Discussion questions
Metric system has only seven basic units, while the US system has more than 300 basic units; thus, it is simpler. In addition, units in metric systems are multiples of 10, therefore, calculations is easier than in US system. Metric systems are universally applied, except in USA.
Perimeter is measured by distance round a figure whose SI units are meters; therefore, the perimeter is given in units of length. However, area is a derived quantity and its magnitude is obtained by multiplication of two units of length. Therefore, its units are given by the product of the units.
Theoretical probability is the ratio of favorable outcomes to total number of outcomes. While, empirical probability is the fraction an event is expected when conducted experimentally. There are professions in which probability is relevant. Doctors use probability to test medicines where the most appropriate method is double blind folded placebo experiments. Also, probability is used by statistician to project the extent to which events are likely to occur, such as population growth subject to various conditions. Lastly, management, probability is used to evaluate decision making and financial risks.
Random sample: in this sampling technique, every participant has an equal chance of being selected.
Systematic sample: in this sampling technique, a random sample is selected, and a certain procedure is used to selected the sample, e.g. every tenth participant
Cluster sampling: in this sampling technique, where groups within the populations are evident, the sample is selected from these groups.
Stratified sampling techniques involve diving the population into strata which are mutually exclusive, then using random or systematic techniques to select the sample from the strata.
Convenience sampling techniques involves selected samples based on a set criteria for suit the objectives of the study.
1. 1mm = 0.001m
2. 9dam = 90m
3. 0.562mm =0.000562m
4. 8cm
5. Grams
6. 1020F = 38.90C
7. 456g
8. 12 in = 30.5 cm
9. 365 lb = 164.3kg
10. A = 5ft *10ft = 50 sq ft = 4.6m2
11. 5.6 m = 5600mm
12. 0.024kl, 0.026hl, 28dal, the smallest quantity is 0.024kl
13. Quantity per day = 2*150mg = 300mg
Per week = 300*7 = 2100mg =210g
14. V = 6 m * 2.3m* 0.36m = 4.968m3
15. A = Lw = 1.9 km * 4.61km = 8.759 km2
1ha = 10000m2 , 8.759 km2 = 8.759 *100 = 875.9 ha
16. V = 18m * 12m * 1.8 m = 388.8m3
V= 388.8kl
17. 210F = -6.10C
18. -550F = -48.30C
19. 60mph = 96.6km/h
20. 300 miles = 482.8km
1.
2. <6 = 1220
<2 = 1220
<8 = 1220
<5 = 580
<3 = 1220
<7= 580
<1 = 580
3. m<1 = 1580
m<2 = 220
m<3 = 1580
m<4 = 1580
m<5 = 220
m<6 = 1580
m<7 = 220
4. 18x + 47 + x =180
19x = 133
X = 7
<1 = 70 and <2 = 1730
5. =
X = 7 *3.1 = 21.7
6. = , h = 60 ft the height of tree
7. Perimeter = 2(16 + 6) = 44 in
Area = bh = 16 * 3 = 48 sq in
8. Area of shaded region = (12 *12) – (3.14 * 6 *6) = 30.96m2
9. V = 4/3 * 3.14 * 5.52 = 696.6cm3
A = 4 * 3.14 * 5.52 = 379.9 cm2
10. V = 149m *149m * 114m = 2530914m3
11. 12. 130.90 supplementary is = 49.10
13. x +14x + 45= 180
15x = 135
X = 9
< 2 = 180-9 = 1710
<1 = 90
14. The triangle is equilateral, the angles are acute
15. 16. (18/12) = QR /20
Qr = 20 * 18 /12 = 30
18/12 = PR/16
PR = 16 *18 /12 = 24
17. 15/10 = a/6 , a = 6 *15/10 = 9
15/10 = b/8 , b = 15*8/10 = 12
18. Circumference = 2*3.14 * 9 = 56.5 in
Area = 3.14 * 9 * 9 = 254.3 sq in
19. Area of shaded region = 3.14 (92 – 62) = 141.30 m2
20. V = 43 * 21 * 21 = 18963 cubic in
V = 10.97 ft3
Questions Unit 7
1. R = 6, Y = 2 , G =3
The odd in favor of red ball is 6 to 6
2. The odd against G33 49:1
3. The odds against selling a car is 0.68 : 0.32, 17: 8
4. 0.7 * $40000 + 0.1* $0 – 0.2*$30000 = $22000
Gain of $22000
5.
a) Probality is equivalent to the area
Probability dart land on $3 = ½ + 1/16 = 9/16
Probability dart land on $10=1/4
Probability dart land on $60 = 1/8
Probability dart land on $70= 1/16
b) (9/16) *3 + (1/4) *10 + (1/8)*60 + 1/16*70 = $16.0625
c) The gambler should pay = 16.0625 /2 = $8.03125
6.
a) P(one boy) = P(BGG) + P(GBG) + P(GGB)
= ( ½ *1/2 * ½) *3
=3/8
b) Probability of atmost two boys = P(one boy) + P(two boys)
P(2Boys) = P(BBG) + P(GBB) + P(BGB) = 3/8
P(one boy) = 3/8
Probability of at most two boys = 3/8 +3/8 = 6/8 = ¾
7.
a) Possible classifications are 8
b) The tree for gender has 2 branches
The tree for hair color has 4 branches
The tree for eye color has 8 branches
c) Size of sample space is 8
P(F. HBL. EBl) = ½ *1/2*1/2 = 1/8
d) The sample space is 8
Probability male with blonde air = (½ *1/2* 1/2 ) + (½ *1/2* 1/2 ) = ¼
8.
a) There are 4 different classifications
b) P(yellow pea) = P(sy) + P(ty) = ½ *1/2 + ½ *1/2 = 1/2
c) P(tall and green pea) = ½*1/2 = ¼
9. P(T1 T1) = 0.5 *0.2 = 0.01
10. The events of birth are not independent
Probability that first child is born with affliction A = 0.007
Probability that second child is born with affliction A = 0.007*0.07 = 0.00049
Probability (fist with affliction and second without) = 0.007 * 0.93 = 0.00651
Probability (fist without affliction and second with) = 0.993 *0.007 =0.006951
Probability (neither is born with affliction A) = 0.993 * 0.993= 0.986
11. The probability that the next person had blond hair = 15/60
12. The probability that the next fish is a grouper = 15/69 =5/13
13. Total number of plants = 697 + 209 = 906
Probality of a plant had white flowers = (697/906) = 0.769
Probability that plant had purple flowers = (209/906) = 0.231
14.
a) The probability that the card selected is 2 = 2/52 = 1/26
b) Probability is a black card = 26/52 = ½
15. Probability of drawing a 10 or king = 4/52 + 4/52 = 8/52 = 2/13
Probability of drawing a diamond = 13/52 = ¼
16. The probability of being dealt kind = 14/52 = 1/13
17. The probability of being dealt a 10 and a queen = 4/52 *4/51 = 4/663
18. Probability that spinner lands on blue = 2/8 = ¼
Probability that spinner lands on red = 2/8 = ¼
19. Probability that spinner lands on blue = 3/10
Probability that spinner lands on brown = 2/10 = 1/5
20. Probability os selecting orange soda = 18/100 =9/50
1. Stratified sampling
2. Random sampling
3. The statement is not valid important information is missing
4. The statement is invalid because of unknown sample size
5.
a) The graph is not misleading
b) The graph does not need to be changed
6. frequency
Lang, S. (2002). Algebra. USA: Springer.
Szecsei, D. (2007). Homework Helpers pre-calculus. USA: Career press.
