Basic Math Questions and Answers

Give all solutions of the nonlinear system of equations including those with nonreal complex components y x 5x 2x y 10 TIB Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Type an ordered pair Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Express complex numbers in terms of i Use a comma to separate answers as needed B There are infinitely many solutions OC The system is inconsistent The solution set is

One frequent customer is located in Miami FL LTL shipments from Atlanta to Miami cost 900 for a 5 000 pound shipment A new employee suggests that the company consider establishing a breakbulk facility in Jacksonville FL to serve customers in the South region including the Miami customer The cost of breaking bulk in Jacksonville is estimated to be 1 200 per truckload shipment received A truckload shipment has capacity for up to 50 000 pounds 10 typical orders The truckload carrier charges by the mile The distance between Atlanta and Jacksonville is 383 miles The carrier charges a rate of 1 95 per mile plus a fuel surcharge of 0 25 per mile An LTL shipment of 5 000 pounds from Jacksonville to Miami is 500 Would adding the breakbulk operation make sense from a cost standpoint Show your calculations and compare

Suppose that v and w are unit vectors If the angle between v and i is a and the angle between w and i is use the idea of the da following equation cos cos acos sin asin Write the i and j components of v in terms of a Since it is a unit vector the v factor has been omitted v cos a i sin aj Write the i and j components of w in terms of Since it is a unit vector the w factor has been omitted w cos Bi sin j Use these expressions to compute the dot product of v and w in terms of a and B V W

Suppose a closed economy with no government spending or taxing is capable of producing an output of 1900 at full employment Suppose also that autonomous consumption is 120 intended investment is 70 and the mpc is 0 50 What is the value of output Y in equilibrium Your Answer

3 You re comparing the potential returns of two different investment options Investment A and Investment B Their projected growth based on a 50 initial deposit is graphed below In artinon a Which investment has a larger growth factor Explain how you know C b Approximately how much will Investment A be worth after 15 years After 20 years how much more is Investment A worth than Investment B d During which time period did the value of Investment A increase the most Years 0 5 i ii Years 5 10Li iii Years 10 15 iv Years 15 20 V Years 20 15 laren 15 e Approximately how long does it take for Investment B to double in value

Mark and Abby played a game which required flipping a coin Mark won when the coin landed heads and Abby won when the coin landed tails Below is the table showing their wins Person Number of Wins Mark 12 Abby 15 1 Find the experimental probability Mark wins Write the probability in simplest form 2 Find the experimental probability Abby wins Write the probability in simplest form

Convert the rectangular equation to a polar equation x y 36

Given v 5i and w 2i 3j find the angle between v and w The angle between v and w is approximately T O round until th final anque Then rou

9 127 Solve the system of equations y x 5 y x 1 9 128 Carmel picks an integer from 1 to 12 as a value for c in the equation y x 4x c What is t probability that the equation will have complex roots

K Given vectors u i 2j and v 5i yj find y so that the angle between the vectors is 60 Points 0 of 1 ya Use a comma to separate answers as needed Do not round until the final answer Then round to three decimal places as needed

Objective 2 2 11 The large square below was divided into smaller squares of equal size 5 6 3 7 7 7 7 4 4 2 6 7 1 7 5 7 7 6 4 3 7 7 3 6 4 2 What fractional part of the large square is represented by the number of small squares that contain the number 7 10 10

or the following vectors a find the dot product yw h find the angle between y and wc o stato

Decompose v into two vectors v and v where v is parallel to w and v is orthogonal to w v i 4j w i 2j v i v i j Simplify your answer

K For the following vectors a find the dot product vw b find the angle between v and w c state whether the vectors are parallel orthogonal or

Find a vector of magnitude 20 that is parallel to 8i 6j The vector is Simplify your answer Type your answer in the form ai bj

9 110 Claude graphs y cos 0 and y cos 0 360 on the same set of axes Does Claude see any difference in the graphs at all Why or why not

