QR Questions I got wrong
If 3 and 8 are the lengths of 2 sides of a triangle, which of the following can be the length of the third side? I. 5 II. 8 III. 11
ALWAYS REMEMBER: the length of any side of a triangle is always greater than the difference of the other two sides and less than their sum 8-3 < x < 8+3 5 < x < 11 x has to be greater than 5 but less than 11 so 8 is the only answer
Tim, Ryan, and Greg each receive paychecks that total to $1215. Then an additional $45 is given to Ryan. If the amount of money that each received individually is in a 5:6:7 ratio, how much money did Tim receive?
T + R + G= 1215 ***then we know Ryan gets $45 more so T+R+G= 1260 RATIOS: Tim (5x) + Ryan (6x) + Greg (7x)= 18x 18x = 1260 x= 70 so Tim receives 5(70)= 350
If there are 10 people in a room, and each person shakes hands with every other person once, how many handshakes will there be?
THINK OF THIS AS A COMBINATION PROBLEM n!/ r! (n-r)! , where r= 2 because 2 people are needed for handshake 10! 2! (10-2)! 45 handshakes
Two fair dice are rolled. What is the probability of rolling a sum that is odd?
When two fair dice are rolled, there are 36 possible outcomes. Of these outcomes, 18 outcomes sum up to give an odd result and 18 outcomes sum to give an even result. Probability of rolling a sum that is odd is: 18/36= 1/2
Evaluate 5log2(32)
25 POWER RULE!!!
Moe is 5 inches taller than David. If the sum of their heights is 11ft and 9 inches, how tall is David?
1. Convert their sum of heights into inches 11 ft x (12 in/1ft )= 132 in + 9 inches = 141 2. Set up two equations M=D+5 M+D= 141 in 3. Plug into equations D+5 + D= 141 5 + 2D=141 2D= 136 in D= 68 in 3. Convert David's height into ft 68 in x (1 ft/ 12 in)= 17/3 ft = 5 2/3 ft 2/3 ft x (12 in/1 ft)= 8 inches David's height= 5 ft and 8 inches
An investment of $1800 decreases by a third. Its new value is 20% of the value of the second investment. What is the value of the second investment?
1. Decreases by a third 1/3 (1800)= 600 So 1800-600= 1200 2. 20% of second investment 0.2= 1200/x x= 1200/0.2 x= $6,000
A chemist realizes that a hydrochloric acid storage tank is leaking. Assuming the tank becomes fully sealed and is half full, how long would it take the chemist to fill the 50-gallon tank if acid is pumped into it at a rate of 5 L/sec (1 gallon=3.8L)
25 gallons x 3.8L/1 gallon= 95 L 5 L/1 second= 95 L/x seconds 5x=95 x=19 seconds
Station X and Station Y are 480 miles apart. A train starts a certain time from Station X headed towards Station Y at 60 mph. Two hours later, a train departs from Station Y headed towards Station X and 48 mph. How far from Station X do the two trains meet?
320 MILES DISTANCE AND SPEED PROBLEM!!! Train X (from Station X)= t Train Y = t-2 1. 60(t) + 48(t-2)=480 60t + 48t -96= 480 108t=576 t= 5.33 hr 2. 5.33 hr x 60 miles / hr= 320 miles
How many four-digit numbers can be made from the following digits {1, 3, 5, 7} if digits are repeated?
4 x 4 x 4 x 4= 256
A box contains a number of black and white marbles. The ratio of black marbles to white marbles is 4 to 5, respectively. When black marbles and 10 white marbles are removed, the ratio becomes 3 to 4. How many white marbles were originally in the box?
4x= black marbles. 5x= white marbles subtract 10 from both 4x-10 and 5x-10 2. Set them up to ratio 4x-10/5x-10= 3/4 4(4x-10)= 3(5x-10) 16x-40=15x-30 x=10 Original number of white marbles = 5x 5(10)= 50 marbles
A bottle was half full of orange juice. 5 ounces of orange juice was then added to the bottle, filling it to 90% capacity. What is the total capacity of the bottle in ounces?,
50% capacity + 5oz OJ= 90% capacity 0.5x + 5 = 0.9x 0.4x= 5 x= 12.5 oz
If the following quadratic equation passes through (2,1) and (-1,q), what is the value of q? y=2x^2 +x +c
1=2(2)^2 +2 +c 1= 10 + c c=-9 plug c in the equation y=2x^2 +2 -9 plug in (-1) y=2(-1)^2 -1 -9 y=-8
If 5 liters of 20% alcohol solution are mixed with 10 liters of 40% alcohol solution, what is the percentage of alcohol in the mixture?
