An airplane is at an elevation of 12000 ft in air. it starts to descend at a rate of 450 feet per minute. a. write and evaluate an expression to show how far the plane will descend in 7 minutes. b. if the airplane, then starts to ascend at a rate of 300 ft/min what would be the airplane's final elevation after 3 minutes.

Answers

Answer 1

Write and evaluate an expression to show how far the plane will descend in 7 minutes. The airplane starts to descend at a rate of 450 feet per minute. After 7 minutes, the airplane will have descended by 450 x 7 = 3,150 feet.

Therefore, the expression for how far the plane will descend in 7 minutes is 450 x 7 = 3,150 ft. If the airplane then starts to ascend at a rate of 300 ft/min what would be the airplane's final elevation after 3 minutes? The airplane started at an elevation of 12,000 feet. It then descended 3,150 feet to an elevation of 8,850 feet (12,000 - 3,150 = 8,850).Next, the airplane starts to ascend at a rate of 300 ft/min for 3 minutes. Therefore, the airplane ascends by 300 x 3 = 900 feet. Finally, the airplane's final elevation would be 8,850 + 900 = 9,750 feet. Given the elevation of the airplane in air as 12,000 ft, it starts to descend at a rate of 450 feet per minute. The question has two parts. The first part is to write and evaluate an expression to show how far the plane will descend in 7 minutes. The second part of the question is to find the airplane's final elevation after 3 minutes if the airplane, then starts to ascend at a rate of 300 ft/min. To find out how far the plane will descend in 7 minutes, we can use the formula D = R * T, where D is the distance, R is the rate, and T is the time. So, the expression for how far the plane will descend in 7 minutes is 450 x 7 = 3,150 ft. Therefore, after 7 minutes, the airplane will have descended by 3,150 feet. To find the final elevation of the airplane after 3 minutes, we have to calculate the elevation of the airplane before it starts ascending. When the airplane starts to descend at a rate of 450 feet per minute, then after 7 minutes it will be at an elevation of 12,000 - 3,150 = 8,850 ft. When the airplane starts ascending, it ascends at a rate of 300 ft/min. So, after 3 minutes, the airplane will have ascended by 3 * 300 = 900 feet. Therefore, the final elevation of the airplane will be 8,850 + 900 = 9,750 feet.

In conclusion, we can say that the airplane will descend by 3,150 feet in 7 minutes. After 7 minutes, the elevation of the airplane will be 8,850 ft. When the airplane starts ascending, it ascends at a rate of 300 ft/min. So, after 3 minutes, the airplane will have ascended by 900 feet, and its final elevation will be 9,750 feet.

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Related Questions



Solve the absolute value inequality -2|x-3| ≤ -16 . Show your work.

Answers

The solution to the absolute value inequality -2|x-3| ≤ -16 is

x ≤ -5 or x ≥ 11.

To solve the absolute value inequality -2|x-3| ≤ -16, we need to isolate the absolute value expression and consider both the positive and negative cases.

Step 1: Remove the negative sign from the inequality by dividing both sides by -2:

|x-3| ≥ 8

Step 2: Consider the positive case:

x-3 ≥ 8

x ≥ 8 + 3

x ≥ 11

Step 3: Consider the negative case:

-(x-3) ≥ 8

-x + 3 ≥ 8

-x ≥ 8 - 3

-x ≥ 5

Step 4: Multiply both sides of the negative case inequality by -1, and reverse the inequality sign:

x ≤ -5

Step 5: Combine the solutions from both cases:

x ≤ -5 or x ≥ 11

Therefore, the solution to the absolute value inequality -2|x-3| ≤ -16 is x ≤ -5 or x ≥ 11.

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Use a calculator to solve the equation 7²ˣ=75 . Round the answer to the nearest hundredth.

Answers

The equation 7²ˣ = 75 and obtain the value of "x" rounded to the nearest hundredth.

To solve the equation 7²ˣ = 75 using a calculator and rounding the answer to the nearest hundredth, you can follow these steps:

1. Enter "7" on the calculator.
2. Press the exponent button (usually "^" or "x^y").
3. Enter the value of "x" on the calculator.
4. Press the equals "=" button.
5. If your calculator has a square root function, you can use it to find the square root of 75. If not, continue to the next step.
6. Divide the result by 7 to isolate the variable "x".
7. Take the logarithm (base 10 or natural logarithm, depending on the calculator) of both sides to solve for "x".
8. Divide the logarithm result by the logarithm of 7 to get the value of "x".
9. Round the value of "x" to the nearest hundredth.

Using these steps, you can solve the equation 7²ˣ = 75 and obtain the value of "x" rounded to the nearest hundredth.

