Example 1 Does y = e* - 2 exist? What is the domain & range of the function ifit does exist? (show full working out)
Example 1 Does y = e* - 2 exist? What is the domain & range of the function ifit 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
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can u solve example1
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A CALCULUS_pdf.pdf
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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 € [0,4x] (show full working out for all intercepts and turning
points).
Example 3
Find the derivative of In(3t² – 2t + 1) and then calculate f +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 Sx<3
f(x) = }k(6 – x), 3 S x56
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)
Example 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 distrībution of the sample proportion
of milk chocolate bars in the sample.
b. Evaluate Pr(0<P< 0.7) and hence evaluate Pr(P<0.7|P>0).
7:34 AM
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10/13/2020
>](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee1dcf8a-1c5c-42e9-8c79-eba0c591ecab%2Fa6179bc4-6fc5-448f-b4a6-6e9ab28cac4c%2Fydymgt8_processed.png&w=3840&q=75)
Transcribed Image Text:D SIMPLE_SAMPLE_QUESTIONS_20 X
A CALCULUS_pdf.pdf
O File | C:/Users/USER/AppData/Local/Microsoft/Windows/INetCache/IE/68NCA10W/SIMPLE_SAMPLE_QUESTIONS_2020[1].pdf
A) Read aloud
V Draw
F Highlight
O Erase
1
of 1
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 € [0,4x] (show full working out for all intercepts and turning
points).
Example 3
Find the derivative of In(3t² – 2t + 1) and then calculate f +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 Sx<3
f(x) = }k(6 – x), 3 S x56
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)
Example 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 distrībution of the sample proportion
of milk chocolate bars in the sample.
b. Evaluate Pr(0<P< 0.7) and hence evaluate Pr(P<0.7|P>0).
7:34 AM
P Type here to search
Hi
321
14
10/13/2020
>
![D SIMPLE_SAMPLE_QUESTIONS_20 X
CALCULUS_pdf.pdf
| +
O File | C:/Users/USER/AppData/Local/Microsoft/Windows/INetCache/IE/68NCA10W/SIMPLE_SAMPLE_QUESTIONS_2020[1].pdf
+
--
A) Read aloud
V Draw
F Highlight
O Erase
1
of 1
The yield of a variety of Farmer Jase's pumpkin patch has a probability density function:
kx, 0 Sx<3
f(x) = }k(6 – x), 3 <x56
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)
Example 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 distrībution table showing the sampling distribution of the sample proportion
of milk chocolate bars in the sample.
b. Evaluate Pr(0<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.
a. Create a probability distrībution 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)
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)
7:34 AM
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321
10/13/2020
>](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee1dcf8a-1c5c-42e9-8c79-eba0c591ecab%2Fa6179bc4-6fc5-448f-b4a6-6e9ab28cac4c%2Fiyyem0c_processed.png&w=3840&q=75)
Transcribed Image Text:D SIMPLE_SAMPLE_QUESTIONS_20 X
CALCULUS_pdf.pdf
| +
O File | C:/Users/USER/AppData/Local/Microsoft/Windows/INetCache/IE/68NCA10W/SIMPLE_SAMPLE_QUESTIONS_2020[1].pdf
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A) Read aloud
V Draw
F Highlight
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1
of 1
The yield of a variety of Farmer Jase's pumpkin patch has a probability density function:
kx, 0 Sx<3
f(x) = }k(6 – x), 3 <x56
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)
Example 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 distrībution table showing the sampling distribution of the sample proportion
of milk chocolate bars in the sample.
b. Evaluate Pr(0<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.
a. Create a probability distrībution 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)
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)
7:34 AM
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321
10/13/2020
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