In ΔABC, the measure of ∠C=90°, the measure of ∠A=5°, and BC = 3 feet. Find the length of CA to the nearest tenth of a foot

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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The length of the arc intercepted by a central angle of 230° on a circle with a radius of 5 feet is approximately 4.02 feet.

To find the length of the arc, denoted as s, on a circle with radius r intercepted by a central angle θ, we can use the formula:

s = (θ/360°) * 2πr

Given:

Radius, r = 5 feet

Central angle, θ = 230°

Substituting the values into the formula, we have:

s = (230°/360°) * 2π * 5

Simplifying the expression:

s = (23/36) * 2π * 5

s = (23/36) * 10π

s = (23/18)π

To round the answer to two decimal places, we can approximate the value of π as 3.14:

s ≈ (23/18) * 3.14

s ≈ 4.02 feet

Therefore, the length of the arc intercepted by a central angle of 230° on a circle with a radius of 5 feet is approximately 4.02 feet.

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The mean absolute deviation (MAD) of the data set, rounded to the nearest tenth, is 5.4 bags of caramel corn.

To calculate the mean absolute deviation, we first find the mean of the data set by adding up all the values and dividing by the total number of nights: (16 + 23 + 32 + 24 + 19 + 27 + 18) / 7 = 19.7 bags.

Next, we find the absolute deviation for each night by subtracting the mean from each data point and taking the absolute value of the difference: |16 - 19.7| = 3.7, |23 - 19.7| = 3.3, |32 - 19.7| = 12.3, |24 - 19.7| = 4.3, |19 - 19.7| = 0.7, |27 - 19.7| = 7.3, |18 - 19.7| = 1.7.

We then calculate the average of these absolute deviations by adding them up and dividing by the total number of nights: (3.7 + 3.3 + 12.3 + 4.3 + 0.7 + 7.3 + 1.7) / 7 = 5.4 bags.

Therefore, the mean absolute deviation of this data set is 5.4 bags of caramel corn. This value represents the average distance between each data point and the mean, providing an indication of the variability or dispersion in the number of bags sold each night at the concession stand.

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The required, Wallace performs graphic design work at the Computer Wholesale Warehouse.

Based on the description provided, Wallace performs visual design or graphic design work at the Computer Wholesale Warehouse. He develops visual impressions of products for advertisements and marketing materials. This involves creating visual elements, such as graphics, images, and layouts, to effectively convey messages and promote products.

Wallace's role at the Computer Wholesale Warehouse involves performing visual design work to create captivating visual impressions of products for advertisements and marketing materials, contributing to the overall effectiveness of their promotional efforts.

Thus, the required, Wallace performs graphic design work at the Computer Wholesale Warehouse.

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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​​

Answer

there's 120 members in total

84 not pensioners

Explaination

36÷30% = 120

70% are not pensioners

so 70% × 120 = 84

or you could minus the pensioners from the total 120-36=84

The solution to the problem is that Omar has 16 apples and 14 bananas. the first row satisfy the condition that Omar has four times as many apples as bananas.

To solve this problem, we are given that Omar has four times as many apples as bananas and a total of 30 pieces of fruit.

Let's represent the number of apples as 'a' and the number of bananas as 'b'.

We know that a + b = 30, as the total number of fruits is 30.

From the given information, we are also told that Omar has four times as many apples as bananas, which can be expressed as a = 4b.

To find the values of 'a' and 'b', we can use the table provided:

Types of Fruit  | a | b | a + b |

-------------------------------

16 apples and 14 bananas

20 apples and 10 bananas

22 apples and 8 bananas

24 apples and 6 bananas

We can observe that in the first row, a = 16 and b = 14. Let's check if these values satisfy the given conditions.

If we add the number of apples and bananas, we get 16 + 14 = 30, which matches the total number of fruits given.

We can also verify that a = 4b: 16 = 4 * 14.

Therefore, the solution to the problem is that Omar has 16 apples and 14 bananas.

It's worth noting that the other rows in the table represent different combinations of apples and bananas that sum up to 30, but only the values in the first row satisfy the condition that Omar has four times as many apples as bananas.

In conclusion, Omar has 16 apples and 14 bananas, as per the given information and by checking the values in the table.

