Mass production focuses on producing: Multiple choice question. a wide variety of products customized products a limited variety of products many products in small amounts

The existence of this relief in the Persian capital city clearly portrays the monumental and artistic nature of the Persian Empire.

The Persian Empire, renowned for its grandeur and opulence, left a rich legacy of architectural and artistic achievements. One of the remarkable features of the Persian Empire was its emphasis on monumental structures and elaborate artistic expressions. The existence of the relief in the Persian capital city stands as a testament to the empire's commitment to showcasing its power, wealth, and cultural sophistication. The relief, with its intricate detailing, impressive scale, and artistic finesse, reflects the grand vision and ambition of the Persian Empire. It serves as a visual representation of the empire's wealth, craftsmanship, and mastery of architectural techniques. The Persian rulers, recognizing the significance of art and architecture in projecting their imperial might, invested considerable resources and talent in creating magnificent structures and artworks. Through the existence of this relief, the Persian Empire conveyed its desire to leave a lasting legacy and demonstrate its dominance in the ancient world. The relief's presence in the capital city symbolizes the empire's cultural and artistic achievements, leaving an enduring impression of the Persian Empire's monumental and artistic nature.

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Option B) If the sum of the squares of the two short sides equals the square of the longest side

The rectangular coordinates for (4. 24, 135°) are (-3, 3). Hence, option a is correct.

To convert the given polar coordinates (4.24, 135°) to rectangular coordinates, we use the formulas,

x = r * cos(θ)

y = r * sin(θ)

Plugging in the values,

x = 4.24 * cos(135°)

y = 4.24 * sin(135°)

Evaluating the trigonometric functions for 135°,

x = 4.24 * (-0.7071) ≈ -3

y = 4.24 * 0.7071 ≈ 3

Therefore, the rectangular coordinates for (4.24, 135°) are approximately (-3, 3). So the answer is a. (-3, 3).

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The loss percentage for the merchant is 2.5%.

The merchant bought a quintal of potatoes, which is equal to 100 kg.

The initial cost of the potatoes is Rs 4000.

The price of potatoes was reduced by Rs 1 per kg.

Initially, the cost of 1 kg of potatoes is Rs 4000 / 100 kg = Rs 40 per kg.

After the reduction, the cost of 1 kg of potatoes becomes Rs 40 - Rs 1 = Rs 39 per kg.

The total cost after the reduction is 100 kg × Rs 39/kg = Rs 3900.

Now, we can calculate the loss

Loss = Initial cost -Final cost

Loss = Rs 4000 - Rs 3900

Loss = Rs 100

To calculate the loss percentage, we can use the formula

Loss percentage = (Loss / Initial cost) × 100

Substituting the values:

Loss percentage = (Rs 100 / Rs 4000) × 100

Loss percentage = 2.5%

Therefore, the loss percentage for the merchant is 2.5%.

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The most likely cause for the change in pH after bubbling CO2 through the solution is the formation of carbonic acid.

When CO2 is bubbled through an aqueous solution, it can react with water to form carbonic acid (H2CO3). This reaction occurs due to the dissolution of CO2 in water, which undergoes a chemical equilibrium process. Carbonic acid is a weak acid that can release hydrogen ions (H+) into the solution, thus lowering the pH. The presence of carbonic acid lowers the pH value compared to the original pH of the solvent.

This phenomenon is commonly observed when CO2 is dissolved in water, such as in carbonated beverages. The carbonic acid formed from the reaction with CO2 contributes to the acidic properties of the solution. Therefore, the most likely cause for the change in pH after bubbling CO2 through the solution is the formation of carbonic acid, leading to a decrease in pH.

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Based on the hypothesis, the correct option is C. No, the Large Counts condition is not met since all expected counts are not greater than 5.

The statement mentions that the politician selects a random sample of 306 voters from her state. However, it also states that the data do not come from a random sample. This contradiction suggests that the random sample condition is not met.

The Large Counts condition for inference states that all expected counts must be greater than 5. In this case, the expected counts are:

Region 1: 103 * 0.4 = 41.2

Region 2: 103 * 0.3 = 30.9

Region 3: 103 * 0.3 = 31.9

As you can see, not all of these expected counts are greater than 5. Therefore, the Large Counts condition is not met and we cannot use the chi-square test for independence to test the politician's hypothesis.

