Questions

Use the properties of logarithms to condense the following logs as much as possib 3 log m logn log b 4 3log a log b

5 4 3 3 3 22 1 2 1 2 3 4 2 3 14 5 6 Identify the function whose graph appears above f x

3 Explain what is happening in this image Which type of immune response will this lead to humoral immunity or cell mediated immunity

2 Consider the function f x y y x 16 i Determine an equation for the tangent plane to the surface z f x y at input 3 2 ii Use part i to estimate the number 1 98 3 3 01 2 16 by hand For fun ask a machine what this number comes out to and compare to your estimate are you close

K Use the results from a survey of a simple random sample of 1038 adults Among the 1038 respondents 88 rated themselves as above average drivers We want to test the claim that more than themselves as above average drivers Complete parts a through e 17 of adults ra 20 a Regardless of the conclusion reached from the hypothesis test is it possible that more than of adults can be above average drivers 20 A Yes Assuming quality of driving can be quantified a distribution that is extremely skewed to the left would be the most promising scenario for more than this proportion of adults to have driving quality that is above the mean B No Assuming quality of driving can be quantified half of all adults must have driving quality less than or equal to the mean OC Yes Assuming quality of driving can be quantified a distribution that is extremely skewed to the right would be the most promising scenario for more than this proportion of adults to have driving quality that is above the mean COD No It is impossible to compare the quality of different adults driving b If we use the same significance level to conduct the hypothesis test using the P value method the critical value method and a confidence interval which method is not always equivalent to the other two A The P value method is not always equivalent to the other two B The confidence interval method is not always equivalent to the other two CC The critical value method is not always equivalent to the other two OD All three methods are always equivalent to each other c It was stated that we can easily remember how to interpret P values with this If the P is low the null must go What does this mean This statement means that if the is low in relation to then one should

engineer takes a sample of 10 batteries and calculates a sample variance of 1 3 hr2 Find a 99 confidence interval on the population variance o 0 b A school district wants to evaluate the effectiveness of a new teaching method for improving students math scores A sample of 25 students is randomly selected and their math scores are measured before and after the new teaching method is implemented The sample standard deviation of the differences in math scores is 5 2 points Find a 90 confidence interval on the population variance o

0 38 If the measure of angle A is 75 and the measure of angle C is 25 in a triangle ABC what is the measure of angle B

In a study of 809 randomly selected medical malpractice lawsuits them were dropped or dismissed Use a 0 01 significance level to test the claim that mos medical malpractice lawsuits are dropped or dismissed Which of the following is the hypothesis test to be conducted OA Ho p 0 5 H p 0 5 c Ho p 0 5 H p 0 5 E Ho p 0 5 H p 0 5 What is the test statistic Z B Ho p 0 5 H p 0 5 OD Ho p 0 5 H p 0 5 OF Ho p 0 5 p H p 0 5

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line about the line x 6 209 Volume TC 3 y x x y

Select the representations that do not change the location of the point 2 Choose the correct answer below Choose all that apply A B C 2 2 7x 3x 4

In a newspaper s survey of 453 people 53 said that we should replace passwords wil biometric security such as fingerprints The accompanying Statdisk display results from test of the claim that half of us say that we should replace passwords with biometric sec Use the normal distribution as an approximation to the binomial distribution Use the dis and a 0 10 significance level to complete parts a through e Sample proportion 0 5298013 Test Statistic z 1 2686 Critical z 1 6449 P value 0 2046 a Is the test two tailed left tailed or right tailed Choose the correct answer below left tailed two tailed right tailed b What is the test statistic Z

b A paint company has developed a new paint formula which should have a faster drying time compared to the old formula Paint drying time is known to be normally distributed and from previous tests it is known that the original paint formula has a mean drying time of 14y 45 min 0 36 min2 The company s R D scientists believe the new formula will have a mean drying time of 2 35 min o 16 min2 that is they expect the new formula to dry an average of 10 min faster than the old formula or that 10 A scientist takes 16 samples of each paint formula and determines the mean drying time for each batch to be X 44 min and X2 36 min respectively Find a 90 confidence interval on the difference in average lifetime between the two populations 12

