Basic Math Questions and Answers

1 18y 1 9y 8y 6 4y 3 4y 3 1 y 1 4y 2 6 3y 6y 6 6y 9y y 1 2 3y CLEAR 4 5y 3y 4 3y 2 2 5y

An object is thrown upward at a speed of 200 feet per second by a machine from a height of 15 feet off the ground The height h of the object after t seconds can be found using the equation h 16t 200t 15 When will the height be 166 feet Select an answer Hint List all of the solutions with commas between them Round to one decimal place Hint Be sure to include the correct units When will the object reach the ground Select an answer Select an answer Question H feet per second seconds Submit feet 0

Find equivalent expre y 10 4 Choose three expressions 3y 4 2y s for 2y 7 5y 6y 3 y 9y 5 9 5y 4y 4 4y 1 2y y y 1 4 4y 4

47 Growth rate If w t is the rate of growth of a child in 10 pounds per year what does f w t dt represent

MSILM What s the Area A rectangle measures 2 meters by 1 meters What is its area 4 8 Solve on paper and check your work on Zearn 4 15 Area m

mmutative Property Step 1 1 x x Step 2 Distributive Property 2 1 2 4 DRAG AND DROP AN ITEM HERE DRAG AND DROP AN ITEM RERE 1 1 3 Reason DRAG AND DROP AN ITEM HERE CLEAR CH Associative Property Explanation Reordering Grouping

Calculate the derivative of the function 5 x x 1 h x h x

Calculate the derivative of the function 3x 9 4x 1 s x Step 1 Recall the Chain Rule If f is a differentiable function of u and u is a differentiable function of x then the composite f u is a Many like to think of the derivative of f expression as the derivative of f of the expression times the 3x 9 4x For the function s x the derivative of s If we think of 3x 9 4x 1 note that s is a composite function with an expression that is rais as u then u is a differentiable function of x and u Apply the Generalized Power Rule to find the derivative of u f x 3x 9 4x1

Tutorial Exercise Calculate dy dx Simplify your answer HINT See Examples 1 and 2 y 2x 5x 1 Step 1 In the given equation y 2x 5x 1 we have the product of two Therefore to differentiate we must first recall tho

Assume that it costs a company approximately

1 Solve the equation over the complex numbers x 64 2 Write the product in the form a bi 2 71 2 7i 3 Use the Quadratic Formula to solve the equation x 8x 6 0 4 Use the Quadratic Formula to solve the equation 2 x 2x 7 0

Crystal borrows money to build an addition to a lab owned by her engineering firm Edison takes out a mortgage for a new house in Cleveland Brian purchases a corporate bond issued by an automotive firm Broo70 a cloud computing company O

tributive Property ommutative Property Step 1 Step 2 1 5 0 9 7 3 2 1 y 1 5 0 9 7 3y 2 1y 1 5 7 3y 0 9 2 1y DRAG AND DROP AN ITEMMERE 1 5 0 9 7 3y 2 1y Reason DRAG AND DROP AN TEM HERE PABAND DROP CLEAR Associative Property Explanation Reordering Grouping

2x 3 x 1 4x 8 10x8x 5 52 4 3 2x 4 5x 7 4x 6 2x 3 7x 5 2x 9 77 x 1 2x 2 4x 1

The daily cost to manufacture generic trinkets for gullible tourists is given by the cost function C x 0 001x 0 5x 550 dollars where x is the number of trinkets a As x increases the marginal cost does which of the following O increases O decreases O increases then decreases decreases then increases b As x increases the average cost does which of the following O increases O decreases O increases then decreases O decreases then increases c The marginal cost is Select the average cost when y 100

Est te income growth based on Today TimeO is year end YE 2014 TICKER P E ttm P E forw PEG EPSO 2014 EPS 2013 Equity Sh Payout 0 2185 What was the growth of earnings for DEF at YE on a trailing year over year basis 0 2248 0 2128 DEF 0 3012 10 8 7 05 1 24 4 16 3 43 19 72 0 29