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Answer:

y = x - 2

Step-by-step explanation:

The slope-intercept form is y = mx + b

-2/5x + 2/5y = -2

2/5y = 2/5x - 2

y = x - 2

Answer:

y=x-5

Step-by-step explanation:

-2/5x+2/5y=-2

+2/5x +2/5x

2/5y=2/5x-2

*5/2 *5/2

10/10y=10/10x-10/2

y=x-5

To convert the masses of copper and chlorine to moles, Avogadro's unit relationships can be utilized.

Avogadro's number (6.022 x 10^23) represents the number of particles (atoms, molecules, ions) in one mole of a substance. Using this concept, the relationship between mass and moles can be established by utilizing the molar mass of the respective elements.

To convert the mass of copper to moles, the molar mass of copper (Cu) is required. The molar mass of copper is determined by adding up the atomic masses of its constituent atoms, which can be found on the periodic table. By dividing the mass of copper by its molar mass, the number of moles of copper can be obtained. Similarly, to convert the mass of chlorine to moles, the molar mass of chlorine (Cl) is used. By dividing the mass of chlorine by its molar mass, the number of moles of chlorine can be determined.

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Tiffany gets 4 minutes of talk time on her cell phone per dollar cost.

If someone gets ' T ' minutes of talk time for the cost $ D so the rate of getting talk time per dollar is given by = T / D.

Given that the Tiffany pays a sum of $ 40 for talking 160 minutes on her cell phone.

So for $ 40 Tiffany gets the talk time of 160 minutes on her cell phone.

For $ 1 Tiffany gets the talk time of = 160 / 40 = 16 / 4 = 4 minutes on her cell phone.

Hence, Tiffany gets 4 minutes of talk time on her cell phone per dollar cost.

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Value falls within the 90% confidence interval for a sample size of 45 is 3.28. The correct option is C.

To determine which value falls within the 90% confidence interval for a sample size of 45, we need to calculate the margin of error and then find the range of values within that interval.

The margin of error (E) can be calculated using the formula:

E = (Z * σ) / √n

Where:

Z is the critical value corresponding to the desired confidence level (in this case, for a 90% confidence level),

σ is the standard deviation, and

n is the sample size.

The critical value for a 90% confidence level can be obtained from a standard normal distribution table, and it is approximately 1.645.

Substituting the given values into the formula, we have:

E = (1.645 * 0.98) / √45

E ≈ 0.309

The confidence interval is then calculated as the sample mean ± the margin of error.

Lower Limit = Sample Mean - E

Lower Limit = 3.56 - 0.309

Lower Limit ≈ 3.251

Upper Limit = Sample Mean + E

Upper Limit = 3.56 + 0.309

Upper Limit ≈ 3.869

From the given answer choices, the value that falls within the 90% confidence interval is:

C. 3.28

Therefore, the correct option is C. 3.28.

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If the HRM Cafe expects to generate $120,000 in annual-revenue, renting space with a monthly cost of 5% of sales which is variable cost would be the cheaper option.

To determine which option costs less for the HRM Cafe, we need to compare the total costs of each option.
Option 1: Fixed costs of $5,000 per month.
This means that the monthly rent will always be $5,000 regardless of how much revenue the cafe generates.
Annual rent cost = $5,000 x 12 months = $60,000
Option 2:Variable costs: 5% of monthly sales.
This means that the monthly rent will be a percentage of the cafe's monthly sales.
Monthly rent cost = 5% x $120,000 (annual revenue) / 12 months = $500
Annual rent cost = $500 x 12 months = $6,000
Comparing the two options, we can see that option 2 (5% of monthly sales) costs less at an annual rent cost of $6,000 compared to option 1's annual rent cost of $60,000.
The variable rent option, which is 5% of monthly sales, costs less for HRM Cafe's second location.

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Answer: its c obviously

Step-by-step explanation:

its easy

Answer:

94.5

Step-by-step explanation:

14 + 54 + 56 + 65 = 189

189 ÷ 2 = 94.5

Hope this helps :)

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The equivalent expression is 31/8

A fraction is simply defined as the portion representing the part of a whole number, a whole element or a whole variable.

In mathematics, there are different types of fractions, These includes;

From the information given, we have that the expression is written as;

3 1/4 - (-5/8)

expand the bracket, we get;

3 1/4 + 5/8

convert the improper fraction

13/4 + 5/8

Find the LCM

26 + 5/8

31/8

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American jurists (fill in the names) defined law as predictions of how a court will decide specific legal questions, based on a functional perspective.

