HEART OF MATHEMATICS
4th Edition
ISBN: 9781119760061
Author: Burger
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 4.4, Problem 7MS
Another angle. Look at the 5-unit super-tile you created in Mindscape 6. Measure the angle between the line determined by the base of the original triangle and the base of the 5-unit super-tile.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
For each given function f(x) find f'(x) using the rules learned in section 9.5.
1. f(x)=x32
32x
2. f(x)=7x+13
3. f(x) =
x4
4. f(x) = √√x³
5. f(x) = 3x²+
3
x2
Apply STATA commands & submit the output for each question
only when indicated below
i. Apply the command egen to create a variable called "wyd"
which is the rowtotal function on variables bwght & faminc.
ii. Apply the list command for the first 10 observations to
show that the code in part i worked. Include the outcome of
this code
iii. Apply the egen command to create a new variable called
"bwghtsum" using the sum function on variable bwght by
the variable high_faminc (Note: need to apply the bysort'
statement)
iv. Apply the "by high_faminc" statement to find the
V.
descriptive statistics of bwght and bwghtsum Include the
output of this code.
Why is there a difference between the standard deviations
of bwght and bwghtsum from part iv of this question?
According to a health information website, the distribution of adults’ diastolic blood pressure (in millimeters of mercury, mmHg) can be modeled by a normal distribution with mean 70 mmHg and standard deviation 20 mmHg.
b. Above what diastolic pressure would classify someone in the highest 1% of blood pressures? Show all calculations used.
Chapter 4 Solutions
HEART OF MATHEMATICS
Ch. 4.1 - The main event. State the Pythagorean Theorem.Ch. 4.1 - Two out of three. If a right triangle has legs of...Ch. 4.1 - Hypotenuse hype. If a right triangle has legs of...Ch. 4.1 - Assesing area. Suppose you know the base of a...Ch. 4.1 - Squares all around. How does the figure below...Ch. 4.1 - Operating on the triangle. Using a straightedge,...Ch. 4.1 - Excite your friends about right triangles....Ch. 4.1 - Easy as 1,2,3? Can there be a right triangle with...Ch. 4.1 - Sky high (S). On a sunny, warm day, a student...Ch. 4.1 - Sand masting (H). The sailboat named Sand Bug has...
Ch. 4.1 - Getting a pole on a bus. For his 13th birthday,...Ch. 4.1 - The Scarecrow (ExH). In the 1939 movie The Wizard...Ch. 4.1 - Rooting through a spiral. Start with a right...Ch. 4.1 - Is it right? (H) Suppose someone tells you that...Ch. 4.1 - Tfrain trouble (H). Train tracks are made of...Ch. 4.1 - Does everyone have what it takes to be a triangle?...Ch. 4.1 - Getting squared away. In our proof of the...Ch. 4.1 - The practical side of Pythagoras. Suppose you are...Ch. 4.1 - Pythagorean pizzas (H). You have a choice at the...Ch. 4.1 - Natural right (S). Suppose r and s are any two...Ch. 4.1 - Well-rounded shapes. Suppose we have two circles...Ch. 4.1 - A Pythagorean Theorem for triangles other than...Ch. 4.1 - With a group of folks. In a small group, discuss...Ch. 4.1 - Double trouble. Suppose you know a right triangle...Ch. 4.1 - K-ple trouble. Suppose you have a right triangle...Ch. 4.1 - Padding around. You have a rectangular patio with...Ch. 4.1 - Pythagoras goes the distance. Plot the points (5,...Ch. 4.1 - Ahoy there! (H) Your exotic sailboat, which you...Ch. 4.2 - Standing guard. Draw the floor plan of a gallery...Ch. 4.2 - Art appreciation. State the Art Gallery Theorem.Ch. 4.2 - Upping the ante. How many guards do you need for a...Ch. 4.2 - Keep it safe. At what vertices would you place...Ch. 