explain how you can use the answer to problem 2 to verify the unit rate is 40

Step-by-step explanation:

f(x) = 2(x+4)(x+2)

= 2[x² + 6x + 8]

= 2x² + 12x + 16

Answer:

r = 11

L = 6

Step-by-step explanation:

7(6) = 42

5(11) = 55

42 + 55 = 97

The algebraic expression "3(7j + 2 - 4j)" can be translated to the verbal expression "Three times the sum of seven times a number, two, and the negation of four times the same number."

The algebraic expression "3(7j + 2 - 4j)" can be translated into a verbal expression as follows: "Take a number, multiply it by seven, add two to the result, subtract four times the same number, and finally multiply the entire expression by three."

To break it down further, let's consider the variable j as the unknown number. Multiplying 7 by j gives us seven times the unknown number, 7j. Adding 2 to this term gives us 7j + 2. Then, subtracting 4j from this sum represents subtracting four times the same unknown number. So, we have 7j + 2 - 4j.

Finally, multiplying the entire expression by 3 gives us 3(7j + 2 - 4j). This means that the entire calculation described above is repeated three times.

In summary, the verbal expression for 3(7j + 2 - 4j) can be stated as "Three times the sum of seven times a number, two, and the negation of four times the same number."

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Work Shown:

x = his age now

x+11 = his age 11 years into the future

x-7 = his age 7 years ago

The equation to set up is

x+11 = 3(x-7)

since his age 11 years into the future is triple that of his age 7 years ago.

-------

Let's solve for x.

x+11 = 3(x-7)

x+11 = 3x-21

x-3x = -21-11

-2x = -32

x = -32/(-2)

x = 16

He is currently 16 years old.

11 years from now he'll be 16+11 = 27, and 7 years ago he was 16-7 = 9.

Note that 9*3 = 27 to help confirm the answer.

Answer:

16

Step-by-step explanation:

3(x-7)=x+11

Plug into equation and find value of x

To simplify √18x⁵ and √2x³, first simplify √18 to get 3√2 and √2x³ to get x√2. Then multiply (3√2)(x√2) to get 3x√4. Simplify √4 to get 2 and multiply 3x(2) to get 6x.

To simplify the expression √18x⁵ and √2x³, we can break it down into smaller parts.
1. Simplify √18 to get 3√2.
2. Simplify √2x³ to get x√2.
3. Multiply the simplified parts together:

(3√2)(x√2) = 3x√4.
4. Simplify √4 to get 2.
5. The final simplified expression is 3x(2) = 6x.

1. √18 can be simplified as √(9 x 2). Since 9 is a perfect square, it simplifies to 3. Therefore, √18 becomes 3√2.
2. Similarly, √2x³ can be simplified as √(2 x x²). The square root of 2 cannot be simplified any further, but x² can be simplified as x. Therefore, √2x³ becomes x√2.
3. To multiply two square roots together, we can multiply the numbers outside the square root and the numbers inside the square root separately. Therefore, (3√2)(x√2) = 3x√(2 x 2) = 3x√4.
4. The square root of 4 is 2, so we can simplify √4 to 2. Therefore, 3x√4 becomes 3x(2) = 6x.

To simplify √18x⁵ and √2x³, first simplify √18 to get 3√2 and √2x³ to get x√2. Then multiply (3√2)(x√2) to get 3x√4. Simplify √4 to get 2 and multiply 3x(2) to get 6x.

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Answer:

15.65 foot

Step-by-step explanation:

Pythagoras theorem can be used

a² + b² = c²

a being 14
b being unknown ( x )
c being 21

hence,

14² + x² = 21²
196 + x² = 441

x = √245  

  = 15.65 foot (answer)

The lifetimes of a certain brand of photographic light are normally distributed with a mean of 210 hours and a standard deviation of 50 hours. We need to find the probability that a particular light will last more than 250 hours.

Given mean = μ = 210 hours. Standard deviation = σ = 50 hours. Let X be the lifetime of a photographic light. X ~ N (μ, σ) = N (210, 50). The probability that a particular light will last more than 250 hours can be calculated as follows: P(X > 250) = 1 - P(X < 250)Let Z be the standard normal variable.

Then, (250 - μ) / σ = (250 - 210) / 50 = 0.8P(X < 250) = P(Z < 0.8). Using the z-table, the probability that Z is less than 0.8 is 0.7881. Therefore, P(X > 250) = 1 - P(X < 250) = 1 - 0.7881 = 0.2119. Hence, the probability that a particular light will last more than 250 hours is 0.2119.

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The given question is incomplete as it does not provide the measurements for the time it takes to complete 5 rotations.

In order to provide a meaningful answer, we need the actual measurements for the time it takes to complete 5 rotations. Without the measurements, it is not possible to analyze the data or draw any conclusions regarding the time taken.

Once the measurements are available, they can be used to calculate the average time taken for 5 rotations. This can be done by summing up the individual measurements and dividing by the number of measurements taken. The average will provide an estimate of the typical time taken for 5 rotations.

Additionally, other statistical measures such as the standard deviation can be calculated to assess the variability or consistency of the measurements. A smaller standard deviation indicates less variability and a higher level of consistency in the time taken for 5 rotations.

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Here are the instructions on how to create a histogram based on the given data.

To create a histogram representing the data, you can follow these steps:

1. Determine the range of the data. Find the minimum and maximum values in the given table.

2. Determine the number of intervals or bins you want to use for the histogram. This can be based on the number of data points and the desired level of detail in the representation. Generally, 5 to 15 bins are used.

3. Divide the range of the data into equal intervals based on the number of bins chosen. Each interval should cover an equal range of values.

4. Count the frequency or number of occurrences of tornadoes within each interval. This will give you the height or frequency of each bar in the histogram.

5. Plot the intervals on the x-axis and the corresponding frequencies on the y-axis. Draw rectangles (bars) for each interval, where the height of the bar represents the frequency.

6. Label the x-axis and y-axis appropriately to provide context for the data being represented.

By following these steps, you can create a histogram to represent the given data on the number of tornadoes recorded in the U.S. in 2008.

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Answer:

if a person pays for both meal then

32.75+39.88

=159.75

noww

14%of 159.75

(14/100)x159.75

=22.36$

noww total cost

=159.75+22.36

=182.115$

Answer:

total cost = 77.82 including tax

Step-by-step explanation:

32.75+39.88= 72.63

72.63/14= 5.19

72.63+5.19

=77.82

Answer:

Approximately 1.6

Step-by-step explanation:

To graph. a function, let use desmos or graphing calculator.

Here the function.

The length of the pendulum as shown here when x=2, is 1.6

The area under the standard normal curve where P(Z > -0.5) is 0.6915. To find this, we can use a standard normal distribution table or a calculator with a normal distribution function.

First, we need to find the z-score associated with -0.5. We know that the mean of the standard normal distribution is 0 and the standard deviation is 1. So, the z-score can be calculated as z = (x - μ) / σ = (-0.5 - 0) / 1 = -0.5. Now, we can look up the area to the right of the z-score -0.5 in a standard normal distribution table. The area is 0.6915, which means that the probability of getting a z-score greater than -0.5 is 0.6915.

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The system has a unique solution for all values of 'a' except a = 1. For a = 1, the system has no solution.

When 'a' is not equal to 1, the system of equations can be solved using standard methods, resulting in a unique solution. The coefficient 'a' affects the slopes of the lines and their intersection point, ensuring a unique solution.

When 'a' is equal to 1, the two equations become identical, and there is no unique solution. The lines representing the equations are parallel and do not intersect.

When 'a' is equal to 0, the second equation becomes redundant and provides no new information. The two equations represent the same line, resulting in an infinite number of solutions.

Therefore, the value of 'a' determines the nature of the solution: unique, no solution, or infinite solutions.

