Transcript
PROBLEM
PROBLEM
A small group has $100 to spend spend for lunch. The The group decided decided to give a tip of 20%(before tax). The sales tax is 7 ½ %. How much should they spend?
x 0.20 x 0.075 x 100
1.275 x 100
What is the reciprocal of 3-i? 1 3i 1
x $78.43
3i
x
3 i 3 i 3 i 9 3i 3i 1
PROBLEM
An un-experienced un-experienced worker unloads unloads a truck within within 1 hour and 40 minutes. Together Together with a trainee they can work for 1 hour. In how many hours can the trainee spend working alone? 1 hour and 40 minutes 100 minutes rt 1 1 1 60 1 100 x
3i 9 1 3 i 10
or 0.3 0.1i
PROBLEM
Find the sixth term of the arithmetic sequence with a1=11 and d=4.
a n a1 (n 1)d a 6 11 (6 1)4
x 150
a 6 31
PROBLEM
0.16 x 0.2815 x 0.2415
Find the general term an, of the arithmetic sequence -8,-3,2...
0.16 x 4.2 0.28 x 3.6 0.12 x 0.6
a n a1 ( n 1)d a n 8 ( n 1)5
x 5
a n 5n 5 8
PROBLEM
a n 5n 13
Peanut and nut mixture contains 40% peanut. How much additional peanut mixture should be added to produce 8 lbs. of 50% peanut?
PROBLEM
A solution of system of linear inequalities is bounded if IT IS ENCLOSED WITHIN A CIRCLE
x
+
100%
8-x
PROBLEM
A mixture containing 16% of a drug is combined to a 28% of a drug to obtain a 15mL of 24% of a mixture. How many 16% of a drug should be added? 16%
40%
+
28% 15-x
=
0.408 x 1 x 0.508 3.2 0.4 x x 4 0.6 x 0.8
24% 15
x 1.33lbs
x
=
50% 8
PROBLEM
PROBLEM
A small boat travelling 5 miles upstream, later back down stream for 1 hour and 40 minutes. The stream current is 4 mph. What is the velocity when it is in still water?
Together John and Michael can paint a wall for 18 minutes. John alone can finish the wall 15 minutes more than Michaels painting. Find the time of each.
1 hour and 40 minutes 1.67 hours
1 1 18 1 t 1 t 2 1 1 18 1 t 2 15 t 2
t u t d 1.67 5 V 4
5 V 4
1.67
t 2 30 min
V ( )2mph
t 1 45 min
PROBLEM
The third term of a geometric progression is 32 and the fifth is 128. Find the first term and the common ratio. a n a1 r n 1 a3 a1 r 31 32 a1 r 31
6 1
a 6 a1 r
128 a1r 6 a1 12.70 r 1.59
1
PROBLEM
Daniel is twice as old as Jimmy. Terry is one year younger than Daniel. If the sum of their age is 44. How old is Daniel? D 2 J J
D
2
D J T 44 D
D
2
T D 1 D 18
D 1 44
PROBLEM
PROBLEM
A Bank contains $1.65 Nickel, Dimes and Quarter. There are twice as many as Nickel as Dimes as and one more Quarter than Nickel. There are how many Quarter.
A woman pays $21.56 in buying a book which is marked 20% off. The sales tax is 8%. How much is the book.
0.05 N 0.10 D 0.25Q 1.65
N 2 D D
N
2
Q N 1
0.80 x SELLING PRICE
N 0.05 N 0.10 0.25 N 1 1.65 2 N 4
x BOOK PRICE 0.80 x 0.080.80 x 21.56
Q 4 1 Q5
x 24.95
PROBLEM PROBLEM
The sum of two positive numbers is 35. There product is 304. What is the smallest number?
A boy got 100 an average in Homework and Test grade which are 97, 99, 100. Homework counts 15%. Each Test grade counts 20% and 25% Final grade. What is the score he should get in Final Exam to have a grade of 90?
x SMALL NUM BER 35 x LARGER NUM BER x35 x 304 35 x x 2 304 x 2 35 x 304 0
x 19 x 16 0
90 1000.15 970.20 990.20 1000.20 0.25 x
x 19 x 63.2
x 16
SMALL NUM BER 16
PROBLEM A matrix is in reduced form containing 0’s in a row is below any ____
non zero element. 1
PROBLEM
PROBLEM
Two balls are drawn in a bag with one red ball, two black balls and three white balls. What is the probability if the first ball is red and the second is white given if that the first drawn ball is return into the bag?
How many ways can you position six person in circular table? C n 1! C 6 1!
P
1 3
P
1
6 6
3 36
C 120ways
PROBLEM
How many permutation can you get in a letter word TENNESSEE?
12 P
9! 2!2!4!
PROBLEM
A student is given a 87% chance to get 98% in the exam given that he was able to solve all problems. But he has also 15% chance of not solving the problem. What is the chance of him getting 95% in the exam?
P 3780ways PROBLEM How many ways can you arrange the l etters in a word “MONDAY”
E 0.870.85 x100
given that the first letter is a vowel.
E 74%
W 2 5 4 3 2 1 W 240ways
PROBLEM How many ways can you arrange the word “MONDAY” wherein the 4
letters are taken at a time?
PROBLEM
There are 7 paintings in a museum with 3 vacant slots. How many ways can you arrange the paintings in the given slot?
7 P 3 210ways
6 P 4 360ways PROBLEM PROBLEM
The 1st and the 10th term of a geometric progression is 1 and 4. Find the 17th term.
What is the mode of the sequence 4 21 11 7 4 8 6 9? 4. IT IS UNIMODAL
a n a1r n 1
4 1r 10
PROBLEM
What is the mode of the sequence 15 6 7 9 3 8 11 15 3 4 9? 15 and 9. BIMODAL
r 4
1
1
1 a17 1 4 9
17 1
a17 11.758
9
PROBLEM 1 3
1 9
What is the sum of the series 1 ?
PROBLEM
What is the median of the sequence 5 6 8 12 13 15? MEDIAN
8 12 2
10
r
a2 a1 1
r r
3 1 1 3
1 a1 1 r 1 1 3 3 S 2 S
PROBLEM
PROBLEM
What is the sum of the first 50 terms of the series 10 85 160 325 ?
A calculator manufacturer wants to earn $18000. They produce the calculator for $6 and sell it for $11. If the overhead runs $150000. What is the number of calculator to be produced?
d a2 a1 85 10 75
S
n2a1 ( n 1) d
2
502(10) (50 1)75 2
x - number of calculator
S 92375
11 x 6 x 150000 18000
PROBLEM
x 33600
The special way in proving hypothesis and rank against the most basic tools in the mathematicians toolbox. MATHEMATICAL INDUCTION
If a man buys gasoline: 10L for 11.50 12L for 12.01 18L for 11.78 average.
PROBLEM
What is
7 8i 4 2i
?
PROBLEM
3 5
23 10
i
Average
1011.5 1212.01 1811.78 10 12 18
Average 11.78
Find the
PROBLEM
PROBLEM
If we partition the division so that the rectangles width is not equal and the height is taken from sublevel, the sum of areas of the rectangles are called: REIMANN SUM
How ways are there to select 3 juniors and 4 seniors from chorus with 10 freshmen, 15 sophomores, 18 juniors and 20 seniors to sing in an all-day chorus?
Solution: (18C3) x (20C4) ANSWER: 3,953,520 way s
PROBLEM
The mean score of the students is 65.3 and the standard deviation of 20.15. Find the two values at which must lie at least 75% of the data.
PROBLEM
How many ways can 5 keys be arranged in a keychain? Solution: (n-1)! (5-1)!
Solution:
ANSWER: 24 ways k=2 65.3 – 2(20.15) = 25 65.3 + 2(20.15) = 105.6
ANSWER: 75% of the d ata lie between 25 and 105.6
PROBLEM
A bracelet has 7 charms. How many arrangements of charms can be made? Solution: (n-1)! (7-1)! ANSWER: 720 ways
PROBLEM
PROBLEM
How many distinguishable permutations can be made from the letters of MISSISSIPPI?
A box contains 3 red marbles and 5 black marbles. A red marble is drawn and was not replaced back to the box. What is the probability that a black marble will drawn?
Solution:
ANSWER:
ANSWER: 34,650
PROBLEM
A man tosses a 1 five-peso coin, 2 one-peso coins, 3 twenty-fivecentavo coins, and 4 ten-centavo coins to 10 boys. In how many ways can the boys profit if each have a coin? Solution:
QUESTION
What occurs when the new coordinate axes have the same direction as and are parallel to the original coordinate axes? ANSWER: Translation of coord inate axes
PROBLEM An office…
Let y = number of offices rented ANSWER: 12,600
PROBLEM
A box contains 3 red marbles and 5 black marbles. A red marble is drawn and replace back to the box before the second drawer. What is the probability that a black marble will dr awn? ANSWER:
rent x offices = 68,400 (1600 + 100y) (40 – y) = 68,400 (y – 22) (y – 2)=0 y=2 rent = 1600 + 100(2) ANSWER: rent = 1800
PROBLEM
PROBLEM
Kelly sells corn dogs in a state fair. Booth rental and equipment total $200 per day. Eacg corn dogs is $35 cents to make and sell for $2 each. How many corn dogs should she sell if she wants $460 profit?
Two men will meet at an intersection. One travels southward while the other travels north. If one of the driver drives 30 mph and the other drives 40mph, when will they be 35 miles apart?
