Questions

Sketch the region enclosed by x 6y and x y 5 Decide whether to integrate with respect to x or y Then find the area of the region

Sketch the region enclosed by x y 20 and a 20 and x y Decide whether to integrate with respect to x or y Then find the area of the region

Determine whether the integral is divergent or convergent If it is convergent evaluate it If it diverges to infinity state your answer as INF If it diverges to negative infinity state your answer as INF If it diverges without being infinity or negative infinity state your answer as DIV 9 5 2 dx 0 x 4 5 2

Determine whether the integral is divergent or convergent If it is convergent evaluate it If not state your answer as divergent 3 dx x 3 3 2

Sketch the region enclosed by the given curves Decide whether to integrate with respect to x or y Then find the area of the region y 5 x y 5 x

In electromagnetic theory the magnetic potential u at a point on the axis of a circular coil is given by where A r a are constants Compute u Hint The integration is a little tricky Substitute x rtan 0 da u Ar a 72 x2 3 2

Determine whether the integral is divergent or convergent If it is convergent evaluate it If not state your answer as divergent 00 3e dx

x 4 x 7 f x 2 x Find the area enclosed between f x 0 7x 10 and g x x from x 4 to x

Determine whether the integral is divergent or convergent If it is convergent evaluate it If not state your answer as divergent L 1 dw 9 w

Find M12 8 7 10 A 53 2 01 5

2 The amount of dry matter in tomatoes measured in grams is the amount of solid content of the fruit subtract the water content The table below shows weights of dry matter in 10 tomatoes grown in soil with different amounts of calcium Ca measured in mg cm Ca in soil mg cm x Weight of dry matter g y 12 13 15 17 18 19 21 22 23 25 2 9 31 47 4 5 47 5 3 6 1 65 62 68 a 1 ii b 1 Find the Pearson s product moment correlation coefficient r for this data 0 96 Comment on the strength of the r value found Strong Poative linear correlation Find the Spearman s rank correlation coefficient r for this data ii Comment on the strength of the r value found c In the context of this question and the data provided comment on if both correla coefficients should be considered when determining the relationships between calcium content and dry matter weight or if one should be used in favour of the

The stockholders equity of Merkovsky Company at the beginning and end of 2016 totaled 127 000 and 137 000 respectively Assets at the beginning of 2016 were 151 000 If the liabilities of Merkovsky Company increased by 67 000 in 2016 how much were total assets at the end of 2016 Use the accounting equation a 218 000 6 228 000 c 74 000 d 221 000

Abdominis abdomen Brachium arm Delta triangular shaped Greek letter Gluteus buttock Maximus largest Minimus smallest Pectoris chest Rectus straight Trapezius trapezoid Bi two Brevis short Femoris thigh Longus long Medius middle Oblique angled Piriform pear shaped Transversus right angles Tri three Rectus femoris Adductor longus Triceps brachii Pronator teres Brachioradialis Extensor carpi ulnaris Biceps femoris

DETAILS Let vec B 4 95m at 60 0 vec C and vec 4 have equal magnitudes The direction angle of vec C is larger than that of vec 4 by 25 0 Let vec 2 A vec B 27 9m and vec 2 B vec C 33 9m Find the magnitude in m and direction in degrees of vec A

cot theta square root 3 0

Question 9 Prove the following statements by Mathematical Induction a 3 6 9 3 1 15 pts b 1222 3 1 c y 5 1 2m 1

Find the length x to the nearest whole number 240 66 38

Solve the formula for the indicated variable B rw x for w The solution is w

Solve Clear fractions first 52 53 7 1 3 3 x 18 6 6 The solution is x Type an integer or a simplified fraction

Jerry left a 2 40 tip on a meal that cost 15 What percent of the meal s cost was the tip What was the total cost of the meal including the tip The tip was of the meal s cost The total cost of the meal including the tip was

Graph the polar equation Create a chart of many ordered pairs in polar form and plot the points to show your work r 4sin20