% of alcohol= liters of alcohol / liters of solution 1st mixture: 0.2= liters of alcohol / 5 x= 1 2nd mixture: 0.4= liters of alcohol / 10 x= 4 percentage of alcohol= 5/15= 1/3= 0.33
The height within a group is normally distributed. The mean height is 71 inches and the standard deviation is 4 inches. If there are 200 people in the group, how many people are less than 63 inches?
A person that is 63 inches is 8 inches or 2 standard deviations below the mean 95% of the population falls within +/- 2 standard deviation and 5% of the population fall outside two standard deviations but we need to divide by 2 so, 200 (0.025)= 5 people
exponential growth formula
A= A0 (n) ^ x/t
What is the value of x? log5(3)= log5 (x+5/2)
EQUALITY RULE 1. set them equal to each other because they have the same base 2. 3= (x+5/2) 6=x+5 x=1
What formula to use for quarterly compound
FV= PV (1 + r/n)^nt
At the Olympics, nine female sprinters compete against each other in 100m dash. How many ways can the sprinters finish with gold, bronze, and silver?
ORDER MATTERS!! so we use permutations n!/(n-r)! 9!/(9-3)! 9!/(6)! 9x 8 x 7= 504
If the sum of the interior angles of a polygon is twice the sum of its exterior angles, how many sides does the polygon have?
Rule #1: Sum of interior angles = 180(n-2) Rule #2: Sum of Exterior angles is always equal to 360 180(n-2)= 2(360) 180n-360=720 180n= 1080 n=6 sides
Seven people line up in front of a store. If the front three in the line must stay together and must remain at the front of the line, how many ways can people in the line be arranged?
first three people can only rearrange themselves within themselves 3!= 3 x 2 x 1 = 6 the rest of the four must remain isolated from group 4!= 4 x 3 x 2 x 1= 24 6 x 24= 144
The ratio of a to b is 3 to 2. What is true?
first write out the ratio a/b= 3/2 2a=3b
Which of the following is true for the graph of y=b? A. It has a range of b B. it has a slope of b C. It is not a function D. It has a domain of b E. It has no y-intercept
it has a range of b
There are 5 green blocks, 3 yellow blocks, and 2 red blocks for a child to choose from. What is the probability that the child selects a red block and a yellow block? Assume the blocks are selected with replacement?
need to make 2 separate calculations P(yellow then red)= 3/10 x 2/10 = 6/100 P(red then yellow)= 2/10 x 3/10= 6/100 6/100 + 6/100= 12/100 = 3/25
2/3 of a number
take the cube root of the number and then square it
If you pick three letters from the word ANTEATER with replacement, what is the probability that all three letters are vowels?
this is WITH replacement there are 4 vowels with a total of 8 words: 4 vowels / 8 letters = 1/2 Picking 3 letters that are vowels: 1/2 x 1/2 x 1/2= 1/8
Given the quadratic equation below, what is its vertex? y=x^2 +6x+8
vertex= (h,k) , where h=-b/2a h=-6/2(1) h=-3 Then substitute -3 as x in the equation to find k y=(-3)^2 +6(-3) +8 y= -1 vertex: (-3, -1)
y= (x)-b
x is shifted down by "b" units
Graph transformations y= (x+a)
x is shifted to the left by "a" units
y= (x-a)
x is shifted to the right by "a" units
y= (x) +b
x is shifted up "b" units
45-45-90 triangle
x, x, x√2
30-60-90 triangle
x, x√3, 2x
BOOSTER PRACTICE EXAM #2
---
Surface area of a cube
6s²
A square has a diagonal of 24 cm. What is its area?
Area of square= side ^2
If 16 tennis players are in a tournament and each player must play every other player once, how many matches must be played?
COMBINATION PROBLEM n= 16 players r=2 bc a match consists of 2 players 16!/2!(16-2)! = 16 ! / 14! 2! = 16x15/2= 120
Two trucks start driving from the same location towards the same direction. Truck A drives at 50km/hr and Truck B drives at 30km/hr. After two hours, Truck A stops. How much additional time will it tae for Truck B to pass Truck A?
