A 2-column table with 6 rows. Column 1 is labeled Sample with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Sample Mean with entries 16. 8, 12. 3, 19. 0, 17. 5, 18. 2, 17. 5. Looking at the means of the samples, which of these values is least likely to be the mean of the population the samples were taken from? 12. 3 18. 4 19. 0 19. 5.

Answer:

Step-by-step explanation:

D)

[tex]\frac{4\sqrt{b} }{\sqrt{3}-b }[/tex]                         > in order to get rid of root on bottom like this, you

                                  need to multiply top and bottom by conjugate

                                  √3 +b

[tex]=\frac{4\sqrt{b} }{\sqrt{3}-b }\frac{\sqrt{3}+b}{\sqrt{3}+b}[/tex]              > Distribute on top and FOIL bottom

[tex]=\frac{4\sqrt{3b}+4b\sqrt{b} }{3 -b^{2} }[/tex]               >This is simplified, you cannot combine anything else

E)

[tex]\frac{3\sqrt{a^{2} } } {\sqrt{3} } / 2a^{\frac{3}{2} }[/tex]                    >√a² = a

[tex]=\frac{3a } {\sqrt{3} } / 2a^{\frac{3}{2} }[/tex]                    >Division of fraction keep change flip

[tex]=\frac{3a } {\sqrt{3} } * \frac{1}{2a^{\frac{3}{2}} }[/tex]                  >Because 2a is not in parenthesis 3/2 exp.

                                     is only for a

[tex]=\frac{3a } {\sqrt{3} } * \frac{1}{2\sqrt{a^{3} } }[/tex]              > You can make 1 set of a² so 1 comes out but 1 stays

[tex]=\frac{3a } {\sqrt{3} } * \frac{1}{2a\sqrt{a } }[/tex]              >put like items under root

[tex]=\frac{3a } {2a\sqrt{3a} }[/tex]                     >multiply top and bottom by root

[tex]=\frac{3a } {2a\sqrt{3a} }*\frac{\sqrt{3a}}{\sqrt{3a}}[/tex]             >multiply

[tex]=\frac{3a\sqrt{3a} } {2a(3a)} }[/tex]                       >3a cancels

[tex]=\frac{\sqrt{3a} } {2a} }[/tex]                           >This is simplified

Three minutes ago, Sergio's water tank had approximately 12 gallons of water before the crack started leaking at a rate of 2 gallons per minute.

Based on the given information, we know that the current water level in the tank is 6 gallons. The leak in the tank is causing a loss of 2 gallons per minute. To determine the water level three minutes ago, we need to calculate the amount of water that was lost during that time.

Since the leak is causing a loss of 2 gallons per minute, we can multiply the rate of leakage by the number of minutes, which in this case is 3. So, 2 gallons per minute multiplied by 3 minutes gives us a loss of 6 gallons during this period.

To find the water level three minutes ago, we need to subtract the amount lost from the current water level. Starting with the current water level of 6 gallons and subtracting the 6 gallons lost, we find that three minutes ago, the tank had approximately 12 gallons of water. Therefore, the initial water level in Sergio's tank three minutes ago was approximately 12 gallons before the crack started leaking.

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Answer:

[tex] \frac{100}{360} = \frac{l}{25.2\pi} [/tex]

[tex]l = \frac{5}{18} (25.2\pi) = 7\pi[/tex]

The exact length of the arc is 7π cm.

The line of best fit is a straight line that best fits the scattered data points on a scatterplot. It is represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.

In this particular case, the equation of the line of best fit is y = -6x + 97, where x represents the number of absences and y represents the final grade.

This means that for every additional absence a student has, their final grade is expected to decrease by 6 points. The y-intercept of 97 means that if a student had zero absences, their predicted final grade would be 97.

It is important to note that the line of best fit is a prediction, and not a definitive statement about the relationship between the variables. While it can provide some insight into the relationship between the number of absences and final grade, there may be other factors that are not taken into account by the model.

Additionally, the equation of the line of best fit is only valid within the range of the data used to create the model. Extrapolating beyond this range may not produce accurate predictions.

Overall, the line of best fit is a useful tool for analyzing relationships between variables, but it should be used with caution and in conjunction with other analyses to get a complete understanding of the relationship between variables.

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Answer:

  27

Step-by-step explanation:

You want to know the ACT composite test score for the 87.49th percentile, given the ACT scores have a mean of 21.0 and a standard deviation of 5.2.