4.2 - Puttoing guards in their place. For each floor...Ch. 4.2 - Guarding the Guggenheim. The Art Gallery Theorem...Ch. 4.2 - TriangulatIng the Louvre (H). Triangulate the...Ch. 4.2 - Triangulating the Clark. Triangulate the floor...Ch. 4.2 - Tricolor me (ExH). For each triangulation, color...Ch. 4.2 - Tricolor hue. For each triangulation, color the...Ch. 4.2 - One-third. Write the number 6 as a sum of three...Ch. 4.2 - Easy watch. Draw a floor plan of a museum with six...Ch. 4.2 - Two watches (S). Draw the floor plan of a museum...Ch. 4.2 - Mirror, mirror on the wall. Consider the floor...Ch. 4.2 - Nine needs three (H). Draw a floor plan for a...Ch. 4.2 - One-third again (ExH). If a natural number is...Ch. 4.2 - Square museum (S). If a museum has only...Ch. 4.2 - Worst squares (H). Draw examples of museums with...Ch. 4.2 - Pie are squared. The circumference of a circle of...Ch. 4.2 - I can see the light. Suppose you are in a...Ch. 4.2 - Less than. Youve tnangulated your polygon and...Ch. 4.2 - Greater than. Youve triangulated your polygon and...Ch. 4.2 - Counting the colors. Your polygon has 40 vertices....Ch. 4.2 - Only red. Twelve of your polygons vertices have...Ch. 4.2 - Totaling triangles. If a polygon has n sides, it...Ch. 4.3 - Defining gold. Explain what makes a rectangle a...Ch. 4.3 - Approximating gold. Which of these numbers is...Ch. 4.3 - Approximating again. Which of the following...Ch. 4.3 - Same solution. Why does the equation l1=1l have...Ch. 4.3 - X marks the unkonw (ExH). Solve eachh equation for...Ch. 4.3 - A cold tall one? Can a Golden Rectangle have a...Ch. 4.3 - Fold the gold (H). Suppose you have a Golden...Ch. 4.3 - Sheets of gold. Suppose you have two sheets of...Ch. 4.3 - Circular logic? (H). Take a Golden Rectangle and...Ch. 4.3 - Growing gold (H). Take a Golden Rectangle and...Ch. 4.3 - Counterfeit gold? Draw a rectangle with its longer...Ch. 4.3 - In the grid (S). Consider the 1010 grid at left....Ch. 4.3 - A nest of gold. Consider the figure of infinitely...Ch. 4.3 - Comparing areas (ExH). Let G be a Golden Rectangle...Ch. 4.3 - Do we get gold? Lets make a rectangle somewhat...Ch. 4.3 - Do we get gold this time? (S) We now describe...Ch. 4.3 - A silver lining? (H) Consider the diagonal in the...Ch. 4.3 - Prob. 20MSCh. 4.3 - Going platinum. Determine the dimensions of a...Ch. 4.3 - Golden triangles. Draw a right triangle with one...Ch. 4.3 - Prob. 23MSCh. 4.3 - Prob. 24MSCh. 4.3 - Prob. 25MSCh. 4.3 - Power beyond the mathematics. Provide several...Ch. 4.3 - Special K. As a student at the University of...Ch. 4.3 - Special x. Find all values of x satisfying the...Ch. 4.3 - In search of x. Solve each equation for x:...Ch. 4.3 - Adding a square. Your school Healthy Eating garden...Ch. 4.3 - Golden Pythagoras (H). If you have a Golden...Ch. 4.4 - To tile or not to tile. Which of the following...Ch. 4.4 - Shifting Into symmetry. Shown below are small...Ch. 4.4 - Prob. 3MSCh. 4.4 - Prob. 4MSCh. 4.4 - Symmetric scaling (ExH). Each of the two patterns...Ch. 4.4 - Build a super. Draw a 1,2,5 right triangle in the...Ch. 4.4 - Another angle. Look at the 5-unit super-tile you...Ch. 4.4 - Super-super. Surround your 5-unit super-tile with...Ch. 4.4 - Expand forever (H). If you continue the process of...Ch. 4.4 - Prob. 10MSCh. 4.4 - Expand again. Take your 4.unit equilateral...Ch. 4.4 - One-answer supers. Here is a Pinwheel Pattern. For...Ch. 4.4 - Prob. 14MSCh. 4.4 - Many answer supers (H). Shown here are pictures of...Ch. 4.4 - Fill er up? (ExH) For each tile below, could...Ch. 4.4 - Prob. 18MSCh. 4.4 - Prob. 19MSCh. 4.4 - Prob. 20MSCh. 4.4 - Penrose tiles. Roger Penrose constructed two tiles...Ch. 4.4 - Expand forever. Why does any shape that can be...Ch. 4.4 - Super total. Recall that the Pinwheel Triangle has...Ch. 4.4 - Prob. 26MSCh. 4.4 - XY-tiles. The trapezoidal tile on the left has one...Ch. 4.4 - School spirit. Your dorm bathroom is tiled using...Ch. 4.4 - T-total (H). Suppose you start with one small...Ch. 4.5 - Its nice to be regular. What makes a polygon a...Ch. 4.5 - Keeping it Platonic. What makes a solid a regular...Ch. 4.5 - Countem up. How many faces, edges, and vertices...Ch. 4.5 - Defending duality. Explain why the cube and the...Ch. 4.5 - The eye of the beholder. Suppose you have models...Ch. 4.5 - Drawing solids. Draw each solid by completing the...Ch. 4.5 - Count. For each of the regular solids, take the...Ch. 4.5 - Soccer counts (ExH). Look at a soccer ball. Take...Ch. 4.5 - A solid slice (S). For each regular solid, imagine...Ch. 4.5 - Siding on the cube. Suppose we start with the...Ch. 4.5 - Cube slices (H). Consider slicing the cube with a...Ch. 4.5 - Dual quads (S). Suppose you have a cube with edges...Ch. 4.5 - Super dual. Suppose you take a cube with edges of...Ch. 4.5 - Self-duals. Suppose you have a tetrahedron having...Ch. 4.5 - Not quite regular (ExH). Suppose you allow...Ch. 4.5 - Truncated solids. Slice off all the vertices of...Ch. 4.5 - Stellated solids. Take each regular solid and...Ch. 4.5 - Prob. 24MSCh. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.6 - Walkind the walk. Here are three walks from corner...Ch. 4.6 - Missing angle in action. The triangles below are...Ch. 4.6 - Slippery X. A triangle is drawn on a sphere. Can...Ch. 4.6 - A triangular trio. The sphere below has three...Ch. 4.6 - Saddle sores. The triangle at right is drawn on a...Ch. 4.6 - Travel agent. In each of the following three...Ch. 4.6 - Travel agent. In each of the following three...Ch. 4.6 - Travel agent. In each of the following three...Ch. 4.6 - Latitude losers (H). In each of the following...Ch. 4.6 - Latitude losers (H). In each of the following...Ch. 4.6 - Latitude losers (H). In each of the following...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Big angles (H). What is the largest value we can...Ch. 4.6 - Many angles (S). Draw three different great...Ch. 4.6 - Quads in a plane. Measure the sum of the angles of...Ch. 4.6 - Quads on the sphere. Below are quadrilaterals on...Ch. 4.6 - Parallel lines (ExH). On a plane, if you draw a...Ch. 4.6 - Cubical spheres (ExH). Take a cube. Put a point in...Ch. 4.6 - Tetrahedral spheres. Lets do a similar calculation...Ch. 4.6 - Dodecahedral spheres. This Mindscape is the same...Ch. 4.6 - Total excess. Using the observations from the...Ch. 4.6 - What is the sum of the three angles? Why? Consider...Ch. 4.6 - What is the sum of the angles of your triangle? Is...Ch. 4.6 - Removing a slice of the pie. Complete the...Ch. 4.6 - Conjuring up a conjecture. Make a conjecture about...Ch. 4.6 - Tetrahedral angles. What is the sum of the angles...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.7 - At one with the univers. Below is a sketch of a...Ch. 4.7 - Are we there yet? Why does the information x=4 not...Ch. 4.7 - Plain places. Plot the following points in the...Ch. 4.7 - Big stack. If you take a huge number of sheets of...Ch. 4.7 - A bigger stack. If you take a huge number of...Ch. 4.7 - On the level in two dimensions. Pictured in the...Ch. 4.7 - On the level in two dimensions (S). Pictured in...Ch. 4.7 - On the level in four dimensions. Pictured in the...Ch. 4.7 - Tearible 2s. In the pictures