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Engineers can be held most morally blameworthy for foreseeable harms resulting from technological innovations, engineers have a responsibility to anticipate the potential consequences of their work,

and to take steps to mitigate those consequences. If they fail to do so, and their work results in harm, they can be held morally blameworthy. When engineers develop new technologies, they have a responsibility to consider the potential consequences of their work.

They need to think about how their technology could be used, and whether it could be used to harm people or the environment.

They also need to consider how their technology could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their work results in harm, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

For example, engineers who develop new weapons systems have a responsibility to consider the potential consequences of their work. They need to think about how their weapons could be used,

and whether they could be used to kill or injure innocent people. They also need to consider how their weapons could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their weapons are used to kill or injure innocent people, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

It is important to note that engineers cannot be held morally blameworthy for unforeseeable harms. This is because they did not have the opportunity to anticipate the harm, and they could not have taken steps to prevent it.

For example, engineers who develop new medical treatments cannot be held morally blameworthy if the treatments have unforeseen side effects. This is because the engineers did not have the opportunity to anticipate the side effects, and they could not have taken steps to prevent them.

In conclusion, engineers can be held morally blameworthy for foreseeable harms resulting from technological innovations.

This is because they have a responsibility to anticipate the potential consequences of their work, and to take steps to mitigate those consequences.

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Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

Answer:

it's 21/4

Step-by-step explanation:

on time 4 learning

p.s. stream sour by Olivia Rodrigo

Answer:

4805.38

Step-by-step explanation:

982×5.47=5371.54

598×78=46,644

5371.54-46644=4805.10

4805.10+28=4805.38

Answer:

x=8

Step-by-step explanation:

3x -5 =2.5x + 3 - (x-4)

3x - 5 = 2.5x + 3 -x+4

3x - 5 = 1.5x +7

1.5x = 12

x =8

The solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.

The given expression is,

x-5=2.5x+3-(x-4)

Simplify the equation by combining like terms.

Start with the terms on the right-hand side of the equation:

2.5x+3-(x-4)

= 2.5x + 3 - x + 4 (distributing the negative sign)

= 1.5x + 7

Now let's combine the terms on the left-hand side of the equation:

3x - 5

Now the reduced equation be,

3x - 5 = 1.5x + 7

Isolate the variable (x) on one side of the equation.

Subtracting 1.5x from both sides:

3x - 1.5x - 5 = 1.5x - 1.5x + 7

1.5x - 5 = 7

Add 5 to both sides:

1.5x - 5 + 5 = 7 + 5

1.5x = 12

Solve for x by dividing both sides by 1.5:

1.5x/1.5 = 12/1.5

x = 8

So the solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.

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Answer:

I agree with Damian and Alex because the formula to find the volume of a sphere is \(\frac{4}{3} \pi r^3\), where \(r\) represents the radius of the sphere. The radius of the given sphere is 6 cm, so the volume of the sphere would be \(\frac{4}{3} \pi* 6^3\) = \(216 * \frac{4}{3} \pi\) = \(288\pi\) (Damian's answer) ≈ 904 \(cm^3\) (Alex's answer), so both Damian and Alex got the right answer.

A blocked design compares different independent variable levels by using homogeneous groups of experimental units.

In this type of experimental design, subjects are divided into homogeneous groups, or blocks, based on similar characteristics or traits. These blocks help to control or account for potential confounding variables that may affect the outcome of the experiment.

By grouping subjects into blocks, researchers can reduce the variability within each group and increase the accuracy of the experimental results. This allows for a more precise comparison of the effects of different levels of the independent variable on the dependent variable. Blocked designs are particularly useful when there are natural groupings within the experimental units or when the variability between units is high.

In summary, a blocked design is a powerful experimental tool that can help researchers account for potential confounding factors and reduce variability among experimental units. By doing so, it enables the accurate comparison of different levels of the independent variable, ultimately leading to more reliable and valid results.

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Step-by-step explanation:

There are 15,504 different committees that can be chosen from the 20-member student council to form a committee of 15 students.

