QR Review

Evaluate the expression 1/4 + 3/8 - 6/16 - 8/32 A. 7/16 B. 1/32 C. 1/8 D. 1/4 E. 0

0 1) Rewriting each fraction with the common denominator of 32: 1/4 ​× 8/8​= 8/32​ 3/8 × 4/4= 12/32 6/16 x 2/2 = 12/32 8/32 2) 8/32 + 12/32 - 12/32 - 8/32 = 0/32 = 0

Which of the following is the value of the expression | 14-3| - |7-16| / 3|(-2) + 1|? A. -20/3 B. -2/3 C. 0 D. 2/3 E. 20/3

2/3

If an electron has a mass of 9.709 x 10-31 kg, and a proton has a mass of 1.672 x 10-27 kg, approximately how many electrons are required to have the same mass as one proton? A. 150,000 B. 1,800 C. 5.4 x 104 D. 5.4 x 10-4 E. 15 x 10-58

1,800 Number of electrons= Mass of one proton/ Mass of one electron Number of electrons= 1.672×10^−27 kg​/9.709×10^−3 Number of electrons= 1.672​/.709 ×10^−27−(−31) Number of electrons≈ 172.064×10^4 Number of electrons≈ 1.72064×10^6 Rounding 1.72 to the nearest hundred gives 1700, so 1800 is closet

What part of an hour is 6 seconds? A. 1/600 B. 1/10 C. 1/360 D. 1/60 E. 1/5

1/600 1) To find what part of an hour 6 seconds is, we can set up the proportion: time in seconds/time in hours= 6/3600 2) Since there are 60 seconds in a minute and 60 minutes in an hour, there are 60 × 60= 3600 seconds in an hour. Simplifying the proportion: 6/3600= 1/600

1 yard

3 feet

Right triangle ABC with right angle at C and AB = 6, BC = 3, find AC. A. 3 B. 6 C. 27 D. 33 E. 3√3

3√3 AC2=AB2 + BC2 AC2= 62 + 32 AC2= 36 + 9 AC2= 45 AC= sqr rt(45​) AC= sqr rt (9×5)​ AC= 3 sqr rt(5​)

A student received test grades of 83, 90, and 88. What was her grade on a fourth test if the average for the four tests is 84? A. 85 B. 80 C. 75 D. 70 E. 65

75 Average = (Sum of all grades) / (Number of grades) We can set up the equation: 84= (83 + 90 + 88 + x)/4 ​84 × 4= 83 + 90 + 88 + x 336= 261 + x x= 336 − 261 x= 75

A tank can be filled by a pipe in 30 minutes and emptied by another pipe in 50 minutes. How many minutes will it take to fill the tank if both pipes are open? A. 45 B. 60 C. 75 D. 80 E. 100

75 1) For the first pipe, the rate of filling is 1/30​ of the tank per minute. For the second pipe, the rate of emptying is 1/50 of the tank per minute. 2) Combined rate= 1​/30 − 1/50 ​3) Time= Volume​/Rate Time= 1/(1/30 ​− 1/50​) = 1 / (5/150 ​− 3/150​)1 ​= 1(2/150​) = 150/2 = 75

1 cm

10 mm

1 foot

12 inches

Five eighths of the employees in a certain company are male. One fifth of these males are single. What percentage of the employees in the company are single males? A. 12.5 B. 20.0 C. 25.0 D. 32.0 E. 62.5

12.5

Which of the following would NOT result in a straight line? A. x = 1/y B. x = 2y+5 C. x = (y+6)/(2) D. x = 5-y E. x = 4(x+3y)

x = 1/y A. x = 1/y represents a hyperbola, not a straight line. B. x = 2y+5 represents a straight line with slope 2 and y-intercept (0,5) C. x = (y+6)/(2) represents a straight line with slope 1/2​ and y-intercept (0,3) D. x = 5-y represents a straight line with slope −1 and y-intercept (0,5) E. x = 4(x+3y) This equation simplifies to x=4x+12y, which rearranges to 3x=12y or x=4y. This equation represents a straight line with slope 1/4​ and y-intercept (0,0).