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Here is my question...next one 70 points (promise)!!!...if i pass thankyou!! :)

luke buys a certain brand of cereal that costs $11 per box. luke changes to a super-saving brand of the same size. the equation shows the price, y, as a function of the number of boxes, x, for the new brand.

y = 9x

part a: how many more dollars is the price of a box of luke's original brand of cereal than the price of a box of the super-saving brand? show your work.

part b: how much money does luke save each month with the change in cereal brand if he buys 6 cereal boxes each month? show your work.

Answers

To find the difference in price between Luke's original brand of cereal and the super-saving brand, we need to subtract the price of the super-saving brand from the price of Luke's original brand.

The price of Luke's original brand is $11 per box, and the price of the super-saving brand is given by the equation

y = 9x.

To find the price of the super-saving brand, substitute

x = 1 into the equation:

y = 9(1) = $9.  

So, the price of Luke's original brand is $11 and the price of the super-saving brand is $9. To find the difference, subtract $9 from $11: $11 - $9 = $2.  Therefore, the price of a box of Luke's original brand of cereal is $2 more than the price of a box of the super-saving brand.

To calculate how much money Luke saves each month with the change in cereal brand, we need to find the difference in cost between buying 6 boxes of Luke's original brand and 6 boxes of the super-saving brand. The cost of 6 boxes of Luke's original brand is $11 x 6 = $66.  The cost of 6 boxes of the super-saving brand is $9 x 6 = $54. To find the savings, subtract $54 from $66: $66 - $54 = $12. Therefore, Luke saves $12 each month with the change in cereal brand if he buys 6 cereal boxes each month.

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The table shows the populations of the San Diego and Detroit metropolitan regions. When were the populations of these regions equal? What was that population?

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The populations of the San Diego and Detroit metropolitan regions were equal in the year 1980, and the population of the two regions was about 2,500,000.

According to the table, the populations of San Diego and Detroit metropolitan regions were equal in the year 1980. The population of the two regions was about 2,500,000.

The table below indicates the populations of San Diego and Detroit metropolitan regions from 1970 to 2000. The population of the San Diego metropolitan region in 1980 was 1,753,434, while the population of the Detroit metropolitan region was 1,747,385. In the year 1980, the populations of both metropolitan regions were equal.A metropolitan area is a significant population concentration consisting of a big city and its surrounding area. San Diego and Detroit are both major metropolitan areas with a lot of people living in them.

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a. If m∠BAD=38 and m∠BCD=50 , find ADC . m∠

Answers

To find the measure of angle ADC (m∠ADC), we can use the fact that the sum of the angles in a triangle is 180 degrees.

Given:
m∠BAD = 38 degrees
m∠BCD = 50 degrees

We know that angle BCD and angle BAD are adjacent angles (they share a common side, CD). Therefore, the sum of their measures is 180 degrees:

m∠BCD + m∠BAD = 180 degrees

Substituting the given values:

50 + 38 = 180

88 = 180

To find m∠ADC, we subtract the sum of angles BCD and BAD from 180 degrees:

m∠ADC = 180 - 88
m∠ADC = 92 degrees

The measure of angle ADC (m∠ADC) is 92 degrees.

Given that m∠BAD is 38 degrees and m∠BCD is 50 degrees, we can find the measure of angle ADC (m∠ADC). To do this, we use the fact that the sum of the angles in a triangle is always 180 degrees. In this case, angles BCD and BAD are adjacent angles, meaning they share a common side, CD.

So, we can write the equation m∠BCD + m∠BAD = 180 degrees. Substituting the given values, we get 50 + 38 = 180. Simplifying this equation, we find that 88 = 180. To find m∠ADC, we subtract the sum of angles BCD and BAD from 180 degrees. Thus, m∠ADC = 180 - 88 = 92 degrees. In conclusion, the measure of angle ADC (m∠ADC) is 92 degrees.

The measure of angle ADC (m∠ADC) is 92 degrees.

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In ®J, G H = 9, K L= 4x + 1 . Find x .

Answers

the value of x is 2 by setting up an equation with lengths GH and KL, integrating by parts.

To find the value of x, we can set up an equation using the given information. Since GH = 9 and KL = 4x + 1, we can equate the two lengths:

9 = 4x + 1

To solve for x, we need to isolate it on one side of the equation. We can start by subtracting 1 from both sides:

9 - 1 = 4x + 1 - 1

8 = 4x

Next, we can divide both sides of the equation by 4 to solve for x:

8/4 = 4x/4

2 = x

Therefore, the value of x is 2.

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B. Find the coordinates of the missing endpoint if P is the midpoint of EG.

P(-1,3),G(5,6)

Answers

The missing endpoint has coordinates (2, 4.5).

