Improve Your Math Modeling Skills with Practice Problems

Consider a capital budgeting problem with seven projects represented by binary (0 or 1) variables $X_{1}, X_{2}, X_{3}, X_{4}, X_{5}, X_{6}, X_{7}$ . Write a constraint modeling the situation in which only 2 of the projects from $1, 2, 3 a n d 4$ must be selected. Write a constraint modeling the situation in which at least 2 of the project from $1, 3, 4, a n d 7$ must be selected. Write a constraint modeling the situation project 3 or 6 must be selected, but not both. Write a constraint modeling the situation in which at most 4 projects from the 7 can be selected.

aortiH 2021-03-08

Answer true or false to each of the following statements and explain your answers. A polynomial regression equation can be estimated using the method of least squares, the same method used in multiple linear regression.

Jerold 2021-03-07

The article “Modeling Arterial Signal Optimization with Enhanced Cell Transmission Formulations presents a new method for timing traffic signals in heavily traveled intersections. The effectiveness of the new method was evaluated in a simulation study. In 50 simulations, the mean improvement in traffic flow in a particular intersection was 654.1 vehicles per hour, with a standard deviation of 311.7 vehicles per hour.
a) Find a $95 %$ confidence interval for the improvement in traffic flow due to the new system.
b) Find a $98 %$ confidence interval for the improvement in traffic flow due to the new system.
c) A traffic engineer states that the mean improvement is between 581.6 and 726.6 vehicles per hour. With what level of confidence can this statement be made?
d) Approximately what sample size is needed so that a $95 %$
confidence interval will specify the mean to within $\pm 50$ vehicles per hour?
e) Approximately what sample size is needed so that a $98 %$ confidence
interval will specify the mean to within $\pm 50$ vehicles per hour?

abondantQ 2021-03-07

Mathematical modeling is about constructing one or two equations that represent real life situations. What are these math models used for? Give at least two equations that have practical applications. Example: The equation $s = 30 h + 1000$ can be used to find your salary given the fact you earn a fixed salary of $1000 per month, plus $30 per hours. Here, s stands for your overall pay, and h denotes the number of hours you put in.

Albarellak 2021-03-07

A good approach to mathematical modeling is a two-stage approach, using a verbal description to form a ?, and then, after assiging labels to the quantities, forming an ?.

Reeves 2021-03-06

Determine the algebraic modeling
Solve for x: $32 {(1.05)}^{x} = 90$

Maiclubk 2021-03-02

Consider a challenge in capital budgeting where six projects are represented by $0 - 1 variables x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, and x_{6} .$
a. Write a constraint modeling a situation in which two of the projects 1, 3, and 6 must be undertaken.
b. In which situation the constraint " $x_{3} - x_{5} = 0$ " is used, explain clearly:
c. Create a constraint to represent a scenario where either roject 2 or 4 must be pursued, but not both
d. Write constraints modeling a situation where project 1 cannot be undertaken IF projects 3. also is NOT undertaken.
e. Explain clearly the situation in which the following 3 constraints are used simulataneously (together):
$x_{4} \leq x_{1}$
$x_{4} \leq x_{3}$
$x_{4} \geq x_{1} + x_{3} - 1$

Efan Halliday 2021-02-25

High IQ Exercise 26 proposes modeling IQ scores with N(100, 16). What IQ would you consider to be unusually high? Explain.

Cheyanne Leigh 2021-02-25

Describe the shape of a scatter plot that suggests modeling the data with an exponential function.

Line 2021-02-24

Lemons and Car Crashes Listed below are annual data for various years. The data are weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population [based on data from “The Trouble with QSAR (or How I Learned to Stop Worrying and Embrace Fallacy),” by Stephen Johnson, Journal of Chemical Information and Modeling, Vol. 48, No. 1]. Is there sufficient evidence to conclude that there is a linear correlation between weights of lemon imports from Mexico and U.S. car fatality rates? Do the results suggest that imported lemons cause car fatalities? $\begin{matrix} L e m o n i m p o r t s & 230 & 265 & 368 & 480 & 630 \\ C r a s h F a t a l i t y R a t e & 159 & 157 & 15.3 & 15.4 & 14.9 \end{matrix}$

pancha3 2021-02-21

Explain the Logistic Modeling of Population Data?

