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23 Dec 2024, 10:50
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total = 32
Ai = 24
Cs = 8
In Ai
with ms/without ms = 5/3
=> with ms = 15
=> without ms = 9
In Cs
with ms/without ms = 3/5
=> with ms = 3
=> without ms = 5
total with ms = p = 18
total without ms = q = 14
ratio p/q = 9/7
Ai = 24
Cs = 8
In Ai
with ms/without ms = 5/3
=> with ms = 15
=> without ms = 9
In Cs
with ms/without ms = 3/5
=> with ms = 3
=> without ms = 5
total with ms = p = 18
total without ms = q = 14
ratio p/q = 9/7
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes
A tech startup has recently expanded its team to 32 employees, focusing on two main areas: artificial intelligence (AI) and cybersecurity. Here's the team composition:
If the ratio of employees with a master's degree to those without is p to q, select for p the possible value of p, and select for q the possible value of q that would be jointly consistent with the given information. Make only two selections, one in each column.
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A tech startup has recently expanded its team to 32 employees, focusing on two main areas: artificial intelligence (AI) and cybersecurity. Here's the team composition:
- 75% of the employees work in AI, while the remaining 25% work in cybersecurity. There is no overlap between these departments.
- In the cybersecurity team, the ratio of employees with a master's degree to those without is 3:5.
- In the AI team, the ratio of employees with a master's degree to those without is 5:3.
If the ratio of employees with a master's degree to those without is p to q, select for p the possible value of p, and select for q the possible value of q that would be jointly consistent with the given information. Make only two selections, one in each column.
23 Dec 2024, 10:52
Kudos
Bookmarks
Total employees = 32
Ai group = 24
Cs group = 8
In Ai
with ms/without ms = 5/3
with ms = 15
without ms = 9
In Cs
with ms/without ms = 3/5
with ms = 3
without ms = 5
total with ms = p = 18
total without ms = q = 14
ratio p/q = 9/7
p = 9
q = 7
Ai group = 24
Cs group = 8
In Ai
with ms/without ms = 5/3
with ms = 15
without ms = 9
In Cs
with ms/without ms = 3/5
with ms = 3
without ms = 5
total with ms = p = 18
total without ms = q = 14
ratio p/q = 9/7
p = 9
q = 7
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes
A tech startup has recently expanded its team to 32 employees, focusing on two main areas: artificial intelligence (AI) and cybersecurity. Here's the team composition:
If the ratio of employees with a master's degree to those without is p to q, select for p the possible value of p, and select for q the possible value of q that would be jointly consistent with the given information. Make only two selections, one in each column.
|
A tech startup has recently expanded its team to 32 employees, focusing on two main areas: artificial intelligence (AI) and cybersecurity. Here's the team composition:
- 75% of the employees work in AI, while the remaining 25% work in cybersecurity. There is no overlap between these departments.
- In the cybersecurity team, the ratio of employees with a master's degree to those without is 3:5.
- In the AI team, the ratio of employees with a master's degree to those without is 5:3.
If the ratio of employees with a master's degree to those without is p to q, select for p the possible value of p, and select for q the possible value of q that would be jointly consistent with the given information. Make only two selections, one in each column.
23 Dec 2024, 10:54
Kudos
Bookmarks
Step-by-Step Solution:
We are tasked with determining the ratio
p:q of employees with a master’s degree to those without a master’s degree across the entire company, based on the provided information.
Step 1: Breakdown of the Teams
The startup has 32 employees divided into two areas:
AI team:
75% of the employees, i.e., 0.75×32=24 employees.
Cybersecurity team: 25% of the employees, i.e.,
0.25×32=8 employees.
Step 2: Master's Degree Ratios
In the cybersecurity team, the ratio of employees with a master’s degree to those without is 3:5.
Total cybersecurity employees = 8.
Using the ratio 3:5, we calculate:
Employees with a master’s degree: 3/8 ×8=3.
Employees without a master’s degree: 5/8 ×8=5.
In the AI team, the ratio of employees with a master’s degree to those without is
5:3.
Total AI employees = 24.
Using the ratio 5:3, we calculate:
Employees with a master’s degree: 5/8 ×24=15.
Employees without a master’s degree: 3/8 ×24=9.
Step 3: Total Master's Degree Counts
Now, combine the numbers for both teams:
Total employees with a master’s degree:
3(cybersecurity)+15(AI)=18.
Total employees without a master’s degree:
5(cybersecurity)+9(AI)=14.
Step 4: Overall Ratio p:q
The ratio of employees with a master’s degree to those without is:
p:q=18:14=9:7.
Final Answer: p=9,q=7.
p=9,q=7
We are tasked with determining the ratio
p:q of employees with a master’s degree to those without a master’s degree across the entire company, based on the provided information.
Step 1: Breakdown of the Teams
The startup has 32 employees divided into two areas:
AI team:
75% of the employees, i.e., 0.75×32=24 employees.
Cybersecurity team: 25% of the employees, i.e.,
0.25×32=8 employees.
Step 2: Master's Degree Ratios
In the cybersecurity team, the ratio of employees with a master’s degree to those without is 3:5.
Total cybersecurity employees = 8.
Using the ratio 3:5, we calculate:
Employees with a master’s degree: 3/8 ×8=3.
Employees without a master’s degree: 5/8 ×8=5.
In the AI team, the ratio of employees with a master’s degree to those without is
5:3.
Total AI employees = 24.
Using the ratio 5:3, we calculate:
Employees with a master’s degree: 5/8 ×24=15.
Employees without a master’s degree: 3/8 ×24=9.
Step 3: Total Master's Degree Counts
Now, combine the numbers for both teams:
Total employees with a master’s degree:
3(cybersecurity)+15(AI)=18.
Total employees without a master’s degree:
5(cybersecurity)+9(AI)=14.
Step 4: Overall Ratio p:q
The ratio of employees with a master’s degree to those without is:
p:q=18:14=9:7.
Final Answer: p=9,q=7.
p=9,q=7