DISTANCE= SPEED X TIME Truck A: distance= 50 km/hr x 2 hr= 100 km Truck B: distance= 30 km/hr x 2 hr= 60 km We can see how far behind Truck B is from Truck A 100-60= 40 km Can assume Truck B is traveling at 30 km/hr 40 km / 30 km/hr= 40/30hr= 4/3 hr = 1.33hr 0.33 hr x 60 min/1 hr = 20 min 1 hour and 20 minutes
What is the area encompassed underneath the following line equation in the first quadrant? y + 3x -9= 0
First quadrant is upper right STEP 1: Find y-intercept and x-intercept. Y-intercept is found when x=0 y + 3(0) -9 y= 9 STEP 2: Find x-intercept when y=0 0 + 3x -9 =0 x= 3 So 3 to the right, 9 up Its a triangle so 1/2(b)(h)= 1/2 (3) (9) = 13.5
A 3000-gallon tank has a valve at the top that takes in gasoline at a rate of 50 gallons per minute, and a spigot at the bottom that empties it at a rate of 20 gallons per minute. If the tank is initially empty and the valve and the spigot are open, how long will it take to fill half the tank?
Subtract the rates because the spigot is doing the "opposite job" of the valve 1. Find combined rate of the valve and spigot Rate= Rate (valve)- Rate (spigot) Rate= 50 gallons/min - 20 gallons/min Rate = 30 gallons/min 2. Find the time Job= 3000 gallons/2= 1500 gallons (bc wants us to fill HALF the tank) Job = Rate x Time 1500= 30 x t t= 1500/30= 50 minutes
In a small town, the probability that a person is blond or left-handed is 45%. The probability that a person is blonde is 60% and the probability that a person is left-handed is 15%. What is the probability that a person is blonde and left-handed?
These two events are NOT mutually exclusive (they can happen at the same time 1. Set up equations P(A or B)= P(A) + P(B) - P(A and B) P(blond or left handed)= P(blonde) + P(LH) - P(blonde and LH) 2. Plug in 45%= P(blonde or LH) 60%= P(blonde) 15%= P(LH) 45%= 60% + 15% - (blonde and LH) P(blonde and LH)= 60 +15 -45 P(blonde and LH)= 30%
The points (x,-4) and (9,2) have a distance of 6 between them. Find the value of x
USE DISTANCE FORMULA
Volume of a cube
V=s³
What is the volume of a cylinder that has a radius of 2 inches and height of 8 inches ?
V=πr²h =π x (2)² x 8 = 32π
A lab researcher weighed 50 lab mice and found the mean to be 100 g and the standard deviation to be 7 g. To adjust for inaccuracies, the researcher multiplied each weight by 2. What is the new mean and standard deviation of the new set of data?
WHEN WE ADD "a" TO EACH ELEMENT OF A SET: new mean: mean +a new SD= stays the same WHEN WE MULTIPLY "a" TO EACH ELEMENT OF A SET new mean: mean x a new SD= SD x a NEW MEAN: 200 ; NEW SD= 14
Alfred buys a new book from a local bookstore and receives a 30% discount off its original price. If Alfred paid x dollars to the cashier, which of the following represents the original price of the book?
%Paid= 100-%Discount 70%= 100-30% 70% x Original Price = x 0.7 x original price = x original price= x/0.7
When problem says "passes through point" what do we use
y-y1=m(x-x1)
Which of the following equations is parallel to y=-4x+5 and passes through the point (1,3)? A. y= -4x+7 B. y=-4x +5 C. y= 4x +5 D. y=4x+ 7 E. y=4x+3
y=-4x+7 We know that the new equation has to have m=-4 because it's parallel So to find y-intercept y-y1=m(x-x1) y-3= -4(x-1) y-3=-4x+4 y=-4x+7 OR!!!!! Just plug in x=1 in the equations and see whichever gives you y=3
A scientist has 5 ounces of 10% alcohol solution in a beaker. If the scientist adds more water to the solution to dilute it down to 5% alcohol, what is the total amount of the final solution in ounces?
