Maths-
SAT
Easy
Question
(15 - 4i) ( 6 - 3 i) = a + bi
In the equation above, a and b are real numbers and
i = 
. What is the value of a ?
The correct answer is: 78
(15 – 4i) (6 – 3i) = 15 × 6 – 4 × 6i – 15 × 3i + 4 × 3i2
= 90 – 24i – 45i + 12i2
= 90 – 24i – 45i – 12
= 78 – 69i
a = 78
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a |
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In spring 2015, three separate studies on the fitness level of tenth graders were conducted in the city of Mistwick. In each study, every student in a group of tenth graders took the same fitness test and received a score on it. The possible scores on the fitness test are the whole numbers from 50 to 100, inclusive. The distribution of the scores for each of the' studies is shown in the table below.
|
Score range |
Study I |
Study II |
Study III |
| 50-59 |
24 |
50 |
88 |
| 60-69 |
36 |
67 |
67 |
| 70-79 |
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52 |
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17 |
39 |
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70.4 |
| Total number of participants |
100 |
200 |
300 |
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• For Study II, 200 tenth graders were selected at random from all tenth graders in Mistwick.
• For Study III, 300 tenth graders from Mistwick volunteered to participate.
No tenth grader participated in more than one of the three studies.
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|
Score range |
Study I |
Study II |
Study III |
| 50-59 |
24 |
50 |
88 |
| 60-69 |
36 |
67 |
67 |
| 70-79 |
22 |
52 |
65 |
| 80-89 |
11 |
14 |
41 |
| 90-100 |
7 |
17 |
39 |
| Mean score |
68.6 |
68.7 |
70.4 |
| Total number of participants |
100 |
200 |
300 |
• For Study I, 100 tenth graders were selected at random from all tenth graders in Mistwick.
• For Study II, 200 tenth graders were selected at random from all tenth graders in Mistwick.
• For Study III, 300 tenth graders from Mistwick volunteered to participate.
No tenth grader participated in more than one of the three studies.
The results of which of the studies can appropriately be generalized to all tenth graders in Mistwick in spring 2015?
maths-sat