Miscellaneous When k k 1 what is the value of k 00 2 3 00 0 2 2 2 3 3 3

Find the work W done by a force of 3 pounds acting in the direction 60 to the horizontal in moving an object 8 feet from 0 0 to 8 0 W foot pounds Round to the nearest whole number as needed Points 0 of 1 CICHLID

For the following vectors a find the dot product vw b find the angle between v and w c state whether the vectors are parallel orthogonal or neither v 3i 4j w 6i 8j a v w Simplify your answer O Points 0 of 1 1 C 2 201 Save

The table below represents the value of an investment account y after x years Which of the equations options do you think represents the account s growth Justify your response using math terms from this lesson X of years O 1 2 3 4 y balance 80 00 84 00 88 20 92 61 97 24 Equation options y 1 05 80 y 80 1 05 y 1 05x 80 y 80x 1 05

Create a second equation to form a system of equations with no solutions 3x 8y 24

Find an equation of the ellipse that has center 3 1 a minor axis of length 6 and a vertex at 10 1 0 0 0

Expand the given function in an appropriate cosine or sine series 0 1 1 f x f x 1 x 0 0 X T 2 1 n

9 Determine two values of k so that each can be factored over the trinomial integers a 9x 15x k b 5y 11y k c 4m 16m kOE d 3w 10w k 2A 18 1 2 THE

Test whether 1 at the a 0 01 level of significance for the sample data shown in the accompanying table Assume that the populations are normally distributed Click the icon to view the data table Determine the null and alternative hypothesis for this test OA Hol 1 H H1 H2 OB Hol1 12 H H1 H OC Ho P1 1 H H1 H Sample Data XI5 Population 1 32 103 5 Population 2 25 1142 X

A scientist claims that pneumonia causes weight loss in mice The table shows the weights in grams of six mice before infection and two days after infection At a 0 10 is there enough evidence to support the scientist s claim Assume the samples are random and dependent and the population is normally distributed Mouse Weight before Weight after What is the claim 2 3 4 5 6 22 7 19 1 21 8 23 6 19 7 23 8 21 2 18 4 21 1 23 3 18 7 22 7 OA Weight loss causes pneumonia in mice OB Pneumonia causes weight gain in mice OC Weight gain causes pneumonia in mice OD Pneumonia causes weight loss in mice Which calculator command would be most appropriate for testing the claim A Z Test tempts tempts tempts tempts tempts tempts

For a canine gourmet company x double bar 45 grams n 10 R bar 6 grams What is the mean and range upper control limits round up final calculations to 2 decimal places O 46 85 10 66 grams O 45 50 1 34 grams O 43 15 1 34 grams O 43 15 8 67 grams

1 pts In a hospital SPC study out of 960 healthcare staff 49 is recorded as absent If n is 64 using p chart formulas what is the upper and lower control limits of this absenteeism process use 4 decimals O 0 051 0 002 O 0 1010 0 031 O 0 1219 0 019 O 0 1335 0 000

Find the Fourier series of f on the given interval f x ex f x sin ha 7L X T X 00 E n Give the number to which the Fourier series converges at a point of discontinuity of f If f is continuous on the given interval enter CC continuous

Find the Fourier series of f on the given interval 8 x 0 f x 0 x 8 f x X X 00 n 1 Give the number to which the Fourier series converges at a point of discontinuity of f If f is continuous on the given interval enter CONTIE continuous

Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis If a hypothesis test is performed how should you interpret a decision that a rejects the null hypothesis or b fails to reject the null hypothesis A researcher claims that the standard deviation of the life of a certain type of lawn mower is more than 2 2 years FRICKCICHI Does the claim represent the null hypothesis or the alternative hypothesis Since the claim a statement of equality it represents the a How should you interpret a decision that rejects the null hypothesis There is evidence to type of lawn mower is more than 2 2 years b How should you interpret a decision that fails to reject the null hypothesis There is evidence to type of lawn mower is more than 2 2 years hypothesis the claim that the standard deviation of the life of a certain the claim that the standard deviation of the life of a certain tempts tempts tempts tempts 68 of 68 que 49 of 49 ques 41 of 41 ques