American jurists Oliver Wendell Holmes Jr. and Benjamin Cardozo are known for their functionalist approach to defining law. They viewed law not merely as a set of abstract principles or rules, but as a prediction of how courts will decide specific legal questions in practice. According to their perspective, the law should be seen as a dynamic and evolving system that adapts to societal changes and reflects the judgments and decisions of the judiciary. By emphasizing the functional aspect of law, Holmes and Cardozo recognized the importance of considering how legal principles are actually applied and interpreted in real-world scenarios. Their approach acknowledges that the interpretation and application of law by judges can vary and evolve over time, depending on factors such as legal precedent, social context, and the specific facts of the cases before them.

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a. The appropriate model for the random variable A is the binomial distribution.

b. The probability that Alex gets at most five questions correct can be calculated using the binomial distribution formula.

c. The probability that Alex gets at least seven questions correct can also be calculated using the binomial distribution formula.

d. The probability that Alex gets no more than three questions correct can be calculated using the binomial distribution formula.

e. E(A/4) represents the expected value of A divided by 4, which is the average number of correct answers Alex is expected to get per question.

f. The probability that Alex scores more than expected would depend on the specific values of the expected value and the distribution of the random variable.

g. The expected value of Alex's total points can be calculated by multiplying the expected number of correct answers by 4 and subtracting the expected number of incorrect answers multiplied by 1.

h. The probability that at least two of the four students will get seven or more questions correct would involve calculating the probabilities for each possible combination of students using the binomial distribution and summing them up.

What is probability?

Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event.

a. The appropriate model for the random variable A, the number of questions Alex gets correct, is the binomial distribution.

b. To find the probability that the number of questions Alex gets correct is at most five, we need to calculate P(A ≤ 5) using the binomial distribution formula.

This involves summing up the probabilities of getting 0, 1, 2, 3, 4, or 5 questions correct. The specific values will depend on the probability of guessing a question correctly.

c. To find the probability that the number of questions Alex gets correct is at least seven, we need to calculate P(A ≥ 7) using the binomial distribution formula. This involves summing up the probabilities of getting 7, 8, 9, ..., 25 questions correct. Again, the specific values will depend on the probability of guessing a question correctly.

d. To find the probability that the number of questions Alex gets correct is no more than three, we need to calculate P(A ≤ 3) using the binomial distribution formula. This involves summing up the probabilities of getting 0, 1, 2, or 3 questions correct.

e. E(A/4) represents the expected value of A divided by 4. The expected value is calculated by multiplying each possible outcome by its probability and summing them up. Dividing by 4 scales down the expected value. The interpretation of E(A/4) is the average number of correct answers Alex is expected to get per question.

f. To find the probability that Alex scores more than expected, we would need to compare the actual number of questions he gets correct to the expected value. The probability would depend on the specific values of the expected value and the distribution of the random variable.

g. If a correct answer is awarded 4 points and an incorrect answer incurs a penalty of 1 point, we can calculate the expected value of Alex's total points by multiplying the expected number of correct answers by 4 and subtracting the expected number of incorrect answers and multiply it by 1.

h. To find the probability that at least two of the four students will get seven or more questions correct, we would need to calculate the probabilities for each possible combination of students getting seven or more questions correct (e.g., 2 students, 3 students, 4 students) using the binomial distribution, and sum them up.

a. The appropriate model for the random variable A is the binomial distribution.

b. The probability that Alex gets at most five questions correct can be calculated using the binomial distribution formula.

c. The probability that Alex gets at least seven questions correct can also be calculated using the binomial distribution formula.

d. The probability that Alex gets no more than three questions correct can be calculated using the binomial distribution formula.

e. E(A/4) represents the expected value of A divided by 4, which is the average number of correct answers Alex is expected to get per question.

f. The probability that Alex scores more than expected would depend on the specific values of the expected value and the distribution of the random variable.

g. The expected value of Alex's total points can be calculated by multiplying the expected number of correct answers by 4 and subtracting the expected number of incorrect answers multiplied by 1.

h. The probability that at least two of the four students will get seven or more questions correct would involve calculating the probabilities for each possible combination of students using the binomial distribution and summing them up.

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Fashion trends influence people's tastes and preferences in clothing.

Fashion trends have a significant impact on the demand for clothing and fashion accessories. They play a crucial role in shaping people's tastes and preferences, which directly affect their purchasing decisions. As fashion trends change, consumers are influenced to adopt new styles, designs, and aesthetics, leading to shifts in their demand for clothing items.

Fashion trends are a non price determinant of demand because they operate independently of the price of the products. Unlike factors like price, income, or availability, fashion trends do not directly affect the quantity demanded at a given price. Instead, they influence consumers' preferences, attitudes, and perceptions towards different clothing options, leading to changes in the overall demand for fashion products.

