Basic Math Questions and Answers

7 y 3 x 2 2 9 y x 3 2 E f x K 8 y x 1 8 6 4 2 6 2 10 y x 2 5 it 2 2 AH

15 1 point Where is the first maximum of y 2 sin x 180 after x 0 d 360 a 90 b 180 C 270

20 4 points A weight hooked onto the end of a spring fixed to a ceiling bounces up and down The weight s height h relative to the ground in metres is given by the formula 0 25 sin 240 90 1 5 where is the time in seconds a What is the weight s initial height b How high off the ground is the weight when it is midway between its highest and lowest points c What is the weight s maximum height d What is the height after 2 5 s

18 4 points The graph of a periodic function is shown a Domain b Range c Period d Amplitude e Phase shift fl Vertical translation YA B 0 2 90 180 270 360

13 1 point Which angles are coterminal a 50 and 100 b 100 and 460 c d 400 and 720 200 and 880

10 1 point Which is true for any AABC sin A sin B sin C b c a b 2ab cos C C b a c 2ac cos B d all of the above

4 points Distances from Ron s house to the grocery store and library are shown Ron in line skates from his house to the grocery store Then he goes to the library and returns home How far does he travel in total Show all the steps Library 5 0 km 135 5 5 km Ron s House Grocery Store

1 point The period of the sine function is 360 and the amplitude is 2

4 1 point Coterminal angles share the same terminal arm when in standard position

7 1 point The amplitude of y 3 sin x is 3

2 1 point Given AABC tan A b Im ME

18 ABC Cleaning Company cleaned 45 offices and incurred operating costs of 2 340 What was the cost to clean each office Select the formula labels then enter the amounts and compute the cost of cleaning each office Total number of services provided Total costs Unit cost per service

How many gallons of a 90 antifreeze solution Strength Gallons of Solutions must be mixed with 90 gallons of 15 antifreeze to get a mixture that is 80 antifreeze Use the six step method You need gallons 90 15 80 X 90 x 90 Gallons of Antifreeze

Factor the following polynomial by grouping If it cannot be factored indicate Not Factorable ax 5bx 5ay 25by

the target with the bullet holes Does this show lack of precision or bias b Draw a second sketch of the target if the shots are both unbiased and precise have little variation The rifleman s aim is not perfect so your sketches should show more than one bullet hole 7 20 Targets Bias or Lack of Precision Again a If a rifleman s gunsight is adjusted correctly but he has shaky arms the bullets might be scattered widely around the bull s eye target Draw a sketch of the target with the bullet holes Does this show variation lack of precision or bias Explain how you can tell from the widths of the graphs which has the largest sample n 40 and which has the smallest sample n 10 amount Each dot in the dotplots represents the proportion of suc cess for one person For instance the dot in Figure A farthest to the right represents a person with an 80 success rate One dotplot rep TRY 7 33 What Is the Proportion of Seniors Example 5 resents an experiment in which each person had 10 trials another shows 20 trials and a third shows 40 trials population of college students is taking an advanced math clas the class are three juniors and two seniors Using numbers 1 2 3 to represent juniors and 4 and 5 to represent seniors sample out replacement Draw a sample of two people four times ond each of parts a b c and d and then fill in the following table a Use the first line reprinted here from the random number table select your sample of two The selections are underlined 02779 72645 86009 00000000000 0000 0000 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Sample Proportion 7 28 ESP Again In the graph for Exercise 7 27 explain how you can tell from the shape of the graphs which has the largest sample size and which has the smallest sample size 6 Calculate the standard error c Use your answers to fill in the blanks We expect t s give or take 7 29 Standard Error Which of the dotplots given in Exercise 7 27 has the largest standard error and which has the smallest stan dard error 7 27 ESP A Zener deck of cards has cards that show one of five different shapes with equal representation so that the probability of selecting any particular shape is 0 20 A card is selected randomly and a person is asked to guess which card has been chosen The graph below shows a computer simulation of experiments in which a person was asked to guess which card had been selected for a large number of trials If the person does not have ESP then his or her proportion of successes should be about 0 20 give or take some SECTION EXERCISES CHAPTER 7 7 32 Far from Fair Which of the graphs in Exercise 7 31 is centered farthest from 0 50 32699 Report the percentage of seniors in the sample Count the numb 4 s and 5 s and divide by the sample size 2 b Use the next line to select your sample of two 31867 85872 91430 45554 Report the percentage of seniors in the sample c Use the next line to select your sample of two 07033 75250 34546 75298 Report the percentage of seniors in the sample d Use the last line to select your sample of two 80623 09084 98948 09541 Report the percentage of seniors in the sample e Fill in the rest of the table below showing the results of the four samples Repetition 1 from part a 2 from part b 3 p Population Proportion of Seniors 2 5 0 4 p Sample Proportion of Seniors 1 2 0 5 Error p 0 5 0 4

Solve the given initial value problem for the Cauchy Euler equation ty t 8ty t 20y t 0 y 1 2 y 1 7 The solution is y t