The Z-table in the first attachment shows you the Z-value of the 87.49th percentile is 1.10+0.05 = 1.15.

The corresponding score is ...

  X = μ +σZ

  X = 21.0 +5.2·1.15 ≈ 27

A learner must earn a score of 27 to be at the 87.49th percentile on the ACT composite test.

<95141404393>

The given options are 1.7 cm, 71, 21, 1.7 cm, 2.2 cm, 4.3 cm, 53, 377, 2.1 cm, 42, 3.2 cm, 3.8 cm, 3.6 cm, 2.9 cm, 2.5 cm, 34, and 8 cm.

The summary of the answer is that the length of the side is 2.2 cm.

In trigonometry, it is common to use the concept of a right triangle to relate the lengths of its sides with the trigonometric functions. However, without additional context or information about the triangle or the specific problem, it is not possible to determine the length of the side accurately.

Among the given options, the length of the side closest to 2.2 cm is 2.2 cm itself. Therefore, based on the options provided, we can conclude that the length of the side is 2.2 cm. However, it is important to note that without further information or context, this is an assumption based solely on the given options and may not be the correct answer in a different context or problem.

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Given, Brad's dinner bill, including a 16% tip, is $10.44. We need to find the amount of the bill before the tip.Let the amount of the bill before the tip be x.So, the bill amount including the tip of 16% will be x + (16/100)x or (116/100)x.

This is because, if x is the bill amount, the tip is 16% of x, which is (16/100)x, then the total bill amount will be x + (16/100)x or (116/100)x.

We know that the bill amount including the tip is $10.44. So,(116/100)x = 10.44=> x = (10.44 × 100)/116= $9 (approx) Therefore, the amount of the bill before the tip is $9. Answer: $9.

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The expression for the perimeter of the quadrilateral is 6x^2 + 14x + 6.

To find the perimeter of the quadrilateral, we need to add up the lengths of all its sides.

The given polynomial expressions represent the lengths of the sides of the quadrilateral:

Side 1: 3x + 5

Side 2: 4x^2 - 7x

Side 3: 5x + 1

Side 4: 2x^2 + 13x

To find the perimeter, we add these side lengths together:

Perimeter = Side 1 + Side 2 + Side 3 + Side 4

= (3x + 5) + (4x^2 - 7x) + (5x + 1) + (2x^2 + 13x)

To simplify, we combine like terms:

Perimeter = 3x + 5 + 4x^2 - 7x + 5x + 1 + 2x^2 + 13x

= (4x^2 + 2x^2) + (3x - 7x + 5x + 13x) + (5 + 1)

= 6x^2 + 14x + 6

Therefore, the expression for the perimeter of the quadrilateral is 6x^2 + 14x + 6.

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The answer is 25. 3. Hence, option B is the correct answer.

Given that the two vertical posts stand side by side. One post is 8 feet tall and the other is 17 feet tall, and a 24-foot post is stretched between the tops of the posts, we need to find how far apart are the posts?We have to use the Pythagorean Theorem to find the distance. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides of the triangle.The figure can be drawn as below:

Here, AB is the 24 foot post, and A and B are the tops of the shorter and the taller post, respectively.

From the figure, we can observe that:

In triangle ABC,

AB² = AC² + BC² (According to Pythagoras theorem)

AC = 8 feet

BC = 17 feet

AB = 24 feet

Substituting the values in the above formula we get,

24² = 8² + 17²

576 = 64 + 289

576 = 353 + BC²

BC² = 576 - 353

BC² = 223

BC = sqrt(223)

The distance between the two posts is the length of the line segment CD, which is BC minus the length of the line segment AD.

Therefore,

Distance between the posts = BC - AD= sqrt(223) - 24= 3.17 ft (approx)

Therefore, the answer is 25. 3. Hence, option B is the correct answer.

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The missing values are:

Original price (OP): Php300.00

Rate of discount (RD): 0.2 or 20%

Based on the given information, we can determine the missing values as follows:

Original price (OP): Let's assume the original price is represented by "x".