If 0 ≤ x ≤ 12 and -2 ≤ y ≤ 9, then 3x-4/4 + 5y^2 is as large as possible when A. x =12 and y =9 B. x =12 and y=0 C. x=12 and y=-12 D. x=0 and y = 9 E. x =0 and y = 0

x = 12 y = 0 Calculate the expression 3x − 4/4​+5y^2 for each option and find the one that yields the maximum value. A. 3(12) − 4/4 + 5(9)^2= 36 − 1 + 405= 440 B. 3(12) − 4/4 + 5(0)^2= 36 − 1 + 0 = 35 C. 3(12) − 4/4 + 5(−12)^2= 36 − 1 + 720= 755 D. 3(0) − 4/4 + 5(9)^2= 0 − 1 + 405= 404 E. 3(0) − 4/4 + 5(0)^2= 0 − 1 + 0= −1 The largest possible value occurs when x=12 and y=−12. However, this point is not within the given range for y, which is −2≤y≤9. Among the given options within the specified ranges for x and y, the largest possible value occurs when x=12 and y=0, yielding a value of 35.

Which line is perpendicular to the x-axis? A. x =3 B. y=3 C.. x=y D. x =7/3 E. x/3

x =3 A line that is perpendicular to the x-axis is a vertical line. This means the line will have an equation of the form x= constant, where the value of x remains constant regardless of the value of y.

45-45-90 Triangles

x, x, x√2

30-60-90 Triangles

x, x√3, 2x

The value of cos (π./3) equals the value of A.- cos (2π./3). B. cos (2π./3). C. cos (6π./3). D. - cos (5π./3). E. cos (4v/3).

- cos (2π./3)

4/3 =

1.33

Odds in favor =

# of favorable outcomes / # of unfavorable outcomes

An investment is made at r percent compounded annually, at the end of n years it will have grown to A = P(1 + r)n. An investment made at 16% compounded annually. It grows to $1,740 at the end of the year. How much was originally invested? A. $150 B. $278.40 C. $1,461.60 D. $1,500 E. $1,700

$1,500 1. Given: Annual interest rate r= 16%= 0.16 Time n=1 year Final amount A = $1,740 2. We want to find the original investment amount P. A=P(1+r)^n $1,740 = P(1 + 0.16)^1 $1,740 = P(1.16) P = $1,740 / 1.16 P = 1,500

The introduction of a new manufacturing process will effect a savings of $1,450.00 per week over the initial 8-week production period. New equipment, however, will cost 1⁄4 of the total savings. How much did equipment cost? A. $11,600.00 B. $2,900.00 C. $725.00 D. $362.50 E. $181.25

$2,900.00 1. Given: Savings per week: $1,450.00 Number of weeks: 8 2. Total savings over 8 weeks: 8 × $1,450.00= $11,600.00 3. We need to find one-fourth of the total savings: 14 × $11,600.00= $2,900.00

(n ways) x (m ways) =

(n x m) ways to do both things

What is 1/4 % of 200? A. 0.05 B. 0.5 C. 5 D. 12.5 E. 50

0.5 1) To calculate 1/4% of 200, we need to convert 1/4% to a decimal. 2) 1/4% is equivalent to 0.25/100 or 0.0025 as a decimal 3) Now, we multiply this decimal by 200: 0.0025 × 200= 0.50

P (event not happening) =

1 - P (event happening)

π / 3

1.05

1 meter

1.1 yards

√2 =

1.4

1 mile

1.6 km

Which of the following is the value of A, if 50 (A/100) = 2A^2? A. 25 B. 1 C. 5/2 D. 1/4 E. 1/2

1/4

1 m

100 cm

1 kg

1000 g

1 km

1000 m

1 L

1000 mL

1 pound

16 ounces

If x pens costs 75 cents and y pencils cost 57 cents, then which equation below can be used to find the cost of 2 pens and 3 pencils? A. 2(75/x) + 3(657/y) B. 3x/75 + 2y/57 C. 75/2x + 57/3y D. 2(x/75) + 3(y/57) E. 3(75/x) + 2(57/y)

2(75/x) + 3(657/y)

If (4/5)x = (2/5)y, then which of the following is equal to y/x? A. 1/2 B. 2/5 C. 25/8 D. 2 E. 3

2 1) 4/5​x= 2/5​y First, we can simplify both sides by multiplying both sides by 5 to get rid of the fractions: 4x=2y Next, divide both sides by 2 to solve for 2x=y 2) Now that we have y=2x, we can substitute this expression into y/x: y/x ​= 2x​/x Finally, we simplify to get the answer: y/x​= 2

