MATH120 Algebra Test

Q1)  Solve each system of equations

3x + 5y = –9

x+ 4y = –10

Q2) Solve each system of equations

2x + 3 = y

x + 2y = –4

Q3) Determine if the system is consistent, independent, dependent or inconsistent:

2x – 5y = 6

–4x + 10y = –1

Q4) Writ the following system as an augmented matrix:

3x – 4y + 4z = 7

x – y – 2z = 2

2x – 3y + 6z = 5

Q5) Solve each system of equations

          2x + 3y = 6

            x = 3

Q6) A restaurant serves two types of fish dinners- small for $5.99 each and large for $8.99.  One day, there were 134 total orders of fish, and the total receipts for these 134 orders was $1024.66. How many small dinners and how many large dinners were ordered?

Q7) Solve each system of equations

x + 3y = 5

2x – y = 3

Q8) Solve each system of equations

x + 2y = 4

x + (1/2)y = 4

Q9) Writ the following system as an augmented matrix:

x + y – z = –2

2x – y + z = 5

–x + 2y + 2z = 1

Q10)  The sum of two integers is 97. Their difference is 43. Find the two numbers.

DETAILED ASSIGNMENT

20200929035638test_2__chapter_4

MATH 645 Exam I

(a) (2 points) Calculate the dot products u · v and v · w or explain why they do not exist.
(b) (3 points) Calculate the norms kuk and kvk of u and v.
(c) (2 points) Using your answers to parts (a) and (b) above, confirm that Schwarz’s Inequality holds
for u and v (in other words, verify that |u · v| ≤ kuk · kvk).

(a) (3 points) Are u, v, and w linearly independent or linearly dependent? Justify/explain your response.
(b) (3 points) Consider the set of all linear combinations of u and v. In R
3
, this set of vectors defines
what type of geometric object?

10. (Bonus, 3 points) A band matrix is a square matrix with nonzero entries only on the main diagonal and
on w of the diagonals above and below the main diagonal, and zeros everywhere else. The matrix B
below is an example of a 5×5 symmetric band matrix with w = 1. Elimination for band matrices is
much cheaper than elimination for ordinary matrices. For a generic n × n band matrix B with exactly
w nonzero bands above and below the main diagonal, approximately how many multiplication and
subtraction operations are necessary for elimination B → U?

DETAILED ASSIGNMENT

20200928074536basic_algebra

SAMPLE ASSIGNMENT

Sample-2

Requirements: Answer each question fully. Use Excel formulas with cell references. Answers must be recorded on the worksheet.

DETAILED ASSIGNMENT

20200917200757major_assignment_2__28121319_29

Prove using Definition 2.14 that lim n2 + 1 = +∞.

n→∞ n+1
2. (5 pts) Which three of the following statements, if combined,

imply that limn→∞ yn = −3? Prove your answer.

(A) x2n ≥ yn2 for every n
(B) yn − xn < n1 for every n
(C) limn→∞ xn = −3

(D) yn2 ≥ x2n for every n
3. (5 pts) Suppose that limn→∞ xn = 1. Prove using the definition

of limit (find N for every ε) that
lim 4xn −1 =−3.

n→∞ xn−2

SAMPLE ASSIGNMENT

Sample-2

The idea that the mind is separate from the brain is called:

答案选项组dualism

monism

epigenetics

psychobiology

标记此问题问题 21 分

The term afferent refers to ______ signals.

答案选项组incoming

outgoing

relay

motor

标记此问题问题 31 分

Neurons fire or they don’t. This is referred to as:

答案选项组the all or none response

depolarization

action potential

refractory period

标记此问题问题 41 分

The role of glial cells is primarily:

答案选项组to provide support and nutrients for neurons.

to process sensory input

to send signals from one brain region to another.

to carry out information processing in the brain.

标记此问题问题 51 分

After a neuron fires there is a brief amount of time before it can fire again. This is called:

答案选项组refractory period

repolarization

threshold of excitation

hyperpolarization

标记此问题问题 61 分

Cajal proposed that the nervous system is made up of separate neurons. This is called the ______ hypothesis.

答案选项组neuron

nerve net

glial

neurogenesis

标记此问题问题 71 分

The human brain contains approximately:

答案选项组100 billion neurons

100 million neurons

1 billion neurons

100,000 neurons

标记此问题问题 81 分

Which type of glial cell provides support for the neuron as well as creates the blood-brain barrier?

答案选项组astrocytes

microglia

ependymal cells

oligodendrocytes

标记此问题问题 91 分

The spaces in between the segments of myelin sheath are called:

答案选项组nodes de Ranvier

dendritic spines

axon terminals

the teledendria

标记此问题问题 101 分

Epigenetics is the study of:

答案选项组how environment influences biology

how our behavior is governed by genetics

how neural messages are transmitted

how thoughts can also be examples of behaviors

标记此问题问题 111 分

Which of the following receives information:

答案选项组dendritic spine

soma

axon collaterals

terminal button

标记此问题问题 121 分

______ help generate myelin in the CNS, whereas ______ help generate myelin in the PNS.

答案选项组Oligodendrocytes; Schwann cells

Schwann cells; oligodendrocytes

Astrocytes; Schwann cells

Oligodendrocytes; microglial cells

标记此问题问题 131 分

One of the main points in psychobiology is that:

答案选项组all behavior is caused by the brain

perception occurs in your senses

mental activity and brain activity are separate from one another

the mind is based on scientific findings

标记此问题问题 141 分

The ______explanation of behavior describes why a behavior evolved as it did.