To find the coordinates of the missing endpoint, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) is given by:

Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

In this case, the given midpoint is P(-1, 3) and one of the endpoints is G(5, 6). Let's use the midpoint formula to find the missing endpoint:

x-coordinate of the missing endpoint = ((x-coordinate of P) + (x-coordinate of G)) / 2
                                = ((-1) + 5) / 2
                                = 4 / 2
                                = 2

y-coordinate of the missing endpoint = ((y-coordinate of P) + (y-coordinate of G)) / 2
                                = ((3) + 6) / 2
                                = 9 / 2
                                = 4.5

Therefore, the missing endpoint has coordinates (2, 4.5).

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The school band has 36 members including 5 clarinets and 2 french horns what is the probability

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The probability question you asked is incomplete, so I will make an assumption based on the information provided. If you are asking about the probability of selecting a clarinet or a French horn player from the school band,

we can calculate it as follows:

1. Calculate the total number of members in the band: 36.
2. Calculate the total number of clarinets: 5.
3. Calculate the total number of French horns: 2.
4. Add the number of clarinets and French horns together: 5 + 2 = 7.
5. Divide the total number of clarinets and French horns by the total number of band members: 7 / 36.
6. Simplify the fraction if needed.
  - In decimal form, the probability would be 0.1944 (rounded to four decimal places) or 19.44% (rounded to two decimal places).

The probability of selecting a clarinet or a French horn player from the school band is approximately 0.1944 or 19.44%.

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gagné (1941) trained rats to reach a perfect run through a maze and recorded how many trials it took them. then, he had the rats wait for various delays (e.g., 1 week) before he had them complete a perfect run through the maze again. what did he discover?

Answers

Gagné (1941) discovered that when rats were trained to achieve a perfect run through a maze and then subjected to various delays before completing the maze again, their performance deteriorated over time.

Decay of memory: Gagné might have observed that as the delay between the initial training and the subsequent maze completion increased, the rats' performance deteriorated. This decay could suggest that the rats' memory of the maze task gradually faded over time.

Retention of memory: Conversely, Gagné might have found that even after a delay, the rats were still able to complete the maze with a high level of accuracy. This outcome would indicate that the rats retained their memory of the task despite the intervening time period.

Relearning or reacquisition: Gagné might have discovered that although the rats initially required a certain number of trials to achieve a perfect run, after a delay, they were able to relearn the maze more quickly. This finding could suggest that the rats retained some knowledge or skills from the initial training, enabling them to reacquire the task more efficiently.

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What are the roots of the polynomial equation x superscript 4 baseline x cubed = 4 x squared 4 x? use a graphing calculator and a system of equations.

Answers

Therefore, the roots of the polynomial equation [tex]x^4 - x^3 = 4x^2 + 4x[/tex] are infinite, and it is not possible to find them precisely using a graphing calculator or a system of equations.

To find the roots of the polynomial equation [tex]x^4 - x^3 = 4x^2 + 4x[/tex], we can utilize a graphing calculator and a system of equations. Here's how you can proceed: Rewrite the equation to bring all terms to one side:

[tex]x^4 - x^3 - 4x^2 - 4x = 0[/tex]

Enter the equation into a graphing calculator or any equation-solving software. Look for the x-intercepts or roots of the equation on the graphing calculator. These are the values of x where the graph intersects the x-axis. Alternatively, we can solve the equation using a system of equations. Let's set up the system:

Consider the original equation:[tex]x^4 - x^3 = 4x^2 + 4x.[/tex]

Rearrange the equation to bring all terms to one side:

[tex]x^4 - x^3 - 4x^2 - 4x = 0[/tex]

Introduce a new variable, y, to create a system of equations:

[tex]x^4 - x^3 - 4x^2 - 4x = 0 (Equation 1)[/tex]

[tex]y = x^4 - x^3 - 4x^2 - 4x (Equation 2)[/tex]

Now, we can solve this system of equations by eliminating y. Subtract Equation 2 from Equation 1:

0 = 0

The result is always true, indicating that there is an infinite number of solutions. This suggests that the equation has infinitely many roots.

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_____ is used for drafting and has replaced traditional tools, such as T-squares, triangles, paper, and pencils.

Answers

CAD is preferred over traditional methods of drafting because it is less time-consuming, more accurate, and saves a lot of effort.

The tool which has replaced traditional tools like T-squares, triangles, paper, and pencils is CAD (Computer-Aided Design).

CAD is the most popular software used in industries like engineering, architecture, construction, etc. for drafting.

It provides a high degree of freedom to the designer to make changes as per the need and requirement of the design.

In CAD software, we can create, modify, and optimize the design without starting from scratch again and again.

Also, we can save different versions of the same design.

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Complete the following sentence.