below, describe how...Ch. 4.7 - Dare not to tear? For the figures in the Tearible...Ch. 4.7 - Unlinking (H). Using the fourth dimension,...Ch. 4.7 - Unknotting. Describe how you would unknot the...Ch. 4.7 - Prob. 13MSCh. 4.7 - Edgy hypercubes (H). Produce drawings of the...Ch. 4.7 - Prob. 15MSCh. 4.7 - Prob. 16MSCh. 4.7 - Doughnuts in dimensions. Suppose we have a...Ch. 4.7 - Assembly required (S). As promised in the...Ch. 4.7 - Slicing the cube. Take a 3-dimensional cube...Ch. 4.7 - Here we celebrate the power of algebra as a...Ch. 4.7 - Here we celebrate the power of algebra as a...Ch. 4.7 - Here we celebrate the power of algebra as a...Ch. 4.7 - Here we celebrate the power of algebra as a...Ch. 4.7 - Here we celebrate the power of algebra as a...
Additional Math Textbook Solutions
Find more solutions based on key concepts
CHECK POINT 1 In a survey on musical tastes, respondents were asked: Do you listed to classical music? Do you l...
Thinking Mathematically (6th Edition)
1. combination of numbers, variables, and operation symbols is called an algebraic______.
Algebra and Trigonometry (6th Edition)
At what points are the functions in Exercise continuous?
University Calculus: Early Transcendentals (4th Edition)
The four flaws in the given survey.
Elementary Statistics
Find how many SDs above the mean price would be predicted to cost.
Intro Stats, Books a la Carte Edition (5th Edition)
ASSESSMENT Find the first five terms in sequences with the following nth terms. a. n2+2 b. 5n+1 c. 10n1 d. 3n2 ...
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Write STATA codes which will generate the outcomes in the questions & submit the output for each question only when indicated below i. ii. iii. iv. V. Write a code which will allow STATA to go to your favorite folder to access your files. Load the birthweight1.dta dataset from your favorite folder and save it under a different filename to protect data integrity. Call the new dataset babywt.dta (make sure to use the replace option). Verify that it contains 2,998 observations and 8 variables. Include the output of this code. Are there missing observations for variable(s) for the variables called bwght, faminc, cigs? How would you know? (You may use more than one code to show your answer(s)) Include the output of your code (s). Write the definitions of these variables: bwght, faminc, male, white, motheduc,cigs; which of these variables are categorical? [Hint: use the labels of the variables & the browse command] Who is this dataset about? Who can use this dataset to answer what kind of…arrow_forwardApply STATA commands & submit the output for each question only when indicated below İ. ii. iii. iv. V. Apply the command summarize on variables bwght and faminc. What is the average birthweight of babies and family income of the respondents? Include the output of this code. Apply the tab command on the variable called male. How many of the babies and what share of babies are male? Include the output of this code. Find the summary statistics (i.e. use the sum command) of the variables bwght and faminc if the babies are white. Include the output of this code. Find the summary statistics (i.e. use the sum command) of the variables bwght and faminc if the babies are male but not white. Include the output of this code. Using your answers to previous subparts of this question: What is the difference between the average birthweight of a baby who is male and a baby who is male but not white? What can you say anything about the difference in family income of the babies that are male and male…arrow_forwardnot use ai pleasearrow_forward
