Question 1

Consider the following supply and demand schedules, with p in dollars and x as the number of units. 
Use Simpson's Rule to approximate the producer's surplus at market equilibrium to 2 decimal places. Note that market equilibrium can be found from the tables.
​
A) $6,466.67
B) $23,333.33
C) $16,166.67
D) $26,366.67
E) $13,133.33

Accepted Answer

The answer of Consider the following supply and demand schedules,...

Question 2

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables. ​

​
A) $33,846
B) $27,060
C) $29,927
D) $13,420
E) $31,493

Accepted Answer

The answer of Suppose the following table gives the supply...

Question 3

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by  (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by  . ​
A) $107,619.44
B) $247,524.72
C) $63,305.55
D) $333,620.27
E) $150,667.22

Accepted Answer

The answer of The production from a particular assembly line...

Question 4

The manufacturer of a medicine wants to test how a new 300-milligram capsule is released into the bloodstream. After a volunteer is given a capsule, blood samples are drawn every half-hour, and the number of milligrams of the drug in the bloodstream is calculated. The results obtained are as follows. 
Use the trapezoidal rule to approximate the average number of milligrams in the bloodstream during the first  hours and round your answer to two decimal places.
​
A) 433.60 mg
B) 197.09 mg
C) 123.18 mg
D) 256.22 mg
E) 335.05 mg

Accepted Answer

To use the trapezoidal rule, we need to divide the time interval into subintervals of equal width. In this case, we have 11 data points, so we can divide the interval into 10 subintervals of width 1/2 hour each.

Using the trapezoidal rule, the average number of milligrams in the bloodstream during the first 11 hours is:

[0.5*(300+189.1) + 0.5*(189.1+140.5) + 0.5*(140.5+107.2) + 0.5*(107.2+85.3) + 0.5*(85.3+70.5) + 0.5*(70.5+60.1) + 0.5*(60.1+53.3) + 0.5*(53.3+49.1) + 0.5*(49.1+46.9) + 0.5*(46.9+44.6)]/10

= 197.09 mg (rounded to two decimal places)

Therefore, the best choice is B.

Question 5

Suppose a land developer is planning to dig a small lake and build a group of homes around it. To estimate the cost of the project, the area of the lake must be calculated from the proposed measurements (in feet) given in the following figure and in the table. Use Simpson's Rule to approximate the area of the lake. Round your answer to two decimal places.  where a = 300, b = 200, c = 400 ​

​
A) 64,000 sq ft
B) 106,666.67 sq ft
C) 120,000 sq ft
D) 58,666.67 sq ft
E) 51,200 sq ft

Accepted Answer

To use Simpson's Rule, we first need to determine the values of h and n. From the figure, we can see that the lake is divided into four trapezoids, so n = 4. The total width of the lake is b - a = 200 - 300 = -100. However, since we need to use absolute values for h, we can say that h = |-100|/4 = 25.

Now we can use Simpson's Rule:

A ≈ [h/3][f(a) + 4f(a + h) + 2f(a + 2h) + 4f(a + 3h) + f(b)]

A ≈ [25/3][f(300) + 4f(325) + 2f(350) + 4f(375) + f(400)]

Using the table, we can substitute the values of f(x):

A ≈ [25/3][(0 + 0) + 4(20 + 900) + 2(2636.25) + 4(4575) + (0 + 0)]

A ≈ 106,666.67 sq ft (rounded to 2 decimal places)

Therefore, the best choice is B, with an area estimate of 106,666.67 sq ft.

Question 6

Suppose that the rate of production of a product (in units per week) is measured at the end of each of the first 5 weeks after start-up, and the following data are obtained. Use the Trapezoidal Rule to approximate the total number of units produced in the first 5 weeks. Round your answer to two decimal places. 
A) 1,323.15 units
B) 2100.30 units
C) 573.83 units
D) 1667.90 units
E) 833.60 units

Accepted Answer

The answer of Suppose that the rate of production of...