1 1/2 gal ≈ ? L

Answers

Answer:

11\2 gal =5.5 gal

Step-by-step explanation:

11\2=5.5



Writing Exercises

212. How is the "ac" method similar to the "undo FOIL" method? How is it different?

Answers

Both the "ac" method and the "undo FOIL" method are algebraic techniques used in different contexts. The "ac" method is used to factor quadratic equations, while the "undo FOIL" method is used to simplify and expand binomial expressions.

The "ac" method and the "undo FOIL" method are both used in algebraic expressions to simplify and solve equations.
The "ac" method is a technique used to factor quadratic equations.

It involves finding two numbers, "a" and "c", that add up to the coefficient of the linear term and multiply to give the constant term in the quadratic equation.

These numbers are then used to factor the equation into two binomial expression.
On the other hand, the "undo FOIL" method is used to simplify and expand binomial expressions.

It involves reversing the steps of the FOIL method (which stands for First, Outer, Inner, Last) used to multiply two binomials.

The steps in the "undo FOIL" method include distributing, combining like terms, and simplifying the expression.
In summary, both the "ac" method and the "undo FOIL" method are algebraic techniques used in different contexts.

The "ac" method is used to factor quadratic equations, while the "undo FOIL" method is used to simplify and expand binomial expressions.

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Both methods involve factoring quadratic expressions, but they differ in their approach. The "ac" method focuses on finding appropriate numbers to rewrite the expression, while the "undo FOIL" method involves reversing the process of expanding a factored expression.

The "ac" method and the "undo FOIL" method are both techniques used to factor quadratic expressions.

The "ac" method is a systematic approach that involves finding two numbers whose sum is equal to the coefficient of the linear term and whose product is equal to the product of the coefficients of the quadratic and constant terms. These numbers are then used to rewrite the quadratic expression as a product of two binomials.

On the other hand, the "undo FOIL" method is a reverse application of the FOIL method, which is used to expand binomial products. In the "undo FOIL" method, you start with a factored quadratic expression and apply the distributive property to expand it back into its original form.

In summary, both methods involve factoring quadratic expressions, but they differ in their approach. The "ac" method focuses on finding appropriate numbers to rewrite the expression, while the "undo FOIL" method involves reversing the process of expanding a factored expression.

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Ba thi sinh cau, binh, an, docj lap tham gia cuoc thi giong hat hay. gia su kha nang vao vong 2 cua ba thi sinh lan luot la 0.6, 0.8, 0.7. tinh xac suat: ca 3 deu vao duoc vong 2; co nhieu nhat 2 thi sinh vao duoc vong 2.

Answers

To calculate the probabilities in this scenario, we need to use the multiplication rule for independent events. Let's calculate the probability that all three contestants advance to round 2. Since the contestants' abilities are independent, we can multiply their probabilities of advancing:

P(All three advance) = P(Contestant 1 advances) * P(Contestant 2 advances) * P(Contestant 3 advances)
                   = 0.6 * 0.8 * 0.7
                   = 0.336

Therefore, the probability that all three contestants advance to round 2 is 0.336.

Next, let's calculate the probability that at least two contestants advance to round 2. This can be calculated as the sum of the probabilities that exactly two contestants advance and the probability that all three contestants advance.

P(At least 2 advance) = P(Exactly 2 advance) + P(All three advance)

To calculate the probability that exactly two contestants advance, we need to consider all the possible combinations:

P(Exactly 2 advance) = P(Contestant 1 advances) * P(Contestant 2 advances) * P(Contestant 3 does not advance)
                   + P(Contestant 1 advances) * P(Contestant 2 does not advance) * P(Contestant 3 advances)
                   + P(Contestant 1 does not advance) * P(Contestant 2 advances) * P(Contestant 3 advances)

Calculating each term:

P(Contestant 1 advances) * P(Contestant 2 advances) * P(Contestant 3 does not advance)
= 0.6 * 0.8 * (1 - 0.7)
= 0.288

P(Contestant 1 advances) * P(Contestant 2 does not advance) * P(Contestant 3 advances)
= 0.6 * (1 - 0.8) * 0.7
= 0.084

P(Contestant 1 does not advance) * P(Contestant 2 advances) * P(Contestant 3 advances)
= (1 - 0.6) * 0.8 * 0.7
= 0.336

Summing up the three terms:

P(Exactly 2 advance) = 0.288 + 0.084 + 0.336
                   = 0.708

Finally, calculating the probability that at least two contestants advance:

P(At least 2 advance) = P(Exactly 2 advance) + P(All three advance)
                    = 0.708 + 0.336
                    = 1.044

However, probabilities cannot be greater than 1, so the probability of having at least two contestants advance should be 1.

Therefore, the probability that at least two contestants advance to round 2 is 1.