Find the indicated quantity assuming that u 4i j v i 3j and w 3i u v uW

B 1 Points Match the polar equation with the graphs labeled I IV 1 r DETAILS Select O III Jo IV

tch the terms to the definitions The Supreme Court ruled in 1954 that separate but 3 equal had no place in education ordered desegregation with all deliberate speed but states continued to resist 10 A New Deal government program that purchased and refinanced home loans in default during the Great Depression became an engine of home ownership and suburban growth in the 1950s Huge growth in birth rates due to higher incomes to support larger families and homes large enough to 6 accommodate them contributed to the professionalization of homemaking in which the role of housewife was viewed as a career The organizers of the Mattachine Society and the Daughters of Bilitis held meetings distributed literature 8 and provided legal and counseling services but had to operate in secret because homosexuality was considered a mental disorder and they risked arrest and abuse Young people discontent with an America rigidly defined fortablo liuo by ric alth 1 Home Owners Loan Corpora

Nathan walked on an asphalt pathway for 12 miles He walked the 12 miles back to his car on a gravel road through the forest On the asphalt he walked 2 miles per hour faster than on the gravel The walk on the gravel took one hour longer than the walk on the asphalt How fast did he walk on the gravel Provide your answer below

AP6 1 11 se make sure to properly format your answers All dollar figures in th 7 All percentage values in the answers need to include a percentage s ow both decimal places 5 06 Use if your filing status is Head of household Complete the row below tha a W c Multiple d Subtraction

A pressure drop of 200 kPa is measured over a 50 m length of 2 mm diameter pipe transporting 30 C water If a laminar flow exists calculate the flow rate Solution 1 At 30 C the kinetic viscosity of water is 0 801 X10 6 2 Reynolds number is calculated as 2496 v 3 Frictional factor for laminar flow is calculated as 0 0256 v 4 From Energy equation pressure drop is equal to total energy loss thus o pressure drop is equivalent to 20 486 m o total frictional loss is equivalent to 32 66 V 1 m o Hence v 0 6265 m s 5 The flow rate is then Q ml s 6 Check the Reynolds number to make sure the flow is laminar Re

Section D Use if your filling status is Head of household Complete the Taxable Income If line 11b is At least 100 000 but not over 160 700 Over 160 700 but not over 204 100 Over 204 100 but not over 510 300 Over 510 300 a Enter the amount from line 11b b Multiplication amount x 24 0 24 x 32 0 32 x 35 0 35 x 37 0 37 c Multiply a by b Calculate the tax for each of the taxable incomes of a head of h a 400 000 115 409 00 h 108 962 22 303 00

Schedule Z If your filing status is Head of household If your taxable income is Over 0 13 850 52 850 84 200 160 700 204 100 510 300 But not over 13 850 52 850 84 200 160 700 204 100 510 300 The tax is X 10 1 385 00 12 6 065 00 22 12 962 00 24 31 322 00 32 45 210 00 35 152 380 00 37 Calculate the tax for each taxable income of a head of house a 400 000 115 409 00 b 10 954 1 095 40 c 108 962 22 303 00

Qu hace la persona Instrucciones Look at the indicated subject pronoun and the picture Decide what form of the verb is CORRECT for that person Then write what it means in English on the line below it 1 Yo 2 Clara y Marisol 3 El gato 4 Nosotros 5 T 6 Vosotros Es hora de desemnar A preguntamos A ayudas A cocinas A habla B pregunta A Descanso A estudian B hablan B descansar B estudia B ayudo B cocin is C pregunto C mira C descansa C estudiamos C ayuda C cocinan

D 15 Question 8 Spider man decides to go for a walk through New York City D t given below is his distance in kilometers from the Empire State Building after hours of walking The relationship is as follows D t 11 5 5t Let D be the inverse function of D Take x to be the output of the function D That is x D t and t D x Which statement best describes D x a The reciprocal of his distance from the Empire State Building in kilometers after walking x hours b The amount of time he has walked in hours when he is x kilometers from the Empire State Building c His distance from the Empire State Building in kilometers after he has walked for x hours d The ratio of the amount of time he has walked in hours to his distance from the Empire State Building in kilometers x

Bob deposited 2000 into an account with 9 1 interest compounded monthly Assuming that no withdrawals are made how much will he have in the account after 4 years Do not round any intermediate computations and round your answer to the nearest cent Balance after 4 years

15 For the each pair of functions below find fog x and gof x and determine whether f and g are inverses of each other f x and g x 1 3x 3x fog x 3x gof x Are fand g inverses Yes No f x x 2 and g x x 2 fog x gof x Are fand g inverses Yes No

uestion 4 15 olve the following inequality Write your answer as an interval or union of ervals 2 7 x 1 x 1

ffice ay April 6 2023 ent event on A concrete mix is designed for an ultimum strength of 4 000 psi in 28 days What will be its strength in 7 days

