Questions

You randomly select and measure the contents of 10 bottles of cough syrup The results in fluid ounces are shown to the 4 216 4 297 4 253 4 245 4 188 right 4 201 4 262 4 242 4 227 4 237 Assume the sample is taken from a normally distributed population Construct 80 confidence intervals for a the population variance o and b the population standard deviation o Interpret the results a The confidence interval for the population variance is Round to six decimal places as needed Interpret the results Select the correct choice below and fill in the answer box es to complete your choice Round to six decimal place as needed 0 OA With 20 confidence it can be said that the population variance is less than OC With 20 confidence it can be said that the population variance is between and OB With 80 confidence it can be said that the population variance is between OD With 80 confidence it can be said that the population variance is greater than and b The confidence interval for the population standard deviation is D Round to four decimal places as needed Interpret the results Select the correct choice below and fill in the answer box es to complete your choice Round to four decimal place as needed OA With 80 confidence you can say that the population standard deviation is between and OB With 80 confidence you can say that the population standard deviation is less than inches inches OC With 20 confidence you can say that the population standard deviation is greater than OD With 20 confidence you can say that the population standard deviation is between and inches inches

45 Show that sin A B is in general not equal to sin A sin B by substituting 30 for A and 60 for B in both expressions and simplifying

41 1 sin t 1 sin t cos t 1 sin t

29 csc B sin B cot B cos B

Prove that each of the following identities is true 1 cos 0 tan 0 sin 2 sec 0 cot 0 csc 0 3 csc 0 tan 0 sec 0 4 tan 0 cot 0 1 tan A 5 sin A sec A cot A 6 cos A CSC A 7 sec 0 cot 0 sin 0 1 8 tan csc 0 cos 0 1 9 cos x csc x tan x cot x sin x 10 sin x sec x csc x tan x 1 11 csc x cot x 1 cot x csc x sec x 12 tan x cos x cot x sin x 1 13 cos x 1 tan x 1 15 1 sin x 1 sin x cos x 14 sin x cot2x 1 1 16 1 cos x 1 cos x sin x 17 cost sint sin t cott 1 18 sint cost sin t cos t sec t csct

Prove that each of the following identities is true 1 cos 0 tan sin 2 sec cot csc 0 3 csc 0 tan 0 sec 0 4 tan cot 0 1 tan A 5 sin A sec A 7 sec 0 cot 0 sin 0 1 cot A 6 cos A CSC A 8 tan csc 0 cos 0 1 9 cos x csc x tan x cot x sin x 10 sin x sec x csc x tan x 1 11 csc x cot x 1 cot x csc x sec x 12 tan x cos x cot x sin x 1 13 cos x 1 tan x 1 14 sin x cot2 x 1 1

Distribution of Earthquakes Mediterranean Himalayan Belt Indonesian Belt Circum Pacific Belt Based on the earthquake distribution what can you say about the dip direction of subduction in the Indonesian Belt Shallow focus O Intermediate focus Deep focus

What causes an Earthquake a The breakdown of material in the core b When stress is less than strength of the rock c Deformation of plastic material d When stress is greater than strength of the roc e When stored elastic energy is released

Why do we study Earthquakes a to know exactly when and where an Earthquake will happen b to help determine exactly how intense an Earthquake will be c to help describe explain assess and possibly help to determine if an Earthquake is likely d because people too indifferent toward Earthquakes e because we have too much time on our hands

Whoever realizes the benefit in question 1 how much will the total benefits that the publi realizes add up to per home sold Less than 10 000 10 000

Congress is now thinking about banning TikTok or forcing its sale to a US based company likely one of the tech giants If this happens what market failure will be worse Adverse selection O Market power O Externalities O Moral hazard

JK J M G K 15 L P

need to transform the integrand first 5 x sin x dx

13 Let A 4 3 be the initial side and B 2 5 be the terminal side a Find the ordered pair for vector AB Find the horizontal and vertical components b Find the magnitude of AB Round o the nearest thousandth 0 Find the direction Round to the nearest thousandth

A rhombus is a parallelogram with four congruent sides perpendicular diagonals and the diagonals bisect a pair of opposite angles A square is a parallelogram with all the properties of a rectangle and rhombus RHOM is a rhombus Find the unknown measures Treat each problem independently 5 If OB 2x 1 and BR 3x 10 then OR 6 If RM 18 then RH OH OM 10 7 If m22 48 then mZMOH M R 4 3 B 8 5 6

Antidifferentiate using a table of integrals You may need to transform the integrand first x e4x dx

For problems 1 9 use rectangle QUAD Treat each problem independently 1 If DP 4x 1 and PA x 13 then DP 2 If m 2 12x 4 and m23 16x 12 then m23 3 If m25 12x 3 and m 6 10x 9 then mZ4 D 4 If m23 18x 8 and m 6 70 4x then mZ6 8 6 4 7 1 3 A

need to transform the integrand first dx 9 252

Find the least common multiple for the following expressions x and x 3 x 3 x x 3 Or 3 3x