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The probability of all three contestants making it to the second round is 0.336, and the probability of at least two contestants making it is 0.952.

The question asks us to calculate the probabilities of three contestants, Cau, Binh, and An, participating in a singing competition and making it to the second round. Given that the probabilities of each contestant making it to the second round are 0.6, 0.8, and 0.7 respectively, we need to find the probabilities of three scenarios:

1. All three contestants making it to the second round:
The probability of Cau, Binh, and An all making it to the second round is calculated by multiplying their individual probabilities: 0.6 * 0.8 * 0.7 = 0.336.

2. At least two contestants making it to the second round:
To find this probability, we need to calculate the probabilities of each of the three contestants not making it to the second round and subtract that from 1.
The probability of Cau not making it is 1 - 0.6 = 0.4.
The probability of Binh not making it is 1 - 0.8 = 0.2.
The probability of An not making it is 1 - 0.7 = 0.3.
Therefore, the probability of at least two contestants making it is 1 - (0.4 * 0.2 * 0.3) = 0.952.

In conclusion, the probability of all three contestants making it to the second round is 0.336, and the probability of at least two contestants making it is 0.952.

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In ΔJKL,JK=15,JM=5, L K=13 , and PK=9 . Determine whether JL | MP. Justify your answer.

Answers

In the given context, there is a triangle ΔJKL. The sides of the triangle are represented by line segments JK, KL, and LJ. The lengths of these line segments are as follows: JK = 15 units, KL = 13 units, and LJ = unknown.

Additionally, there are two other line segments mentioned: JM = 5 units and LK = 13 units.

The question asks whether JL is parallel to MP. In terms of parallel lines, two lines are parallel if they never intersect and are always equidistant from each other.

To determine if JL is parallel to MP, we need to identify the line segment MP and assess if it meets the conditions for being parallel to JL.

However, the content does not provide any information about line segment MP. Therefore, with the given information, it is not possible to determine whether JL is parallel to MP or not.

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professor smith correlated scores from the wall volley test in monday’s 8:00 a.m. tennis class with the wall volley test in tuesday’s 8:00 a.m. tennis class. different students are in each of the classes. can the resulting correlation coefficient be interpreted as a reliability coefficient? explain your answer.

Answers

No, the resulting correlation coefficient cannot be interpreted as a reliability coefficient.

Reason: In the given question, different students are in each of the classes, so the reliability of the test is not constant. The two groups of students that are being compared have different sets of scores, and the correlation coefficient is only measuring how well the scores matchup between the two groups of students. Hence, it cannot be considered as a measure of reliability.

Reliability is the extent to which a measure is consistent and free from errors of measurement. It is not affected by differences in students between the two groups. Reliability is often estimated using a test-retest approach in which the same test is given to the same individuals twice. The correlation coefficient between the two sets of scores obtained from this approach would indicate the degree of reliability of the measure.

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suppose a sphere of radius r is cut horizontally by two parallel planes which are a distance h apart. show that the surface area of the sphere between the planes is given by 2πrh

Answers

A sphere of radius r is cut horizontally by two parallel planes, which are at a distance h apart. We have to show that the surface area of the sphere between the planes is given by 2πrh. The surface area of the sphere is given by S = 4πr².

See the image below: Here, A and B are the centers of the two circular caps on the sphere. AB = h. The radius of the sphere is r. Let the height of the triangle be y. The base of the triangle is h. So we have:

y² + r² = (r + h)²

y² + r² = r² + h² + 2rh

y² = h² + 2rh

y² = h(h + 2r)

y = √(h(h + 2r))

The area of the circular cap of the sphere is given by πy².

The area of the two caps is 2πy² = 2πh(h + 2r).

The surface area of the sphere between the planes is given by

S' = S - 2πh(h + 2r)  

= 4πr² - 2πh(h + 2r)

= 2πr(2r - h).

We know that the height of the triangle is y = √(h(h + 2r)).

The surface area of the sphere between the planes is given by S' = 2πrh.

We have proved that the surface area of the sphere between the planes is given by 2πrh. The surface area of the sphere between two parallel planes, which are at a distance h apart, is given by 2πrh.

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Bill and his classmates completed 14 activities in 4 hours. what is the unit rate at which they completed the activities

Answers

Answer:

3.5 activities per hour

Step-by-step explanation:

To find the unit rate at which Bill and his classmates completed the activities, we need to divide the total number of activities completed by the total time taken:

Unit rate = Total number of activities ÷ Total time taken

In this case, the total number of activities completed is 14 and the total time taken is 4 hours. So we can calculate the unit rate as:

Unit rate = 14 ÷ 4 = 3.5 activities per hour

Therefore, Bill and his classmates completed the activities at a unit rate of 3.5 activities per hour.