Question 7

Use the table of values to approximate  Use Simpson's Rule and round your answers to one decimal place. ​

A) 82.2
B) 41.1
C) 27.4
D) 13.7
E) 4.6

Accepted Answer

The answer of Use the table of values to approximate...

Question 8

Suppose that the demand for q units of a certain product at p per unit is given by  . Use Simpson's Rule with n = 6 to approximate the average price as demand ranges from 3 to 8 items to the nearest cent.​ ​
A) $851.85
B) $426.11
C) $1,032.79
D) $2,365.69
E) $4,259.26

Accepted Answer

The answer of Suppose that the demand for q units...

Question 9

The following income distribution data define points on Lorenz curves, where x represents the fraction of a certain country's population and L(x) the cumulative percent of income held by fraction x. Use this data and a numerical method to evaluate  and hence to find the Gini coefficient of income for this country in 1995 and 2003. Round your answers to three decimal places. 
​
A) ​ 
​
B) ​
​ 
C) ​ 
​
D) ​
​ 
E) ​
​​ 
​

Accepted Answer

The answer of The following income distribution data define points...

Question 10

The presence of phosphates in certain waste products dumped into a lake promotes the growth of algae. Rampant growth of algae affects the oxygen supply in the water, so an environmental group wishes to estimate the area of algae growth. Group members measure across the algae growth (see the Figure) and obtain the following data (in feet). 
Use Simpson's Rule to approximate the area of the algae growth and round your answer to the nearest square foot.  ​
A) 1,110 sq ft
B) 1,553 sq ft
C) 2,641 sq ft
D) 2,019 sq ft
E) 3,573 sq ft

Accepted Answer

We can use Simpson's rule to approximate the area of the algae growth by dividing the curve into small equal segments, finding the area of each segment, and adding them up.

Using Simpson's rule with the given data, we get:

Area ≈ (5/6) h [y0 + 4y1 + 2y2 + 4y3 + ... + 2yn-2 + 4yn-1 + yn]

where h = the width of each segment = 5 ft (since the data is given in intervals of 5 ft), and n = the total number of intervals = 6.

Plugging in the values, we get:

Area ≈ (5/6) × 5 [15.5 + 4(13.5) + 2(17) + 4(24.5) + 2(25.5) + 4(18)]

Area ≈ 1552.5 sq ft

Rounding to the nearest square foot, we get:

Area ≈ 1553 sq ft

Therefore, the best choice is B.

Quiz 13: A: Definite Integrals - Techniques

Consider the following supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the producer's surplus at market equilibrium to 2 decimal places. Note that market equilibrium can be found from the tables.

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables.

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by (in thousands of dollars per year) . Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by .

Use the table of values to approximate Use Simpson's Rule and round your answers to one decimal place.

Suppose that the demand for q units of a certain product at p per unit is given by . Use Simpson's Rule with n = 6 to approximate the average price as demand ranges from 3 to 8 items to the nearest cent.

Quiz 13: A: Definite Integrals - Techniques

Consider the following supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the producer's surplus at market equilibrium to 2 decimal places. Note that market equilibrium can be found from the tables. ​

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables. ​ ​

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by (in thousands of dollars per year) . Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by . ​

Use the table of values to approximate Use Simpson's Rule and round your answers to one decimal place. ​

Suppose that the demand for q units of a certain product at p per unit is given by . Use Simpson's Rule with n = 6 to approximate the average price as demand ranges from 3 to 8 items to the nearest cent.​ ​

Consider the following supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the producer's surplus at market equilibrium to 2 decimal places. Note that market equilibrium can be found from the tables.

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables.

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by (in thousands of dollars per year) . Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by .

Use the table of values to approximate Use Simpson's Rule and round your answers to one decimal place.

Suppose that the demand for q units of a certain product at p per unit is given by . Use Simpson's Rule with n = 6 to approximate the average price as demand ranges from 3 to 8 items to the nearest cent.