a.
The domain and the range of the relation between the number of AA batteries and the corresponding price.
a.
Answer to Problem 1RE
The domain and the range of the relation between the number of AA batteries and the corresponding price are
Explanation of Solution
Given:
The price of a pack of 8 batteries is $6.30.
The price of a pack of 16 batteries is $13.99.
The price of a pack of 20 batteries is $12.32.
The price of a pack of 24 batteries is $13.99.
Calculation:
The relation between the number of batteries and the price can be defined as 8 is mapped to $6.30, 16 is mapped to $13.99, 20 is mapped to $12.32 and 24 is mapped to $13.99.
The domain of the relation between the number of AA batteries and the corresponding price consists of different values of the number of batteries.
Hence, the domain of the given relation is
The range of the relation between the number of AA batteries and the corresponding price consists of different values of the price of batteries.
Hence, the range of the given relation is
b.
The relationship between the number of batteries and the corresponding price as a set of ordered pairs.
b.
Answer to Problem 1RE
The relationship between the number of batteries and the corresponding price expressed as a set of ordered pairs is
Explanation of Solution
Take the first coordinate as the number of batteries in a pack and the second coordinate as the corresponding price.
Obtain the relationship between the number of batteries and price as a set of ordered pairs as shown below.
Hence, the relationship between the number of batteries and the corresponding price expressed as a set of ordered pairs is
c.
The relationship between the number of batteries and the corresponding price as a mapping.
c.
Explanation of Solution
Use the variable x for the number of batteries and y for the price.
Take x values as the 8, 16, 20 and 24.
Take y values as $6.30, $12.32 and $13.99.
Obtain the relationship between the number of batteries and their price as a mapping as shown in Figure 1.
From Figure 1, it can be observed that a pack of 16 batteries and a pack of 24 batteries have the same price $13.99.
d.
The relationship between the number of batteries and the corresponding price as a graph.
d.
Explanation of Solution
Take the number of batteries along the x-axis and the corresponding price along the y-axis.
Plot the points
From Figure 2, it can be observed that a pack of 16 batteries and a pack of 24 batteries have the same price $13.99.
Want to see more full solutions like this?
Chapter 3 Solutions
Pearson eText Algebra and Trigonometry -- Instant Access (Pearson+)
- Q.1) Classify the following statements as a true or false statements: Q a. A simple ring R is simple as a right R-module. b. Every ideal of ZZ is small ideal. very den to is lovaginz c. A nontrivial direct summand of a module cannot be large or small submodule. d. The sum of a finite family of small submodules of a module M is small in M. e. The direct product of a finite family of projective modules is projective f. The sum of a finite family of large submodules of a module M is large in M. g. Zz contains no minimal submodules. h. Qz has no minimal and no maximal submodules. i. Every divisible Z-module is injective. j. Every projective module is a free module. a homomorp cements Q.4) Give an example and explain your claim in each case: a) A module M which has a largest proper submodule, is directly indecomposable. b) A free subset of a module. c) A finite free module. d) A module contains no a direct summand. e) A short split exact sequence of modules.arrow_forwardListen ANALYZING RELATIONSHIPS Describe the x-values for which (a) f is increasing or decreasing, (b) f(x) > 0 and (c) f(x) <0. y Af -2 1 2 4x a. The function is increasing when and decreasing whenarrow_forwardBy forming the augmented matrix corresponding to this system of equations and usingGaussian elimination, find the values of t and u that imply the system:(i) is inconsistent.(ii) has infinitely many solutions.(iii) has a unique solutiona=2 b=1arrow_forwardif a=2 and b=1 1) Calculate 49(B-1)2+7B−1AT+7ATB−1+(AT)2 2)Find a matrix C such that (B − 2C)-1=A 3) Find a non-diagonal matrix E ̸= B such that det(AB) = det(AE)arrow_forwardWrite the equation line shown on the graph in slope, intercept form.arrow_forward1.2.15. (!) Let W be a closed walk of length at least 1 that does not contain a cycle. Prove that some edge of W repeats immediately (once in each direction).arrow_forward1.2.18. (!) Let G be the graph whose vertex set is the set of k-tuples with elements in (0, 1), with x adjacent to y if x and y differ in exactly two positions. Determine the number of components of G.arrow_forward1.2.17. (!) Let G,, be the graph whose vertices are the permutations of (1,..., n}, with two permutations a₁, ..., a,, and b₁, ..., b, adjacent if they differ by interchanging a pair of adjacent entries (G3 shown below). Prove that G,, is connected. 132 123 213 312 321 231arrow_forward1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k components, where k is the greatest common divisor of {n, r,s}.arrow_forward1.2.20. (!) Let u be a cut-vertex of a simple graph G. Prove that G - v is connected. עarrow_forward1.2.12. (-) Convert the proof at 1.2.32 to an procedure for finding an Eulerian circuit in a connected even graph.arrow_forward1.2.16. Let e be an edge appearing an odd number of times in a closed walk W. Prove that W contains the edges of a cycle through c.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education