Basic Math Questions and Answers

7 POINTS 8 SOLVE THE FOLLOWING PROBLEMS A IN HOW MANY WAYS CAN THE LETTERS OF THE WORD TRACK BE ARRANGED PAGE 4 OF 13 B A STUDENT MUST SELECT AND ANSWER SIX OUT OF TEN QUESTIONS ON AN EXAM IN HOW MANY WAYS CAN THIS BE DONE C A TEACHER DECIDES TO GIVE SIX IDENTICAL PRIZES TO 6 OF THE 20 STUDENTS IN HIS CLASS IN HOW MANY WAYS CAN THIS BE DONE D HOW MANY DISTINCT ARRANGEMENTS CAN BE MADE WITH THE LETTERS IN THE WORD CONNECTION E HOW MANY AUTOMOBILE LICENSE PLATES CAN BE MADE IF EACH PLATE CONTAINS 3 DIFFERENT DIGITS FOLLOWED BY 3 DIFFERENT LETTERS F IF A BASEBALL TEAM CONSISTS OF 18 PLAYERS HOW MANY POSSIBLE GROUPS OF 9 MAN TEAMS ARE POSSIBLE G HOW MANY DIFFERENT COMMITTEES CAN BE FORMED FROM 4 TEACHERS AND 20 STUDENTS IF THE COMMITTEE IS TO CONSIST OF TWO TEACHERS AND THREE STUDENTS

6 POINTS 2 A SINGLE CARD IS DRAWN AT RANDOM FROM THE PROBABILITY OF DRAWING THE FOLLOW LOWEST TERMS A A DIAMOND OR A 5

7 POINTS 14 ANSWER THE FOLLOWING QUESTIONS ABOUT MEAS A WHICH 2 MEASURES OF CENTRAL TENDENCY AR SCORES B WHICH MEASURE OF CENTRAL TENDENCY IS USE WORKS WELL WITH MANY STATISTICAL METHOD C WHAT MEASURE OF CENTRAL TENDENCY MIGHT DATA

3 POINTS 3 TWO DICE ARE ROLLED USE THE TAB DETERMINE THE PROBABILITIES OF R A NOT LESS THAN 9

3 POINTS 23 WRITE EACH STATEMENT A A 40 OF 60 IS WHAT NUM

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3 POINTS 9 HOW MANY 7 DIGIT TELEPHONE BE ZERO AND A THE TELEPHONE NUMBER M BOKO

12 4 Homework K The figure illustrates a normal distribution for the prices paid for particular model of a new car Th is 12 000 and the standard devi 500

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Calculate the producers surplus for the supply equation at the indicated unit price p HINT See Example 2 Round your answer to the nearest cent p 80 e 0 01q p 120

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In Exercises 15 24 use a double angle formula to find the exact value of eac expression 15 1 2 sin 75 2 tan 75 16 1 tan 75 17 2 cos 105 1 18 1 2 sin 165 2 tan 165 19 1 tan 1651 20 2 cos 165 1 21 1 2 sin2 22 2 cos 23 8 2 tan 1 tan 24 12 sin 5TT 12 1 5T 12 7 12

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In gradually varied flow the channel bottom water surface and EGL are parallel Select one True O False

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A rectangular channel has a bottom width of 3 78 ft longitudinal bottom slope of 0 001 and a Manning roughness factor of 0 016 If the critical depth in the channel is 1 18ft what is the flow rate in the channel in cfs

Find the range for the group of data items 21 22 23 24 25 The range is Simplify your answer

Consider the following orthogonal set of vectors 5 13 12 13 V V 12 13 5 13 Determine whether the given orthogonal set of vectors is orthonormal

Determine whether A is diagonalizable 202 A 022 220 avy d peppua e fond de pag

Show that A and B are not similar matrices 2 A 3 6 3 2 B Just type the result write your solution steps on the worksheet next assignment

Of students scoring in the 30s on a practice test the following study times resulted in certain test scores In the accompanying table x represents study time in hours and y represents the final test score Write a logarithmic regression equation for this set of data rounding all coefficients to the nearest ten thousandth Using this equation find an estimated test score for a student who studied 22 hours to the nearest integer

5 Determine the intercepts of the line 5x 9 8y 3

4 What is the slope of the line to 2 y 2 2

3 Fill the output b when the input a is 6 b 1 7a b

1 Complete the equation of the line through 6 5 and 3 3 Use exact numbers

8 Find the equation of the line Use exact numbers y B S No co 6 7 84 up co H

A 8 0 kg piece of metal displaces 1 2 L of water when submerged Part A Find its density Express your answer to two significant figures and include the appropriate unit H PSIC