Rate of discount (RD): We know that the amount of discount (AD) is Php60.00, and we can calculate the rate of discount as follows:

AD = OP * RD

60 = x * RD

Sale Price (SP): The sale price is calculated by subtracting the amount of discount from the original price:

SP = OP - AD

240 = x - 60

To find the missing values, we need to solve the system of equations formed by the two equations above:

Equation 1: 60 = x * RD

Equation 2: 240 = x - 60

From Equation 2, we can rearrange it to solve for x:

x = 240 + 60

x = 300

Substituting x = 300 into Equation 1, we can solve for the rate of discount:

60 = 300 * RD

RD = 60 / 300

RD = 0.2

Therefore, the missing values are:

Original price (OP): Php300.00

Rate of discount (RD): 0.2 or 20%

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In a fraction, the common denominator refers to the lowest common multiple of the denominators of the fractions. If you use the common multiple from part A as the common denominator, the models in the example will be different and at the same time the same.

A common multiple is the product of two or more factors that are common. In other words, it is a number that is a multiple of two or more integers.

Let's take an example of finding the common multiple of 6 and 8:

The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, ...

The multiples of 8 are: 8, 16, 24, 32, 40, 48, ...

Therefore, the common multiples of 6 and 8 are: 24, 48, 72, 96, 120, 144, ...

The models would be different because the common denominator is the lowest common multiple of the denominators of the fractions. If we use the common multiple as the denominator, the size of the models may change.

Let's take an example:

Suppose we have two fractions, 1/2 and 2/3. The denominators are 2 and 3. The common multiple is 6.

If we use 6 as the common denominator, the fractions become:

1/2 = 3/6 (we multiplied the numerator and denominator by 3)

2/3 = 4/6 (we multiplied the numerator and denominator by 2)

The models would be different because the sizes are based on the denominators of the fractions. If we change the denominator, the size of the model may also change.

The models would be the same because they represent the same fractions.

Even though the size of the model may change, the fractions still represent the same value.

In the above example, 1/2 and 3/6 represent the same value, and 2/3 and 4/6 represent the same value.

Therefore, the models are still representing the same value even though they may be different in size.

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Average seawater salinity = 3.5%100g of salt has been left after seawater has evaporatedThe mass of salt dissolved in 100g of seawater will be 3.5g (since salinity is 3.5%)Let x be the mass of seawater that needs to be evaporated to leave 100g of salt.

According to the law of conservation of mass,Mass of salt in the solution before = Mass of salt in the solution afterTherefore, 100g of salt that has been left after evaporation was originally dissolved in x grams of seawater.

Therefore, the mass of salt in that seawater would have been 3.5% of x.Using the above information, we can write an equation as follows:0.035x = 100g Therefore, about 2857.14 g or 2.85714 kg of seawater needs to have evaporated to leave 100 g of salt.

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The measurement that is more accurate but less precise than 5.3 pounds is 5 pounds.

Accuracy refers to how close a measurement is to the true value, while precision refers to the level of consistency or reproducibility of a measurement.

In this scenario, the scale measured a 4.5-pound brick as weighing 5.3 pounds. Comparing this measurement to the true value, we can say that it is not accurate because it overestimates the weight of the brick. However, it is relatively precise because it provides a specific value (5.3 pounds) rather than a range of values.

To find a measurement that is more accurate but less precise than 5.3 pounds, we look for a value that is closer to the true weight of the brick (4.5 pounds) but still lacks precision. Among the given options, 5 pounds is the closest value to the true weight of the brick, making it more accurate. However, it is less precise because it represents a rounded value without indicating any decimals.

Therefore, among the options provided, 5 pounds is the measurement that is more accurate but less precise than 5.3 pounds.

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By converting -1 2/3 to an improper fraction, we get -5/3. To add these fractions, we need to find a common denominator, which is 6. Adding the fractions gives us 5/6. Therefore, -1 2/3 - (-5/6) is equal to 5/6.

To perform the addition and subtraction of rational numbers, we start by converting -1 2/3 to an improper fraction. We multiply the whole number (-1) by the denominator of the fraction (3), which gives us -3. Adding the result to the numerator (2) gives us -3 + 2 = -1. So, -1 2/3 can be represented as -5/3.

Next, we rewrite the expression as -5/3 - (-5/6). When we subtract a negative number, it is equivalent to adding the positive value. So, -(-5/6) becomes +5/6.

To add fractions, we need a common denominator. In this case, the common denominator is 6. We multiply the numerator and denominator of -5/3 by 2 to get -10/6. Therefore, the expression becomes -10/6 + 5/6.Now that the fractions have the same denominator, we can add the numerators. -10/6 + 5/6 equals -5/6.

Hence, the final result of -1 2/3 - (-5/6) is 5/6.

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The factored form of the expression 12x^4 - 42x^3 - 90x^2 is 6x^2(x - 5)(2x + 3).