答案选项组functional

physiological

ontological

evolutionary

标记此问题问题 151 分

Some brain structures are able to create new neurons. This is called:

答案选项组neurogenesis

synaptogenesis

neuroplasticity

synaptic pruning

标记此问题问题 161 分

One theory that explains behavior focuses on how a behavior developed. This approach is called the:

答案选项组ontological

physiological

functional

evolutionary

标记此问题问题 171 分

Dendritic spines can appear, change shape, disappear, etc. This is an example of:

答案选项组neuroplasticity

neurogenesis

flexibility

epigenetics

标记此问题问题 181 分

The electrical charge that travels down the cell and passes information on is called:

答案选项组the action potential

the function of afferent neurons

the refractory period

the resting membrane potential

标记此问题问题 191 分

Efferent neurons are also called:

答案选项组motor neurons

interneurons

sensory neurons

action potentials

标记此问题问题 201 分

The finger like extensions at the end of the axon are called:

答案选项组telodendria

axon collaterals

dendritic spines

oligodendrocytes

标记此问题问题 211 分

Which of the following letters indicates the location of the cell body?

答案选项组C

A

D

B

标记此问题问题 221 分

Which of the following letters indicates where the action potential begins?

答案选项组A

B

D

E

标记此问题问题 231 分

Which of the following letters indicates the part of the neuron that conveys information to other neurons ?

答案选项组D

E

C

A

标记此问题问题 241 分

Which of the following letters indicates the part of the neuron that regenerates the electrical charge traveling down the axon?

答案选项组E

A

D

B

标记此问题问题 251 分

Which of the following letters indicates the part of the neuron that helps regulate the firing of the neuron?

SAMPLE ASSIGNMENT

Sample-2

1. Locate the point on the line segment between ?(3, −5) and ?(13, −15) given that the point is 4/5 of the
way from ? to ?. Show your work.

3. Find the exact area and circumference of a circle whose diameter is 8 meters. Show your work.

4. Briefly explain the Law of Detachment. Write a statement that is concluded using the Law of Detachment for
the following statements.
If Jillian gets a raise, then she will buy a new car. Jillian got a raise.

DETAILED ASSIGNMENT

20200917182837geometry_exam_student_version_rev__3_

Question 2

You’re planning on making 6 meatloafs for a party. You go to the store to buy breadcrumbs, and see they are sold by the canister. What information do you need to figure out how many canisters to buy? Select all that apply. (this would be an essay question on the real exam)

A.How long it takes to make the recipe.

B.The amount of bread crumbs required for the recipe, times 6.

C.The amount of bread crumbs contained in each canister.

D.The other ingredients required for the recipe.

E.The amount of meat required for the recipe.

F.The amount of bread crumbs needed in other recipes.

QUESTION 3

You plan to make 8 pecan pies, all of which require 1 1/2 cups of pecans. You buy the pecans from the bulk section, where there is a scale to weigh them, but no measuring cups. According to the label, 1 cup of pecans weighs 98 grams. How many grams of pecans do you need to make all the pies? Round to the nearest 10th if necessary. Remember to label.

ANSWER:

QUESTION 4

Lambert created a triangular garden on his property. Two of the sides have the same length, while the final side is twice as long as they are. How long are the shorter sides if he needed 88 feet of fencing to enclose the garden?

ANSWER:

QUESTION 5

When Samantha first checked the price of an adjustable bed online, it was $800. Several months later, the price had dropped to $500. Find the absolute change (include a negative sign if applicable). $ANSWER

QUESTION 6

When Samantha first checked the price of an adjustable bed online, it was $800. Several months later, the price had dropped to $500. Find the relative (include a negative sign if applicable). ANSWER%

QUESTION 7

A recipe normally calls for 3/4 cup sugar, 2 Tablespoon baking powder, 1/2 cup milk, and 2 cups flour. Val only has 1 1/2 cups flour, and doesn’t have time to run to the store just now. How much of the other ingredients should he use?

Reminder: there are 16 Tablespoons in 1 cup, and 3 teaspoons in 1 Tablespoon

Use this preference schedule for the questions on this page.

QUESTION 8

Who wins by the Plurality Method?

A.C

B.B

C.A

D.D

QUESTION 9

Enter the number of points B would get using the Borda Count method.

ANSWER:

QUESTION 10

Who wins by the Borda Count Method?

A.B

B.C

C.A

D.D

QUESTION 11

Who gets eliminated first using Plurality with Elimination (aka Instant-Run-Off Voting)?

A.C

B.D

C.B

D.A

QUESTION 12

Who wins by Plurality with Elimination?