Fashion trends can create a sense of novelty, social acceptance, and personal expression, driving consumers to seek out specific styles or brands that align with the current trends. This influence on people's tastes and preferences in clothing can result in shifts in demand curves as consumer preferences change over time. Therefore, fashion trends are a significant nonprice determinant of demand in the fashion industry.

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For the given linear regression, the predicted value of y when t = 17 is approximately 73.3352.

What is regression?

Regression is a statistical modeling technique used to investigate the relationship between a dependent variable and one or more independent variables.

To predict the value of y when t = 17 using the given linear regression model, we can use the estimated intercept and time coefficients.

The partial computer output provides the following information for the regression model:

Variable | Estimate | T-Value | Probability

Intercept | 18.100 | 4.45 | 0.001

Time | 3.2456 | 7.71 | 0.000

In this case, the regression model can be represented as:

y = 18.100 + 3.2456t

To predict the value of y when t = 17, we substitute t = 17 into the equation and calculate the corresponding value of y:

y = 18.100 + 3.2456 * 17

y ≈ 18.100 + 55.2352

y ≈ 73.3352

Therefore, the predicted value of y when t = 17 is approximately 73.3352.

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The standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin is:

[tex]y=-\frac{1}{3}x^{2}[/tex]

What is the equation of the parabola with a vertex at the origin and a vertical axis, which passes through the point (-3, -3)?

The equation of the parabola in standard form is [tex]y=-\frac{1}{3}x^{2}[/tex]. This equation represents a parabola with a vertex at the origin (0, 0) and a vertical axis. Additionally, it passes through the point (-3, -3), satisfying the given characteristics.

To find the standard form of the equation of a parabola with a vertex at the origin and a vertical axis, we can use the general equation of a parabola:

y=[tex]a(x-h)^{2}[/tex]+k

where (h, k) = the vertex of the parabola.

Since the vertex is at the origin , the equation becomes:

y=a[tex]x^{2}[/tex]

Now, we need to find the value of 'a' using the given point on the parabola (-3, -3).

These values are satisfied the equation, we have:

[tex]-3=a(-3)^2[/tex]

Simplifying:

−3=9a

Dividing both sides by 9:

[tex]a=-\frac{1}{3}[/tex]

Therefore, the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin is:

[tex]y=-\frac{1}{3}x^{2}[/tex]

Hence, the equation  in standard form is:[tex]y=-\frac{1}{3}x^{2}[/tex]  

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The concentration of quinine in mg/L can be determined by calculating the difference in fluorescence intensity and using the given information. In this case, the concentration of quinine is approximately 6.5 mg/L.

The relationship between the concentration of quinine and its fluorescence intensity can be described using a linear equation. By comparing the fluorescence intensities at two different concentrations, we can determine the concentration of quinine in mg/L.

The change in fluorescence intensity is given by:

ΔI = I2 - I1

In this case, ΔI = 6.5 units - 3.7 units = 2.8 units.

ΔI = mΔC

where m is the slope of the line, representing the change in intensity per unit change in concentration.

Rearranging the equation, we have:

m = ΔI / ΔC

Substituting the values, we get:

m = 2.8 units / 4.0 mg/L

m ≈ 0.7 units/mg/L

Now, we can find the concentration of quinine by rearranging the linear equation:

ΔC = ΔI / m

ΔC = 2.8 units / 0.7 units/mg/L

ΔC ≈ 4.0 mg/L

Therefore, the concentration of quinine in mg/L is approximately 6.5 mg/L.

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The logo that fits the requirement is the triangle logo i.e. logo 2

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

The figures that represent the logos

For the triangle logo, we have

Area = 1/2 * 10 * 12

Convert units to meters using the scale

Area = 1/2 * (0.3 * 10) * (0.3 * 12)

Evaluate

Area = 5.4 sq meters

Also, we have

Width = 10 cm * 0.3

Width = 3.0 meters

For the logo 1, we have

Area = 2 * 8 * 3 + 6 * (12 - 2 * 3)

Convert units to meters using the scale

Area = 2 * 8 * 0.3 * 3 * 0.3 + 6 * 0.3 * (12 * 0.3 - 2 * 3 * 0.3)

Evaluate

Area = 7.56 sq meters

Also, we have

Width = 12 cm * 0.3

Width = 3.6 meters

Hence, the logo that fits the requirement is the triangle logo i.e. logo 2

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The value of the side in Monica's roof that is marked with a question mark would be = 8.3ft. That is option B.

