Question 1:
There are 180 primary schools in a country area having an average of 30 or more people under the age of 21 per class. A sample of 30 schools drawn using systematic sampling with an interval of k = 6.
Serial number |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
No. of students |
60 |
200 |
45 |
50 |
40 |
79 |
35 |
41 |
30 |
120 |
Serial number |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
No. of students |
300 |
65 |
111 |
120 |
200 |
42 |
51 |
67 |
32 |
40 |
Serial number |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
No. of students |
46 |
55 |
250 |
100 |
63 |
90 |
47 |
82 |
31 |
50 |
In: Advanced Math
what combinations using only 0, 1,2, then transform that number to base 3, can give 7 when doing modulus division 9. Need a number x in base 10 that when transformed in base 3, where x%9 = 7
In: Advanced Math
Solve the given initial value problem by undetermined coefficients (annihilator approach).
y'' − 4y' + 4y = e^4x + xe^−2x
y(0) = 1
y'(0) = −1
In: Advanced Math
Lab Assignment
Part B - Recurrence Intervals
Data from the chart below was collected at the USGS site and includes the 20 largest discharge events for Sweetwater Creek at station 02337000 from January 1, 2008 through May 1, 2015, excluding the dramatic 2009 flood (we will learn more about that later). In order to create a flood-frequency graph, you must first calculate the recurrence interval (one is calculated below as an example). A recurrence interval refers to the average time period within which a given flood event will be equaled or exceeded once. To calculate it, first evaluate the rank of the flood, with a “1” going to the highest discharge event and a “20” going to the lowest discharge event. Calculate the recurrence interval using the following equation:
RI = (n+1) ÷ m
where, RI = Recurrence Interval (years)
n = number of years of records (in this case, 8)
m = rank of flood. Peak Discharge Date |
Discharge (cubic ft/sec = cfs) |
Rank |
Recurrence Interval (years) |
08/27/2008 |
5,140 |
||
03/02/2009 |
2,360 |
||
10/13/2009 |
3,290 |
||
11/12/2009 |
6,120 |
1 |
9 |
12/03/2009 |
2,860 |
||
12/10/2009 |
2,170 |
||
12/19/2009 |
3,830 |
||
12/26/2009 |
2,650 |
||
01/25/2010 |
2,500 |
||
02/06/2010 |
3,680 |
||
03/12/2010 |
3,600 |
||
03/10/2011 |
2,350 |
||
04/17/2011 |
3,100 |
||
02/24/2013 |
2,060 |
||
02/27/2013 |
2,190 |
||
05/06/2013 |
3,610 |
||
12/23/2013 |
3,790 |
||
04/08/2014 |
4,170 |
||
01/05/2015 |
3,970 |
||
04/20/2015 |
2,940 |
In: Advanced Math
General Ford produces cars in Los Angeles and Detroit and has a warehouse in Atlanta. The company supplies cars to customers in Houston and Tampa. The costs of shipping a car between various points are listed in the file P05_54.xlsx, where a blank means that a shipment is not allowed. Los Angeles can produce up to 1600 cars, and Detroit can produce up to 3200 cars. Houston must receive 1800 cars, and Tampa must receive 2900 cars. a. Determine how to minimize the cost of meeting demands in Houston and Tampa. b. Modify the answer to part a if no shipments through Atlanta are allowed.
unit shipping cost | |||||||||
to | |||||||||
LA | Detroit | Atlanta | Houston | Tampa | |||||
from | LA | $97 | $95 | $125 | $156 | ||||
Detroit | $94 | $103 | $110 | $148 | |||||
Atlanta | $87 | $100 | $95 | $56 | |||||
Houston | $129 | $103 | $88 | $100 | |||||
Tampa | $147 | $145 | $60 | $103 | |||||
network formulation | flow balance contraints | ||||||||
origin | destination | cost | flow | location | index | net flow in/out | Required | ||
1 | 2 | $97 | LA | 1 | <= | ||||
1 | 3 | $95 | Detroit | 2 | <= | ||||
1 | 4 | $125 | Atlanta | 3 | = | ||||
1 | 5 | $156 | Houston | 4 | = | ||||
2 | 1 | $94 | Tampa | 5 | = | ||||
2 | 3 | $103 | |||||||
2 | 4 | $110 | |||||||
2 | 5 | $148 | |||||||
3 | 1 | $87 | |||||||
3 | 2 | $100 | |||||||
3 | 4 | $95 | |||||||
3 | 5 | $56 | |||||||
4 | 1 | $129 | |||||||
4 | 2 | $103 | |||||||
4 | 3 | $88 | |||||||
4 | 5 | $100 | |||||||
5 | 1 | $147 | |||||||
5 | 2 | $145 | |||||||
5 | 3 | $60 | |||||||
5 | 4 | $103 |
total cost
In: Advanced Math
What are the primary differences among the CF valuation model, asset-based valuation model, and multiples valuation model?