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The surface area of the cuboid is 324 cm2, the volume of the cuboid is 360 cm3. And the Area of kite = (5 × 6.403)/2 = 16.008 cm²2a)

Solution: Length of cuboid = l = 12cmWidth of cuboid = b = 6cmHeight of cuboid = h = 5cmSurface area of cuboid = 2 (lb + bh + lh)

By substituting the given values of l, b and h, we get:

Surface area of cuboid = 2 (12 × 6 + 6 × 5 + 12 × 5) = 2 (72 + 30 + 60) = 2 × 162 = 324 cm2∴ The surface area of the cuboid is 324 cm2.Length of diagonal of cuboid, d =√l2 + b2 + h2By substituting the given values of l, b and h, we get:d =√12² + 6² + 5²=√144 + 36 + 25=√205=14.317 cm (approx)∴

The length of diagonal of the cuboid is 14.317 cm.

Volume of cuboid = lbh

By substituting the given values of l, b and h, we get:

Volume of cuboid = 12 × 6 × 5 = 360 cm3∴

The volume of the cuboid is 360 cm3.

(2b) Calculation of the area of a kite when its sides are 8cm and 6cm, and its vertical diagonal is 5cm.Given, sides of the kite are 8cm and 6cm respectively. Vertical diagonal of kite = 5cmArea of kite = (Product of diagonals)/2By using Pythagoras theorem on a kite, we have:

Horizontal diagonal of kite, d =√(52 + 42)=√41 = 6.403 cm

Area of kite = (Product of diagonals)/2

By substituting the given values of vertical diagonal and horizontal diagonal, we get:

Area of kite = (5 × 6.403)/2 = 16.008 cm²2a)

Surface area of cuboid = 2 (lb + bh + lh)

Length of diagonal of cuboid, d =√l2 + b2 + h2Volume of cuboid = lbh2b) Area of kite = (Product of diagonals)/2.

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The approximate form of the expression for all values of t is simply

To find an approximate form of the expression [tex]3(1.25)^{t/5}[/tex] for all values of t, we can simplify it by evaluating the exponent.

First, let's simplify

= [tex]3(1.25)^{t/5}[/tex]

= [tex]3 \sqrt[5]{1.25} ^{t}[/tex]

= 3 * (1.05)ˣ (Assuming x = t)

Now, let's rewrite the expression:

3(1.05)ˣ

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The weight in Newtons that the scale reads when the elevator is in different scenarios can be calculated using the formula W = mg, where W = weight, m=  mass, and g = the acceleration due to gravity.

a. When the elevator is at rest, there is no acceleration, so the weight will be equal to the gravitational force acting on the person. The weight can be calculated as W = mg, where m is the mass of the person (85 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Thus, the weight is W = 85 kg * 9.8 m/s^2.

b. the weight will remain the same as the gravitational force, which is calculated using the formula W = mg.  c. The acceleration is still zero, and the weight will be the same as the gravitational force, calculated using the formula W = mg.

d. We need to consider the net force acting on the person. The net force will be the sum of the gravitational force and the force due to the acceleration. The weight can be calculated as W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the upward acceleration (3 m/s^2).

e. We calculate the weight similarly to case d. The weight is W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the downward acceleration (-4 m/s^2) since it acts in the opposite direction.

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The hour hand will stop at the 9 o'clock position.A clock typically has 12 hours marked on its face, and a complete revolution of the hour hand corresponds to 12 hours or 360 degrees.

To determine where the hour hand will stop after making 3/4 of a revolution clockwise, we need to calculate the angle it will cover in a equation.

A full revolution is 360 degrees, so 3/4 of a revolution is (3/4) * 360 = 270 degrees.

Starting at the 12 o'clock position, the hour hand will move clockwise, and after covering 270 degrees, it will stop at a new position.

To find the location on the clock where the hour hand stops, we divide 270 degrees by the angle covered by each hour mark on the clock face. Since the hour hand moves 30 degrees for each hour (360 degrees divided by 12 hours), we divide 270 by 30:

270 degrees / 30 degrees per hour = 9 hours.

Therefore, the hour hand will stop at the 9 o'clock position.

To summarize, if the hour hand starts at 12 and makes 3/4 of a revolution clockwise, it will stop at the 9 o'clock position.

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Mary's holiday pay for four weeks, including leave loading at 17.5% would be $7,840.

To calculate Mary's holiday pay for 4 weeks, including leave loading at 17.5%, we need to use the following formula:H = W x RWhere, H represents the holiday pay, W represents the weeks worked, and R represents the rate of holiday pay as a percentage of the gross earnings.So, we can start by calculating Mary's gross earnings for four weeks:Gross Earnings = Weekly Earnings x Weeks WorkedGross Earnings = $800 x 4Gross Earnings = $3,200Next, we need to calculate Mary's leave loading at 17.5%:Leave Loading = Gross Earnings x 17.5%Leave Loading = $3,200 x 17.5%Leave Loading = $560Finally, we can calculate Mary's holiday pay using the formula:H = W x RHoliday Pay = Gross Earnings + Leave LoadingHoliday Pay = $3,200 + $560Holiday Pay = $3,760Therefore, Mary's holiday pay for 4 weeks, including leave loading at 17.5% would be $7,840.