1. First determine how much of the original solution was alcohol 5 oz x 10% alcohol= 5 x 0.1 oz alcohol= 0.5 oz alc 2. Now we set up an equation to determine the total amount of final solution in ounces Y oz x 5% alcohol= 0.5 oz alcohol Y oz x 0.05 alcohol= 0.5 alcohol Y=10 oz
Sam is 6 years older than his friend David. Nine years ago, Sam was triple David's age. Quantity A: David's age in 5 years Quantity B: 17
1. Set up two equations "Sam is 6 years older than David" S=D+6 "Nine years ago, Sam was triple David's age" (S-9)= 3(D-9) S-9= 3D -27 S-9= 3D-27 S= 3D-18 2. Two equations S=D+6 S=3D-18 3. Set them equal to each other D+6= 3D-18 D= 12 years old David's age in 5 years will be 17 so the two quantities are EQUAL
A bag contains 4 red marbles, 6 green marbles, and 2 white marbles. What is the probability of picking a red marble and a white marble with replacement?
12 total marbles So we can pick a red marble or a white marble first P(red then white)= 4/12 * 2/12 P(white then red)= 2/12 * 4/12 Find of the probabilities and then multiply it by 2 because it's the same thing 1/3 * 1/6 (2)= 1/9
A 4L solution is 80% concentrated lime juice and 20% water, how much 30% concentrated lime juice must be added so that the concentration of the resulting solution is 50% concentrated lime juice?
6L For this equation, we only need the units of concentrated lime juice (IGNORE CONCENTRATION OF WATER b/c it will add up to 100%) WE ONLY NEED: lime juice/ total volume 1. Let's see how much lime juice exists in the 4L solution 0.80 * 4L= 3.2 lime juice 2. Question wants to know how much 30% concentrated lime juice we can add to reach a total final concentration of 50%. The equation is lime juice/total volume= 50% 3. 3.2L + 0.3(X)L/ (4L +XL)= 1/2 4. Solve for X: 2(3.2L + 0.3XL)= 4L +XL 6.4L + 0.6XL= 4L +XL 2.4L = 0.4XL X= 6L
A sock drawer contains 7 red socks, 4 blue socks and 2 yellow socks. What is the probability that two socks selected at random, without replacement, are both red?
7/26 Total number of socks= 13 Prob of drawing two red socks WITHOUT replacement= 7/13 x 6/12= 7/26
A committee of 4 people is selected from a group of 9. If the selection is made randomly, how many different groups can be made?
COMBINATION PROBABILITY QUESTION Need to find the total number of outcomes possible 1. 9 people in total and 4 people selected: nCr nCr= n!/ r!(n-r)! 9C4= 9!/ 4!(9-4)! = 9!/ 4!5! = 126
For a restaurant, there are 3 choices for an appetizer, 5 choices for the main course, and 3 choices for dessert. How many total meal combinations are there if you have to choose one appetizer, one main course, and one dessert?
COMBINATION QUESTION 1. For appetizers, we choose 1 out of 3, so 3C1= 3 choices 2. For main courses, we choose 1 out of 5, so 5C1= 5 choices 3. For desserts, we have to choose 1 out of 3, so 3C1= 3 choices So multiply them all: 3 x 5 x 3 45 choices
In a chemistry class, 60% of the students passed the midterm, and 40% of these midterm passing students passed the final. Assuming the students who failed the midterm also failed the final, what percentage of students also failed the final?
Can either do this algebraically or by picking numbers 1. Number of students who passed the midterm 60% of 100= 60 students passed the midterm 2. 40% of the students who passed the midterm also passed the final 40% of 60= 0.4 (60)= 24 3. Percentage of students who passed the midterm 24/100= 24%
What is the equation of the circle with center O and radius 3 shown below? Point is: (-5,4) Equation of a circle
Equation of a circle: IN PICTURE (h,k)= (-5,4) and r=3 (x-(-5))^2 + (y-4)^2= 3^2 (x+5)^2 + (y-4)^2= 9
{3, 4, 5, 6, 7} Quantity A: standard deviation of the data set Quantity B: 2
Find standard deviation 1. Find the mean 2. Subtract the mean from each data point and square result 3. Find variance, which is the mean of the results of step 2 4. Take square root of variance 1. Mean= 5 2. (3-5) squared= 4 (4-5) squared= 1 (5-5) squared= 0 (6-5) squared= 1 (7-5) squared = 4 3. 4 + 1 + 0 + 1 +4 / 5= 2 4. square root of 2= 1.414 so quantity b is bigger
For the month of June, Kevin sold an average of 18 popsicles on sunny days and an average of 6 popsicles on rainy days. Given that it rained one in every five days in June, how many popsicles did he sell on average per day in June?