The equivalent factored form of the expression 12x^4 - 42x^3 - 90x^2 is 6x^2(x - 5)(2x + 3).

To find the factored form, we need to factor out the greatest common factor (GCF) from the given expression. The GCF of the coefficients 12, 42, and 90 is 6, and the GCF of the variables x^4, x^3, and x^2 is x^2.

Factoring out the GCF, we have:

6x^2(2x^2 - 7x - 15)

Next, we need to factor the quadratic expression within the parentheses. We are looking for two binomials that, when multiplied together, result in 2x^2 - 7x - 15.

The factors can be found by considering two numbers whose product is -30 (the product of the coefficient of x^2, 2, and the constant term, -15) and whose sum is -7 (the coefficient of x, -7).

By trial and error, we can determine that the factors are (2x + 3) and (x - 5).

Thus, the factored form of the expression 12x^4 - 42x^3 - 90x^2 is 6x^2(x - 5)(2x + 3).

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a) The radian measure is 5π radians.

b) The radian measure is (3πr)/2 radians.

To determine the radian measure corresponding to a certain number of orbits in a circular orbit, we need to know the circumference of the orbit.

The circumference of a circle is given by the formula C = 2πr, where C represents the circumference and r represents the radius.

Let's assume the radius of the circular orbit is denoted by "r."

(a) To find the radian measure for 2.5 orbits:

The total angle covered in 2.5 orbits is equivalent to 2.5 times the full circumference of the orbit.

Angle = 2.5 * (2πr) = 5πr

Therefore, the radian measure corresponding to 2.5 orbits is 5π radians.

(b) To find the radian measure for 3/2 orbit:

The total angle covered in 3/2 of an orbit is equivalent to (3/2) times the full circumference of the orbit.

Angle = (3/2) * (2πr) = 3πr/2

Therefore, the radian measure corresponding to 3/2 of an orbit is (3πr)/2 radians.

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The number of pages read in 72 minutes is 144 pages.

When given a table of values, the relationship between the values ​​is often expressed as a rule or an equation. A formula that links the number of pages in a book to the number of minutes it takes to read it is often used in book reviews or book reports.  

Rule relating to the minutes, x, to the number of pages, y

Let us assume that reading x minutes corresponds to y pages. In other words, we want to identify an equation or formula that links the two variables.

The number of pages read in one minute is calculated by dividing the total number of pages by the total time it takes to read them.

y / x = k, where k is the constant of variation, or the number of pages that can be read in one minute. If the number of pages is directly proportional to the number of minutes, then the k value remains constant.

If we solve for y, we get the following:

y = kx

When the minutes equal 72, we will find the number of pages.

We know that k is a constant, so we may use any of the given (x, y) pairs.

The given minute value is x, and we want to find the corresponding page value, y.

Let us assume that 120 pages can be read in 60 minutes.

We may solve for k using this information:120 / 60 = k2 = k

Now that we know k, we may use the equation to determine the number of pages that can be read in 72 minutes:

y = kx

y = 2 * 72y = 144

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Given the information provided, we need to determine the length of the bridge (a) and the distance between the two people.

The person at point Q is 30 meters away from the bridge, and the angle between the bridge and the line of sight from P to Q is 70.9 degrees.

To solve this problem, we can use trigonometry. We can consider the triangle formed by the bridge, point P, and point Q. The angle at point P is 70.9 degrees, and the side opposite to this angle is the length of the bridge (a). The side adjacent to this angle is the distance between the two people.

Using trigonometric functions, we can set up the following equation:

tan(70.9 degrees) = a / 30 meters

By rearranging the equation, we can solve for a:

a = 30 meters * tan(70.9 degrees)

This gives us the length of the bridge.

To find the distance between the two people, we can use the Pythagorean theorem. The distance between the two people is the hypotenuse of the triangle formed by the bridge, point P, and point Q. Using the length of the bridge (a) and the distance from point Q to the bridge (30 meters), we can calculate the distance between the two people using the equation:

Distance = sqrt(a^2 + 30^2)

By substituting the value of a, we can calculate the final answer for the distance between the two people, rounding to two decimal places if necessary.

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The person has completed 14.4 problems in the math review packet, which is 60% of the total 24 problems.