Optometry school applicants decreased by 25% during a 4-year period. During the same time, the number of first-year openings in optometry school increased by 12%. If the ratio of applicants to first-year student openings had been 3 to 1, then which of the following would be the approximate ratio at the end of the 4-year period? A. 1.5 to 1 B. 2 to 1 C. 3 to 2 D. 4 to 3 E. 6 to 5

2 to 1 1) The initial ratio of applicants to first-year student openings is 3 to 1, A0​​= 3/1 2) Now, let's find the ratio of applicants to first-year student openings after 4 years, denoted as A/O​: A/O ​=0.75 x (3/1)/ 1.12 = 2.25/1.12 = 2

1 kg

2.2 lbs

1 inch

2.54 cm

If the perimeter of a square is 20, then what is the area of the square? A. 5 B. 10 C. 20 D. 25 E. 100

25 1)Given that the perimeter of the square is 20, we can set up the equation: 4s= 20 2)Solving for the side length s: s= 20/4 ​= 5 3) Area = s^2 = 5^ = 25

If sq rt(x-25) = 7 - 5, then which of the following is the value of x? A.4 B. 27 C. 29 D. 49 E. 729

29 1.Given: sq rt (x−25)​=7−5 We simplify the right side of the equation: 7−5= 2 Substitute this into the equation: sq rt (x−25)​= 2 2) Square both sides to isolate x−25: sqr rt(x−25​)^2 = 2^2 x−25= 4 x= 4+25 x= 29

If 2/x + 3/5 = 4/3, then which of the following is the value of x? A. 30/11 B. 30/29 C. 11/30 D. -11/6 E. -5/2

30/11 1) Multiply all terms in the equation by the least common denominator (LCD) to clear the fractions. The LCD is 15x: 15x(2/x​) + 15x(3/5​)= 15x(4/3​) 2) Simplify each term: 15 × 2 + 3x × 3= 5x × 4 30 + 9x= 20x 9x − 20x= −30 −11x= −30 x= −30/-11​ x= 30/11​

If 2x + y = 7 and x - 4y = 4, then x equals which of the following? A. -15/9 B. -1/9 C. 7/16 D. 11/9 E. 32/9

32/9 1) {2x + y= 7 x −4y= 4​ 2) Multiply both sides of the second equation by 2 to make the coefficients of x the same in both equations: = {2x + y= 7 2x − 8y= 8​ 3) Subtract the second equation from the first equation: (2x+y) − (2x−8y)= 7−8 2x +y − 2x + 8y= −1 9y= −1 4) Solve for y: y= −1/9 5) 2x + (−1/9​)= 7 2x −1/9 = 7 2x= 7 + 1/9 ​2x= 63/9 ​+ 1/9 ​2x= 64/9 ​x= 32/9​

Sum of Interior angles of Quadrilateral

360°

If 1/3 + 5/(x - 1) = 8, then which of the following is the value of x? A. 8/13 B. 8/5 C. 38/28 D. 38/23 E. 38

38/23 1) 3(x−1) × 1/3​+ 3(x−1) × 5/x−1​= 8 × 3(x−1) x − 1 + 15= 24(x−1) x + 14= 24x − 24 24x − x= 14 + 24 23x= 38 x = 38/23

1 mile

5280 feet

Express the product (2x + 5y)^2 in simple form A. 4x^2 + 25y^2 B. 4x^2 + 20xy + 25y^2 C. 4x^2+10y+25y^2 D. 4x^2 - 20xy + 25y^2 E. 4x+25y

4x^2 + 20xy + 25y^2 To express 2(2x+5y)^2 in simple form, we can use the formula for squaring a binomial: ((a+b)^2= a^2 + 2ab + b^2 Where a=2x and b=5y. Substituting a and b into the formula: (2x+5y)^2=(2x)^2 + 2(2x)(5y) + (5y)^2 Simplifying each term: 2(2x)^2=4x^2 2(2x)(5y)= 20xy (5y)^2= 25y^2 Putting it all together: 2(2x+5y)^2= 4x^2 + 20xy + 25y^2

A standard deck of cards has:

52 cards 4 suits (Spades, Hearts, Clubs, Diamonds) 13 Cards in each suit. (A, 2-10, J, Q, K)

