economic forces. Value is a concept that can be applied to many different aspects of life, including economic goods, personal relationships, and objects. Value is determined by how much someone is willing to pay for something or how much someone needs something. In economics, value is determined by the market, which is based on supply and demand. In personal relationships, value is determined by the mutual respect, trust, and understanding between two people. In objects, value is determined by the sentiment and meaning it holds for the owner. Ultimately, value is a perception of worth, and its true value is subjective.

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The percentage of women in a study reported in the Dove consumer insight perceived their actual beauty to fall short of their ideal is 96%.

Explanation:

The percentage of women in a study reported in the Dove consumer insight perceived their actual beauty to fall short of their ideal is 96%. There is a prevalent stereotype in society that women should look a certain way, such as being thin and having flawless skin, which can cause women to feel self-conscious and dissatisfied with their appearance. Dove's mission is to help women feel more confident and happy in their skin, regardless of their size or skin type.

To that aim, they conducted a study where 96% of women perceived their actual beauty to fall short of their ideal. Dove's Real Beauty campaign has been very popular in recent years, encouraging women to embrace their natural beauty and feel proud of who they are.

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Number of wolves hunting in medium-sized packs) to perform these calculations and obtain the percentage.

To find the percent of wolves that are neither female nor hunt in medium-sized packs, follow these steps:
1. Determine the total number of wolves.
2. Identify the number of female wolves and those that hunt in medium-sized packs.
3. Subtract the number of wolves that fit into either category from the total number of wolves.
4. Divide the remaining number of wolves by the total number and multiply by 100 to get the percentage.
Please provide the necessary data (total number of wolves, number of female wolves, and number of wolves hunting in medium-sized packs) to perform these calculations and obtain the percentage.

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The expected value (the mean of the distribution) for someone who buys a ticket can be calculated by adding up the total amount of money in the raffle and then dividing that by the number of tickets sold, which in this case in $6.68.

In this scenario, a ticket costs $5. The prize for winning the raffle is $1400 plus the cost of the ticket, which is $5.

The total value of the raffle is equal to the sum of the prize and the total amount of money raised from the tickets. The amount raised from the tickets is the number of tickets sold multiplied by the cost of the ticket.

Therefore, the total value of the raffle is equal to: $1400 + ($5 × 833) = $1400 + $4165 = $5565

The expected value of a ticket is the total value of the raffle divided by the number of tickets sold.

Therefore, the expected value of a ticket is:$5565 / 833 = $6.68

Therefore, the expected value (the mean of the distribution) for someone who buys a ticket is $6.68.

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The least likely event from given events is Option B: A randomly selected student who is freshmen owns a skateboard.

The event whose occurence is minimum is least likely event.

Suppose there are finite elementary events in sample space of considered experiment and all are equally likely.

Then, we want to find the probability of an event E.

Then, its probability is given as

P(E) = Number of favourable cases/ Number of total cases = n(E)/n(S)

where favorable cases are the elementary events who belong to E, and total cases are size of sample space.

For two events A and B, by chain rule, we have:

P(A∩B) = P(B)P(A|B) = P(A)P(A|B)

How to find the conditional probability:

Suppose that there are two events A and B. Then suppose the conditional probability are:

P(A|B) = probability of occurrence of A given B has already occurred.

P(B|A) = probability of occurrence of B given A has already occurred.

We can then use the chain rule to find them, or Bayes theorem also helps in finding these probabilities.

We are given the table of joint relative frequency:

We take events as A, A' and B and B'

Important probabilities which will be used are evaluated as:

P(A) = n(A)/n(S) = 150/1200 = 1/8

P(B) = n(B)/n(S) = 250/1200 = 5/24

P(A') = 1 - P(A) = 7/8

P(B') = 1 - P(B) = 1 - 5/24 = 19/24

P(A∩B) = n(A∩B) / n(S) = 40/1200 = 1/30

P(A'∩B') = n(A'∩B') / n(S) = 840/1200 = 7/10

P(A'∩B) = n(A'∩B) / n(S) = 210/1200 = 7/40

Evaluating probabilities of choices given, we get:

Case 1: E = A random selected student who owns skateboard is freshmen

P(E) = ?