Estimating the Difference Between Two Means Known Variance a A car manufacturer outsources production of a certain automotive component The company has found a cheaper supplier supplier 2 but wants to make sure that the component is of the same quality The standard deviations in component lifetimes are known to be 1 000 miles and o 1 500 miles respectively 50 components from each supplier are tested and the average lifetime for the new supplier s component is 1 050 miles shorter compared to the original supplier s component that is X X 1 050 Find a 95 confidence interval on the difference in average lifetime between the two populations H

Let R be the region bounded by x 4 y 4x 7 y 2x 19 To find the volume of the solid when R is revolved around the z axis evaluate the integral 4 4x 66x 312x x dx

Find the volume formed by rotating about the y axis the region enclosed by x 7y and y3 x with y 0

C Question 5 of 14 Step 1 of 1 6 21 Correct Determine the implied domain of the following function Express your answer in interval notation Answer x 6 f x X 3

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified lin about the line 6 Volume y x x y

The test statistic of z 1 14 is obtained when testing the claim that p 0 26 This is a right tailed test Using a 0 05 significance level complete parts a and b Click here to view the standard normal distribution table for negative z scores Click here to view the standard normal distribution table for positive z scores a Find the critical value s Select the correct choice below and fill in the answer box es within your choice Round to two decimal places as needed OA There are two critical values the lower critical value is is OB There is one critical value the critical value is and the upper critical valu

Claim The mean systolic blood pressure of all healthy adults is less than than 121 mm Hg Sample data For 277 healthy adults the mean systolic blood pressure level is 120 72 mm and the standard deviation is 15 17 mm Hg The null and alternative hypotheses are Ho H 121 and H 121 Find the value of the test statistic The value of the test statistic is Round to two decimal places as needed

Claim The standard deviation of pulse rates of adult males is more than 10 bpm For a fanc sample of 171 adult males the pulse rates have a standard deviation of 11 5 bpm Complet parts a and b below a Express the original claim in symbolic form bpm Type an integer or a decimal Do not round

A formal hypothesis test is to be conducted to test the claim that the wait times at the Spa Mountain ride in Walt Disney World have a mean equal to 35 minutes Complete parts a through d a What is the null hypothesis and how is it denoted minute s Type an integer or a decimal Do not round

2 8 points Determine if T is a linear transformation T R R T x y x y x y

In order to image small objects with high resolution select all possible methods Lower electron gun current Use a smaller spot size Move up the specimen closer to the objective lens Increase the accelerating voltage Increase the image contrast

d the local maximum and minimum values and saddle point s of the function You are encouraged viewpoint that reveals all the important aspects of the function Enter your answers as comma s f x y x xy y 8y maximum value s l minimum value s 8 16 dle point s x y 3 3

To avoid charging effect in SEM imaging select all possible methods Coat with metals Coat with carbon Decrease the voltage Decrease the chamber vacuum Use a larger aperture

A matrix is give 18 9 01 a Determine whether the matrix is in row echelon form Yes No b Determine whether the matrix is in reduced row echelon form Yes No c Write the system of equations for which the given matrix is the augmented matrix Enter each answer in terms of x ar 9 7

Solve the system of linear equations If the system is dependent express your answer in terms of t where x x t y y t and z t If the system is inconsistent enter INCONSISTENT x 2y 3z 8 2x 4y6z 16 3x 7y 2z 31 x y z

Solve the system of linear equations If the system is dependent express your answer in terms of t where x x t y y t and z t If the system is inconsistent enter INCONSIS 2x y 3z x y z x 17 7z 18 3x 2y z 20

The system of linear equations has a unique solution Find the solution using Gaussian elimination or Gauss Jordan elimination y z 8 x 2x 3y 2z 16 3z 4 x y z 4x y

Find the volume of a pyramid with height 23 and rectangular base with dimensions 3 and 9 using integration

Find the volume of the solid obtained by rotating the region bounded by y x y 0 and x 3 about the y axis V

