Question 1

Find the area of the region under the given curve  over the indicated interval. 
A)  sq units
B)  sq units
C)  sq units
D)  sq units

Accepted Answer

The answer of Find the area of the region under...

Question 2

Evaluate the following improper integral whenever it is convergent. 
A)5
B)6
C)7
D)9
E)the integral is divergent

Accepted Answer

The answer of Evaluate the following improper integral whenever it...

Question 3

The life span of a certain plant species (in days) is described by the probability density function  Find the probability that a plant of this species will live for 95 days or less.Please round the answer to the nearest thousandth if necessary.  __________
Find the probability that a plant of this species will live more than 130 days.Please round the answer to the nearest thousandth if necessary.  __________
Find the probability that a plant of this species will live more than 60 days but less than 150 days.Please round the answer to the nearest thousandth if necessary.  __________

Accepted Answer

The answer of The life span of a certain plant...

Question 4

Find the area of the region bounded by the x-axis and the graph of the function. 
A)  sq units
B)  sq units
C)  sq units
D)  sq units
E)  sq units

Accepted Answer

The answer of Find the area of the region bounded...

Question 5

The number of streets in the downtown section of a certain city that need repairs in a given year is a random variable with a distribution described by the probability density function  Find the probability that at most half of the streets will need repairs in any given year.

Accepted Answer

The answer of The number of streets in the downtown...

Question 6

Find the area of the region under the given curve  over the indicated interval. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the area of the region under...

Question 7

Find the area of the region under the given curve  over the indicated interval. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The area under a curve can be found using definite integration. Integrating 11eb12b0_a947_0598_b394_f396d97e342c_TB7866_11 over the interval 11eb12b0_a947_0599_b394_f1b6ec4f283c_TB7866_11 gives:

11eb12b0_a947_2cab_b394_2d14df02067d_TB7866_11

This matches with option B.

Question 8

Find the area of the region bounded by the x-axis and the graph of the function 
A)4 sq units
B)  sq unit
C)  sq unit
D)0 sq units

Accepted Answer

The answer of Find the area of the region bounded...

Question 9

Find the area of the region under the given curve  over the indicated interval. 
A)10 sq units
B)12 sq units
C)9 sq units
D)6 sq units

Accepted Answer

To find the area under the curve, we need to integrate the function over the given interval. 
∫(11x-x²)dx from x=1 to x=2
= [(11/2)x² - (1/3)x³] from x=1 to x=2
= [(11/2)(2²) - (1/3)(2³)] - [(11/2)(1²) - (1/3)(1³)]
= (22/2 - 8/3) - (11/2 - 1/3)
= 9/2 - 17/6
= 27/6 - 17/6
= 10/6
= 5/3
Therefore, the area is 5/3 square units, which is closest to 9 square units, making choice C the best answer.

Question 10

Determine whether the given function is a probability density function on the specified interval.

Accepted Answer

The answer of Determine whether the given function is a...

Question 11

Find the area of the region under the given curve  over the indicated interval. 
A)  sq unit
B)  sq unit
C)  sq unit
D)  sq units
E)  sq unit

Accepted Answer

The answer of Find the area of the region under...

Question 12

Determine whether the statement is true or false.
If  is a probability density function of a continuous random variable  in the interval  , then the expected value of  is given by

Accepted Answer

The answer of Determine whether the statement is true or...

Question 13

Show that the function  is a probability density function on the interval  .

Accepted Answer

The answer of Show that the function  is a...

Question 14

The amount of time t (in seconds) it takes a motorist to react to a road emergency is a continuous random variable with probability density function  What is the expected reaction time for a motorist chosen at random?

Accepted Answer

The answer of The amount of time t (in seconds)...

Question 15

Find the area of the region under the given curve  over the indicated interval. 
A)  sq unit
B)  sq units
C)  sq unit
D)  sq unit
E)  sq unit

Accepted Answer

To find the area under the curve, we need to integrate the function with respect to x from the lower limit to the upper limit of the given interval. Using integration, we get:

∫(11eb12b0_a946_b771_b394_951f91c6e80a_TB7866_11)dx = [11eb12b0_a946_de86_b394_915349a5d6f9_TB7866_11*x] from 11eb12b0_a946_b772_b394_d102c2720b62_TB7866_11 to 11eb12b0_a946_b773_b394_fc7a3ee4a4c7_TB7866_11

Substituting the limits of integration, we get:

[11eb12b0_a946_de86_b394_915349a5d6f9_TB7866_11*(11eb12b0_a946_b773_b394_fc7a3ee4a4c7_TB7866_11 - 11eb12b0_a946_b772_b394_d102c2720b62_TB7866_11)]

Simplifying the expression using arithmetic operations, we get:

11eb12b0_a946_de84_b394_27678bbb12fd_TB7866_11 square units

Thus, the correct choice is B.

Question 16

Determine whether the statement is true or false.
If  exists, then  exists and  .

Accepted Answer

The answer of Determine whether the statement is true or...

Question 17

National Welding uses industrial robots in some of its assembly-line operations.Management has determined that, on average, a robot breaks down after 1,000 hours of use and that the lengths of time between breakdowns are exponentially distributed.
a.What is the probability that a robot selected at random will break down between 300 and 600 hours of use?
Round your answer to two decimal places.
b.What is the probability that a robot will break down after 1,100 hours of use?
Round your answer to two decimal places.

Accepted Answer

The answer of National Welding uses industrial robots in some...

Question 18

a.Determine the value of the constant k so that the function  is a probability density function on the interval  .  __________
b.If x is a continuous random variable with the probability density function given in part (a), find the probability that x will assume a value greater than 1.
Round your answer to four decimal places.

Accepted Answer

The answer of a.Determine the value of the constant k...

Question 19

Evaluate the following improper integral whenever it is convergent. 
A)17
B)26
C)8
D)18
E)the integral is divergent

Accepted Answer

The answer of Evaluate the following improper integral whenever it...

Question 20

Find the area of the region under the curve  over the indicated interval. 
A)  sq units
B)  sq units
C)  sq units
D)  sq units
E)  sq units

Accepted Answer

The answer of Find the area of the region under...

Quiz 7: Additional Topics in Integration

Find the area of the region under the given curve over the indicated interval.

Evaluate the following improper integral whenever it is convergent.

Find the area of the region bounded by the x-axis and the graph of the function.

The number of streets in the downtown section of a certain city that need repairs in a given year is a random variable with a distribution described by the probability density function Find the probability that at most half of the streets will need repairs in any given year.

Find the area of the region under the given curve over the indicated interval.

Find the area of the region under the given curve over the indicated interval.

Find the area of the region bounded by the x-axis and the graph of the function

Find the area of the region under the given curve over the indicated interval.

Determine whether the given function is a probability density function on the specified interval.

Find the area of the region under the given curve over the indicated interval.

Determine whether the statement is true or false. If is a probability density function of a continuous random variable in the interval , then the expected value of is given by

Show that the function is a probability density function on the interval .

The amount of time t (in seconds) it takes a motorist to react to a road emergency is a continuous random variable with probability density function What is the expected reaction time for a motorist chosen at random?

Find the area of the region under the given curve over the indicated interval.

Determine whether the statement is true or false. If exists, then exists and .

Evaluate the following improper integral whenever it is convergent.

Find the area of the region under the curve over the indicated interval.