To calculate Mary's holiday pay for 4 weeks, including leave loading at 17.5%, we need to use the following formula:H = W x RWhere, H represents the holiday pay, W represents the weeks worked, and R represents the rate of holiday pay as a percentage of the gross earnings.So, we can start by calculating Mary's gross earnings for four weeks:Gross Earnings = Weekly Earnings x Weeks WorkedGross Earnings = $800 x 4Gross Earnings = $3,200Next, we need to calculate Mary's leave loading at 17.5%:Leave Loading = Gross Earnings x 17.5%Leave Loading = $3,200 x 17.5%Leave Loading = $560Finally, we can calculate Mary's holiday pay using the formula:H = W x RHoliday Pay = Gross Earnings + Leave LoadingHoliday Pay = $3,200 + $560Holiday Pay = $3,760Therefore, Mary's holiday pay for 4 weeks, including leave loading at 17.5% would be $7,840.

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the ball will be in the air for approximately 1.34 seconds before it reaches the ground.

To determine the time the ball is in the air, we can use the given gravity equation -16t^2 + subzero (initial height), where t represents time and subzero represents the initial height of the ball. In this case, the initial height is 45 ft above the ground.Setting up the equation, we have:

-16t^2 + 45 = 0

To solve for t, we need to isolate t on one side of the equation. Rearranging the equation, we get:

16t^2 = 45

Dividing both sides by 16, we have:

t^2 = 45/16

Taking the square root of both sides, we find:

t = √(45/16)

Evaluating the square root, we get:

t ≈ 1.34 seconds

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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

Answer:

The correct answer is:

C.) 3000(1.035^(1/52))^t

This expression represents the equivalent exponential expression that identifies the weekly growth rate of the population. The exponent 1/52 represents the conversion from years to weeks, as there are 52 weeks in a year.

Step-by-step explanation:

The logarithm base 12 can be expressed as log12 or in exponential form as 12^x = y, where x is the exponent and y is the result.

The logarithm function is the inverse of exponentiation. It represents the exponent to which a given base (in this case, 12) must be raised to obtain a certain value. There are four different ways to express log12:

Logarithmic form: log12(y) - This notation indicates that the logarithm base 12 is being applied to a value y.

Exponential form: 12^x = y - In this form, the base 12 is raised to an exponent x to produce a value y.

Fractional exponent form: y^(1/12) - The fractional exponent represents the root of y with a base of 12. It is equivalent to log12(y).

Common logarithm form: log(y) / log(12) - If the logarithm base 12 function is not directly available, we can use the common logarithm (base 10) or any other logarithmic base and apply the change of base formula. The result is the logarithm of y divided by the logarithm of 12.

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To build the frame of the rectangle long jump pit with a length of 9.54 meters and a width of 2.75 meters, a total of 24.58 meters of wood is needed.

The frame of the rectangle consists of four sides, two of which are the length and two are the width. To determine the amount of wood needed, we calculate the perimeter of the rectangle.

The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width.

Substituting the given values, we have P = 2(9.54) + 2(2.75) = 19.08 + 5.50 = 24.58 meters.

Therefore, to build the frame of the rectangle long jump pit, a total of 24.58 meters of wood is needed.

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To calculate the number of cones that need to be sold in order to break even, we need to use the formula, Break-even point = Fixed costs / (Selling price per unit - Variable cost per unit).

Here, the fixed cost is the cost of the freezer which is $200. The variable cost per unit is the cost of making each single-scoop ice cream cone which is $0.45. The selling price per unit is $1.25.Substituting the values in the formula, we get, Break-even point = $200 / ($1.25 - $0.45) = $200 / $0.8 = 250 cones Therefore, 250 cones need to be sold in order to break even.

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The value of the given expression is approximately 71.31.

[tex]$$75 - 12(20 ÷ 2.5) ÷ 26$$[/tex]

The Order of Operations states that the sequence of steps in which we carry out the operations of a given problem.

So, we follow the Order of Operations to solve this expression.

Firstly, we will evaluate the parentheses:

[tex]$$20 ÷ 2.5 = 8$$[/tex]

Now, the given expression becomes:

[tex]$$75 - 12 × 8 ÷ 26$$[/tex]

Then, we will evaluate multiplication and division in order from left to right.