Khadija Wells 2021-02-19

An equation that expresses a relationship between two or more variables, such as $H = \frac{9}{10} (220 - a)$ ,
is called $\frac{a}{a n} ? .$ The process of finding such equations to describe real-world phenomena is called mathematical ? .
Such equations, together with the meaning assigned to the variables, are called mathematical ? .

Anish Buchanan 2021-02-12

A famous NBA player appears at a local hot spot an average once every month. What is the probability that he will make an appearce at this same local that hot spot more than 2 times in a three month span?

slaggingV 2021-02-11

Determine the algebraic modeling which of the following data sets are linear and which are exponential. For the linear sets, determine the slope. For the exponential sets, determine the growth factor or the decay factor
a) $\begin{array}{cc} x & - 2 & - 1 & 0 & 1 & 2 & 3 & 4 \\ y & \frac{1}{9} & \frac{1}{3} & 1 & 3 & 9 & 27 & 81 \end{array}$

b) $\begin{array}{cc} x & - 2 & - 1 & 0 & 1 & 2 & 3 & 4 \\ y & 2 & 2.6 & 3.2 & 3.8 & 4.4 & 5.0 & 5.6 \end{array}$

c) $\begin{array}{cc} x & - 2 & - 1 & 0 & 1 & 2 & 3 & 4 \\ y & 3.00 & 5.0 & 7 & 9 & 11 & 13 & 15 \end{array}$

d) $\begin{array}{cc} x & - 2 & - 1 & 0 & 1 & 2 & 3 & 4 \\ y & 5.25 & 2.1 & 0.84 & 0.336 & 0.1344 & 0.5376 & 0.021504 \end{array}$

Cheyanne Leigh 2021-02-11

The stature of men is normally distributed, with a mean of 69.0 inches and a standard deviation of 2.8 inches. The height of women is normally distributed, with a mean of 63.6 inches and a standard deviation of 2.5 inches. Modeling academy standards require women to be models taller than 66 inches (or 5 feet 6 inches). What percentage of women meet this requirement?

OlmekinjP 2021-02-10

One type of Iodine disintegrates continuously at a constant rate of 8.6% per day. Suppose the original amount, $P_{0}$ , is 10 grams, and let be measured in days. Because the Iodine is decaying continuously at a constant rate, we use the model $P = P_{0} e^{k t}$ for the decay equation, where k is the rate of continuous decay. Using the given information, write the decay equation for this type of Iodine.

djeljenike 2021-02-06

Consider that algebraic modeling For the function $f (x) = 34 {(1.024)}^{x}$
1) The function is an increasing exponential function because it is the form $y = a b^{x}$ and ?
2) The growth rate is ?
3) Thrawth factor is ?

usagirl007A 2021-02-05

A population of 6 mice doubles every 4 weeks. When will this population reach 120 mice? Use an algebraic solving process.

DofotheroU 2021-02-02

Determine the algebraic modeling If you invest $8,600 in an account paying $8, 4 %$ annual interest rate, compounded continuously, how much money will be in the account at the end of 11 years?

glasskerfu 2021-01-31

Evaluate the line integral $\oint_{C} \frac{y}{{(x - 1)}^{2} + 4 y^{2}} d x + \frac{- (x - 1)}{{(x - 1)}^{2} + 4 y^{2}} d y$ where C is circle defined by $x^{2} + y^{2} = 27$

Since Math modeling problems can be encountered anywhere from AI-based solutions to programming and design, questions that relate to this area of Algebra are always in demand. You can see various Math modeling examples below that provide help and solutions to various problems. While it may not address your particular challenge, taking a look at some solutions will always provide a great starting point. See several Math modeling questions first and compare them to see the rationality and the use of equations that make things easier.

Algebra II

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