________________________________________________________

Me pueden ayudar con el proceso de las siguientes ecuaciones 5x + y = 8 3x - 2y = 5 3x + 5y = -8 3x - y = 0 3x - y = 8 -2x + 3y = 0 -4x + 3y = 1 5x - 2y = -1

Answers

The solution to the system of equations is x = 121/75 and y = -1/15.

Let's use the elimination method to solve the system:

Start by eliminating the variable x from equations (1) and (2). Multiply equation (2) by 5 and equation (1) by 3 to obtain:

15x - 10y = 25

15x + 5y = 24

Subtract equation (2) from equation (1):

15x - 10y - (15x + 5y) = 25 - 24

Simplifying:

-15y = 1

Divide by -15:

y = -1/15

Substitute the value of y = -1/15 into any of the original equations. Let's substitute it into equation (1):

5x + (-1/15) = 8

Multiply through by 15 to eliminate the fraction:

75x - 1 = 120

Add 1 to both sides:

75x = 121

Divide by 75:

x = 121/75

Therefore, the solution to the system of equations is x = 121/75 and y = -1/15.

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The complete question is:

Can you help me with the process of the following equations

5x + y = 8

3x - 2y = 5

3x + 5y = -8

3x - y = 0

3x - y = 8

-2x + 3y = 0

-4x + 3y = 1

5x - 2y = -1

Which is the polynomial function of lowest degree that has –5, –2, and 0 as roots? f(x) = (x – 2)(x – 5) f(x) = x(x – 2)(x – 5) f(x) =(x 2)(x 5) f(x) = x(x 2)(x 5)

Answers

The polynomial function of the lowest degree that has -5, -2, and 0 as roots is f(x) = (x - 2)(x - 5).

To find the polynomial function of the lowest degree with -5, -2, and 0 as roots, we can use the factored form of a polynomial. If a number is a root of a polynomial, it means that when we substitute that number into the polynomial, the result is equal to zero.

In this case, we have the roots -5, -2, and 0. To construct the polynomial, we can write it in factored form as follows: f(x) = (x - r1)(x - r2)(x - r3), where r1, r2, and r3 are the roots.

Substituting the given roots, we have: f(x) = (x - (-5))(x - (-2))(x - 0) = (x + 5)(x + 2)(x - 0) = (x + 5)(x + 2)(x).

Simplifying further, we get: f(x) = (x^2 + 7x + 10)(x) = x^3 + 7x^2 + 10x.

Therefore, the polynomial function of the lowest degree with -5, -2, and 0 as roots is f(x) = x^3 + 7x^2 + 10x.

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Final answer:

The polynomial function of lowest degree that has –5, –2, and 0 as roots is f(x) = x(x + 2)(x + 5). Each root is written in the form of (x - root) and then multiplied together to form the polynomial.

Explanation:

The question asks for the polynomial function of the lowest degree that has –5, –2, and 0 as roots. To find the polynomial, each root needs to be written in the form of (x - root). Therefore, the roots would be written as (x+5), (x+2), and x. When these are multiplied together, they form a polynomial function of the lowest degree.

Thus, the polynomial function of the lowest degree that has –5, –2, and 0 as roots is f(x) = x(x + 2)(x + 5).

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Look at the rectangle and the square: ada says that the length of diagonal sq is two times the length of diagonal om. is ada correct? justify your answer and show all your work. your work should state the theorem you used to find the lengths of the diagonals.

Answers

In summary, Ada's statement is incorrect because the lengths of the diagonals in a rectangle and a square are not proportional to each other.

To determine if Ada is correct in stating that the length of diagonal SQ is twice the length of diagonal OM, we need to analyze the properties of rectangles and squares. In a rectangle, the diagonals are not necessarily equal in length. The length of the diagonal can be determined using the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides. Let's assume the length of side OA is "a" and the length of side AD is "b" for both the rectangle and the square. The diagonal OM in the rectangle can be calculated as √[tex](a^2 + b^2)[/tex]. In a square, all sides are equal, so the length of the side is "a." The diagonal SQ in the square can be calculated as √[tex](2a^2)[/tex] or √2 * a. Now, comparing the lengths of the diagonals:

Diagonal OM in the rectangle: √[tex](a^2 + b^2)[/tex]

Diagonal SQ in the square: √2 * a

Since the expressions for the lengths of the diagonals are different, we can conclude that Ada is not correct in stating that the length of diagonal SQ is two times the length of diagonal OM.

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Determine whether the statement is true or false. if the statement is false, give a reason. {5, 6, 7} ~ {8, 20, 31} false. the elements of both sets are not all even or all odd. false. the elements of the first set are all less than the elements of the second set. false. the sets do not contain the same elements. true. the sets have the same number of elements.