12 × 8 = 96

So, the given expression becomes:

[tex]$$75 - 96 ÷ 26$$[/tex]

Evaluating division, we get:

[tex]$$75 - 3.6923$$[/tex]

Now, we will add and subtract from left to right.

[tex]75 − 3.6923 ≈ 71.31[/tex]

Therefore, the value of the given expression is approximately 71.31.

So, the required  is approximately 71.31.

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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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The question provides that the blades of a ceiling fan rotate around a fixed axis and begin to rotate with a constant angular acceleration such that they are rotating at 10 revolutions per second after a certain period of time.

After 60 turns, the fan will be rotating at 15 revolutions per second.

Solution:The given data is:Initial angular speed, ω₁ = 0 (since they start from rest)

Final angular speed, ω₂ = 15 revolutions/sec

Angular acceleration, α = constant

Number of revolutions for the first part, n₁ = 60

Number of revolutions for the second part, n₂ = (total revolutions) - (n₁) = (60 + 10) - 60 = 10 revolutions

Using the formula for the angular velocity, ω = ω₀ + αt

and the formula for the number of revolutions, n = ωt / 2π

We can find out the time required to reach a final speed of 15 rev/s as follows:15 = 0 + αt ⇒ t = 15 / α

The total time required to reach a speed of 15 rev/s would be the sum of the time required to reach a speed of 10 rev/s and the time required to reach 15 rev/s.t = t₁ + t₂ ⇒ t₂ = t - t₁

We can find the value of t₁ from the formula for the number of revolutions during the first part of the motion as follows:n₁ = ω₁t₁ / 2π0 = αt₁² / 2 + ω₁t₁ / 2π ⇒ t₁ = 0

Using the formula for the number of revolutions, we can find the value of t₂ as follows:n₂ = (ω₁t₂ + 1/2 αt₂²) / 2π ⇒ t₂ = 20/α

The value of α can be found by equating the two formulas for t₂ obtained above:

20/α = 15 / α + t₁⇒ α = 100 / 3 rad/s²

We can now substitute this value in the formulas for t and t₂ to find the times required to reach speeds of 10 and 15 rev/s respectively.t₁ = 0 s, t₂ = 60 / 3 = 20 s

Answer: The time required for the blades of the ceiling fan to rotate with a constant angular acceleration before rotating at 10 revolutions per second is 0 seconds and the time required to reach a speed of 15 revolutions per second is 20 seconds.

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To find the value of x in the given problem, we can start by calculating the area of the rectangular box. The area of a rectangular box is given by the formula A = 2lw + 2lh + 2wh, where l represents the length, w represents the width, and h represents the height. In this case, the area is given as 29,946 in².

The first step is to substitute the given values into the formula:

29,946 = 2(x)(5x - 1) + 2(x)(2x + 3) + 2(5x - 1)(2x + 3).

Next, we simplify the equation and distribute the terms:

29,946 = 2(5x² - x) + 2(2x² + 3x) + 2(10x² + 15x - 2x - 3).

After combining like terms, we have:

29,946 = 10x² - 2x + 4x² + 6x + 20x² + 30x - 4x - 6.

Combining similar terms further, we get:

29,946 = 34x² + 40x - 6.

Now, we can rearrange the equation and set it equal to zero:

34x² + 40x - 29,946 = 0.

To solve this quadratic equation, we can either factor it or use the quadratic formula. However, since the equation is not easily factorable, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a).

By substituting the values a = 34, b = 40, and c = -29,946 into the quadratic formula, we can find the two possible values of x. However, since we are looking for a real-world length, we can discard any negative or non-real solutions.

After solving the equation, we find that x is approximately equal to 24.4 or x ≈ -29.36. Since negative values are not meaningful in the context of length, we can conclude that the value of x for which the rectangular box has the given area of 29,946 in² is approximately 24.4 inches.

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The node(s) with the highest degree will have the highest integer value in the dictionary.To determine the node(s) with the highest degree in a graph, a dictionary can be used to store the node_id as the key and the node degree as the value.  

To find the node(s) with the highest degree in a graph, we need to calculate the degree of each node and store the results in a dictionary. The dictionary will have the node_id as the key and the node degree as the value. The degree of a node in a graph is the number of edges connected to that node. By iterating through each node in the graph and counting the number of edges, we can determine the degree of each node. After calculating the degrees of all nodes and storing them in the dictionary, we can find the maximum degree value in the dictionary. This value represents the highest degree among all nodes in the graph. Next, we can extract all the nodes from the dictionary that have this maximum degree value. These nodes will be the ones with the highest degree in the graph. In case of a tie where multiple nodes have the same highest degree, the dictionary will contain multiple key-value pairs with the same maximum degree value. Therefore, the returned result will be a dictionary with the node_id(s) as the key(s) and the highest degree as the value.

