EBK ALGEBRA 2
11th Edition
ISBN: 9780544714304
Author: Larson
Publisher: HMH PUB
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Chapter 2, Problem 21TP
Solution
(a.)
A model for the total number of hospital beds in U.S. hospitals.
It has been determined that the model for the total number of hospital beds in United States from 1980 to 2002, is given as
Given:
The number of hospitals in the United States from 1980 to 2002 is given as,
The average number of hospital beds in each hospital from 1980 to 2002 is given as,
Here,
Concept used:
The total number of hospital beds is the product of the average number of hospital beds in each hospital and the total number of hospitals.
Calculation:
The number of hospitals in the United States from 1980 to 2002 is given as,
The average number of hospital beds in each hospital from 1980 to 2002 is given as,
Then, it follows that the total number of hospital beds from 1980 to 2002 is given as,
Put the required values in the above expression to get,
Here,
This is the required model for the total number of hospital beds in United States from 1980 to 2002.
Conclusion:
It has been determined that the model for the total number of hospital beds in United States from 1980 to 2002, is given as
(b.)
The number of beds in the U.S. hospitals in 1995, according to the obtained model.
It has been determined that the number of beds in the U.S. hospitals in 1995, according to the obtained model, is
Given:
The number of hospitals in the United States from 1980 to 2002 is given as,
The average number of hospital beds in each hospital from 1980 to 2002 is given as,
Here,
Concept used:
The number of beds in the U.S. hospitals in 1995, according to the obtained model, can be determined by plugging in the required value of
Calculation:
As determined previously, in part (a), the model for the total number of hospital beds in United States from 1980 to 2002, is given as,
Then, the year 1995 is represented by
Put
Solving,
This implies that the number of beds in the U.S. hospitals in 1995, according to the obtained model, is
Since the number of beds must be a whole number, the obtained value can be rounded off to the nearest whole number to get the number of beds in the U.S. hospitals in 1995, according to the obtained model as
Conclusion:
It has been determined that the number of beds in the U.S. hospitals in 1995, according to the obtained model, is
(c.)
How the model changes if the number of hospital beds is required in thousands.
It has been determined that the model for the number of beds in the U.S. hospitals in thousands, is given as
Given:
The number of hospitals in the United States from 1980 to 2002 is given as,
The average number of hospital beds in each hospital from 1980 to 2002 is given as,
Here,
Concept used:
If the number of hospital beds is required in thousands, then the obtained model which gives the number of hospital beds in units has to be divided by thousand.
Calculation:
As determined previously, in part (a), the model for the total number of hospital beds in United States from 1980 to 2002, is given as,
If the number of hospital beds is determined in thousands, then multiplying it by thousand should give the number of hospital beds in units.
Then, the obtained model which gives the number of hospital beds in units should be divided by thousand to produce the model which gives the number of hospital beds in thousands.
So, the required model is,
Conclusion:
It has been determined that the model for the number of beds in the U.S. hospitals in thousands, is given as
Chapter 2 Solutions
EBK ALGEBRA 2
Ch. 2.1 - Prob. 1GPCh. 2.1 - Prob. 2GPCh. 2.1 - Prob. 3GPCh. 2.1 - Prob. 4GPCh. 2.1 - Prob. 5GPCh. 2.1 - Prob. 6GPCh. 2.1 - Prob. 7GPCh. 2.1 - Prob. 8GPCh. 2.1 - Prob. 1ECh. 2.1 - Prob. 2E
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- 26 5G II. 8:44 ☐ myportal.aum.edu.kw ENGLISH العربية RH Problem 2 [20 points]: Find the Reduced Row 1 4 7 Echelon Form of the matrix -1 0-1 3 04 Problem 3 [30 points]: Consider the following linear system: x+2y=1 -2x+2my=0 a) Write the linear system in the matrix form: A.X=b. b) For m=1, find the inverse of A, using the definition of the inverse. In this case, deduce the solution of the system. c) Use the definition of the inverse to find the values of m for which A is not invertible. 7 A▾ III G B I Ff▾ < ↑arrow_forwardFind the future values of the ordinary annuities at the given annual rate r compounded as indicated. The payments are made to coincide with the periods of compounding. (Round your answer to the nearest cent.) PMT = $140, r = 4.5%, compounded weekly for 15 yearsarrow_forwardI want a mathematical relationship with all the details, not explanations and definitionsarrow_forward
- 4 sinx cos2x+4 cos x sin2x-1=0arrow_forwardFor the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) 6 -2 -[47] A = -3 1 P = Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal. P-1AP =arrow_forward(e) Without using a membership table, show that (A N B) U (A N B) = A. State all the rules used.arrow_forward
- The function r has vertical asymptotes x =____________ (smaller value) and x = __________ (larger value)arrow_forwardProblem 1. 1.1. In each of the below, find a complete list of subgroups of the group G and write down their orders. a) The group G = Z/48Z b) The group G of rotations in D14. c) The group G = Z13 of 13-th roots of unity in C. 1.2. Find all elements x of the group G from 1.1 b) which generate G. 1.3. Let H = [[20]) ℃ Z/48Z. Using only order, determine which of the subgroups from your solution to 1.1 a) H coincides with.arrow_forwardmy teacher told me the answer was 4a⁷b⁶ because of the product of a power how can I tell the truth us there any laws in math please provide the law to correct her tyarrow_forward
- a=1 b=41)Find the vector and parametric scalar equations of the line L. Show that Q does not lieon L. 2)Without performing any numerical calculations, express d in terms of sin(θ) and |P Q| andhence show that d = |P Q × v(v with a hat)|. Proceed to use your points P and Q and the vector v(hat) to find d. 3)Find the point R such that PR =(P Q · v(hat)/|v(hat)| 2⃗ ) * v(hat). Confirm that R lies on the line L. Interpret the vector P R. Finally, verify that d = |RQ|.arrow_forwardDirections: Use your knowledge of properties of quadratic equations to answer each question. Show all work and label your answers with appropriate units. Round any decimals to the nearest hundredths place. 1. The hypotenuse of a right triangle is 5 centimeters longer than one leg and 10 centimeters longer than the other leg. What are the dimensions of the triangle? 2. The profit of a cell phone manufacturer is found by the function y = -2x²+ 108x+75, where x is the price of the cell phone. At what price should the manufacturer sell the phone to maximize its profits? What will the maximum profit be? 3. A farmer wants to build a fence around a rectangular area of his farm with one side of the region against his barn. He has 76 feet of fencing to use for the three remaining sides. What dimensions will make the largest area for the region? 4. A 13-foot ladder is leaning against a building, forming a right triangle. The height where the ladder touches the building is 7 feet more than the…arrow_forwardConsider the linear system: x12x2ax3 - 3x1 + x2 3x3 -3x14x2+7x3 a) For what value of a we can not solve the above system using Cramer's Rule? a b) If we take a 3 what will be the value of x₁? x1 = == 4. =-7 ==arrow_forward
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