A visible-factor number is a natural number that is divisible by each of its nonzero digits, for example, 424 or 505. How many visible-factor numbers are less than 100?
In: Advanced Math
In: Computer Science
Let P1 = number of Product 1 to be produced
P2 = number of Product 2 to be produced
P3 = number of Product 3 to be produced
P4 = number of Product 4 to be produced
Maximize 15P1 + 20P2 + 24P3 + 15P4 Total profit
Subject to
8P1 + 12P2 + 10P3 + 8P4 ≤ 3000 Material requirement constraint
4P1 + 3P2 + 2P3 + 3P4 ≤ 1000 Labor hours constraint
P2 > 120 Minimum quantity needed for Product 2 constraint
And P1, P2, P3, P4 ≥ 0 Non-negativity constraints.
(a) What are the ranges of optimality for the profit of Product 1, Product 2, Product 3, and Product 4?
(b) Find the shadow prices of the three constraints and interpret their meanings. What are the ranges in which each of these shadow prices is valid?
(c) If the profit contribution of Product 3 changes from $24 per unit to $50 per unit, what will be the optimal solution? What will be the new total profit? (Note: Answer this question by using the sensitivity results given above. Do not solve the problem again).
(d) Which resource should be obtained in larger quantity to increase the profit most? (Note: Answer this question using the sensitivity results given above. Do not solve the problem again).
In: Statistics and Probability
Number 5 (8 pts) An analysis of variance on the mean number of hours that Glendon students sleep the night after consuming either one of two different brands of energy drinks or an herbal tea at lunch indicates that the means are not all the same. Further data is gathered, with the following results
| Treatment | SAMPLE SIZE | Mean number of hours of sleep | Standard deviation of hours of sleep |
| DRINK A | 21 | 7.5 | 0.5 |
| DRINK B | 21 | 7.8 | 0.3 |
| HERBAL | 21 | 8 | 0.6 |
Use a contrast to test at a 5% level of significance whether the energy drinks lead to a lower number of mean hours of sleep than the herbal tea.
In: Statistics and Probability
Number 5 (8 pts) An analysis of variance on the mean number of hours that Glendon students sleep the night after consuming either one of two different brands of energy drinks or an herbal tea at lunch indicates that the means are not all the same. Further data is gathered, with the following results
| Treatment | SAMPLE SIZE | Mean number of hours of sleep | Standard deviation of hours of sleep |
| DRINK A | 21 | 7.5 | 0.5 |
| DRINK B | 21 | 7.8 | 0.3 |
| HERBAL | 21 | 8 | 0.6 |
Use a contrast to test at a 5% level of significance whether the energy drinks lead to a lower number of mean hours of sleep than the herbal tea.
In: Statistics and Probability
In: Chemistry
Let x be the number of years after 2007 and y represent the number of students enrolled at WWCC. Answer the following
given the data that enrollment was 2055 in the year 2007, 2244 in 2008, 2512 in 2009, and 2715 in 2010.
(a) Find the least-squares line for the data using Excel and submit your file in Canvas.
(b) Using partial derivatives, verify the formula you obtained in Excel.
(c) Find the least-squares error E.
In: Math
(a) True or false: An element’s number of valence electrons is the same as its atomic number.
(b) How many valence electrons does a nitrogen atom possess?
(c) An atom has the electron configuration 1s 2 2s 2 2p6 3s 2 3p2 . How many valence electrons does the atom have?
In: Chemistry
Define a class called Rational for rational numbers. A
rational number is a number that can be represented as the quotient
of two integers. For example, /2, 3/4, 64/2, and so forth are all
rational numbers.
Represent rational numbers as two private values of type int, numfor the numerator and den for the denominator. The class has a default constructor with default values (num = 0,den = 1), a copy constructor, an assignment operator and three friend functions for operator overloading +, << and >>.
In + operator, the sum of a/b and c/d is (a*d+b*c)/bd. In >> operator, if the user enter 0 for the denominator, output error message and prompt user to type again (use while loop). In << operator, output a rational number in the format a/b. If a = 0, just output 0. If b = 1, just output a. If the number is a/-b, output –a/b. If the number is –a/-b, output a/b. In the main function, declare two objects and use operator >> and assign data for them. Then sum the two numbers and display the results. Sample output:
Enter two integers: 3 0
Error: the denominator cannot be 0. Try again.
Enter two integers: 2 3
Enter two integers: 3 -4
2/3 + -3/4 = -1/12
(2 bonus marks) Add a private member function with function prototype void normalize( ) to normalize the values stored so that, after normalization, the denominator is positive and the numerator and denominator are as small as possible. For example, after normalization 4/-8 would be represented the same as -1/2. You must email me your code for this part.
In: Computer Science
The City Council has gathered data on the number of minor traffic accidents and the number of youth football games that occur in a town over a weekend
X (Soccer Games) 20 30 10 12 15 25 24
Y (minor accdnt) . 6 9 4 5 7 8 9
Plot the data
Develop the estimating equation that describes the data
Predict the number of minor traffic accidents that will occur on a weekend during which 33 soccer games takes place
In: Statistics and Probability