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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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The equation represents a line that is perpendicular to the line represented by 2x − y = 7 is y = −(1/2)x + b

The equation represents a line that is perpendicular to the line represented by 2x − y = 7 is y = 2x + b.

Explanation: The given equation of line is 2x − y = 7.

We can rearrange the given equation of line in slope-intercept form, y = mx + b ,

where m is the slope of the line and b is the y-intercept of the line.

Rewrite the given equation of line, 2x − y = 7, in slope-intercept form:

First, add  y  to both sides of the equation to isolate the variable y:

2x − y + y = 7 + y

Simplify to get: 2x = y + 7

Then, subtract 7 from both sides to isolate y.

So, 2x − 7 = y or y = 2x − 7

We now have the slope-intercept form, where m = 2 is the slope and b = −7 is the y-intercept of the line.

Thus, the slope of the line 2x − y = 7 is m = 2.

Now, to find the equation of line that is perpendicular to 2x − y = 7, we need to flip the sign of the slope and switch the places of m and n (as the product of slopes of two perpendicular lines is −1).

Therefore, the slope of the line that is perpendicular to the line 2x − y = 7 is m = −1/2 (flip the sign of the slope) and

the equation of the line can be written as: y = −(1/2)x + b.

So, the answer is: The equation represents a line that is perpendicular to the line represented by 2x − y = 7 is y = −(1/2)x + b.

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The problem requires adding two measurements in different units, 2 ft 5 in and 9 in. We need to determine the sum of these measurements.

To add the given measurements, we should first convert them to a consistent unit. In this case, we will convert everything to inches since the second measurement is already in inches.

1 foot is equal to 12 inches, so 2 ft is equal to 2 * 12 = 24 inches. Therefore, 2 ft 5 in can be written as 24 in + 5 in. Adding 24 in and 5 in, we get 29 in. Thus, the sum of 2 ft 5 in and 9 in is 29 inches. In conclusion, when we add 2 ft 5 in and 9 in, the result is 29 inches.

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Based on the above, the length of the arch should be approximately 7.85 meters.

To know the length of the arch, one need to calculate the circumference of the semicircle.

The circumference of a full circle is: C = 2πr

Note that the semicircle is (180°), so one need to divide the circumference by 2 to get the length of the arch:

Length of the arch = C/2 = (2πr)/2 = πr

Given the radius (r) of 2.5m, one need to substitute the value into the formula:

Length of the arch = π × 2.5

= 3.14 × 2.5

=7.85 meters

Therefore, the architect should build the arch with a length of about 7.85 meters.

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An architect designs the main arch of the nave of a church in the shape of a semicircle (180°), with a radius of 2.5m. How long should that arch be built?

To solve the given problem we have to add the quantities of blue and yellow paint that were used by Gunther to make the mural.We are given that:Gunther used 3 3/5 pints of blue paint and 2 1/10 pints of yellow paint to make a mural.To add these two quantities we need to find a common denominator.

Here, the common denominator is 10.As such, we have to convert the mixed numbers to improper fractions.3 3/5 = (3 × 5 + 3)/5 = 18/5 2 1/10 = (2 × 10 + 1)/10 = 21/10Now, we can add the two fractions to get the total amount of paint used:18/5 + 21/10 = (36 + 21)/10 = 57/10 Therefore, Gunther used a total of 57/10 pints of paint to make the mural.Now, let's simplify this answer.

We can simplify the fraction by dividing both the numerator and denominator by the greatest common factor of 57 and 10, which is 1.57/10 = 5.7Thus, Gunther used 5.7 pints of paint to make the mural.In conclusion, Gunther used 3 3/5 pints of blue paint and 2 1/10 pints of yellow paint, or a total of 5.7 pints of paint to make the mural.

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Answer:

I believe it's A

Step-by-step explanation:

In 15 minutes, a water pump capable of pumping 13.2 gallons of water per minute will remove a total of 198 gallons of water from the pool.

If a water pump can pump 13.2 gallons of water in a pool every minute, we can calculate the amount of water it will remove in 15 minutes by multiplying the pumping rate by the duration. Therefore, 13.2 gallons/minute x 15 minutes = 198 gallons. During the 15-minute period, the water pump will continue to operate at a constant rate, removing water from the pool. Each minute, 13.2 gallons of water will be pumped out. When we multiply this rate by the duration of 15 minutes, we find that a total of 198 gallons of water will be removed from the pool. It's important to note that this calculation assumes a constant pumping rate without any interruptions or changes in efficiency.

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