P(E) = P(B|A) = P(A∩B) / P(A) = 1/30 ÷ 1/8 = 4/15

Case 2: E = A random selected student who is freshmen owns skateboard:

P(E) = P(A|B) = P(A∩B) / P(B) = 1/30 ÷ 5/24 = 4/25

Case 3: E = A random selected student who doesn't owns skateboard is freshmen

P(E) = P(B|A') = P(A'∩B) / P(A') = 7/40 ÷ 19/24 = 21/95

Case 4: E = A randomly selected student who doesn't owns skateboard is not freshmen

P(E) = P(B'|A') = P(A'∩B') / P(A') = 7/10 ÷ 19/24 = 84/95

So, the least probability is for second case.

Question - Seth is analyzing number of students in class and high school who own skateboards. He puts the data in table shown. Given information in table, which event is least likely?

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0%.

The area of a regular hexagon is given by A = (3√3/2)s2, where s is the length of one side of the hexagon. To calculate the percent of the area of the original hexagon that was removed, we need to calculate the area of the dodecagon and subtract it from the area of the hexagon.

The area of a regular dodecagon is given by A = 3(3 + 2√3)s2, where s is the length of one side of the dodecagon.

Let's assume that the side length of the original hexagon is s, and the side length of the resulting dodecagon is sd. Since each of the isosceles triangles removed has base length of s and height of s/2, we can find the side length of the dodecagon as sd = √3s.

Substituting this into the area formula for the dodecagon, we get:
Ad = 3(3 + 2√3)sd2

Ad = 3(3 + 2√3) (√3s)2

Ad = 3(3 + 2√3)(3s2)

Ad = 27s2

Therefore, the area of the dodecagon is 27 times the area of the original hexagon.

The percent of the area of the original hexagon that was removed is given by the following formula:
Percent removed = 100 x (Ahex - Adod) / Ahex

Percent removed = 100 x (Ahex - 27Ahex) / Ahex

Percent removed = 100 x (1 - 27) / 1

Percent removed = 100 x (-26) / 1

Percent removed = -2600 / 1

Percent removed = -2600%

Since the percent of the area of the original hexagon that was removed cannot be negative, the correct answer is 0%.

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The appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."

What is variability?

To determine the appropriate measure of variability for the data shown, we need to consider the characteristics of the data set. Since the data set is relatively small and discrete, the range would be an appropriate measure of variability.

To calculate the range, we subtract the smallest value from the largest value:

Largest value: 58

Smallest value: 10

Range = Largest value - Smallest value = 58 - 10 = 48

Therefore, the appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."

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Answer:

There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).

Step-by-step explanation:

The dimensions of the rectangle are 6 ft by 5.5 ft, and n = 6.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

We know that the area of a rectangle is given by:

Area = Length x Width

Since the problem does not specify the shape of the rectangle, we cannot assume that it is a square. Therefore, we need to find two numbers whose product is 33.

The factors of 33 are 1, 3, 11, and 33. None of these factors is equal to 3, so we cannot simply multiply 3 by a factor of 33 to get the length of the rectangle. Therefore, we need to use a different approach.

One way to find two numbers whose product is 33 is to start with the square root of 33 and round up and down to the nearest integer. The two resulting integers will be close to the factors of 33 and will multiply to give 33.

The square root of 33 is approximately 5.74. Rounding up and down to the nearest integer gives:

Length = 6 ft

Width = 33 ÷ 6 = 5.5 ft (approximately)

The product of these two numbers is:

6 ft x 5.5 ft ≈ 33 sq ft

Therefore, the dimensions of the rectangle are 6 ft by 5.5 ft, and n = 6.

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