To determine the number of problems completed by the person, we multiply the total number of problems (24) by the percentage completed (60% or 0.60). Mathematically, 24 * 0.60 = 14.4. Therefore, the person has finished 14.4 problems in the math review packet. Since you cannot have a fraction of a problem, we can round down to the nearest whole number, which gives us 14 problems completed. It's worth noting that the person has completed 60% of the packet, indicating that they have more problems left to solve. If they wish to complete the entire packet, they still have 24 - 14 = 10 problems remaining. The completion percentage provides a measure of progress, allowing the person to gauge how much work is left and plan their time accordingly.

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The equation will have all three terms (ax^2+bx+c) if the quadratic equation (x−r)(x+r) is expanded.

When we expand (x−r)(x+r), we get x^2 - r^2. This means that the resulting quadratic equation will have a quadratic term (x^2) and a constant term (-r^2).

However, to have opposite solutions, the constant term (-r^2) should be equal to zero. This implies that r = 0, making the constant term zero.

Therefore, the quadratic equation with opposite solutions, obtained by multiplying (x−r)(x+r), will have a quadratic term (ax^2), a linear term (bx), and a constant term (c) where c = 0.

Hence, the correct answer is option 3: a quadratic term and a linear term only (ax^2+bx).

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Answer:

I believe it's A

Step-by-step explanation:

To calculate a 15% tip for a restaurant bill of $42.40, we multiply the bill amount by 0.15 to find the tip amount. The result will provide the tip amount, which can be added to the bill to get the total amount to pay. Therefore, a 15% tip for a restaurant bill of $42.40 is $6.36.

To calculate a 15% tip, we take 15% of the bill amount. The tip amount is found by multiplying the bill amount by the decimal equivalent of 15%, which is 0.15.

Given the restaurant bill of $42.40, we can find the tip amount by performing the calculation: $42.40 * 0.15 = $6.36.

Therefore, a 15% tip for a restaurant bill of $42.40 is $6.36.

To check if the answer is reasonable, we can consider the percentage amount and the total bill. A 15% tip is generally considered an average or moderate tip amount. Given the bill of $42.40, a tip of $6.36 seems reasonable in relation to the bill total.

However, tipping customs may vary in different regions or based on personal preferences. It is always advisable to consider the overall service quality and local tipping practices when determining an appropriate tip amount.

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y = 5x

This equation implies that each box of cookies costs $5.

To write an equation that models the relationship between the cost, y, of buying boxes of cookies, x, we need the values from the table. Since you haven't provided the specific values in the table, I'll give you an example equation based on a general scenario.

Let's assume that the cost of buying boxes of cookies follows a linear relationship with the number of boxes purchased. In this case, the equation can be written in the form:

y = mx + b

Where:

y represents the cost of buying boxes of cookies.

x represents the number of boxes purchased.

m represents the slope of the line, which indicates the rate of change in the cost per box.

b represents the y-intercept, which is the initial cost when no boxes are purchased.

You would need to substitute the actual values from your table into this equation to create a specific model for your situation. For instance, if the table shows the following data:

Boxes (x) Cost (y)

1            5

2            10

3            15

4            20

We can use these values to find the slope (m) and y-intercept (b) using linear regression techniques. Then, the equation that models this situation would be:

y = 5x

This equation implies that each box of cookies costs $5.

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In the given scenario where x > y > 2, the expressions from least to greatest value are: (x^3y^26)^(-2), (x^2y^5)^(-2), (9xy)^2, and (5x^4y^3)^3.



To determine the order of the expressions from least to greatest value when x > y > 2, we can simplify each expression and compare their values.

1. (x^3y^26)^(-2):

  Simplifying the expression, we have (x^(-6)y^(-52)).

  Since x > y > 2, x^(-6) > 1 and y^(-52) > 1, which means the expression is less than 1.

2. (x^2y^5)^(-2):

  Simplifying, we get (x^(-4)y^(-10)).

  Similar to the previous expression, x^(-4) > 1 and y^(-10) > 1, making this expression also less than 1.

3. (5x^4y^3)^3:

  Simplifying gives (125x^12y^9).

  Since x > y > 2, x^12 > y^12 and y^9 > 2^9, we can conclude that this expression is the greatest.

4. (9xy)^2:

  Simplifying, we have (81x^2y^2).

  Since x > y > 2, 81x^2 > 4x^2 and 81y^2 > 4y^2, this expression is greater than (x^3y^26)^(-2) and (x^2y^5)^(-2), but smaller than (5x^4y^3)^3.

Therefore, the order of the expressions from least to greatest value is:

(x^3y^26)^(-2) < (x^2y^5)^(-2) < (9xy)^2 < (5x^4y^3)^3.

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The average speed of the trip to the recycling plant is approximately 48 km/h.

