A. 3(2x-3)-5(2+x) B. -2(2x+3)(x+2)-(x+2) C. 3(2-x)+3(2-x) 2. Solve and check each of the following equation. i.3x+5=29 ii. x-1=14 3. Solve each of the following questions. i. 2(x+2)-3(2-x)=2(x-3) ii. -3(2-2x)-(x+2)=2x+3 iii. 2/3(x+2)=7/8(2-x) iv. 4/3(2-x)=3/5(x+3) v. 5[x-(4x-5)]-2=2-7x iii. x=21 4. Locate each of the following on the coordinate plane bra​

The first 3 consecutive odd numbers are 1,3,5. x and x + 2 are consecutive odd numbers if x is an odd number.

Consecutive numbers are those that always appear in the same order, from smallest to largest.

For instance:

The numbers 1, 2, 3, 4, 5, 6, and so on are consecutive.

consecutive odd numbers:

Let's call the odd number "x." The subsequent term becomes "x + 4" and the next consecutive odd number becomes "x + 2."

Numbers that begin with 1, 3, 5, 7, or 9 are considered odd. 1, 3, 5, 7, 9, 11, 13, 15, and so on are examples of consecutive odd numbers.

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The solution to the inequality are the region in the shaded area and the graph is attached

From the question, we have the following parameters that can be used in our computation:

y ≥3(0.8)^x

y ≥ x² - 5

Represent properly

y ≥ 3(0.8)^x

y ≥ x² - 5

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)

None of the options represent the shaded area (see attachment)

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The given function is;\($$t=2000(385+71te^{-6.2t})$$\). The given formula shows the expected gift income for each year within a period of 5 years.

We are asked to determine whether the board of trustees expects the gift income to increase or decrease over the five-year period.

(a) The graph of the given function is;\(t=2000(385+71te^{-6.2t})\)\(\frac{t}{2000}=385+71te^{-6.2t}\)

Now, we can input this into a graphing utility like Desmos to obtain the following graph;

From the graph, we can see that the function has an increasing trend. Therefore, we can conclude that the board of trustees expects the gift income to increase over the five-year period.

(b) To find the expected total gift income over the five-year period, we need to integrate the function from 0 to 5. Therefore, we have;

\(\begin{aligned}\int_{0}^{5}t&=2000\int_{0}^{5}(385+71te^{-6.2t})dt\\ &=2000\Bigg[385t-12e^{-6.2t}(13t+50)\Bigg]_{0}^{5}\\ &=2000\Bigg[1925-12e^{-31}(65+50)\Bigg]\\ &=749049.17 \text{ dollars}\end{aligned}\)

Therefore, the expected total gift income over the five-year period is 749049.17 dollars. (rounded to two decimal places)

(c) The average annual gift income over the five-year period is the total gift income divided by the number of years. Therefore, we have;

\(\text{Average annual gift income}=\frac{\text{Total gift income}}{\text{Number of years}}=\frac{749049.17}{5}=149809.83\)

Therefore, the average annual gift income over the five-year period is 149809.83 dollars. (rounded to two decimal places

The board of trustees expects the gift income to increase over the five-year period. The expected total gift income over the five-year period is 749049.17 dollars, while the average annual gift income over the five-year period is 149809.83 dollars.

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The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106

A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.

Rectangles' essential characteristics are as follows:

A rectangle is a parallelogram.

The Perimeter of the rectangle is 2a + 2b where a and b are the two sides

Now , if w is the width of the rectangle then, the length is 4w given in problem.

Perimeter,

2w + 2* 4w

As it is given in the problem

2w + 2* 4w ≤ 106

The first model of inequality satisfy the problem.

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IF YOU CHECK YOU WILL FIND THAT THIS IS A DIFFERENCE OF TWO SQUARES

\( = (5 - 3x)(5 + 3x)\)

ATTACHED IS THE SOLUTION

Answer:

a) 0.25x

b) (0.25x+5)*3

Step-by-step explanation:

The number of ways she can select her new vehicle is:3 (options for type) x 3 (options for make) x 5 (options for color) = 45.Therefore, Laura has 45 ways to select her new vehicle.

Laura is shopping for a new car. She has to make three decisions: type (sedan, SUV, or pickup truck), make (Ford, GM, or Chrysler), and color (black, white, red, silver, or yellow). In how many ways can she select her new vehicle? In order to find the number of ways Laura can select her new vehicle, we have to count the number of possibilities for each decision and then multiply them together.

So, let's start by counting the possibilities for the type of car she wants to buy. Since there are three types of cars she can buy, Laura has three options for the type of car she wants to buy. Now, let's consider the make of the car she wants to buy. Since there are three makes to choose from, Laura has three options for the make of the car she wants to buy. Finally, let's consider the color of the car she wants to buy.

Since there are five colors to choose from, Laura has five options for the color of the car she wants to buy. To find the total number of ways Laura can select her new vehicle, we simply need to multiply the number of possibilities for each decision.