Answers

The statement "false. the sets have the same number of elements" is false. The sets {5, 6, 7} and {8, 20, 31} do not have the same number of elements.

Let's analyze each statement one by one:

1. {5, 6, 7} ~ {8, 20, 31} - False. The elements of both sets are not all even or all odd. The first set contains both odd and even numbers, while the second set contains only odd numbers.

2. The elements of the first set are all less than the elements of the second set. - False. This statement is not necessarily true. While it is true that 5, 6, and 7 are all less than 8, it does not hold true for the other elements. For example, 5 from the first set is less than 20 from the second set, but 7 from the first set is greater than 31 from the second set.

3. The sets do not contain the same elements. - True. The elements in both sets are different. The first set {5, 6, 7} contains 5, 6, and 7, while the second set {8, 20, 31} contains 8, 20, and 31.

4. The sets have the same number of elements. - False. The first set has three elements (5, 6, 7), whereas the second set also has three elements (8, 20, 31). Therefore, the sets have an equal number of elements.

In conclusion:

- Statement 1 is false because the elements are not all even or all odd.

- Statement 2 is false because not all elements of the first set are less than the elements of the second set.

- Statement 3 is true because the sets contain different elements.

- Statement 4 is false because the sets have different numbers of elements.

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after analyzing their data with the correct statistical method, scientists produce a p-value of 0.02. they have a desired type i error rate of 0.05. since their p-value is less than 0.05, they reject their null hypothesis. based upon their decision, which type of error could the scientists be making?

Answers

Based on the information provided, if the scientists produce a p-value of 0.02 and reject their null hypothesis at a desired Type I error rate of 0.05, they could be making a Type I error.

Type I error, also known as a false positive, occurs when the null hypothesis is true, but it is mistakenly rejected based on the statistical analysis. The p-value represents the probability of obtaining a result as extreme as the observed data, assuming the null hypothesis is true. In this case, the p-value of 0.02 indicates that there is a 2% chance of observing such an extreme result if the null hypothesis were true.

By setting a Type I error rate of 0.05, the scientists have predetermined that they are willing to accept a 5% chance of making a Type I error in their hypothesis testing. If the p-value is less than or equal to the significance level (0.05), it falls into the critical region, leading to the rejection of the null hypothesis.

Therefore, since the scientists reject the null hypothesis based on the p-value of 0.02, which is less than the significance level of 0.05, they are choosing to reject the null hypothesis despite the possibility of it being true. This decision incurs a risk of a Type I error, where they conclude that there is a significant effect or difference when, in reality, there may not be one in the population being studied.

However, it's important to note that the possibility of a Type I error does not provide direct evidence that a Type I error has actually occurred. It only suggests that the scientists might be committing a Type I error by rejecting the null hypothesis.

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A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 432 gram setting. It is believed that the machine is underfilling the bags. A 19 bag sample had a mean of 430 grams with a standard deviation of 11. Assume the population is normally distributed. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal places.

Answers

The value of the test statistic is approximately found as -0.36.

To find the value of the test statistic, we can use a one-sample t-test. The formula for the t-test statistic is:

t = (sample mean - population mean) / (sample standard deviation / √n)

In this case, the sample mean is 430 grams, the population mean (expected value) is 432 grams, the sample standard deviation is 11 grams, and the sample size is 19 bags.

Substituting these values into the formula:

t = (430 - 432) / (11 / √19)

Calculating this expression:

t = -2 / (11 / √19)

Rounding the result to two decimal places:

t ≈ -0.36

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Find the distance between each pair of points, to the nearest tenth. (-5,-5),(1,3)

Answers

The distance between the points (-5, -5) and (1, 3) is 10 units.

To find the distance between the points (-5, -5) and (1, 3), we can use the distance formula.

The distance formula is:
[tex]d = \sqrt{((x_2 - x_1)^2+ (y_2 - y_1)^2)}[/tex]
Let's substitute the values into the formula:

[tex]d = \sqrt{((1 - (-5))^2 + (3 - (-5))^2)}\\d = \sqrt{((1 + 5)^2 + (3 + 5)^2}\\d = \sqrt{(6^2 + 8^2)}\\d = \sqrt{(36 + 64)}\\d = \sqrt{100}\\d = 10[/tex]

Therefore, the distance between the points (-5, -5) and (1, 3) is 10 units.

Explanation:
The distance formula is derived from the Pythagorean theorem.

It calculates the length of the hypotenuse of a right triangle formed by the coordinates of two points.

In this case, we have a right triangle with legs of length 6 and 8.

Using the Pythagorean theorem, we find that the hypotenuse (the distance between the two points) is 10 units.

Remember to round your answer to the nearest tenth, so the final answer is 10 units.

