Concept explainers
The bar graph shows the amount, in billions of dollars, that the United States government spent on human resources and total budget outlays for six selected years, (Human resources include education, health, Medicare. Social Security, and veterans benefits and services.)
Source: Office of Management and Budget
The function p(x) = 1.75x2 – 15.9x + 160 models the amount. p(x), in billions of dollars, that the United States government spent on human resources x years after 1970. The function q(x) = 2.1x2 - 3.5x+ 296 models total budget expenditures, q(x), in billions of dollars, x years after 1970.
a. Use p and q to write a rational function that models the fraction of total budget outlays spent on human resources x years after 1970.
b. Use the data displayed by the bar graph to find the percentage of federal expenditures spent on human resources in 2010. Round to the nearest percent.
c. Use the rational function from part (a) to find the percentage of federal expenditures spent on human resources in 2010. Round to the nearest percent. Does this underestimate or overestimate the actual percent that you found in part (b)? By how much?
d. What is the equation of the horizontal asymptote associated with the rational function in part (a)? If trends modeled by the function continue, what percentage of the federal budget will be spent on human resources over time? Round to the nearest percent.

Want to see the full answer?
Check out a sample textbook solution
Chapter 3 Solutions
COLLEGE MATH.CUSTOM BDL W/ MML
- Practice Assignment 5.6 Rational Functions M Practice Assig Practice Assignment 5.6 Rational Functions Score: 120/150 Answered: 12/15 Question 10 A Write an equation for the function graphed below 5 + 4 1 2 H + + -7 -6 -5 -4 -3 -2 -1 2 34567 | -2 ర y = Question Help: Video Message instructor Post to forum Submit Questionarrow_forwardit's not algebra 4th gradearrow_forwardCan you tell me if I answered and showed my work correctlyarrow_forward
- Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N then dim M = dim N but the converse need not to be true. B: Let A and B two balanced subsets of a linear space X, show that whether An B and AUB are balanced sets or nor verly A:LeLM be a subset of a linear space X, show that M is a hyperplane of X iff there exists fe X'/[0] and a EF such that M = {x Ex/f(x) = = a}. B:Show that every two norms on finite dimension linear space are equivalent C: Let f be a linear function from a normed space X in to a normed space Y, show that continuous at x, EX iff for any sequence (x) in X converge to x, then the sequence (f(x)) converge to (f(x)) in Y.arrow_forward2/26 Delta Math | Schoology X Unit 4: Importance of Education X Speech at the United Nations b x Book Thief Part 7 Summaries x + > CA Materials pdsd.schoology.com/external_tool/3157780380/launch ☆ MC Updates Grades Members BrainPOP Canva for Education DeltaMath Discovery Education FactCite Gale In Context: High Sc. Graw McGraw Hill K-12 SSO Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form. Click twice to plot each segment. Click a segment to delete it. 10 9 8 5 сл y Hill Nearpod 3 2 Newsela -10 -9 -8 -7 b -5 -4-3-2 -1 1 23 4 5 b 7 89 10 Scholastic Digital Mana. World Book Online Information Grading periods MP3: 2025-01-25-2025-03- 31, MP4: 2025-04-01-2025- 06-13 ← 2 M -> C % 95 54 # m e 4 7 巴 DELL A t y & * ) 7 8 9 . i L Feb 27 12:19 US + 11arrow_forwardLet & be linear map from as Pacex into aspace and {X1, X2, – 1— x3 basis for x show that f a one-to-one isf {f(x1), f (xx); — F (Kn) } linearly independent. மம் let M be a Proper sub space of aspace X then M is ahyper space iff for any text&M X=. C) let X be a linear space and fe X1{0} Show that is bjective or not and why? ***********arrow_forward
- Q₁/(a) Let S and T be subsets of a vector space X over a field F such that SCT,show that whether (1) if S generate X then T generate X or not. (2) if T generate X then S generate X or not. (b) Let X be a vector space over a field F and A,B are subsets of X such that A is convex set and B is affine set, show that whether AnB is convex set or not, and if f be a function from X into a space Y then f(B) is an affine set or not. /(a) Let M and N be two hyperspaces of a space X write a condition to prove MUN is a hyperspace of X and condition to get that MUN is not hyperspace of X. Write with prove application n Panach theoremarrow_forwardMatch the division problem on the left with the correct quotient on the left. Note that the denominators of the reminders are omitted and replaced with R. 1) (k3-10k²+k+1) ÷ (k − 1) 2) (k4-4k-28k45k+26)+(k+7) 3) (20k+222-7k+7)+(5k-2) 4) (3+63-15k +32k-25)+(k+4) 5) (317k 13) ÷ (k+4) - 6) (k-k+8k+5)+(k+1) 7) (4-12k+6) + (k-3) 8) (3k+4k3 + 15k + 10) ÷ (3k+4) A) 3k3-6k29k - 4 B) 4k2 + 6 R 7 C)²-9k-8- R D) 4k2+6x+1+ E) 10 Elk³-5-12 R 9 F) k² - 4k R 9 R G) k3-3k2-7k+4 H) k³-k²+8 - 3 R - R 9 Rarrow_forwardAnswer choices are: 35 7 -324 4 -9 19494 5 684 3 -17 -3 20 81 15 8 -1 185193arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL