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The rectangular pice has a wide of 24 inches and 40 inches long so we can calculate the area of the rectangle:

Now they say that Lenna folds the piece of fabric along its diagonal so the triangle will have halve of the area of the triangle, so que so we can divide the area of the trangle by 2

So the triangle has an area o

A relation could be a function or it could not. Since b. (6, 8) and d. (4, 3), the connection would no longer be a function.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

You can choose the components of combos in any order.

Permutations and combinations can be mixed up.

So, given is the ordered pair:

(x, y) = (1, 2); (2, 3); (4, 5); (6, 7); (12, 13)

All of the x-values in a relation must be distinct for it to be a function (i.e. no repetition)

The x values of choices (b) and (d) already exist in the ordered pair, namely (6,7) and (d), from the list of alternatives given (4,5)

Accordingly, (b) and (d) would prevent the relation from being a function.

Therefore, a relation could be a function or it could not. Since b. (6, 8) and d. (4, 3), the connection would no longer be a function.

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Correct question:

A bakery sells different packages of muffins. The number of muffins, x, and the price in dollars, y, of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.

{(1,2),(2,3),(4,5),(6,7),(12,13)}

The bakery is considering adding a new package of muffins. which ordered pairs would make the relation NOT a function? Choose all that are correct.

a. (10,13)

b. (6,8)

c. (8,12)

d. (4,3)

e. (24,18)

Dimensions of the enclosure that is most economical to construct are approximately L = 6.79 feet and W = 29.43 feet, rounded to two decimal places.

Let's assume that the rectangular area to be enclosed has dimensions length "L" and width "W", respectively.

We know that the area of the rectangle is 200 square feet:

L x W = 200

We also know that we need to enclose three sides of the rectangle with material that costs 6 dollars per foot, and one side with material that costs 14 dollars per foot.

The total cost, C, of the fencing can be expressed as:

C = 6(2L + W) + 14L

where 2L + W represents the length of the three sides that cost 6 dollars per foot, and L represents the length of the fourth side that costs 14 dollars per foot.

We can simplify this equation to:

C = 26L + 6W

using the equation L x W = 200.

Now we can use the method of calculus to find the minimum value of C. We take the derivative of C with respect to L, set it equal to zero, and solve for L.

dC/dL = 26 = 0

L = 0

This result means that the value of L that minimizes C is L = 0, which is obviously not a valid solution. This implies that the minimum value of C occurs at a critical point where dC/dL is undefined.

To find this critical point, we can use the equation L x W = 200 to eliminate one variable. Solving for W in terms of L, we get:

W = 200/L

Substituting this expression for W into the equation for C, we get:

C = 26L + 6(200/L)

Now we can take the derivative of C with respect to L and set it equal to zero:

dC/dL = 26 - 1200/L² = 0

Solving for L, we get:

L = √(46.15)

Substituting this value for L back into the equation for W, we get:

W = 200/√(46.15)

Therefore, the dimensions of the enclosure that is most economical to construct are approximately L = 6.79 feet and W = 29.43 feet, rounded to two decimal places.

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Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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Answer:

C

Step-by-step explanation:

First you have to find h'(x). To find it you have to use the multiplication differentiation rule. Therefore h'(x) is...

h'(x) = f(x)g'(x) + g(x)f'(x)

Then plug 2 into the equation

h'(2) = f(2)g'(2) +g(2)f'(2)

Then you use the graphs to find out the numerals for the equation

f(2) = 4

g(2) = 5

To find the derivative of these functions, you have to find the slope of the line at the point where x = 2

f'(2) = 2

g'(2) = 1

Then finally you plug that all into the equation we made at the beginning and get the answer

h'(2) = 4 x 1 + 5 x 2 = 14

So the answer is C

*If you are taking the AP exam on monday good luck! I am taking it too! :D

Answer:

Yes, he can.

Step-by-step explanation:

To find the sale, you need to times the sale percentage by the original price so

60 x 0.50 = 30

Then you subtract the original price by the sale price so

60 - 30 = 30

So the with the sale, the price is $30.

Now the tax

Do the same

30 x 0.045 = 1.35

Now instead of subtracting you add so

30 + 1.35 = $31.35

Yes, he can afford it.

4x + 8y = 16

4x = 16 - 8y

4x = 4 (4 - 2y)

x = 4( 4 - 2y)/4

X = 4 - 2y

X = -2y + 4

Answer:

x/7 + 9 = 6

Step-by-step explanation:

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From the given diagram, it can be seen that John made a mistake while drawing the electric field lines for the configuration of two charges. The electric field lines should start from the positive charge and end at the negative charge and they do not cross each other.

However, in the diagram, the electric field lines are starting from the negative charge and ending at the positive charge. This is incorrect as the direction of the electric field is from the positive to the negative charge.

Additionally, the electric field lines should not cross each other. In the given diagram, the electric field lines are crossing each other, which is incorrect. The electric field lines should be evenly spaced and should not intersect with each other.

In conclusion, John made two mistakes while drawing the electric field lines for the configuration of two charges.

The first mistake is that the electric field lines are starting from the negative charge and ending at the positive charge, which is incorrect.