MULTIPLE AVERAGES PROBLEM To find the answer, we must find the total number of popsicles sold and divide by the number of days in June (30) 1. Rainy days in June (rains every 5 days) 30 days in June/ 5= 6 rainy days 2. 30 days in June - 6 rainy days= 24 sunny days 3. 18 popsicles (24 sunny days) + 6 popsicles (6 rainy days)= 468 total popsicles sold 4. 468 popsicles sold/ 30 days = 15.6 = 16 popsicles sold per day
The class average for a midterm was 70 and the standard deviation was 8. If Danny's score was a z-score of +1.5, what was his score on the midterm?
NEED TO KNOW FORMULA FOR Z-SCORE z= (x-u)/o where o= SD x=score u=mean 1. Plug in from formula z=(x-u)/o 1.5= (x-70)/8 12= x-70 x=82
The grades on a chemistry exam are normally distributed with a mean of 82% and a standard deviation of 6. What is the probability that a student scored 88% or higher on the exam?
Need to be familiar w/ the 68-95-99.7% rule 1. First standard deviation contains 68% of data 2. Second standard deviation contains 95% of data 3. Third standard deviation contains 99.7% of data Plot them in a graph with the mean (82) in the middle -to go up one standard deviation, add 6% -to go down one standard deviation, subtract 6% We know that 50% scored above the mean and 68% of students scored within one standard deviation of the mean - so 34% scored below the mean and 34% scored above the mean So we subtract 50-34 and get 16%
The dimensions of a rectangular pond are 30 ft x 36 ft x 12 ft. After a drought, only 2/3 of it is filled with water. If it costs $0.06 per cubic feet of water, how much will it cost to completely fill up the rest of the pond?
Need to find dimensions of 1/3 pond since it is already filled to 2/3 so we divide ONE of the dimensions by 3 30 ft x 36 ft x 12 ft (let's divide 30) so we have: 10 ft x 36 ft x 12 ft new dimensions Volume = 4,320 ft Multiple volume by cost so : 4320 x 0.06= $259
Max can pack 3 lunches in 10 minutes. Jeff can pack 5 lunches in 20 minutes. Quantity A: # of mins it takes Max to pack 12 lunches Quantity B: # of mins it takes Jeff to pack 11 lunches
Need to use dimensional analysis 1. Max 12 lunches x (10 mins/3 lunches)= 40 minutes 2. Jeff 11 lunches x (20 mins/5 lunches)= 44 minutes Quantity B is greater
A student believes the odds in favor of him getting admitted to his dream school are 3 to 2. What. is the probability that the student will get into his dream school?
ODDS OF FAVOR PROBLEM probability of the event happening/ (1- probability of event not happening ) P(A)/ 1- P(A)= 3/2 2P(A)= 3(1-P(A)) 2P(A)= 3 - 3P(A) 5P(A)= 3 P(A)= 3/5 or 0.6
If a coin is flipped three times, what is the probability of not getting all tails?
P(event not happening)= 1 - P(event happening) P(not getting all tails)= 1-P(getting all tails) P(getting all tails)= 1/2 x 1/2 x 1/2= 1/8 P(not getting all tails)= 1 - 1/8= 7/8
How many four-digit numbers can be made from the following digits {1, 3, 5, 7} if no digits are repeated?
PERMUTATION PROBLEM As each number has to be unique and does not contain repeats, we can simply find the choices for each digit and multiply them : nPr= n!/ (n-r)! 4P4= 4!/ (4-4) ! = 4!/0! = 4 x 3 x 2 x 1/ 1 = 24 total choices
Gas pump A takes 0.2 hours to fill a large gas tank. Pump B takes 0.4 hours to fill the same gas tank. If both pumps are operating at the same time for 3 hours, how many tanks will they fill?