- Pidgeonhole Principle 1. The floor of x, written [x], also called the integral part, integer part, or greatest integer, is defined as the greatest integer less than or equal to x. Similarly the ceiling of x, written [x], is the smallest integer greater than or equal to x. Try figuring out the answers to the following: (a) [2.1] (b) [2] (c) [2.9] (d) [2.1] (e) [2] (f) [2.9] 2. The simple pidgeonhole principle states that, if you have N places and k items (k> N), then at least one hole must have more than one item in it. We tried this with chairs and students: Assume you have N = 12 chairs and k = 18 students. Then at least one chair must have more than one student on it. 3. The general pidgeonhole principle states that, if you have N places and k items, then at least one hole must have [] items or more in it. Try this out with (a) n = 10 chairs and k = 15 students (b) n = 10 chairs and k = 23 students (c) n = 10 chairs and k = 20 students 4. There are 34 problems on these pages, and we…arrow_forwardDetermine if the set of vectors is linearly independent or linearly dependent. linearly independent O linearly dependent Save Answer Q2.2 1 Point Determine if the set of vectors spans R³. they span R³ they do not span R³ Save Answer 23 Q2.3 1 Point Determine if the set of vectors is linearly independent or linearly dependent. linearly independent O linearly dependent Save Answer 1111 1110 Q2.4 1 Point Determine if the set of vectors spans R4. O they span R4 they do not span IR4 1000; 111O'arrow_forwardThe everything combined problem Suppose that a computer science laboratory has 15 workstations and 10 servers. A cable can be used to directly connect a workstation to a server. For each server, only one direct connection to that server can be active at any time. 1. How many cables would you need to connect each station to each server? 2. How many stations can be used at one time? 3. How many stations can not be used at any one time? 4. How many ways are there to pick 10 stations out of 15? 5. (This one is tricky) We want to guarantee that at any time any set of 10 or fewer workstations can simultaneously access different servers via direct connections. What is the minimum number of direct connections needed to achieve this goal?arrow_forward
- Can you help me with D and Earrow_forwardQ1.1 1 Point Any set {V1, V2, V3, V4} that consists of four different vectors from R cannot possibly span Rº. True False Save Answerarrow_forwardFind: lim x →-6 f (x) limx-4 f (x) lim x-1 f (x) lim x →4 f (x) (-6,3) • (-1,5) -8 -7 (-6,-2) 4+ (4,5) (4,2) • (-1,1) -6arrow_forward
- 3 2 Find: ƒ(1) lim f(x) 14-x 2 ƒ(2) lim f(x) x-2- lim f(x) x+2+ lim f(x) x→4 3 y=f(x)arrow_forwardFor each graph below, state whether it represents a function. Graph 1 24y Graph 2 Graph 3 4 2 -8 -6 -4 -2 -2 2 4 6 Function? ○ Yes ○ No ○ Yes ○ No Graph 4 Graph 5 8 Function? Yes No Yes No -2. ○ Yes ○ No Graph 6 4 + 2 4 -8 -6 -4 -2 2 4 6 8 Yes -4++ Noarrow_forwardStudents were asked to simplify the expression (secØ - cosØ)/secØ Two students' work is given.Student A: step 1 secØ/secØ - cosØ/secØstep 2 cosØ/1 - (1/cosØ)step 3 1 - cos^2Østep 4 sin^2ØStudent B: step 1 (1/cosØ)-cosØ)/secØstep 2 (1 - cos^2Ø/cosØ)/secØstep 3 sin^2Ø/cos^2Østep 4 tan^2ØPart A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused.Part B: Complete the student's solution correctly, beginning with the location of the error.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Trigonometric Ratios; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9-eHMMpQC2k;License: Standard YouTube License, CC-BY