What is 271403 rounded to the neradt hundred thousand

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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To find out how many children and how many adults attended the event, we can set up a system of equations based on the given information.

Let's use the variables c and a to represent the number of children and adults, respectively. The total number of people who attended the event is 100, and the total amount collected at the door is $626. Each child ticket costs $5, and each adult ticket costs $8. By setting up and solving a system of equations, we can determine the values of c and a.

Let c represent the number of children and a represent the number of adults who attended the event. We can set up the following system of equations based on the given information:

Equation 1: c + a = 100 (total number of people who attended the event)

Equation 2: 5c + 8a = 626 (total amount collected at the door)

We can solve this system of equations using various methods such as substitution, elimination, or matrix methods. Here, we'll solve it using the substitution method.

From Equation 1, we have c = 100 - a. Substitute this value into Equation 2:

5(100 - a) + 8a = 626

500 - 5a + 8a = 626

3a = 126

a = 42

Substitute the value of a into Equation 1:

c + 42 = 100

c = 58

Therefore, 58 children and 42 adults attended the event.

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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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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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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 solution of the given system of equations is (2, -10).

The given system of equations is:

y = 4x - 5

We need to solve the system of equations given by

Step 1: We need to substitute

y = 4x - 5 into the second equation.

4x - y = 5 becomes

4x - (4x - 5) = 5

Simplifying the above equation will give us:-

y + 4x - 4x = 5 + 5y = -10

Hence, the solution of the given system of equations is

(x, y) = (2, -10).

Steps 2 and 3 to solve the system of equations are:

Step 2: Substitute

y = 4x - 5 into the second equation. This gives us:

4x - (4x - 5) = 5

Simplifying the above equation will give us:-

y + 4x - 4x = 5 + 5

Step 3: Solve the simplified equation to get the value of y.-

y = 10y = -10

Thus, the solution of the given system of equations is (2, -10).

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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 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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In the function f(x) = 1/x, when x is close to zero, the value of f(x) approaches positive or negative infinity. As x approaches zero from the positive side (x → 0+).

The function f(x) = 1/x becomes increasingly large and approaches positive infinity. This is because dividing a positive number by a very small positive number yields a very large positive result.

On the other hand, as x approaches zero from the negative side (x → 0-), the function f(x) = 1/x also becomes increasingly large but in the negative direction, approaching negative infinity. Dividing a negative number by a very small negative number yields a very large negative result.

However, it is important to note that the function f(x) = 1/x is undefined at x = 0 since division by zero is undefined in mathematics. Therefore, we say that the function has a vertical asymptote at x = 0, meaning that the function gets arbitrarily close to positive or negative infinity as x approaches zero, but it never actually reaches zero. In conclusion, when x is close to zero in the function f(x) = 1/x, the value of f(x) could be positive or negative infinity depending on whether x approaches zero from the positive or negative side, respectively.

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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.

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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 graph that represents the ordered pairs of the first five terms of the patterns from the table is the line graph.

The graph that represents the ordered pairs of the first five terms of the patterns from the table is the **line graph**.

The x-values in the table are increasing by 3 each time, while the y-values are increasing by 6 each time. This means that the ordered pairs are forming a straight line. The line graph is the only graph that shows a straight line.

The other graphs are either curves or not straight lines. The **scatter plot** shows a cloud of points that are not evenly distributed. The **bar graph** shows a series of vertical bars that are not evenly spaced. The **histogram** shows a series of horizontal bars that are not evenly spaced.

Here is a table of the first five terms of the patterns from the table, along with the corresponding ordered pairs:

X | Y | Ordered Pair

-- | -- | --

0 | 0 | (0, 0)

3 | 6 | (3, 6)

6 | 12 | (6, 12)

9 | 18 | (9, 18)

12 | 24 | (12, 24)

As you can see, the ordered pairs form a straight line.

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The division expression is 7 divided into 3 which can be represented in unit form as follows; 7 ÷ 3 = 2 R1, this means that 7 divided by 3 equals 2, with a remainder of 1.

The remainder is the value left after an integer has been divided by a divisor, such as the number left over after a long division of 7 ÷ 3. Therefore, the value of circle plus circle is given by the formula: $$\text{Circle plus Circle} = πr_1^2 + πr_2^2$$ where r1 and r2 are the radii of the two circles respectively. If the values of the radii are provided, then we can substitute them in the above formula to find the value of circle plus circle.

The area of a circle is given by the formula A = πr² where A is the area of the circle and r is the radius. Therefore, the formula for the value of circle plus circle is given by Circle plus Circle = πr1² + πr2² where r1 and r2 are the radii of the two circles respectively. As we already know that a circle is a geometric figure having no end. It has many properties. One of its properties is that its area can be measured. When we talk about the area of a circle, we are referring to the region enclosed by it. The area of a circle is given by the formula: A = πr², where A is the area of the circle and r is its radius. The symbol π represents the constant pi, which is approximately equal to 3.14. Therefore, the area of a circle is proportional to the square of its radius. If we have two circles with radii r1 and r2, then the area of the first circle is given by A1 = πr1², and the area of the second circle is given by A2 = πr2².

