# Franco begins to save for a new Lego set that costs $65. His parents gave him$35 towards the cost and he plans to save $5 per week. Define all unknown variables. Write an equation modeling the total amount he has saved. Question Modeling asked 2021-01-16 Franco begins to save for a new Lego set that costs$65. His parents gave him $35 towards the cost and he plans to save$5 per week. Define all unknown variables. Write an equation modeling the total amount he has saved. 2021-01-17
Given, Franco begins to save $65 for a new Lego set, and his parents give$35 towards cost.
Franco's plan to save $5 per week we have to find the equation of modeling the total amount he has saved. Here Franco begins to save$65 for a new Lego set , say it as Y.
Franco save $5 per week ,say it as m. The amount of weeks is to save the$5 to be multiply it by m, say as X.
Franco's parents give him $35, say it as C The equation is $$\displaystyle{Y}={m}{X}+{C}$$ i.e. $$\displaystyle{65}={5}{X}+{35}$$ The equation of modeling the total amount he has saved is $$\displaystyle{65}={5}{X}+{35}$$ ### Relevant Questions asked 2021-02-19 Write a recursive rule and an explicit rule for an arithmetic sequence that models a situation. Then use the rule to answer the question. Jack begins an exercise routine for 10 minutes each day. Each week he plans to add 10 minutes per day to his exercise routine. For how many minutes will he exercise for each day on the 7th week? asked 2020-10-28 Determine the algebraic modeling a. One type of Iodine disintegrates continuously at a constant rate of $$\displaystyle{8.6}\%$$ per day. Suppose the original amount, $$\displaystyle{P}_{{0}}$$, is 10 grams, and let t be measured in days. Because the Iodine is decaying continuously at a constant rate, we use the model $$\displaystyle{P}={P}_{{0}}{e}^{k}{t}$$ 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. b. Use your equation to determine the half-life ofthis type of Fodine, That is, find ‘out how many days it will take for half of the original amount to be left. Show an algebraic solution using logs. asked 2021-03-07 Mathematical modeling is about constructing one or two equations that represent real life situations. What are these math models used for? Provide at least two equations that can be used in the real world. For 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 represents the total salary and h is the number of hours you worked. asked 2021-01-27 Marcus rowed 20 miles downstream in 2 hours. The trip back, however, took him 4 hours. Find the rate that Marcus rows in still water and the rate of the current. If x is Marcus's rowing speed, and y is the speed of the river current, construct one equation modeling his downstream trip and another modeling his upstream trip using x and y. The downstream equation is: Distance 20, Rate $$x\ +\ y,$$ Time 2 The upstream equation is: Distance 20, Rate $$x\ -\ y,$$ Time$ You just bought a new car for $22,000. Assume that the value of your new car depreciates at a constant $$12\ \%$$ per year. 1) The decay rate is square 2) The decay factor is square 3) The equation of the function that represents the value, V(t), of the car in dollars t years from now is $$V\ =\ \Box$$ (Write an expression that completes the function's equation.) asked 2021-01-19 Determine the algebraic modeling The personnel costs in the city of Greenberg were$9,500,000 in 2009. In the recent past the personnel costs have increased at the rate of $$4.2\%$$ annually.
To model this, the city manager uses the function $$\displaystyle{C}{\left({t}\right)}={9.5}{\left({1}{042}\right)}^{t}\text{where}\ {C}{\left({t}\right)}$$ is the annual personnel costs,in millions of dollars, t years past 2009
1) Write the equation that can be solved to find in what year the personnel costs will be double the 2009 personnel costs.
2) Then solve the equation numerically (use the Table feature of your calculator) or graphically and determine the year. 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 $$\displaystyle{95}\%$$ confidence interval for the improvement in traffic flow due to the new system.
b) Find a $$\displaystyle{98}\%$$ 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 $$\displaystyle{95}\%$$
confidence interval will specify the mean to within $$\displaystyle\pm\ {50}$$ vehicles per hour?
e) Approximately what sample size is needed so that a $$\displaystyle{98}\%$$ confidence
interval will specify the mean to within $$\displaystyle\pm\ {50}$$ vehicles per hour? A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like a stirred tank. Suppose the blood volume is a four-liter tank that initially has a zero concentration of a particular drug. At time $$\displaystyle{t}={0}$$, an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500 mg/L. The inflow rate is 0.06 L/min. Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant. a. Write an initial value problem that models the mass of the drug in the blood, for $$\displaystyle{t}\ \geq\ {0}$$. Solve the initial value problem, and graph both the mass of the drug and the concentration of the drug. c. What is the steady-state mass of the drug in the blood? d. After how many minutes does the drug mass reach 90% of its steady-state level? 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 $$P = P_0e^{kt}$$ 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. 