Suppose that 65 000 is invested at 4 interest compounded quarterly a Find the function for the amount to which the investment grows after t years b Graph the function c Find the amount of money in the account at t 0 2 8 and 10 years d When will the amount of money in the account reach 100 000

7 Randy Coplin owes the bank 8 500 To repay the debt he paid a fixed amount back to the bank each month After 12 months his remaining debt was 6460 How much did Randy Coplin pay each month t 4 0 6 8 Function 1 is defined by the equation r t 9 Function 2 is defined by the following table How long did it take Randy to pay back his entire debt Write an equation to help solve this question r 9 6 4 5 10 1 5 Which function has a greater y intercept Why

6 Mikoto graphed shown below the relationship between the temperature in Degrees Celsius ar her cat s change in weight in g over the last ten days What is the meaning of peint A Choose 1 answer a At 9 degrees celsius below zero Mikoto s cat lost 2 g At 9 degrees celsius above zero Mikoto s cat lost 2g b C At 9 degrees celsius below zero Mikoto s cat gained 2g d At 9 degrees celsius above zero Mikoto s cat gained 2g

Hank invested 700 in a CD that had a 7 5 APR and was compounded quarterly If Hank had the CD for 12 years what would the total worth of the CD be at the end of 12 years

213 Situation 1 Four friends James Gloria Aman and Celeste go on vacation together 1 On the first day they decide to go enjoy the outdoors Gloria goes for a hike They start at sea level and end on a mountain top at 1 000 ft above sea level Aman goes diving and gets 15 feet below sea level Celeste and James decide to nap on the beach next to the ocean right at sea level Draw a representation of each person s location using a number line Write an expression to represent the distance between Aman and Gloria

9 Graph a line from the equation y 6 5x 1 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 1 2 3 5 6 7 8 9 1 2 3 4 5 6 7 8 9 What is the slope of the line through 2 2 and 9 3 X nich 10 Two anchors one red and one blue started rising toward the surface at the same time They each rose at a constant speed The red anchor started rising from an altitude of 80 meters below the surface After 30 seconds it was 60 meters below the surface

5 Rearrange the equation so r is the independent variable 10q 5r 30 6 The table compares the amount of homework Mr Moyo gave to his class and th number of students who completed them for several different occasions Can the number of students who completed their homework be represented as a function of the homework s size Explain your answer Homework of questions 5 8 6 10 4 7 Complete of students 30 24 26 20 32 25 26

6 What is the y intercept of y 4x 7 Complete the equation of the line through 3 8 and 6 4 y 8 Find the equation of the line Use exact numbers y LI 8 6 4 3 2 A 6 7 8 9 Stosmodis

along with the completed Mini QPA 1 Graph the line and write an equation that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is 0 4 In other words a change of 1 unit in x corresponds to a change of 0 4 units in y XS E 9 8 the equation is 13 y 9 8 7 6 5 4 1 HNWA 3 2 1 1 2 3 4 5 6 7 8 9 supo edt o nottules out of butov alears alolamo 1 2 3 4 5 6 7 8 9 Conikere to see art ai feriWA X

A 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 B 5 Plot the points 3 4 and 6 4 on the coordinate plane below What is the distance between these two points Units 9 8 7 3 2 1 Y 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 123 4 5 6 7 89 X E

1 Karl set out to Alaska on his truck The amount of fuel remaining in the truck s tank in liters as a function of distance ar driven in kilometers is graphed Fuel liters 500 450 400 350 300 250 200 150 100 50 100 200 400 500 600 700 300 Distance kilometers 800 Ypatbee shyde anw fost vol and best of her sal i bib gool wol How much fuel did the truck consume every 100 kilometers

d 6 Determine the intercepts of the line 8 14 y intercept x intercept h 0 6 0 4 y d vsq 0 4 0 2 0 2 0 2 0 6 0 8 012 vbne x yd ben SW Siqueini 101001

An exponential function f a ab passes through the points 0 10000 and 3 640 What are the values of a and b a 0 4 b 10000 X

2 What ordered pair x y is a solution to this equation 5x 2y 30 3 2x 3y 5x y Complete the missing value in the solution to the equation 0 4 What is the slope of the line 3 2 2 Y 61

Determine minimal conditions on the real constant u so that 0 0 is a center for the linear system x ux y y x Uy E

Greetings I need to answer this exercise if it is true or false Please explain step by step what is the correct way to do it Thank you 7 3 4 2 11 5