Bonus Graph all asymptotes of the rational function f x 10 5 x x 5 x 1 10 50 0 5 10 5 10

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Question 2 Solve the following inequality Write your answer as an interval or union of intervals x 16 x 1 x 2 0

3x 12x Graph the rational function h x 2 5271 X2 5X 4 Include asymptotes intercepts holes and sketch the general shape of the graph Vertical Asymptote s 10 5 10 5 0 5 10 5 3x 12x 10 Horizontal Asymptote s x intercept s y intercept s Hole s Domain Range 15

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be atter essional d Thursd What is the diameter of a No 7 bar and En 8 What is the nominal weight of regular reinforced concrete

Which expression is equal to 29 OA 20 13 4 A O B 20 13 4 Oc 20 4 13 O D 13 4 20

Find the product 5 7 9 9 O O O O A B C 12 9 35 9 35 81 2 3

Evaluate 7 34 x 3 24 6 O A 90 O O B 105 c 113 135

Rosa s age is equal to O C B C D 8 years 9 years 18 years 24 years 1 of her uncle s age Her uncle is 27 years old What is Rosa s age 3

3 Let s use an example to explain what s happening when we a List out every three scoop cone choosing from the Vanilla V and Strawberry S there are 24 different M V S C MCV CMV Cvm mvc vm C MVS MSV VMS Smvy Vsm s MCS MSC CMS smc csm CV S CSV VCS SCV NSC NMS VSM SMV CVM vemay possible way V b From your list group all cones that would represer flavors mc mus CSU myc SCM our list and grouping to explain why we div

14 23 Packages having a weight of 50 lb are delivered to the chute at VA 3 ft s using a conveyor belt Determine their speeds when they reach points B C and D Also calculate the normal force of the chute on the packages at B and C Neglect friction and the size of the packages VA 3 ft s A 30 30 5 ft B 5 ft 30 C 30 5 ft D

the lowest population growth rates Determine in how many years each event can occur Use the model P P 1 r where P is the population from the table as of 2020 t is the number of years after 2020 P is the projected population and r is the growth rate State Growth rate Growth rate Population in millions in 96 0 08 12 298 0 08 0 621 0 03 11 467 0 30 0 36 D IN 1 Nevada 2 Arizona 3 Utah 4 Idaho 5 Georgia 2 93 2 81 2 55 2 43 2 17 P 1 499 Po 1 0243 Equation P 1 499 1 0243 2 Population in millions 2 565 6 339 2 645 1 499 9 545 Fill in the information from the table and solve Round all answers to the nearest year 1 In what year would Idaho s population reach 2 million 17 points total 2 2 149961424 3 2 Equation 9 072 State 46 New York 47 Vermont 48 Ohio 49 Michigan 50 Rhode Island 1 334 1419 105 11334 1 499 100 1 334 3 1 71 12 2032 2 What year would Michigan s population be decreased to 9 072 million 17 points total 9 072 2 10 072 2 997 P Po 1 r p 1499 3 43 1 9343 1 0239 10 072 1997 L0 6 t year year 10 072 1 058 00 2 43 3 43 2020112 2032

c Use mental math to ev 12 4 4 7 7 7 Describe your reasoning d Use mental math to 1 98 4 96 2

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b Consider the following Write the percent represer 20

MY NOTES PRACTICE AND Severely obese persons BMI 2 40 have a greatly increased risk of diabetes heart disease and many other ailments that are very expensive to treat The table gives the percent of Americans are severely obese from the year 1990 and projected to 2030 1990 2000 2010 2015 2020 Year Severely Obese y 0 8 22 4 9 6 4 7 9 9 5 11 1 a Find an exponential function that models the data with x equal to the number of years after 1990 and y equal to the percent Round your numerical values to three decimal places 2025 2030 X You re right b Does the unrounded model overestimate or underestimate the percent of severely obese Americans in 2020 The model overestimates the projected total O The model underestimates the projected total c According to the unrounded model in what year are 8 1 of Americans expected to be severely obese 2022 You re right

How many students need to be in a class in order for at least two students to receive the same grade on an exam that is graded on a scale 0 to 40 points Your Answer

How many strings of length 7 can be formed from the letters a b c d and e that contain at least one e 16 384 78 125 40 320 61 741