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The approximate radius of the bike wheel is 11.0 inches.

If a bike wheel covers a total of 69.08 inches after one complete rotation, we can use the formula for the circumference of a circle to find the approximate radius of the bike wheel.

Circumference = 2piradius

where pi is approximately 3.14.

We are given that the circumference is 69.08 inches, so we can plug in these values and solve for the radius:

69.08 = 23.14radius

Dividing both sides by 2*pi, we get:

radius = 69.08 / (2*3.14) ≈ 11.0 inches

Therefore, the approximate radius of the bike wheel is 11.0 inches.

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Nicholas scooped a few gumballs into his bag and found that it weighed 0.76 pounds.

Nicholas's bag of gumballs weighs 0.76 pounds. This weight includes the combined mass of the gumballs and the bag itself. The weight measurement indicates the force exerted by the bag due to the gravitational pull of the Earth. To determine the weight of just the gumballs, Nicholas would need to subtract the weight of the bag from the total weight.

To find the weight of the bag, Nicholas could use a scale or balance to measure an empty bag of the same type. Once he knows the weight of the empty bag, he can subtract that weight from the total weight of the bag with the gumballs. The result will give him the weight of the gumballs alone.

It's important to note that the weight of the gumballs may vary depending on their size, density, and the material of the bag. Different types of gumballs may have different weights. To get an accurate measurement, Nicholas should use a precise weighing instrument and account for any external factors that could affect the weight, such as moisture or contaminants.

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The solutions to the equation f(x) = g(x) are x = 1/65. Hence, this is our final answer.

We have the following functions to graph:f(x)=−32x and ​g(x)=(12)x−1.Similarly, to graph the above functions we would require a table of values. For this we set x = −2, −1, 0, 1, 2 and solve for f(x) and g(x):x -2 -1 0 1 2f(x) 192 96 0 −32 −64g(x) 0.25 0.5 1 2 4Once we get the table of values, we can then graph the functions on the same coordinate plane.

We have the graph as below:Graph of f(x) = −32x and g(x) = (1/2)x−1Now to get the solutions to the equation f(x) = g(x), we equate the two expressions:−32x = (1/2)x−1Multiplying both sides by 2, we get:-64x = x - 1Collecting like terms, we get:-65x = -1Dividing both sides by -65, we get:x = 1/65

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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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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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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 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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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:

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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See text below

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?

Jordan's pet grooming business has a monthly cost function of C - $12p+ $2100. The monthly cost function for Jordan's pet-grooming company is C - $12p+ $2100.

His Revenue is given by the function R - $62p, where C is the total costper month, R is the total revenue he receives each month and x is the number of pets he grooms in a month. We need to find out how many pets must he groom each month to break even.Let's set revenue equal to costs, and solve for p.R = C62p = 12p + 2100p = (12p + 2100) / 62p = 0.1935p ≈ 19.35 petsJordan must groom approximately 19.35 pets each month to break even. The nearest whole number is 19.

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Answer:

I believe it's A

Step-by-step explanation:

The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.

A cylinder's surface area is the overall area or region that the shape's surface covers. A cylinder's total surface area comprises both the area of the curved surface and the area of the two flat surfaces since there are two flat surfaces and one curved surface.

The formula for a particular cylinder's total surface area is as follows:

TSA = 2πr (h + r)

Given that;

One link in a chain was made from a cylinder that has a radius of 2.5 cm and a height of 22 cm.

Hence, The plastic coating would be needed to coat the surface of the chain is,

2 × 3.14 × 2.5 × 22

= 345.4 cm²

So, The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.

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The correct representation of the equation "z minus 6 = 1.4" in words is "The difference of a number and z is the same as one and four-tenths."

The equation "z minus 6 = 1.4" can be represented in words as "The difference of a number and z is the same as one and four-tenths." This representation accurately conveys the meaning of the equation.

Let's break down the equation to understand its components. "z minus 6" represents the difference between the number z and 6. The equal sign indicates that this difference is equal to "1.4", which means one and four-tenths.

Now let's analyze the answer choices:

"The difference of a number and z is the same as one and four-tenths." This choice correctly represents the equation, expressing that the difference between a number and z is equal to 1.4.

"A number subtracted from one and four-tenths is equal to six." This choice represents a different equation, where a number is subtracted from 1.4, resulting in six. It does not match the original equation.

"Six less than a number is the same as one and four-tenths." This choice represents a different equation, where six is subtracted from a number, resulting in 1.4. It does not match the original equation.

"Six decreased by a number is equal to one and four-tenths." This choice represents a different equation, where six is decreased by a number, resulting in 1.4. It does not match the original equation.

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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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Answer:

y = 1.5x + 4

The slope is 1.5, and the y-intercept is 4.