12 ### Problem StatementA psychologist uses two types of boxes with mice and rats. The amount of time (in minutes) that each mouse and each rat spends in each box per day is given in the table below. The questions to be answered are:1. What is the maximum number of mice and rats that can be used in the experiment?2. How many mice and how many rats produce this maximum?### Table InformationThe table provided consists of three columns:1. **Time Needed Per Animal:** - For **Box A**, each mouse requires 20 minutes, and each rat requires 10 minutes. - For **Box B**, each mouse requires 10 minutes, and each rat requires 20 minutes.2. **Maximum Time Available per Day:** - Box A has 900 minutes available per day. - Box B has 840 minutes available per day.| | Time Needed Per Mouse | Time Needed Per Rat | Maximum Time Available per Day ||---|-----------------------|---------------------|--------------------------------|| Box A | 20 min | 10 min | 900 min || Box B | 10 min | 20 min | 840 min |The challenge is to determine the optimal number of mice and rats that can be accommodated within the given daily time limits for both boxes.

let number of Mice = x and number of Rats = y Box A Box B

Answered: A psychologist uses two types of boxes…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter1: Expressions And Functions

Section1.5: Descriptive Modeling And Accuracy

Problem 11PPS

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Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.
Cell Phone Plans Gwendolyn is mulling over the three cell phone plans shown in the table. Gigabytes GB of data included Monthly Cost Each additional megabytes MB Plan A Plan B Plan C 1 1 1 25.00 40.00 60.00 2.00 1.50 1.00 From past experience, Gwendolyn knows that she will always use more than 1GB of cell phone data every month. aMake table of values that shows the cost of each plan for 1 GB to 4 GB, in 500 MB increments. bFind formulas that give Gwendolyns monthly cost for each plan, assuming that she uses x gigabytes of data per month where x1. cWhat is the charge from each plan when Gwendolyn uses 2.2 GB? 3.7 GB? 4.9 GB? d Use your formulas from part b to determine the number of gigabytes of data usage for which: (i) Plan A and Plan B give the same cost. (ii) Plan A and Plan C give the same cost. (iii) Plan B and Plan C give the same cost.

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