At 7:00 a.m. a student leaves his home in his automobile to drive to school 28 miles away. He averages 50 mph until 7:30 a.m. when his car breaks down. The student has to walk and run the rest of the way. If he wants to arrive at school at 8:00 a.m. how fast, in mph, must he travel on foot? A. 3 B. 4 C. 5 D. 6 E. 7

6 mph 1) Calculate the distance covered by car in 30 minutes: Distance=Speed × Time Distance= 50 mph × 0.5 hour =25 miles 2) Calculate the remaining distance to cover on foot: 28−25= 3 3) Calculate the time available for walking/running: The student must arrive at school by 8:00 a.m., which means he has 1 hour (from 7:30 a.m. to 8:00 a.m.) to cover the remaining 3 miles. 4) Calculate the required speed for walking/running: Speed=Distance/Time Speed= 3 miles/0.5 hours​ = 6 mph

A theater charges $5.00 admission for adults and $2.50 for children. At one showing 240 admissions brought a total of $800. How many adults attended the showing? A. 40 B. 80 C. 120 D. 160 E. 266

80 1) Given: The total number of admissions equation: A + C= 240 A = 240 - A The total revenue equation: 5A + 2.5C= 800 2) 5 (240 - C ) + 2.5C = 800 1200 - 5C + 2.5 C = 800 1200 - 2.5 C = 800 -2.5 C = -400 C = -400/-2.5 C = 160 3) A+160= 240 A= 240−160 A=80

Two cars start at the same point and travel north and west at the rate of 24 and 32 mph respectively. How far apart are they at the end of 2 hours? A. 64 B. 80 C. 112 D. 116 E. 100

80 1) We know that distance = speed × time. Therefore, the distance traveled by each car after 2 hours is: For the car traveling north: dn= 24 mph × 2 hours= 48 miles For the car traveling west: dw= 32 mph × 2 hours= 64 miles 2) Now, using the Pythagorean theorem, the distance between the two cars is given by: Distance= sqr rt( dn^2 + dw^2) Distance= sqr rt (48^2 + 64^2) Distance= sqr rt (2304 + 4096​) Distance= sqr rt (6400) Distance= 80 miles

Three consecutive odd numbers have a sum of 51. What is the largest of these numbers? A.15 B.17 C.18 D.9 E.21

9

Distance Rate Formula

= (speed)(time)

Time Rate Formula

= distance/speed

Speed Formula

= distance/time

Are of Rectangle

A= lw

Area of a triangle

A=1/2bh

The dental hygienist at a certain office is paid H dollars a week. The dental assistant works 36 hours a week at A dollars per hour, and the receptionist works 40 hours a week and receives R dollars every other week. Which of the following represents the weekly payroll for these three employees? A. H/3 + 36A + 40R/3 B. H + 36A + 40R/3 C. H/3 + 12A + R/6 D. 5H + 36 + 20R E. H/3 + 12A + 40R

H + 36A + 40R/3 This expression represents the sum of the weekly earnings for the dental hygienist (H dollars), the dental assistant (36A dollars), and the receptionist (whose bi-weekly earnings are 40R/3​ dollars). This expression matches the correct format for the weekly payroll of the three employees.

Range

Highst - Lowest

Median

Middle number

Non- Mutually Exclusive: P (A or B)=

P (A) + P(B) - P (A and B)

Mutually Exclusive: P (A or B)=

P(A) + P(B)

Rate Formula

Rate = Work/Time

Change in Percent

[ difference / original ] x 100% [ y - x / x ] x 100%

Mixture Problems

c1v1 + c2v2 = c(v1 + v2)

Diameter of Circle

d= 2r

Mode

most frequently occurring score

Permutations Equation

n!/(n-r)!

Combinations Equation

n!/r!(n-r)!

P(Outcome A) = outcomes of A/total outcomes

outcomes of A/total outcomes

Mean

sum of all values/ # of values

Z-score formula

z = (x - μ)/σ

Variance

σ^2

A rectangular room is 3 meters wide, 4 meters long and 2 meters high. How far is it from the northeast corner at the floor to the southwest corner at the ceiling? A. √29 meters B. √11 meters C. √9 meters D. 9 meters E. 5 meters

√29 meters d= a^2 + b^2 + c^2​ d= sqr rt (3^2 + 4^2 + 2^2) d = sqrt rt ( 9 + 16 + 4) d= ​√29