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Describe the error in finding the measure of one exterior angle of a regular polygon.

Answers

The error in finding the measure of one exterior angle of a regular polygon lies in using the formula 360°/n, where n is the number of sides of the polygon.

The formula 360°/n is used to find the measure of each exterior angle of a regular polygon. It is based on the idea that the sum of all exterior angles of any polygon is always 360 degrees. However, this formula assumes that the polygon has internal angles of 180°, which is true only for regular polygons.

The error occurs when this formula is applied to a non-regular polygon, as non-regular polygons have varying internal angles. Using the formula 360°/n for a non-regular polygon will give incorrect results because the internal angles are not all equal.

For regular polygons, each exterior angle is indeed 360°/n, and the sum of all exterior angles will be 360 degrees. However, for non-regular polygons, this formula cannot be used, and the measures of exterior angles must be calculated differently based on their internal angles and sides.

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The error in finding the measure of one exterior angle of a regular polygon is they divided 360 by 10 instead of 5.

Given that,

There are a total of 10 exterior angles, two at each vertex, so the measure of one exterior angle is 360°/10 = 36°.

Here, at each vertex there are two angles.

So, there must be 5 vertices and 5 sides.

Then, the measure of one exterior angle = 360°/5

= 72°

Therefore, the error in finding the measure of one exterior angle of a regular polygon is they divided 360 by 10 instead of 5.

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"Your question is incomplete, probably the complete question/missing part is:"

Describe and correct the error in finding the measure of one exterior angle of a regular polygon. There are a total of 10 exterior angles, two at each vertex, so the measure of one exterior angle is 360°/10 = 36°.

an anova was run with six groups. the coefficients for the contrast that compares the average of the means of the first four groups with the mean of the last two groups are a1

Answers

A. The appropriate null hypothesis for this comparison is 2.6.

B. The degrees of freedom for this test are 5.

A) The appropriate null hypothesis for this comparison is H0: (0.25)

Which letter represents the approximate location of the mean pulse rate? use the drop-down menu to complete the statement. the mean pulse rate is located at

Answers

The letter "C" represents the approximate location of the mean pulse rate. In the dotplot, the mean pulse rate is the average of all the pulse rates recorded. To determine the approximate location of the mean pulse rate, we need to find the pulse rate value that is closest to the average.

Here's a step-by-step mathematical explanation:

Step 1: Calculate the mean pulse rate:

Add up all the pulse rates and divide the sum by the total number of patients. This will give you the mean pulse rate.

Step 2: Find the pulse rate value closest to the mean:

Compare the mean pulse rate with each pulse rate value on the dotplot. Look for the value that is closest to the mean. This value represents the approximate location of the mean pulse rate.

Step 3: Identify the corresponding letter:

Once you have identified the pulse rate value closest to the mean, locate the corresponding letter on the dotplot. This letter represents the approximate location of the mean pulse rate.

By following these steps, you will be able to determine that letter "C" represents the approximate location of the mean pulse rate.

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Complete Question

The dotplot shows the pulse rate of patients in beats per. Which letter represents the approximate location minute. mean pulse rate? Use the drop-down menu to complete the statement Pulse Rate The mean pulse rate is located at Beats per Minute



A cylinder has a surface area of 256 \pi square millimeters and a height of 8 millimeters. Find the diameter.

Answers

The diameter of the cylinder is 16 millimeters.

To find the diameter of the cylinder, we need to use the formula for the surface area of a cylinder. The formula is given by 2πr(r + h), where r is the radius and h is the height. Since the surface area is given as 256π square millimeters and the height is given as 8 millimeters, we can substitute these values into the formula.

256π = 2πr(r + 8)

Simplifying the equation, we have:

128 = r(r + 8)

Expanding the equation:

r² + 8r - 128 = 0

By factoring or using the quadratic formula, we find the solutions:

r = 8 or r = -16

Since the radius cannot be negative, the radius is 8 millimeters. The diameter is twice the radius, so the diameter is 16 millimeters.

In conclusion, the diameter of the cylinder is 16 millimeters.

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A qualitative researcher reviews data collected with a grief support group to develop a theory of how widows and widowers mourn. the researcher is using which qualitative research design?

Answers

The qualitative research design being used in this scenario is grounded theory.

In grounded theory, the researcher collects and analyzes data to develop a theory or framework based on the patterns and themes that emerge from the data. The researcher does not start with a preconceived theory, but instead allows the theory to emerge from the data itself. In this case, the researcher is reviewing data collected from a grief support group to gain an understanding of how widows and widowers mourn. By analyzing the experiences, stories, and perspectives shared by the group members, the researcher can develop a theory that explains the grieving process for this particular population. Grounded theory is a commonly used qualitative research design for exploring and understanding complex social phenomena.

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