A.C

B.A

C.D

D.B

QUESTION 13

Who wins by Copeland’s Method (Pairwise Comparisons)?

A.A

B.C

C.D

D.B

QUESTION 14

Is the winner by Copeland’s Method a Condorcet Candidate?

A.Yes. Anyone who wins by Copeland’s Method is the Condorcet Candidate

B.No. While that candidate won, they did not beat every other candidate.

C.No. Copeland’s method has nothing to do with the Condorcet Candidate.

D.Yes. That candidate beat every other candidate when compared directly.

QUESTION 15

Which methods (if any) violated the Condorcet criterion for this schedule? Select all that apply.

A.Plurality with Elimination

B.None. There was a Condorcet Candidate, but that candidate won with every method.

C.Copeland’s Method

D.Borda Count

E.None. There was no Condorcet Candidate.

F.Plurality

QUESTION 16

Match each description with the correct fairness criterion condition.

QUESTION 17

Consider the voting scheme below:

{12: 8, 4, 1, 1, 1}

Which of the options below is accurate for this system?

A.Player 1 is a dictator, and the other players are dummy players.

B.Only Player 1 has veto power.

C.Player 1 and Player 2 both have veto power, but the other players can still matter.

D.Player 1 and Player 2 both have veto power, and the remaining players are dummy players.

QUESTION 18

Consider the voting system: {8: 4, 2, 2, 2}

How much power does player 1 have by Banzhaf’s Method? Enter your answer as a percent. Round to the nearest whole percent if necessary. ____ %

(Hint: there are 4 winning coalitions)

ANSWER:

QUESTION 19

Consider the voting system: {8: 4, 2, 2, 2}

How much power do players 2, 3, and 4 each have by Banzhaf’s Method? Enter your answer as a percent. Round to the nearest whole percent if necessary. ANSWER%

(Hint: there are 4 winning coalitions)

QUESTION 20

Consider the voting system: {8: 4, 4, 2}

How much power do players 1 and 2 each have by the Shapley Shubik Method? Enter your answer as a percent. Round to the nearest whole percent if necessary. ____ %

Here are the sequential coalitions for 3 players:

< P1, P2, P3 > < P1, P3, P2 > < P2, P1, P3 >

< P2, P3, P1 > < P3, P1, P2 > < P3, P2, P1 >

ANSWER:

QUESTION 21

Consider the voting system: {8: 4, 4, 2}

How much power does player3 have by the Shapley Shubik Method? Enter your answer as a percent. Round to the nearest whole percent if necessary. ____ %

Here are the sequential coalitions for 3 players:

< P1, P2, P3 > < P1, P3, P2 > < P2, P1, P3 >

< P2, P3, P1 > < P3, P1, P2 > < P3, P2, P1 >

ANSWER:

SAMPLE ASSIGNMENT

Sample-2

Question 1 (Two-dimension Parity Check, 20%). Consider the following two-dimension parity check, with original data in a
4 × 4 matrix. For each row and column, we generate a parity bit, forming a 5 × 5 matrix. The parity bits are in the last column
and last row. Then, the 25 bits will be transmitted through a bit-flipping channel. For simplification, we assume that each original
bit is flipped with probability p independently; p is a small probability; the parity bits are not flipped at all.
(1) [3%] Assume the following bits are sent:
1 1 0 0 0
1 1 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
(1)
and the following bits are received
0 0 0 0 0
0 0 0 0 0
0 0 1 0 0
0 0 0 0 0
0 0 0 0 0
(1)
Then, what does the receiver do and why?

(2) [3%] The example in (1) shows one case that the receiver believes there is one bit error and the error can be corrected, but
the fixed bits are still wrong. Please give another example: (a) there are 9 bits flipped; (b) the receiver believes there is one bit
error and the error can be corrected; and (c) the fixed bits are still wrong.
(3) [3%] If two original data bits are flipped, can the receive detect errors? can the receiver recover the errors? Why or why not.
(4) [3%] Give an example where there are bit error(s) but the receiver cannot even detect the error(s).
(5) [8%+ up to 4% bonus] Calculate the following probabilities (as a function of p): (a) The receiver believes there is one bit
error and the error can be corrected, and the fixed bits are correct. (b) The receiver believes there is one bit error and the error
can be corrected, but the fixed bits are wrong. For (b), you will get full mark if your answer is sufficiently close to the accurate
solution (i.e., consider those “common” error patterns but ignore those “rare” error patterns). Bonus marks will be given if your
answer is more accurate.

DETAILED ASSIGNMENT

20200917111615comp9121_assignment1_2020_part_1

1. Which method would you expect to give a better separation of a mixture of two liquids: simple
distillation or fractional distillation? Provide a brief explanation for your choice.

2. Explain why, during the course of a distillation, you may see a dramatic drop in vapor
temperature when there is still a significant amount of liquid that needs to be distilled. If this
happens, what would you need to do to ensure that the rest of the liquid is distilled?

DETAILED ASSIGNMENT

20200917061549chem_231_distillation_assignment_f20