Solve using the multiplication principle Don t forget to perform a check 2 8 7x 35 The solution is x Simplify your answer Type an integer or a fraction

Solve for m ag q m The solution is m Simplify your answer

Determine whether 11 is a solution of the equation 5 x 1 50 Is 11 a solution O No Yes

Translate to an inequality Use the variable x for the price of the amusement park ticket The price of an amusement park ticket is no less than 20 The inequality is

What point on the line y 3x 10 is closest to the origin Let D be the distance between the two polots What is the objective function in terms of the x coordinat D Type an expression The interval of interest of the function is Simplify your answer Type your answer in interval notation The point on the line y 3x 10 closest to the origin is Type an ordered pair Simplify your answer Type Integers or simplified fractions

The monthly incomes for 12 randomly selected people each with a bachelor s degree in economics are shown on the right Complete parts a through c below Assume the population is normally distributed 4450 93 459 4455 89 4151 48 3727 53 4283 44 4527 81 4407 28 3946 27 4023 68 4221 55 a Find the sample mean x 4263 3 Round to one decimal place as needed b Find the sample standard deviation S Round to one decimal place as needed

B If DE 16x 3 EF 9x 11 and DF 52 find HG E D H

The polynomial of degree 5 P x has leading coefficient 1 has roots of multiplicity 2 at x 4 and x 0 and a root of multiplicity 1 at x 5 Find a possible formula for P x P x

Verify the identity cot csct csct sint To verify the identity start with the more complicated side and transform it to look like the other side Choose the correct transformations and transform the expression at each step cot 2 csct csct Do not simplify csct sint

Use the standard normal distribution or the t distribution to construct a 95 co interval for the population mean Justify your decision If neither distribution can be used explain why Interpret the results In a random sample of 12 mortgage institutions the mean interest rate was 3 62 and the standard deviation was 0 48 Assume the interest rates are normally distributed Which distribution should be used to construct the confidence interval OA Use a normal distribution because the interest rates are normally distributed and is known OB Use a t distribution because the interest rates are normally distributed and is known OC Use a normal distribution because n 30 and the interest rates are normally distributed D Use a t distribution because it is a random sample is unknown and the interest rates are normally distributed O E Cannot use the standard normal distribution or the t distribution because is unknown n 30 and the interest rates are not normally distributed Select the correct choice below and if necessary fill in any answer boxes to complete your choice A The 95 confidence interval is 5 28 7 12 Round to two decimal places as needed B Neither distribution can be used to construct the confidence interval

1 point A street light is at the top of a 13 5 ft tall pole A man 5 3 ft tall walks away from the pole with a speed of 5 0 feet sec along a straight path How fast is the tip of his shadow moving when he is 40 feet from the pole Your answer 1 962962 ft sec Hint Draw a picture and use similar triangles

EXAMPLE history past present ng 1 source geography clue 2 government goods civics 3 culture economics money 4 geography South America inquiry 5 ocean events river 6 money culture 7 citizenship rights customs ocean 8 history monarchy democracy 2 Complete the sentences Use correct capital letters 1 Culture 2 historian is the study of the physical features of Earth is the study of the rights and Words to us historian culture responsibilities of citizens geograp 3 90graphy is the study of money resources goods econom civic ever and services 4 A events 5 economics and way of life studies history includes information about customs In history class you study civics from the past

UNIT 1 EXAMPLE You hear I m Gia I study life science You write I m Gia I study 1 Hi I m Ben I study planets and the life 2 Hello I m Mrs Park In my class you learn about 3 I m Matt I study 4 Hi I m Amy You are in my 5 Good morning I m Mr Dunn Welcome to 6 Hello I m Mr Reed I teach 7 Hey I m Nate My class focuses on the Ea science sonsize to livi engin univ non appli phy things things science class 5 Listen Write yes or no D EXAMPLE You hear Science is a way to solve problems You write yes 1 2 3 science of s

3 1 2 2 Complete the sentences 4 1 Life science is the study of universe things 2 Scientists nprast things when they think about what is different 3 Earth and space scientists study our planet and the empor 4 Scientists ving Words to use universe contrast non living things when they think about what is the same 5 Physical science is the study of non living things living compare at the science steps in order Investigate together Discuss your ideas

Write an equation for the function graphed below 7 6 5 4 3 2 2 3 4 6

Divide Check your answer by showing that the product of the divisor and the quotient plus the remainder is the dividend 6y 2 2y 3 2y 2

Find the missing length in the simila triangles 16 Find the missing length in the similar triangles 18 6 12 15 9

Nolan Walker decided to buy a used snowmobile since his credit union was offering such low interest rates He borrowed 3 100 at 3 75 on December 26 2021 and paid it off February 21 2023 How much did he pay in interest Assume ordinary interest and no leap year Use Days in a year table Note Do not round intermediate calculations Round your answer to the nearest cent Interest paid

Translate the statement into a confidence interval Approximate the level of confidence In a survey of 3336 adults in a country 44 believe the economy is getting better Three weeks prior to this survey 56 believed that the economy was getting better The survey s margin of error is 1 Use the results from the newer survey The confidence interval for the proportion is D Round to three decimal places as needed

5 A city is planning a new children s park Two contractors are bidding for the project Contractor A will construct the playground for 2 500 000 and estimates annual maintenance to cost 100 000 Contractor B will construct the playground for 3 500 000 and annual maintenance will be 75 500 In both cases the contractors will maintain the park for 20 years The relevant rate of interest is 8 On the basis of NPV analysis which contractor would you recommend

On April 5 2022 Janeen Camoct took out an 10 25 loan for 31 000 The loan is due March 9 2023 Use ordinary interest to calculate the interest What total amount will Janeen pay on March 9 2023 Ignore leap year Use Days in a year table Note Do not round intermediate calculations Round your answer to the nearest cent Maturity value

es On April 5 2022 Janeen Camoct took out an 10 25 loan for 31 000 The loan is due March 9 2023 Janeen s terms are ordinary interest Sabrina Bowers took out the same loan as Janeen Sabrina s terms however are exact interest Ignore leap year Use Days in a year table a What is Sabrina s difference in interest Note Do not round intermediate calculations Round your answer to the nearest cent Difference b What will Sabrina pay on March 9 2023 Note Do not round intermediate calculations Round your answer to the nearest cent Amount

Question 4 Find the derivatives of the following functions a 7 pts f x log4 x 4x 1 10 e 10

In a random sample of 8 people the mean commute time to work was 33 5 minutes and the standard deviation was 7 4 minutes A 98 confidence interval using the t distribution was calculated to be 25 7 41 3 After researching commute times to work it was found that the population standard deviation is 8 8 minutes Find the margin of error and construct a 98 confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known Compare the results The margin of error of is Round to two decimal places as needed

Harold Hill borrowed 15 200 to pay for his child s education at Riverside Community College Harold must repay the loan at the end of 10 months in one payment with 4 interest a How much interest must Harold pay Note Do not round intermediate calculation Round your answer to the nearest cent Interest to pay b What is the maturity value Note Do not round intermediate calculation Round your answer to the nearest cent

Question 3 Find an equation of the tangent line to the given curve at the giver point sin xy x y at 0 0

Look at the graph 101 50 10 5 0 5 10 5 10 What is the equation of the horizontal asymptote

Nolan Walker decided to buy a used snowmobile since his credit union was offering such low interest rates He borrowed 3 100 at 3 75 on December 26 2021 and paid it off February 21 2023 How much did he pay in interest Assume ordinary interest and no leap year Use Days in a year table Note Do not round intermediate calculations Round your answer to the nearest cent Interact poid

Translate the statement into a confidence interval Approximate the level of confidence In a survey of 1069 adults in a country 74 said being able to speak the language is at the core of national identity The survey s margin of error is 3 7 The confidence interval for the proportion is CD Round to three decimal places as needed