To calculate the number of different committees that can be chosen from a 20-member student council to form a committee of 15 students, we can use the combination formula.

The number of combinations of selecting 'r' items from a set of 'n' items is given by the formula:

C(n, r) = n! / (r!(n - r)!)

In this case, we want to select 15 students from a pool of 20 members, so the formula becomes:

C(20, 15) = 20! / (15!(20 - 15)!)

Calculating this value:

C(20, 15) = 20! / (15! * 5!)

The factorial notation represents the product of all positive integers up to a given number. Evaluating the factorials:

20! = 20 * 19 * 18 * 17 * 16 * 15!

15! = 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5!

By canceling out common factors:

C(20, 15) = (20 * 19 * 18 * 17 * 16) / (5 * 4 * 3 * 2 * 1)

Simplifying:

C(20, 15) = 15,504

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Answer:

1/3

Step-by-step explanation:

2/5 times 1/3 equals 1/3

Quadrilaterals ABCD and EFGH are similar.To determine if quadrilaterals ABCD and EFGH are similar, we need to compare their corresponding sides and angles.

Quadrilateral ABCD has side lengths of AB = 2, BC = 2, CD = 2, and DA = 2. The lengths of its sides are equal, and its angles are all 90 degrees. Quadrilateral EFGH has side lengths of EF = 6, FG = 6, GH = 6, and HE = 6. The lengths of its sides are equal, and its angles are all 90 degrees. From the side lengths and angles, we can see that both quadrilaterals have the same shape, a rectangle. Therefore, quadrilaterals ABCD and EFGH are similar.

Similarity means that corresponding angles are equal, and corresponding sides are in proportion. In this case, both the angles and side lengths are the same for both quadrilaterals, confirming their similarity.

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It's generally reasonable to assume that enhancing the speed of execution can positively impact customer satisfaction. Quicker order executions can lead to reduced slippage, improved trade efficiency, and a better overall trading experience. Customers often value fast and reliable execution when it comes to brokerage services.

To determine the potential impact on overall satisfaction rating, several factors would need to be considered, including but not limited to:

Other aspects of the brokerage service: Speed of execution is just one aspect of brokerage services. Factors like customer support, platform usability, account management features, pricing, research tools, and investment options also contribute to overall satisfaction. Improving one aspect may not guarantee a significant increase in overall satisfaction if other areas remain unchanged.

Individual preferences and priorities: Different customers prioritize different features in their brokerage services. While some might highly value speed of execution, others may focus on different aspects such as cost-effectiveness, available investment options, or educational resources. The impact on overall satisfaction would depend on how important speed of execution is to the customer base as a whole.

Competitors' performance: The competitiveness of the market plays a role in shaping customers' expectations. If the average speed of execution rating for other surveyed brokerage firms is relatively high, matching that average may positively impact satisfaction. However, if the sector's overall speed of execution rating is generally low, merely reaching the average might not suffice to significantly boost satisfaction.

It's essential for brokerage firms to consider these factors comprehensively and conduct customer surveys or market research to assess the potential impact on overall satisfaction accurately.

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Answer:

f(8) is 34

Step-by-step explanation:

8*5 is 40, and 40 - 6 is 34

Answer:

34

Step-by-step explanation:

f(x) = 5x-6 then find f(8)

f(8) = 5(8) - 6

f(8) = 40 -6

f(8) = 34

Answer:

38°

Step-by-step explanation:

4x-9=3x+29 ------- because corresponding angles are equal

x=38°

Answer:

\(x=6\)

Step-by-step explanation:

\(8.6 + 5.6x - 1.5 = 40.7\\5.6x = 33.6\\x=6\)

Answer:

Step-by-step explanation:

solve for x

8.6 + 5.6x - 1.5 = 40.7

5.6x = 40.7 - 8.6 + 1.5

5.6x = 33.6

x = 33.6 : 5.6

x = 6

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

check

8.6 + 5.6 * 6 - 1.5 = 40.7

40.7 = 40.7

the answer is good