Example 1 Does y = e9-** - 2 exist? What is the domain & range of the function if it does exist? (show full working out)
Example 1 Does y = e9-** - 2 exist? What is the domain & range of the function if it does exist? (show full working out)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Only 1st 4th 5th 6th
![Example 1
Does y = e9-x* – 2 exist? What is the domain & range of the function if it does exist? (show full working out)
Example 2
Sketch a graph for y = 2 sin (x +) + 1, x € [0,47] (show full working out for all intercepts and turning
points).
Example 3
9r-2
Find the derivative of In(3t3 – 2t + 1) and then calculate f
3t-2t+1
+ 3 dt (use integration by recognition).
Example 4
The probability of winning a prize in a game of chance is 0.48. What is the least number of games that must be
played to ensure that the probability of winning at least twice is more than 0.95?
Example 5
The yield of a variety of Farmer Jase's pumpkin patch has a probability density function:
kx,0 <x<3
f(x) = }k(6 – x), 3 <x< 6
0, x <0 or x >6
a. Find the variance
b. Find the probability Pr(u – 1<X<µ+1)
c. Find the value of a such that Pr(X > a) = 0.6, giving your answer correct to one decimal place.
Example 6
In a small factory producing bamboo products, the standard acceptable measurement for a bamboo straws'
lengths are between 10.085 cm and 12.075 cm. Alexis has noticed that 6% of the straws are rejected for being
too short and another 6% are rejected for being too tall. What is the mean and standard deviation of
distribution assuming that the straws' lengths are normally distributed? (2dp)
Еxample 7
A sample of four chocolate bars are randomly selected from a box of ten. Six of the chocolates in the box are
milk chocolate. (without replacement)
a. Create a probability distribution table showing the sampling distribution of the sample proportion
of milk chocolate bars in the sample.
b. Evaluate Pr(o<P< 0.7) and hence evaluate Pr(P < 0.7|P > 0).
Example 8
In a particular university, the probability that any one student is male is 0.65. Four students are selected at
random from this university as a sample.
Create a probability distribution table showing the sampling distribution of the sample proportion
of female students in the sample. (4dp)
b. Find Pr(P < 0.65| P>0). (4dp)
a.
Example 9
A study is done in Sydney to estimate the proportion of people living there who have travelled outside of
Australia. Previous research has found that this proportion is equal to roughly 28%.
a. Find the minimum sample size needed for the study in order to obtain a minimum of 5% margin of
error in an approximate 95% confidence interval for this proportion. (use k=1.96)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54fb0c70-0115-4b7d-8310-ccc146613760%2F2040a048-46dc-405e-bd71-3cc3db31200b%2Ft9c0l9m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Example 1
Does y = e9-x* – 2 exist? What is the domain & range of the function if it does exist? (show full working out)
Example 2
Sketch a graph for y = 2 sin (x +) + 1, x € [0,47] (show full working out for all intercepts and turning
points).
Example 3
9r-2
Find the derivative of In(3t3 – 2t + 1) and then calculate f
3t-2t+1
+ 3 dt (use integration by recognition).
Example 4
The probability of winning a prize in a game of chance is 0.48. What is the least number of games that must be
played to ensure that the probability of winning at least twice is more than 0.95?
Example 5
The yield of a variety of Farmer Jase's pumpkin patch has a probability density function:
kx,0 <x<3
f(x) = }k(6 – x), 3 <x< 6
0, x <0 or x >6
a. Find the variance
b. Find the probability Pr(u – 1<X<µ+1)
c. Find the value of a such that Pr(X > a) = 0.6, giving your answer correct to one decimal place.
Example 6
In a small factory producing bamboo products, the standard acceptable measurement for a bamboo straws'
lengths are between 10.085 cm and 12.075 cm. Alexis has noticed that 6% of the straws are rejected for being
too short and another 6% are rejected for being too tall. What is the mean and standard deviation of
distribution assuming that the straws' lengths are normally distributed? (2dp)
Еxample 7
A sample of four chocolate bars are randomly selected from a box of ten. Six of the chocolates in the box are
milk chocolate. (without replacement)
a. Create a probability distribution table showing the sampling distribution of the sample proportion
of milk chocolate bars in the sample.
b. Evaluate Pr(o<P< 0.7) and hence evaluate Pr(P < 0.7|P > 0).
Example 8
In a particular university, the probability that any one student is male is 0.65. Four students are selected at
random from this university as a sample.
Create a probability distribution table showing the sampling distribution of the sample proportion
of female students in the sample. (4dp)
b. Find Pr(P < 0.65| P>0). (4dp)
a.
Example 9
A study is done in Sydney to estimate the proportion of people living there who have travelled outside of
Australia. Previous research has found that this proportion is equal to roughly 28%.
a. Find the minimum sample size needed for the study in order to obtain a minimum of 5% margin of
error in an approximate 95% confidence interval for this proportion. (use k=1.96)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