To find the average speed of the trip to the recycling plant, we need to calculate the total distance traveled and divide it by the total time taken. Let's denote the average speed of the trip there as "x".

On the return trip, Amanda averaged 40 km/h, and it took her 5 hours. Therefore, the distance traveled on the return trip is 40 km/h * 5 hours = 200 km.

Since the distance traveled to the recycling plant is the same as the distance traveled back, the total distance traveled is 2 * 200 km = 400 km.

The total time for the round trip is 4 hours for the trip there and 5 hours for the trip back, which gives a total time of 9 hours.

To find the average speed, we divide the total distance (400 km) by the total time (9 hours): x = 400 km / 9 hours ≈ 44.44 km/h.

Rounding this value to the nearest kilometer, the average speed of the trip to the recycling plant is approximately 48 km/h.

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The simplified ratio is: 3 : 1. This means that for every 3 liters of white paint, 1 liter of red paint is used in the mixture.

To find the ratio of white paint to red paint, we need to compare the amounts of white paint and red paint used. The given information states that mixing pink paint requires 3 liters of white paint and 1 liter of red paint.

The ratio of white paint to red paint can be expressed as:

White : Red

To simplify this ratio to its lowest terms, we need to find the greatest common divisor (GCD) of the two numbers (3 and 1) and divide both numbers by it.

The GCD of 3 and 1 is 1, as there are no common factors other than 1. Therefore, we divide both numbers by 1:

3 ÷ 1 = 3

1 ÷ 1 = 1

The ratio 3 : 1 represents the proportional relationship between white paint and red paint in terms of liters. It indicates that for every 3 liters of white paint, only 1 liter of red paint is needed to achieve the desired mixture.

This ratio is already in its simplest form since the GCD of 3 and 1 is 1, and there are no further common factors to divide both numbers by.

In conclusion, the ratio of white paint to red paint in the mixture is 3 : 1.

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The expressions that represent a 20% discount off the price of an item that originally costs d dollars are A. 0.8d and C. d-0.2d.

A 20% discount off the original price means that the discounted price is equal to 80% (100% - 20%) of the original price. Therefore, we can calculate the discounted price by multiplying the original price (d) by 0.8 (representing 80%).

Expression A (0.8d) represents the discounted price as 80% of the original price (d), so it is correct. Expression C, d-0.2d" represents a 20% discount off the price of an item that originally costs d dollars.

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Full question is:

Select all the expressions below which represent a 20% discount off the price of an item that originally costs d dollars.

A. 0.8d

B. d-0.2

C. d-0.2d

D. 1-0.2d​​

Devika poured out 4.2 ounces of water, which is approximately 35% of the water in the full bottle.

To find out how much water was in the full bottle, we can set up a proportion.

Let x represent the amount of water in the full bottle (in ounces). We know that 4.2 ounces is 35% of x.

We can set up the proportion:

4.2 / x = 35 / 100

To solve for x, we can cross-multiply:

4.2 * 100 = 35 * x

420 = 35x

Dividing both sides of the equation by 35:

420 / 35 = x

12 = x

Therefore, there were approximately 12 ounces of water in the full bottle.

So, Devika estimated that she poured out about 35% of the water in the full bottle, which corresponds to approximately 4.2 ounces.

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An engineer is designing a storage compartment in an aircraft. The compartment's volume is 72 cubic meters. The width is 2 meters longer than the length. The height is 1 meter less than the length. the dimensions of the compartment are 4m × 6m × 3m.

Find the dimensions of the compartment. Solution:The volume of a rectangular prism is given by;[tex]`V= l × w × h`[/tex] Given that the compartment's volume is 72 cubic meters, let's substitute[tex]`V = 72`[/tex]

cubic meters;[tex]`l × w × h = 72`[/tex]

We also know that;[tex]w = l + 2h = l - 1[/tex]

Substituting w and h in terms of l, we get;[tex]`l(l+2)(l-1) = 72`[/tex]Expanding,

we get;[tex]`l(l²-1) + 2(l²-1) = 72`[/tex]

Simplifying, we get;[tex]`l³ + l² - 2l - 74 = 0`[/tex]

We will use trial and error method to find one of the roots,`l= 4`.

By substitution, we get;[tex]w = 4 + 2 = 6m h = 4 - 1 = 3m[/tex]

Thus, the compartment dimensions are 4m × 6m × 3m. The width is 6 meters, the length is 4 meters, and the height is 3 meters.

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