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zalisa [80]
3 years ago
15

In the statistic department of UCI, there are 60 graduate students in total, 45 PhD students and 15 master students. Among maste

r students, 40% of them are international students. Among PhD students, 20% are international students. (a) What is the proportion of international students in the statistic department? (b) What is the proportion of master students among all domestic students.
Mathematics
1 answer:
astra-53 [7]3 years ago
6 0

Answer:

(a) The proportion of international students in the statistic department is 25%.

(b) The proportion of master students among all domestic students is 20%.

Step-by-step explanation:

The following can first be obtained from the question:

Total number of graduate students = 60

Number of PhD students = 45

Number of Master students = 15

Percentage of international students among the master students = 40%

Percentage of international students among the PhD students = 20%

Number of international master students = Number of Master students * Percentage of international students among the master students = 15 * 40% = 6

Number of international PhD students = Number of PhD students * Percentage of international students among the PhD students = 45 * 20% = 9

The questions can now be answered as follows:

(a) What is the proportion of international students in the statistic department?

This can be calculated as follows:

Total number of international students = Number of international master students + Number of international PhD students = 6 + 9 = 15

Total number of graduate students = 60

Proportion of international students in the statistic department = Total number of international students / Total number of graduate students = 15 / 60 = 0.25, or 25%

Therefore, the proportion of international students in the statistic department is 25%.

(b) What is the proportion of master students among all domestic students.

This can be calculated as follows:

Total number of graduate students = 60

Total number of international students = Number of international master students + Number of international PhD students = 6 + 9 = 15

Total number of domestic students = Total number of graduate students - Total number of international students = 60 - 15 = 45

Number of Master students = 15

Number of international master students = Number of Master students * Percentage of international students among the master students = 15 * 40% = 6

Number of domestic master students = Number of Master students - Number of international master students = 15 - 6 = 9

Proportion of master students among all domestic students = Number of domestic master students / Total number of domestic students = 9 / 45 = 0.20, or 20%

Therefore, the proportion of master students among all domestic students is 20%.

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(2) Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-2, 2) and point (4, 4) rounde
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