Letx=corn dogs to sell each day Revenue=2x
rt=35 (30+40)t=35 t=0.5 or 30 minutes
Ans. x≥400 PROBLEM PROBLEM
Linda has $16,000 to invest. Part of her money is envested with a bond of 5% and 6 %. How much should she invest in 6 % if she wants an annual profit of $937.50? Let x=invested in 6 % 16000-x = invested in 5% 0.0625x + 0.05(16000-x) = 937.50 X=11,000
There are $8.75 nickels, dimes and quarters. There 5 more dimes than nickel and 4 more quarters than dimes. How many dimes are there? 0.05N+0.10D+0.25Q=8.75 5+N=D Q=4+D 0.05(D-5)+0.10D+0.25(4+D)=8.75 D=20
PROBLEM
PROBLEM
A working student earns $8 per week. How many hours should she work per week to earn $120 to $200?
A polar equation r = a represents
120≤ ≤200
circle
with center at the origin
PROBLEM
A polar equation
represents
lemniscate
15
hours
PROBLEM
PROBLEM
A polar equation r = a csc θ represents Horizontal line PROBLEM
A polar equation θ = a represents a PROBLEM cos ( α – β ) – cos ( α + β ) =
Line
through the origin
sin α sin β PROBLEM
PROBLEM
=
A polar equation r = a cos θ represents Circle
tangent to the y-axis
PROBLEM
PROBLEM
Melinda had a 6 mile hike or 1 hour 45 min. she first walked for 4mph and then he finished her walk at 3mph. Find the distance that she walked after finishing the 4mph walk.
A 16-team… The bowling officials has P8000 budget for the prizes. If the prize given to the 16th place is P275, find the prize given to the first place.
t T 1.75hrs
S
t T t 1 t 2
8000
1.75
x 4
6 x 3
x 3
n
2
(a1 a n ) 16 2
(a1 275)
S 725
PROBLEM
Factor (81-x4) completely (9 x 2 )(9 x 2 )
PROBLEM According to Hooke’s law you can stretch a _____ to F=4.2x. if 7 F 14 , Find the Value of x.
(9 x 2 )(3 x)(3 x)
PROBLEM
7 4.2
4.2 x
14
4.2 4.2 x 5 to 10 3 3
The Government gives P500 taken from the lottery… If P 500 is given to an individual and that individual spends 80% of it, and the receivers of that money also spends 80% of what they received, and the cycle continues forever, Find the total amount of money used. S
400
1 0. 8 S 2000
PROBLEM
PROBLEM
Find the sum of a 20 term G.P. if the first term is 1 and r=2.
A bridge deck consisting of 52 cards. If you were to pick 3 cards, what is the probability that the cards are diamond?
S S
n a1 ( r 1)
r 1 1(2 20 1)
2 1 S 1048575
PROBLEM
th
Total outcome: 52C3 = 22,100 Successful outcome: 13C3 = 286 P = successful outcome / total outcome = 286/22,100 = 0.0129
20
Find the 16 term of the expansion (x-2)
PROBLEM
20 C 161 x 20161 ( 2)161
Answer: cot β 508035072 x
5
PROBLEM PROBLEM
There are 15 contestants in a contest. In how many ways the three winners are to be chosen? 15C3 =
455 ways
Answer: sin α
PROBLEM
PROBLEM
A circle with a radius, r, is inscribed in an irregular triangle having a side of 5 cm, 7cm and 10 cm. Determine the radius of the circle.
Tickets of a concert are consecutively numbered. Manny sold tickets numbered 168-358. How many did he sell?
S=
Solution: an = an + (n-1)d 358 = 168 + (n-1)(1)
= 11 2
A = A = r=
= 16.248 cm = 2.954 cm
an = 359 tickets
PROBLEM
PROBLEM
Probability of getting exactly 3 tails in 5 throws. P = 5C3(1/2)3(1/2)5-3
Answer:
tan 3β
PROBLEM
Answer:
P=5/16
PROBLEM 2cosαcosβ
A standard 52-deck card, how many 5-hand card will have 3aces and 2kings? C1 = 4C3 = 4 C1 = 4C3 = 6 C = (4)(6) = 24 hand
PROBLEM In a single dice, find the probability of getting at least 3 two’s in 4
throws. P1 = 4C3(1/6)3(5/6)4-3 = 5/324 P 2= 4C4(1/6)4(5/6)4-4 = 1/216 P = P1 + P2 = 13/648 PROBLEM
In throwing a 2-dice, find the probability of getting the sum of the two dice greater than 10. P1 = 2/36 ; for 5 and 6 output of the dice. P2 = 1/36 ; for 6 and 6 output of the dice. P = P1 + P2 = ( 2/36) + (1/36) P= 1/12 PROBLEM
Find the combination of 5 object taken 1,2,3,4, and 5. C = 2n – 1 C = 25 – 1 C = 31