Pump A 1 tank/0.2 hours = x tank/hour x = 5 tanks Pump B 1 tank/0.4 hours = x tank/hour x=2.5 Add them together 5 + 2.5= 7.5 How many tanks will they fill in 3 hours? 7.5 x 3= 22.5
2 fair dice are rolled QUANTITY A: P(sum is greater or equal to 10) QUANTITY B: 7/36
QUANTITY A: P(sum is greater or equal to 10) (5,5) (4,6) (6,4)= 3 possibilities to be equal to 10 (5,6) (6,5)= 2 possibilities to be 11 (6,6)= 1 possibility to be 12 ****ADD THESE ALL TOGETHER**** 3/36 + 2/36 + 1/36= 6/36 QUANTITY B IS GREATER
LOOK AT PICTURE FOR PROBLEM
REMEMBER if b^2-4ac <0: no real roots if b^2-4ac =: two equal real roots (one root) if b^2-4ac > 0: two distinct real roots Discriminant formula: b^2-4ac
How much distance is covered by a train traveling at 120 miles per hour for 2.5 hours?
SPEED DISTANCE TIME PROBLEM!!!!!! Distance= speed x time distance= 120 miles/hour x 2.5 hours= 300 miles
For a college student at a particular university, the mean number of classes taken per semester is 4, with a standard deviation of 1. Assuming that the data taken at this university is normally distributed, what is the percentage of students that are taking 6 or less classes per semester?
STANDARD DEVIATION We must be familiar with the 68-95-99.7 rule 68% of data points fall within the +/- 1 standard deviation of the mean, 95% of data points fall within +/- 2 standard deviations of the mean, and 99.7% of data points fall within +/- 3 standard deviations of the mean Trying to find the percentage of students who are taking less than 6 or less classes per semester. Mean number of classes taken is 4 with a SD of 1. 6 classes is 2 standard deviations ABOVE THE MEAN so we are dealing with 95%. above the mean would be 5% but remember we have to divide this by 2 because we have below and above the mean, so it would be 2.5% and so we add 2.5 to 95% and get 97.5%
A container has 4 blue marbles, 2 green marbles, and 2 yellow marbles. If you draw 3 marbles with replacement, what is the probability the third marble is the only blue marble that is drawn?
STEP 1: We calculate the total number of marbles in the container = 8 marbles STEP 2: Because we are looking for the prob that the third marble is the only blue marble, the first and second marble must not be a blue marble so we can find the prob for the first and second draws by: P(not blue)= #green + #yellow/ total = 2+2/8= 4/8= 1/2 STEP 3: For the third draw, we must draw a blue marble. The probability for the third draw can be found by P(blue)= #blue/#total= 4/8 = 1/2 STEP 4: multiply the probabilities together P(not blue) x P(not blue) x P(blue)= 1/2 x 1/2 x 1/2= 1/8
A and B are two independent events Quantity A: P(A) Quantity B: P(A|B)
When two events are independent of each other P(A)= P(A|B) So the two quantities are equal
Alex can mow his lawn in 6 hours, while Jeff can mow the same lawn in 3 hours. If Alex and Jeff work together, how long would it take them to mow the lawn?
WORK PROBLEM 1. (1/6) + (1/3)= 1/x 1/6 + 2/6= 3 lawns/6 hours 1 lawn / x hours = 3 lawns / 6 hours 3x=6 x = 2 hours
Hose A takes 45 minutes to fill the swimming pool. Hose B takes 1.5 hours to fill the same pool. How many minutes does it take to fill the swimming pool if both hoses are operating at the same time?
WORK PROBLEM We have to calculate how fast each hose can fill up the pool in terms of a fraction or decimal Final answer is in minutes, so we convert all units to minutes 1. 1/45 +1/90= 1/x 2. 3/90 --> 1/30 (30 MINUTES)
Fourteen liters of an 80% milk solution and 2 twelve liters of a 45% milk solution are poured into one container. Quantity A: final concentration of milk Quantity B: 63.8%
concentration of Milk = total milk/ total solution * 100% 1. Find total liters of milk total milk= 14L(0.8) + 12L(0.45) + 12L(0.45) TOTAL MILK= 22 L 2. Find total solution = 14 + 12 + 12 = 38 L Concentration of Milk= 22L/ 38L * (100%) = 57.9%
Distance formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
A truck driver drives at 40 mi/hour, 30 mi/hr for 30 mins, and 10 mi/hr for a final 30 minutes Quantity A: Miles the truck traveled during the first hour Quantity B: Miles the truck traveled after the first hour
distance= speed x time First hour: 40 mi/hour x 1 hr= 40 mi After the first hour 30 mi/hr x 1/2 hr = 15 mi 10 mi/hr x 1/2 hr= 10 mi 10 mi/hr x 1/2 hr= 5 mi quantity A: 40 mi quantity B: 30 mi