To determine the missing length of Monica's roof the following steps should be taken as follows:

Jeff's roof = 3× Monica's roof

That is the dimensions of Monica's roof is three times Jeff's roof

Therefore, the missing length of Monica's roof = 24.9/3 = 8.3ft.

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Answer: The person above me is correct!

B) 8.3

Step-by-step explanation: 24.9 divided by 3 equals 8.3!

The true direction of the plane with the wind is approximately 63.19 degrees, and its true speed is approximately 245.94 mph.

To find the true direction and speed of the plane with the wind, we need to consider the vector addition of the plane's velocity and the wind's velocity.

First, let's break down the velocities into their respective components. The plane's velocity of 280 mph at a bearing of 150 degrees can be divided into two components: a northward component and an eastward component. Using trigonometry, we can calculate these components as follows:

Plane's northward component = 280 mph * sin(150) = -140 mph

Plane's eastward component = 280 mph * cos(150) = -241.66 mph

The wind's velocity of 40 mph in the direction of N30E can also be divided into two components:

Wind's northward component = 40 mph * cos(30) = 34.64 mph

Wind's eastward component = 40 mph * sin(30) = 20 mph

Now, we can add the respective components of the plane's velocity and the wind's velocity to obtain the true direction and speed of the plane with the wind:

Northward component: -140 mph + 34.64 mph = -105.36 mph

Eastward component: -241.66 mph + 20 mph = -221.66 mph

Using these components, we can calculate the true direction and speed of the plane with the wind. The true direction can be found using the inverse tangent function:

True direction = arctan(Eastward component / Northward component) = arctan(-221.66 mph / -105.36 mph) ≈ 63.19 degrees

The true speed of the plane with the wind can be calculated using the Pythagorean theorem:

True speed = sqrt((Northward component)^2 + (Eastward component)^2) = sqrt((-105.36 mph)^2 + (-221.66 mph)^2) ≈ 245.94 mph

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The situation described can be modeled by a linear function.

In a linear function, the relationship between the variables is constant and can be represented by a straight line on a graph. In this case, as Sarah's visits to the chiropractor increase, her fees decrease by a fixed amount of $5 each time. This means that there is a constant rate of change between the number of visits and the corresponding decrease in fees.

Let's say the number of visits is represented by the variable 'x' and the fees by the variable 'y'. The relationship can be expressed as:

y = mx + b

Where 'm' represents the rate of change (in this case, -5 because the fees decrease by $5) and 'b' represents the initial fee or the y-intercept.

Therefore, the situation of Sarah's fees decreasing by $5 each time she visits the chiropractor can be modeled by a linear function.

The length of the longest side is 50 units based on the stated length of sides and perimeter.

As per the relation between sides of triangle and it's perimeter, the formula is -

Side + side + side = perimeter

Keeping the values in formula to find the value of x

6x + 8x + 2 + 10x = 122

Performing addition on Left Hand Side of the equation

24x + 2 = 122

Rearranging the equation

24x = 122 - 2

Subtract the values

24x = 120

x = 120/24

Performing division on Right Hand Side

x = 5

Length of each side = 6×5 + ((8×5)+2), 10×5

Length = 30, 42, 50

Hence, the length of the longest side is 50.

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To compute the budgeted direct labor cost for July at Zhang Industries, we multiply the number of units produced in July (220 units) by the direct labor hours per unit (1.5 hours) and the direct labor rate ($12.20 per hour).

To calculate the budgeted direct labor cost for July, we use the formula:

Budgeted Direct Labor Cost = Number of Units * Direct Labor Hours per Unit * Direct Labor Rate

In this case, the number of units produced in July is 220 units, the direct labor hours per unit is 1.5 hours, and the direct labor rate is $12.20 per hour.

Budgeted Direct Labor Cost = 220 * 1.5 * $12.20

Simplifying the equation:

Budgeted Direct Labor Cost = $4,026

Therefore, the budgeted direct labor cost for July at Zhang Industries is $4,026. This represents the expected cost of direct labor based on the production volume and labor rate for that month. It accounts for the labor hours required to produce the units and the corresponding cost per hour.

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The mass of the aluminum can be calculated using the change in volume and the density. the mass of the aluminum is approximately 9.415 grams.

The change in volume when the aluminum is added to the graduated cylinder is equal to the volume of the aluminum. The change in volume is obtained by subtracting the initial volume (10.0 mL) from the final volume (13.5 mL), resulting in 3.5 mL.