Antidifferentiate using the table of integrals You may need to transform the integrand first sin 4t cos 5t dt

need to transform the integrand first 2 dz 4 x 6

need to transform the integrand first sec x dx

A kite is a quadrilateral with two pairs of adjacent congruent sides LMNP is a kite Find the unknown measures 12 If MN 4x 5 and NP 6x 1 then MN 13 If mZLMP 58 and mZLPM 7x 2 then x 14 If mZMON 8x 14 then x M

Antidifferentiate the following function using the table of integrals You may need to transform the integrand first 2 cos t dt

0 A trapezoid is a quadrilateral with exactly one pair of parallel sides In an isosceles trapezoid the legs both pairs of base angles and the diagonals are congruent TRAP is an isosceles trapezoid Find the unknown measures T O If TP 2x 3 and RA 3x 2 then TP If mZTPA 63 then mZRAP and m PTR P R

ABCD is a parallelogram Find each unknown measure 3 If DE 6 then EB DB B E C D 4 If AD 3x 6 and BC x 18 then x AD A E D

Simplify x 7x 30 823 6422 3 8 08 2 3 4 x 8 2 3 4 x 8 0 2 3 O 4 x 8 8x2 4x 40

Simplify x x 20 2 3x 15 8x 16 4 x 4 3 8 x 4 3 3 x 4 8 8 x 2

Which expression is equivalent to the complex fraction 2 7 2 1 2 2 3 0 7 2x 1 7 3 2 3 2x 1 2 2 7 3 2x 1 2 7 2 2z 3

What is the area of the figure Round to the nearest tenth 9 ft 5 ft 13 ft O 55 0 ft O 81 0 ft O 45 0 ft C 1080 2

In the vicinity of a bonfire the temperature 7 in C at a distance of x meters from the center of the fire is given by T x 500 000 x 400 At what range distances from the fire s center is the temperature less than 370 C Assume x is positive Round your values to one decimal place Enter your answer using interval nota m

Solve the inequality Enter your answer using interval notation x4 34x272 0

Find the domain of the given function Enter your answer using interval notation 4 X g x 4 x

Solve the inequality Enter your answer using interval notation x 2 X 3 X 1 X 2

Solve the inequality Enter your answer using interval notation X 1 X 11 0

Solve the inequality Enter your answer using interval notation 4 1 1 5 S X X

Suppose that antibiotics are injected into a patient to treat a sinus infection The antibiotics circulate in the blood slowly diffusing into the sinus cavity while simultaneously being blood by the liver In a future chapter we will derive a model for the concentration of the antibiotic in the sinus cavity as a function of time since the injection c t e at e t a where a 0 b At what time does the inflection point occur 2 t In d B B

After an antibiotic tablet is taken the concentration of the antibiotic in the bloodstream is modeled by the function C t 8 e 0 4t e 0 6 where the time t is measured in hours and C is measured in g mL What is the maximum concentration of the antibiotic during the first 12 hours Round your answer to four decimal place pg mL

Use logarithmic differentiation to differentiate the following functio x 1 6x 1 4x 1 f x 8x 1

College students take different course loads Many colleges determine the number of Full time equivalent students F by using the formula F students enroll for a given semester where n is the total number of credits in which 15 If students on a campus register for a total of 36075 credits how many full time equivalent students does the campus have The campus has 2405 full time equivalent students Solve the formula for n n

Determine whether 11 is a solution of the equation 7 x 1 70 Is 11 a solution Yes No

A hotel purchases a large photo for its newly renovated lobby The perimeter of the photo is 360 in The width is 5 in more than four times the height Find the dimensions of the photo The height of the photo is Simplify your answer Type an integer or a decimal The width of the photo is 4h 5

Caleb paid 27 50 including a 5 sales tax for a security wallet How much did the wallet itself cost The wallet originally cost Round to the nearest cent

Simplify the following expression Write as a single logarithm or monomial 12 In 36 12 In 36

possible Miranda s financial aid stipulates that her tuition not exceed 1200 If her college charges a 125 registration fee for the term plus 250 per course what is the greatest number of courses for whie Miranda can register Miranda can register for at most courses Your answer should be a whole number

TASK 2 Modelling a function 1 The following function h x 2 x 12 5 has undergone a horizontal transition o the right a vertical transition up by 3 and stretched by the factor of 4 What would be function 3 marks

o finance her community college education Sarah takes out a loan for 2200 After a year Sarah decides to pay off the interest which is 8 of 2200 How much will she pay Sarah will pay

Solve using the addition principle Don t forget to perform a check 5 4 2 5 x The solution is x Type an integer or a decimal

olve using the multiplication principle Don t orget to perform a check 6 7x 50 28 The solution is x Type an integer or a decimal

Translate to an algebraic expression A driver drove at a speed of 52 mph for t hours How far did the driver go The algebraic expression 52 mph at t hours is d miles