State the dimension of the matrix 21 18

State the dimension of the matrix 612

A matrix is given in row echelon form 1 0 2 4 1 2 5 14 0 0 1 4 a Write the system of equations for which the given matrix is the augmented matrix Enter each answer in terms of x y and z 5 14 b Use back substitution to solve the system x y z

The graphs of x 8 y f x solid and y g x dashed are shown the graph is not drawn to scale Region One B A a The intersection points are A 8 4 B 8 7 and C 1 5 Suppose Region One is revolved around the x axis Using the method of washers the volume can be computed by evaluating the integral

Let R be the region bounded by 5 y 2x 10 y 3x 25 To find the volume of the solid when R is revolved around the x axis evaluate the integral dx The volume of the solid formed when R is revolved around the x axis is Type pi to enter

Find the volume of the solid obtained by rotating the region bounded by the g curves about the specified axis 2 y x y 1 about y 3

Find the volume of the solid obtained by rotating the region above the x axis bounded by y x and 5about the y axis y

As a hardworking student plagued by too much homework you spend all night doing math homework By 6am you imagine yourself to be a region bounded by y 722 x 0 x 2 y 0 As you grow more and more tired the world begins to spin around you However according to Newton there is no difference between the world spinning around you and you spinning around the world Unfortunately you are so tired that you think the world is the x axis What is the volume of the solid you the region create by spinning about the x axis

In ELISA the enzyme horseradish peroxidase HRP is bound to the region of the secondary antibody well of microtiter plate SARS CoV 2 antigen the tested sample

Why is it necessary to wash the samples repeatedly in ELISA To enhance the interaction between antibody and antigen To remove any proteins or antibodies which are unbound To increase samples concentration To make the sample clean Question 6 1 point Listen An antibody is Are also called immunoglobulins or lgs Made up of variable domains and a constant domain Composed of glycoproteins All of the above Y shaped in antigens

bodies are unique and respond to a specific antigen Where does the antigen attach to the antibody structure The variable domains Fab The binding site the variable domains and the Fab The binding site Fc Question 8 1 point Listen Microneutralization is the gold standard but it is labor intensive and time consuming and requires at least 5 days to get results True

How many types of controls do you need to have in the Microneutralization Assay One Virus Control Two Sample Control and Virus Control Two Virus Control and Cell Control No controls are need

What is the purpose of the ELISA test for this lab To detect COVID 19 virus from serum in people who might have been infected To produce COVID 19 antibody from serum in people who have been infected To detect COVID 19 antibody from serum in people who might have been infected To isolate COVID 19 virus from serum in people who have been infected

Use a graphing utility to graph the function include two full periods Graph the corresponding reciprocal function in the same viewing window y csc 4x 4 y y UU UU 2 2 2 2 y 2 2 2 2 2 y 4 2 X

Use the graph of the function to answer each question 2 x 2 f x csc x 2 3 2 a Find all x intercepts of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE x b Find all y intercepts of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE y c Find the intervals on which the graph of y f x is increasing and the intervals on which the graph of y f x is decreasing Enter your answers using interval notation If an answer does not exist enter DNE increasing decreasing d Find all relative extrema if any of the graph of y f x Enter your answers as a comma separated list of ordered pairs If an answer does not exist enter DNE relative minima relative maxima e Find all vertical asymptotes if any of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE

Match each of the Maclaurin series with right function 1 2 n 0 n 0 1 22n2n 2n 1 2x2n 1 2n 1 3 2 n 0 4 n 0 n 1 2x2n 1 2n 1 A 2 arctan r B e2 G Cos 2x

The function f x sin 4x has a Maclaurin series Find the first 4 nonzero terms in the series that is write down the Taylor polynomial with 4 nonzero terms

Write the improper integral L as a limit or limits of proper integrals 0 2 x 1 da lim lim I S x 1 de lim L 20 dx x 1 2 da lim 8110 I da Jo 2 1 2 lim 2 1 2 da lim 8 100 da x 1 0 lim a10 dx lim da 2 1 2 22 1 2

15 a 0 048 yards b 0 063 yards c 0 075 yards