optional replacement math test
1 2 3 4 5 6 1 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6 A single die is rolled twice. The 36 equally-likely outcomes are shown to the right. Find the probability of getting two numbers whose sum is 4.
(1, 3), (3,1), (2,2) 3/36 = 1/12
(10 - 4)!
(10-4)= 6 6! = 6*5*4*3*2*1= 720
[Spinner has: 1 yellow, 2 green, 3 red] Assume that it is equally probable that the pointer will land on any one of the colored regions. If the pointer lands on a borderline, spin again. If the spinner is spun once, find the probability that the pointer lands in a yellow region.
1/6
A club with eleven members is to choose three officers: president, vice-president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?
11*10*9= 990
License plates in a particular state display 3 letters followed by 2 numbers. How many different license plates can be manufactured for this state?
26*26*26*10*10= 1757600
Find the range for the group of data items. 23, 23, 26, 26, 29,
29 - 23 = 6
An ice cream store sells 4 drinks, in 3 sizes, and 6 flavors. In how many ways can a customer order a drink?
4*3*6= 72
In a race in which five automobiles are entered and there are no ties, in how many ways can the first three finishers come in?
5*4*3= 60
In how many ways can the digits in the number 9,663,333 be arranged?
7!/ 1!2!4! = 105
[Spinner has: 8 equal sections 1-8] It is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an odd number or a number less than 8.
7/8
The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is $15,000 and the standard deviation is $500. Use the 68-95-99.7 Rule to find the percentage of buyers who paid between $13,500 and
99.7 divided by 2 = 49.85%
Use the following graph to describe a circuit that begins and ends at vertex H.
A circuit in a graph is a path that begins and ends at the same vertex. {doesn't always mean every vertex}
A student earns $14 per hour for tutoring and $9 per hour as a teacher's aide. Let x= the number of hours each week spent tutoring and y= the number of hours each week spent as a teacher's aide. A)Write the objective function that describes total weekly earnings. z= ________ B)The student is bound by three constraints. Write an inequality for each constraint. 1. To have enough time for studies, the student can work no more than 24 hours per week. _______ 2. The tutoring center requires that each tutor spend at least two hours per week tutoring. ______ 3. The tutoring center requires that each tutor spend no more than eight hours per week tutoring. _______ C)graph D) Evaluate the objective function for total weekly earnings at each of the four vertices of the graphed region. [The vertices should occur at (2,0), (8,0), (2,22), (8,16)]. E) Complete the missing portions of the statement below. The students can earn the maximum amount per week by tutoring for __ hours per week and working as a teacher's aide for ___ hours per week. The maximum amount that the student can earn each week is ___
A) z= 14x + 9y B) 1. x + y </ 24 2. x>/ 2 3. x</ 8 C) D)28, 112, 226, 256 E) The students can earn the maximum amount per week by tutoring for 8 hours per week and working as a teacher's aide for 16 hours per week. The maximum amount that the student can earn each week is $256
Use the data 8, 9, 10, 12, 13, 14. Without actually computing the standard deviation, determine the value below that best approximates the standard deviation.
A. 12 B. 24 C. 2 D. 6 ANSWER: C.2
A(0,8), B(4,9), C(6,0), D(0,0) The objective function is z=60x+40y. A. Find the value of the objective function at each corner of the graphed region. B. Find the maximum value of the objective function. C. Find the minimum value of the objective function.
A. The value of the objective function at point A is 320. The value of the objective function at point B is 600. The value of the objective function at point C is 360. The value of the objective function at point D is 0. B. The maximum value of the objective function is 600. C. The minimum value of the objective function is 0.
A sales director who lives in city A is required to fly to regional offices in cities B, C, D, and E. The weighted graph shows the one-way airfares between any two cities. Use the Nearest Neighbor Method, with starting vertex A, to find an approximate solution. What is the total cost for this Hamilton circuit?
Start at A, smallest option.... until back at A. Add all the sides of the circuit to get price.
The government of a large city needs to determine whether the city's residents will support the removal of the city's university. The government decides to conduct a survey of a sample of the city's residents. Which one of the following procedures would be the most appropriate for obtaining a sample of the city's residents?
Survey a random sample of persons within each neighborhood.