The second mistake is that the electric field lines are crossing each other, which is also incorrect.

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You can convert from scientific notation to simple notation using the fact that negative powers can be converted to division.

The correct option is given by

Option C. The greatest number is 8. 2 × 10-3. It is 2,000 times greater than the smallest number.

Suppose you have got \(a^{-b}\)

Then we have

\(a^{-b} = \dfrac{1}{a^b}\)

\(8.2 \times 10^{-3} = \dfrac{8.2}{10^3} = \dfrac{8.2}{1000} = 0.0082\\\\5.2 \times 10^{-6} = \dfrac{5.2}{10^6} = \dfrac{5.2}{1000000} = 0.0000052\\\\4.1 \times 10^{-6} = \dfrac{4.1}{10^6} = \dfrac{4.1}{1000000} = 0.0000041\)

Thus, we can see that

The greatest number among given numbers is \(8.2 \times 10^{-3}\)

The smallest number among the given numbers is \(4.1 \times 10^{-6}\)

Dividing greatest number by smallest to see how many times the greatest number is greater than the smallest number

\(\dfrac{8.2 \times 10^{-3}}{4.1 \times 10^{-6}} =\dfrac{8.2}{4.1} \times \dfrac{10^{-3}}{10^{-6}} = 2 \times 10^{-3 - (-6)} = 2 \times 10^3 = 2000\)

Remember that when base are same, and there is division, then power gets subtracted, that's why we got \(\dfrac{10^{-3}}{10^{-6}} = 10^{-3 - (-6)} = 10^3\)

Thus, we have the greatest number 2000 times bigger than the smallest number among the numbers given.

Thus, the correct option is

Option C. The greatest number is 8. 2 × \(10^{-3}\). It is 2,000 times greater than the smallest number.

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12 minutes .

The tank takes 12 minute for the water level to measure 9 inches deep.

Given tank measurement = 15 inches .

it decreases 0.5 inches every minute.

We have to the minute at which water level reaches 9 inches deep,

Here the difference of inches is 6 inches .

15 inches - 6 inches = 9 inches

To find minute ,

  6 / 0.5 = 12 minute .

The tank takes 12 minute to measure 9 inches deep.

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Answer:

y = -1/5x - 1

Answer:

a. h=5
b. A=.5(b)(h). So, 18=.5(6)(h+1). If I plug in 5 as h and solve, 18=.5(6)(6) which can be simplified to 18=(.5)(36). So, h is 5.  

Step-by-step explanation:

Since the area = 18, and the formula for area is .5(b)(h), I can start solving by plugging in the numbers I have. 18=.5(6)(h+1). I multiply both sides by 2 to get rid of the .5, getting 36=6(h+1). I divide by 6 on both sides, getting 6=h+1. I subract 1 on both sides to get h=5

Answer:

a. h=5

b. A=.5(b)(h)

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

3x+12+3x+18=7x+10
6x+30=7x+10
x=20
Angle 3 = 7(20)+10

Angle 3 = 150

The basic characteristics of an independent-measures, or a between-subjects, research study are that it requires a separate sample for each of the treatments or populations being studied. This means that participants are only exposed to one treatment or condition and are not crossed over into other conditions.

Additionally, an independent-measures study requires each individual in each sample to be matched with a corresponding individual in each other sample to ensure that the groups are comparable in terms of relevant characteristics such as age, gender, and prior experience.

Finally, an independent-measures study requires observation of each individual in the sample before and after the treatment is applied to measure any changes that occur as a result of the treatment. These characteristics are essential for ensuring the validity and reliability of the research results.

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Answer:  The graph is shown below. It is nonlinear

==========================================================

Explanation:

I used GeoGebra to make the graph. Desmos is another option I recommend.

The equation we graph is y = (1/2)^x since we're splitting the paper in half each time. This is an exponential decay function. Note how the curve slopes downhill when moving to the right.

It appears the curve touches or crosses the x axis; which is misleading. Instead, the curve is getting closer and closer to this horizontal asymptote. It will never reach the x axis. Think of it like an electric fence.

As the graph indicates, we don't have a straight line. Therefore, the function isn't linear. It's a nonlinear curve.

Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

The time it takes for an orchestra to perform a symphony is not dependent on the number of players. Therefore, the number of players does not directly affect the duration of the performance. In this case, it took the 120-player orchestra 40 minutes to play Beethoven's 9th Symphony.

Assuming that the tempo and performance style remain constant, it is reasonable to assume that a 60-player orchestra would also take 40 minutes to perform the same symphony. The time it takes to play a symphony is primarily determined by the composer's tempo markings and the musicians' interpretation of those markings. Therefore, reducing the number of players does not necessarily mean a shorter performance time.

In summary, the number of players in an orchestra does not determine the time it takes to perform a symphony. The performance time is influenced by factors such as the composer's tempo markings and the musicians' interpretation. Hence, a 60-player orchestra would likely take the same amount of time, approximately 40 minutes, to play Beethoven's 9th Symphony.

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Answer:

b

Step-by-step explanation: