Basic Math Questions and Answers

Find the area of the shaded region in square units y 8 7 6 5 4 3 2 1 fix 1 3 x 1 square units 2 3 4 5 6 X

Determine the area in square units of the trapezoid shown in the figure Consider lengths to be standard units 17 12 13

Melvin made the three drawings below Li E Which drawings contain EF I II and III o I only o II and III o I and II

Match each drawing on the left with its correct geometric notation on the right Some of the answer choices on the right will not be used AB fft AB AB BA

A large building shaped like a box is 60 m high with a face that is 70 m wide A strong wind blows directly at the face of the building exerting a pressure of 170 N m at the ground and increasing with height according to P y 170 2y where y is the height above the ground Calculate the total force on the building which is a measure of the resistance that must be included in the design of the building Find the width function w y for each value of y on the face of the building w y Use integers or decimals for any numbers in the equation CHIB

2 Use the graph of y f x to sketch a graph of each function a y f x f x I

8 Give the Instructions for preparing a two fold serial dilution of serum using 0 5 mL serum and 0 5 mL saline in each of five numbered tubes

Determine the area of the shaded region in square units y 5 5 54 4 5 4 3 5 3 2 5 2 1 5 1 0 5 1 square units 2 3 4 5 6 7 X

Solve the following application involving the area of a rectangle What is the height of the figure shown 23 6 units h units A 221 84 square units

The figure to the right shows the shape and dimensions of a small dam Assuming the water level is at the top of the dam find the total force on the face of the dam Use 1000 kg m for the density of water and 9 8 m s for the acceleration due to gravity 3 OA W y y 9 12m Find the width function w y for each value of y on the face of the dam Place the origin at the center of the base of the dam with the y axis going in the vertical direction and the x axis going in the horizontal direction Choose the correct answer below OB w y 18y 2 OC w y y 9 OD w y 81y 6 m 9m

The figure shows the shape and dimension of a small dam Assuming the water level is at the top of the dam and that the shape of the dam is an isosceles triangle find the total force on the face of the dam Use 1000 kg m for the density of water and 9 8 m s for the acceleration due to gravity 4 OA W y 27 CITR 2 O c w y 27Y Find the width function w y for each value of y on the face of the dam Place the origin at the vertex at the bottom of the dam with the y axis extending up in the vertical direction to the center of the the dam and the x axis going in the horizontal direction Choose the correct answer 27 O B w y y 4 m 27 OD W y Y 27 m

Consider the following scenario From 1990 to 1999 the amount spent to purchase a car exported to a particular country increased at a rate of 1 870 each successive year The increase in amount spent to purchase a car exported to this country from 1990 to 1999 can be represented by the rate function 1 87 f x 10 0 x 9 otherwise where x represents the number of years since 1990 and f x represents the rate of change in the amount spent to purchase a car exported to this country in thousands of dollars per year Calculate the area under f x on the interval 4 x 7 Interpret the result The area under f x on the interval 4 x 7 describes the amount spent to purchase a car exported to this country in thousands of dollars in 1997 The area under f x on the interval 4 x 7 describes the total increase in the rate of change of the amount spent to purchase a car exported to this country in thousands of dollars between 1994 to 1997 The area under f x on the interval 4 x 7 describes the rate of change of the amount spent to purchase a car exported to this country in thousands of dollars in 1997 The area under f x on the interval 4 x 7 describes the total increase in the amount spent to purchase a car exported to this country in thousands of dollars between 1994 to 1997

Determine the area in square units under the constant function on the indicated interval 2 6 0 square units Graph the result 6 5 4 3 2 1 5 4 3 2 f x 1 1 1 2 1 x 8 otherwise 10 3 4 5 on the interval 1 5 x 4 2 T 6 4 7 L 2 3 4 5 6 7 I 8 I 8 X 6 5 4 3 2 1 5 4 3 2 1 1 4 2 3 1 2 3 4 5 10 6 7 8 4 5 6 7 8 X X

Determine the area in square units under the constant function on the indicated interval 1 4 0 square units Graph the result y 2 1 5 0 5 2 1 5 1 0 5 f x 2 4 6 2 4 6 00 4 x 17 otherwise for x 6 7 10 12 14 16 18 20 8 10 12 14 16 18 20 X 2 1 5 1 0 5 2 1 5 1 0 5 2 4 2 4 6 6 8 10 12 14 16 18 20 8 10 12 14 16 18 20 X X

Determine the area in square units under the constant function on the indicated interval 1 2 Graph the result y 31 8 14 111 212 318 14 118 0 x 8 0 otherwise P x 81 square units 12 3 1 2 3 4 4 5 12 on the interval 2 x 7 6 7 8 6 7 8 HIN 318 111 118 HIN 1 318 4 11 00 2 3 4 2 3 4 4 10 5 in 5 10 6 4 6 78 7 8

Determine the area of the shaded region in square units 4 5 4 3 5 3 2 5 2 1 5 1 0 5 1 square units 2 3 4 5 67

Solve the following application involving the area of a rectangle What is the length of the base of the figure A 28 56 square units b unite 11 9 units

of 45 miles per hour For a standard office building suppose that the elevators reach an average speed that is given by m in the equation Solve for m m 3 Need He Interpret the result This is the Select speed in miles per hour of an elevator in a standard office building Submit Ans 0 Points Y NOTES Suppose tha by x in the Solve for x x Interpret th This is the Tapidly 25 6 m 3 7 Need He Select average minimum maximum our in a quarter mile give

6 How would 1 L of a 10 solution of chlorine bleach be prepared

Your dog groomer charges 0 30 per pound plus a 20 appointment fee for any dog that weighs less than or equal to 40 pounds For any additional weight over 40 pounds your groomer charges 0 40 per pound 3x 20 f x 0 x 40 x 40 Find the missing piece for the piecewise function that describes this scenario 4x 20 O 4 x 40 32 4x 4x 32

12 If 0 5 mL of serum is added to 4 5 mL of saline what is the dilution

The graph of y f x gives the speed limit y along a country road after traveling x miles a What are the highest and lowest speed limits along this stretch of road b Estimate the miles of road with a speed limit of 50 mph c Evaluate f 4 and f 8 a What are the maximum and minimum speed limits along this stretch of highway Maximum mph Minimum mph Type integers or decimals Speed Limit in mph Ay 80 70 60 50 40 30 20 10 0 0 O 4 12 8 Distance in miles 16 20

Without dental insurance the average cost in dollars of having Invisalign dental braces is given by m in the equation 5 381 20 m 210 1 28 Solve for m Interpret the result This is the Select cost in dollars of having Invisalign braces Select average maximum exact

On average the radius of the Earth is about 6 371 000 meters Use this table to convert this distance to megameters Writ your answer in standard notation Mm

A standard definition SD movie typically uses about 1 500 000 000 bytes of storage space Use this table to convert this numbe to megabytes Write your answer using standard notation megabytes

Find the area of the shaded region in square units y 6 5 4 3 2 1 f x x 1 square units 2 3 4 5 6 X

Use the formula A nd for the surface area A of a sphere whose diameter measures d This formula yields the surface area in square units The Hoberman Sphere is a mechanical toy that expands from 5 9 inches in diameter when it is fully closed to 30 1 inches diameter when fully expanded What is the difference in the surface area of a Hoberman sphere from when it is fully clos when it is fully expanded in in Round the result to three decimal places

Determine the area of the shaded region in square units 3 5 39 2 5 2 1 5 1 0 5 1 square units 2 3 4 5 1 6 7

8 4 580

12 5 5

Cash Accounts Receivable Supplies Land Office Equipment Accumulated Depreciation Accounts Payable Salaries Payable Common Stock Retained Earnings Dividends Fees Earned Salary Expense Supplies Expense Depreciation Expense Miscellaneous Expense 11 370 27 080 2 870 23 020 21 660 3 520 19 770 2 170 111 460 3 010 7 310 9 100 18 520 73 520 111 460 350 2 410 1 440 4 200 2 410 1 440 350 4 200 11 370 27 080 460 23 020 21 660 3 520 20 120 2 410 1 440 2 170 113 250 4 450 7 310 350 9 100 18 520 73 520 113 250

2 246

7 4 888

10 5 77

3 2 644

2 2 402

Use expansion by cofactors to find the determinant of the matrix 44005 0 1 2 3 7 00254 00366 00005

Find the determinant of the triangular matrix 3 0 7 5 3 6 2 0 0

Use expansion by cofactors to find the determinant of the matrix 31 4 23 2 3 0 1

E15 9 Prepare a cost of goods manufactured schedule and partial financial statements At May 31 2025 the accounts of Lopez Company show the following 1 May 1 inventories finished goods 12 600 work in process 14 700 and raw materials 8 200 2 May 31 inventories finished goods 9 500 work in process 15 900 and raw materials 7 100 3 Debit postings to work in process were direct materials 62 400 direct labor 50 000 and manufacturing overhead applied 40 000 Sales revenue totaled 215 000 4 Instructions a b C Prepare a condensed cost of goods manufactured schedule for May 2025 Prepare an income statement for May 2025 through gross profit Indicate the balance sheet presentation of the manufacturing inventories at May 31 2025 NOTE Enter a formula a cell reference or a value if you are unable to reference a cell into the yellow shaded input cells a LOPEZ COMPANY Cost of Goods Manufactured Schedule For the Month Ended May 31 2025 Work in process May 1 Direct materials used Direct labor Manufacturing overhead applied Total manufacturing costs Total cost of work in process Less Work in process May 31 Cost of goods manufactured

The weekly demand function for high definition televisions is given by p d x 350 4x where x is the number of thousands of televisions and p is in dollars Find the average rate of change of the unit price as the quantity demanded goes from 3000 televisions to 5000 televisions X dollars per one thousand televisions 32 000 Submit Answer

x 6x 36x x Determine the number of discontinuities of f x Consider the function f x 1 Determine the values of x at which f x has a discontinuity Enter your answer as a comma separated list of values The order of the values does not matter Enter DNE if f x does not hav discontinuities 0 K

3 What is the final balance in an account that had an initial invest of 1000 and earns 10 per year simple interest for 4 years

1 Susan deposited 1000 in an account earning 5 per annum simple interest How much interest did she earn after 3 months 2 After 10 years Adele earned 100 in interest from her initial investment If the bank s simple

Ex You deposit 600 into an account that earns simple annual interest After 2 years you now have 648 in your account What is the interest rate

4 Consider a compressible fluidic system of air with input pressure of P and output pressure of P and R 10 Pa sec Ng and G 10 kg Pa write the differential equation of the system RF

You are painting a room that is 14 feet long 12 feet wide and 8 feet high On the walls of the room there are two windows that are each 2 feet wide and 5 feet tall and a door that is 4 feet wide and 7 feet tall A gallon of paint covers 350 square feet How many gallons of paint do you need to cover the 4 walls with one coat of paint not including the windows and the door Round your answer up to the nearest whole number

A hoodlum throws a stone vertically downward with an initial speed of 10 0 m s from the roof of a building 48 0 m above the ground a How long does it take the stone to reach the ground b What is the speed of the stone at impact a Number i 5 Mual Units Unite S no la

You may need to use the appropriate technology to answer this question Consider the following hypothesis test Ho M M 0 Hai My M2 0 The following results are from independent samples taken from two populations Sample 1 Sample 2 n 35 7 40 X 13 6 X1 x 10 1 S 5 1 S 8 6 a What is the value of the test statistic Use x x Round your answer to three decimal places 2 178 X b What is the degrees of freedom for the t distribution Round your answer down to the nearest integer c What is the p value Round your answer to four decimal places p value d At a 0 05 what is your conclusion O Reject Ho There is insufficient evidence to conclude that 0 O Do not Reject Ho There is insufficient evidence to conclude that 0 O Reject Ho There is sufficient evidence to conclude that 0 O Do not Reject Ho There is sufficient evidence to conclude that 0

2 Given the equation y 4 5 a Does this equation represent growth or decay b What is the growth or decay factor c What is the initial value d What is the range