Find the degree of each vertex in the graph.
The degree of a vertex is the number of edges at that vertex. If a loop connects a vertex to itself, that loop contributes 2 to the degree of the vertex.
Intelligence quotas on two different tests are normally distributed. Test A has a mean of 100 and a standard deviation of 13. Test B has a mean of 100 and a standard deviation of 16. Use z-scores to determine which person has the higher IQ: an individual who scores 135 on Test A or an individual who scores 27 on Test B.
The individual who scores 135 on Test A.
Use the display of data items to find the mean, median, mode, and midrange. [Stems: 3, 7, 9] [leaves: 6, 9, 5, 7, 4, 2, 2, 9, 9, 3]
The mean of the data is 66.3 -add all together and divide by number of data items The median of the data is 72. -in the middle The mode is of the data is 72. -occurs the most The midrange of the data is 66. - lowest data value + highest data value divided by two
Use the table below to find the percentage of data items in a normal distribution that lie a. below and b. above a z-score of 0.2. z-score 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Percentile 53.98 57.93 61.79 65.54 69.15 72.57 75.80 78.81 81.59 84.13
a)57.93 b) 100- 57.93= 42.07
A graph is given to the right. a. Explain why the graph has at least one Euler path. b. Use trial and error or Fleury's Algorithm to find one such path.
a. Euler's Theorem can be used to determine if a graph contains Euler paths or Euler circuits. For connectedgraphs, the following statements are true. 1. If a graph has exactly two odd vertices, then it has at least one Euler path, but no Euler circuit. Each Euler path must start at one of the odd vertices and end at the other one. 2. If a graph has no odd vertices (all even vertices), then it has at least one Euler circuit (which, by definition, is also an Euler path). An Euler circuit can start and end at any vertex. 3. If a graph has more than two odd vertices, then it has no Euler paths and no Euler circuits. NEED REVIEW!!!!
Use the complete, weighted graph shown to the right to find the total weight of the following Hamilton circuit.
add the sides of the letters given
5!, called 5 _______ is the product of all positive integers from _______ down through _______. By definition, 0!=_______.
factorial, 5, 1, 1
A method for finding the maximum or minimum value of a quantity that is subject to various limitations is called
linear programming
A random sample of 37 male college students is selected. Each student is asked his height (to the nearest inch). The heights are shown in the frequency distribution below. Construct a histogram and a frequency polygon for the data. Height 66,67, 68, 69, 70, 71, 72, 73, 74, 75 Frequency 3, 4, 2, 3, 4, 7, 3, 6, 2, 3
match the numbers on graphs
Evaluate the expression. 6C2 * 8C1/24C3
nCr= n!/(n-r)!r!
Use the formula for nPr to evaluate the following expression. 4P4
nPr= n!/(n-r)! 4p4= 4!= 24 over (4-4)!= 0!= 1 24/1
The graph models the baseball schedule for a week. The vertices represent the teams. Each game played is represented as an edge between two teams. How many games are scheduled for Kansas City during the week? List the teams that they are playing. How many times are they playing each of these teams?
step 1: count lines from kansas city step 2: Examine all of the edges connected to Kansas City. Each team that Kansas City is connected to is a team Kansas City is playing this week. step 3: To determine how many times Kansas City is playing each of these teams this week, count the edges (if any) connecting the two vertices.
Find the standard deviation for the group of data items. 13, 9, 13, 9, 13, 9, 13, 9
step 1: find mean step 2: chart of data items - mean = deviation step 3: square the deviation step 4: deviation^2 divided by number data items (n) - 1 step 5: square root
The diagram on the right is a floor plan. Letting vertices represent the room and theoutside, and edges represent the connecting doors, which graph correctly models the floor plan?
step 1: First, arrange the vertices representing the rooms (and outside). {dots where the letters are} step 2: Next, draw the edges showing which rooms are connected by doors to vertex G. step 3: Next, draw the edges showing which rooms are connected by doors to vertex D step 4: Draw any remaining edges that may be necessary. Which graph correctly models the floor plan?
Determine whether the graph is a tree. If the graph is not a tree, give the reason why. a. | | b. --------c. (no dashed line)
this graph is a tree