In: Advanced Math
1. Show that if u is harmonic in a domain Ω, then also
the derivatives of
u of any order are harmonic in Ω. (Hint: To get the result for any
order
you may want to use induction).
In: Advanced Math
Gabriella and Steve have adjusted gross incomes of $47 comma 200 and $32 comma 700, respectively. Assume that each person takes one exemption and the standard deduction. Answer parts (a) through (c) below.
Tax Rate |
Single |
Married Filing Jointly |
---|---|---|
10% |
up to $8,925 |
up to $17,850 |
15% |
up to $36,250 |
up to $72,500 |
25% |
up to $87,850 |
up to $146,400 |
28% |
up to $183,250 |
up to $223,050 |
Standard Deduction |
$6100 |
$12,200 |
Exemptions (per person) |
$3900 |
$3900 |
a. Calculate the tax owed by the couple if they delay their marriage until next year so they can each file a tax return at the single tax rate this year.
The couple owes ______
(Simplify your answer. Round to the nearest dollar as needed.)
b. Calculate the tax owed by the couple if they marry before the end of the year and file a joint return.
The couple owes____________
(Simplify your answer. Round to the nearest dollar as needed.)
c. Does the couple face a "marriage penalty" if they marry before the end of the year?
In: Advanced Math
In: Advanced Math
The following table lists a portion of Major League Baseball’s (MLB’s) leading pitchers, each pitcher’s salary (In $ millions), and earned run average (ERA) for 2008. Salary ERA J. Santana 17.0 2.28 C. Lee 3.0 2.39 ⋮ ⋮ ⋮ C. Hamels 0.2 3.00 Click here for the Excel Data File a-1. Estimate the model: Salary = β0 + β1ERA + ε. (Negative values should be indicated by a minus sign. Enter your answers, in millions, rounded to 2 decimal places.) Salaryˆ= + ERA a-2. Interpret the coefficient of ERA. A one-unit increase in ERA, predicted salary decreases by $3.20 million. A one-unit increase in ERA, predicted salary increases by $3.20 million. A one-unit increase in ERA, predicted salary decreases by $11.92 million. A one-unit increase in ERA, predicted salary increases by $11.92 million. b. Use the estimated model to predict salary for each player, given his ERA. For example, use the sample regression equation to predict the salary for J. Santana with ERA = 2.28. (Round coefficient estimates to at least 4 decimal places and final answers, in millions, to 2 decimal places.) c. Derive the corresponding residuals. (Negative values should be indicated by a minus sign. Round coefficient estimates to at least 4 decimal places and final answers, in millions, to 2 decimal places.)
In: Advanced Math
Solve x(y^2+U)Ux -y(x^2+U)Uy =(x^2-y^2)U, U(x,-x)=1
In: Advanced Math
In: Advanced Math
3. The Krov band is touring the UK. They have played eight dates and already their tour is a great success. Total post-gig sales (merchandising, CDs etc.) on each date have been:
Date no. |
Sales (£000s) |
|||
1 |
3 |
|||
2 |
7 |
|||
3 |
15 |
|||
4 |
14 |
|||
5 |
18 |
|||
6 |
21 |
|||
7 |
16 |
|||
8 |
22 |
|||
9 |
||||
In: Advanced Math
data:
weight in lb | Mat-A | Mat-B |
49 | 13.2 | 14 |
51 | 8.2 | 8.8 |
46 | 10.9 | 11.2 |
50 | 14.3 | 14.2 |
51 | 10.7 | 11.8 |
47 | 6.6 | 6.4 |
44 | 9.5 | 9.8 |
47 | 10.8 | 11.3 |
46 | 8.8 | 9.3 |
In: Advanced Math
For each of the following data sets, write a system of equations to determine the coefficients of the natural cubic spline passing through the given points.
x| 2 4 7
-------------
y| 2 8 12
In: Advanced Math