Since the density of aluminum is given as 2.69 g/mL, we can use this information to calculate the mass of the aluminum. The density of a substance is defined as the mass per unit volume. Therefore, we can multiply the density by the volume to obtain the mass.

Using the given density of 2.69 g/mL and the volume of 3.5 mL, the mass of the aluminum can be calculated as follows:

Mass = Density x Volume = 2.69 g/mL x 3.5 mL = 9.415 g

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The upper bound of the prediction interval is approximately 41.1.

The upper bound of a prediction interval in a linear regression model can be calculated by adding the product of the critical value ([tex]\frac{t\alpha }{2}[/tex]) and the standard error (SE) to the fitted value (y). The critical value represents the desired level of confidence, such as 95%, and the standard error quantifies the variability of the model. By combining these components, the upper bound of the prediction interval provides a range within which a new observation is likely to fall, accounting for the uncertainty associated with the regression model.

To find the upper bound of the prediction interval, we can use the formula:

[tex]Upper Bound = y +(\frac{t\alpha }{2})* SE[/tex]

where y is the fitted value at x = 6, t[tex]\alpha[/tex]/2 is the critical value for a 95% confidence level (with degrees of freedom n - 2), and SE is the standard error.

Given information:

SSE = 552

n = 21

sx = 27.45

[tex]\bar x[/tex] = 9

y = 29.82

To calculate the standard error (SE) using the formula:

[tex]SE = \sqrt\frac{SSE}{ (n - 2)}[/tex]

[tex]SE = \sqrt\frac{552}{(21 - 2)}[/tex]

[tex]SE = \sqrt\frac{552}{ 19}[/tex]

SE ≈ 5.39

To find the critical value t[tex]\alpha[/tex]/2 for a 95% confidence level with degrees of freedom (n - 2). Since n = 21, degrees of freedom = 21 - 2 = 19.

Using statistical tables or a calculator, the tα/2 value for a 95% confidence level with 19 degrees of freedom is approximately 2.093.

Now, we can calculate the upper bound of the prediction interval:

[tex]Upper Bound = y + \frac{t\alpha }{2} * SE[/tex]

Upper Bound = 29.82 + (2.093 *5.39)

Calculating:

Upper Bound ≈ 29.82 + 11.28

Upper Bound ≈ 41.1

Therefore, the upper bound of the prediction interval, rounded to two decimal places, is approximately 41.1

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Answer:

The width of the flower bed is 3.5 m

Step-by-step Explanation:

(2x + 8) * (2x + 4) = 165

Step 1:  Expand equation by multiplying and adding 2x * 2x, 2x * 4, 8 * 2x, and 8 * 4:

(2x * 2x) + (2x * 4) + (8 * 2x) + (8 * 4) = 165

2x^2 + 8x + 16x + 32 = 165

2x^2 + 24x + 32 = 165

Step 2:  Subtract 165 from both sides to prepare quadratic for solving:

(2x^2 + 24x + 32 = 165) - 165

2x^2 + 24x - 133 = 0

Step 3:  Solve with quadratic equation:

Currently 2x^2 + 24x - 133 = 0 in standard form, whose general equation is:

ax^2 + bx + c = 0

Thus, in 2x^2 + 24x - 133 = 0, 2 is a, 24 is b, and -133 c.

The quadratic equation is:

[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

(Remember that the +/- comes from the fact that there can be both a positive and negative solution to a quadratic.

Let's find the positive solution then the negative solution:

Step 4:  Find positive solution:

[tex]x=\frac{-24+\sqrt{24^2-4(2)(-133)} }{2(4)}\\ \\x=\frac{-24+\sqrt{2704} }{8}\\ x=(-24/8)+(52/8)\\x=-3+6.5\\x=3.5[/tex]

Step 5:  Find negative solution:

[tex]x=\frac{-24-\sqrt{24^2-4(2)(-133)} }{2(4)}\\ \\x=\frac{-24-\sqrt{2704} }{8}\\ x=(-24/8)-(52/8)\\x=-3-6.5\\x=-9.5[/tex]

We can't have a negative measure, so the width of the flower bed is 3.5 m.

Optional Step 6:  Check validity of answer:

We can check that 3.5 is the correct answer by plugging in 3.5 for x in (2x + 8)(2x + 4) = 165 and checking that we get 165 on both sides:

(2 * 3.5 + 8)(2 * 3.5 + 4) = 165

(7 + 8)(7 + 4) = 165

(15)(11) = 165

165 = 165

Thus, our answer is correct.