Find a general solution to the differential equation using the method of variation of parameters y 25y sec 5t The general solution is y t

a c d b 8 1 9 rational irrational integer natural meaningless 0000 00000 X rational irrational integer natural meaningless 36 6 rational irrational integer natural meaningless 3 0 rational irrational Is one or more of the following types of numbers rational irrational integer natural If the expression is meaningless so state Select all that apply

am n a n m Va m or am n am 1 n am For this problem we will use the first form because we will be taking the square root first and both 25 and 36 are perfect squares 35 25 Step 2 Simplify using the fact that V 25 36 5 6 a vb 3 25 Step 3 Use the fact that a b m am bm to fully simplify the expression and complete the problem If the solution is not a real number enter NOT REAL 53 36 5 6

onditional statement premise 1 A premise 2 conclusion is a tautology then the argument is a n conditional statement premise 1 A premise 2 conclusion is a tautology then the argument is a n argum argum

Perform the indicated operation and simplify 98 2x x 7x 6 x x 2 2x 8 x 4x 12 x 14x 49

Write the answer without using exponents a 73 b 2 7

Simplify the expression with all exponents positive 94 92 9

Replace the radical with a fractional exponent Do not simplify

Tutorial Exercise Find the power and root if they are real numbers 3 2 25 36 Step 1 We can evaluate expressions of the form am n in two ways am n a n m or am n am 1 n Nam For this problem we will use the first form because we will be taking the square root first and both 25 and 36 are perfect squares 2513 2 5 3 25 36

Tutorial Exercise Simplify by combining like terms 17pq 6p2 8pq 4p Step 1 We simplify the expression by combining like terms Notice that we have two different types of like terms pq and

Factor the expression as a product of binomials x 1 24x 23

Simplify the fraction 42x6y8 6x6z

1 Fisgard Lighthouse in British Columbia is Canada s oldest West Coast lighthouse Riaz needs to know the height of the lighthouse This diagram shows the length of the shadows cast by Riaz and by the lighthouse at the same time 0 1 62 m 32 4 m 3 6 m a The sunlight is hitting the ground at the same angle in both triangles How do you know the triangles are similar b What is the height of the lighthouse to the nearest tenth of a metre

A central angle is an angle whose whose are radii of that circle The degree measure of an arc of a circle is equal to the of the central angle that intercepts it mAB 75 is at the center of a circle and 75 0 A

In this question you may take for granted that sine is a continuous function Show that there exists some x 0 2 such that sin x 3 10

A B C D E If tan 7 cos a B cos a B cos a B cos a B cos a where a and where B 3 find cos a B 3 11 a a B T B Cos C B 11 4

A steel shaft 4ft long that has a diameter of 3 in is subjected to a torque of 18 kip ft Determine the angle of twist Use G 12 10 6 a 3 12 b 1 23 c 2 62 d 6 22

Evaluate the sum where S 2 5 6 j jes

Which of the following sequences IS NOT a solution of the recurrence relation below 3a 4a a I n n 1 a n 1 12 a 1 n n 2 Da 4 1 721 O 4

The sequence a a n 4 is a solution of the recurrence relation a 8a n n n 1 O True O False 71 16a n 2

Select all terms of the sequence a a 1 1 a 2 Da 1 O q 2 Da 1 Da 1 0 100 2

Generate the first six terms of the sequence defined by the recurrence relations 0 a na n a3 a n 1 an 2 90 1 a

16 2 Which of the following communication methods are classified as crushing and which are classified as grinding ball mill jaw crusher hammer mill and roller mill

Select one What is the equation of the rational function whose graph is shown above Oy x 1 x 2 x 3 x 4 y x 1 x 2 x 3 x 4 x 1 x 2 x 3 x 4 Oy x 1 x 2 x 3 x 4 Oy

1 a De Select one Function Behavior Question 7 What function is represented by this graph 7 6 5 4 O 2 3 f x 3x f x 3 X y f x 5 Of x 3 x 2

The line RCT is a tangent to the circle angle ADC 135 angle OCB 34 angle TCD 26 Work out angle RCB angle ABC angle OAD O O O 1 1 3 B R O 34 C 26 A D 135 T

Let a 2 5 Find all Leave your answer in simplest radical form la 7 la 29 la 5 llall 28 la 50

A B C D E You have 22 pieces of Halloween candy and want to eat 4 of them In how many different ways can you choose 4 pieces Order does not matter 4 22 175560 7315 24

3 In a 2018 study research finds that 45 of people own an iPhone It is hypothesized that every year that percentage gets higher Therefore in 2019 a research company completed a study and found that 480 of 1023 people owned an iphone a State the null and alternative hypothesis b Find the p value Round to the nearest tenth c Using a 5 significance level state a conclusion to either reject or fail to reject

Let y 70 b 12 and c 11 Solve triangle ABC

Given annual returns of 12 8 10 and 6 what is the arithmetic average what is the geometric average of the returns in question 8 What is the standard deviation of the returns in question 8

A 3 D Let a 3 and ax 1 k 2 a Find the third term of the recursively defined infinite sequence a3 27 a3 35 a3 36 a3 33 a 60

The area of the triangle below is 11 78 square centimeters What is the length of base 3 8 cm

You make a sandwich for lunch You have a choice of 2 types of bread 3 types of meat and 3 condiments How many different types of sandwiches can you make A 8 B 18 C 24 D 36 48 E