A company has recorded the last five days of daily demand on its only product Those values are 120 125 124 128 and 133 The time from when an order is placed to when it arrives at the company from its vendor is 5 days Assuming the basic fixed order quantity inventory model fits this situation and no safety stock is needed which of the following is the reorder point quantity ROP 950 O 126 120 O 630

The brain volumes cm of 20 brains have a mean of 1081 8 cm and a standard deviation of 128 3 cm Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high For such data would a brain volume of 1378 4 cm be significantly high Significantly low values are 825 2 cm or lower Type an integer or a decimal Do not round Significantly high values are cm or higher Type an integer or a decimal Do not round

Convert the rectangular equation to a polar equation x y 4

Convert the polar equation to a rectangular equation Then use a rectangular coordinate system to graph the rectangular equation 0 5x 6 5T The rectangular equation for 0 is y 6 Choose the correct graph of the rectangular equation below O A O C B D

Given v 3i and w 9i 2j find the angle between v and w point s possible

v 7i 5j w 10i 8j v w 110 Simplify your answer

A vector w has initial point 2 3 and terminal point 6 4 Write w in component form W 0 0 X 15

Given vectors a 4 3 and b 2 1 find 3a 4b Write your answer in component form 3a 4b 00 X 15

A vector s has initial point 5 3 and terminal point 1 2 Write s in component form S 70

The titer of a rangi is 17 s and is a 17 34 Find its length and width engen

K Listed below are the numbers of years that archbishops and monarchs in a certain country lived after their election or coronation Assume that the two samples are independent simple random samples selected from normally distributed populations Do not assume that the population standard deviations are equal Use a 0 05 significance level to test the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation All measurements are in years Click the icon to view the table of longevities of archbishops and monarchs What are the null and alternative hypotheses Assume that population 1 consists of the longevity of archbishops and population 2 consists of the longevity of monarchs OA Ho H1 H2 H H1 H C Hoi H1 H2 H H1 H2 ngevities of Archbishops and Monarchs chbishops 14 17 14 12 15 11 15 15 17 1 18 OB Ho H1 H2 H H H H OD Ho H H H1 H2 18 9 15 11 11 D X tempts tempts tempts tempts tempts tempts

of two The primary concern for performing a hypothesis test to compare the means and H populations is deciding whether the mean of Population 1 is greater than the mean of Population 2 a Determine the null and alternative hypotheses Note Always place the mean of Population 1 on the left b Classify the hypothesis test as two tailed left tailed or right tailed a Complete the hypotheses Ho P1 Ha P1 H H b This hypothesis test is tailed te ter tem tem

Sample 1 The number of hours 37 kids spend talking on a cell phone in a week Sample 2 The number of hours 39 adults spend talking on a cell phone in a week Choose the correct answer below OA The two given samples are independent because the same people were sampled OB The two given samples are dependent because different people were sampled OC The two given samples are independent because different people were sampled OD The two given samples are dependent because the same people were sampled

Write an expression for the apparent nth term an of the sequence 9 10 10 11 11 12 12 13 13 14

The histogram to the right represents the weights in pounds of members of a certain high school programming team How many team members are included in the histogram The histogram represents programming team members 4 2 110 120 130 140 150 160 170

If v 2i 6j and w 8i 24j find projwv Then decompose v into two vectors v and v where v is parallel to w and v is orthogonal to w projwv 10 1 C

Given v 7i 9j and w i j a Find projwv b Decompose v into two vectors v and v where v is parallel to w and v is orthogonal to w

Question 7 6 7 41 Given u i j v 10i 4j and w 8j find proju v W O Points 0 of

Determine whether v and w are parallel orthogonal or neither v 2i 5j w 4i 7j Are vectors v and w parallel orthogonal or neither A Orthogonal B Neither