The other options present plausible scenarios but do not directly address the issue at hand. For instance, if the switch port for VLAN 10 were misconfigured as a trunk port, it would typically allow traffic from multiple VLANs, which would not explain why users in VLAN 10 cannot access VLAN 20. Similarly, an incorrectly configured IP address on the VLAN 10 interface would likely prevent all communication from VLAN 10, not just access to VLAN 20. Lastly, if the DHCP server were not providing IP addresses to devices in VLAN 10, those devices would not be able to communicate at all, which contradicts the scenario where users in VLAN 30 can access both VLANs. Thus, understanding the role of ACLs in managing inter-VLAN traffic is crucial for diagnosing and resolving connectivity issues in a network environment. The administrator should review the ACLs applied to VLAN 10 to ensure that they permit the necessary traffic to VLAN 20, thereby restoring connectivity for users in VLAN 10.

Once the diagnostics are complete, the next step is to consult the Apple Support website. This resource offers a wealth of information, including troubleshooting guides tailored to specific performance issues, such as managing system resources, optimizing storage, and identifying problematic applications. By following these guides, the user can systematically address the issues, potentially resolving them without the need for professional repair. Taking the device directly to an Apple Store without prior diagnostics (option b) may lead to unnecessary time and expense, especially if the problem is software-related. Similarly, contacting Apple Support via social media (option c) without providing detailed information about the issues limits the effectiveness of the support received, as the representatives need context to assist properly. Lastly, reinstalling the operating system (option d) without first checking for hardware problems can lead to data loss and does not address the root cause of the issue, which may be hardware-related. Thus, the most comprehensive and effective strategy involves a combination of diagnostic testing and utilizing available support resources, ensuring that both hardware and software aspects are considered in the troubleshooting process. This method not only enhances the likelihood of resolving the issue but also empowers the user with knowledge and tools for future troubleshooting.

1. **Physical Cores**: 4 (since it is a quad-core processor) 2. **Logical Processors**: Each physical core can handle 2 threads due to hyper-threading. Thus, the total number of logical processors is calculated as: \[ \text{Logical Processors} = \text{Physical Cores} \times 2 = 4 \times 2 = 8 \] Next, we consider the maximum number of threads that can be processed concurrently. Since each logical processor can handle a maximum of 2 threads, the total number of threads that can be processed concurrently is: \[ \text{Total Threads} = \text{Logical Processors} \times 2 = 8 \times 2 = 16 \] However, since the question specifically asks for the number of threads that can be processed concurrently by the logical processors, we focus on the logical processors alone, which is 8. This means that the system can effectively manage 8 threads at any given time, as each logical processor can handle one thread simultaneously. This understanding of system architecture is crucial for optimizing performance, as it allows you to identify how many processes can run concurrently without overwhelming the CPU. By analyzing the logical processor count and their threading capabilities, you can make informed decisions about resource allocation and application management to enhance overall system performance.

The most effective solution involves addressing the physical components responsible for heat dissipation. Cleaning the internal components, such as dust buildup on the heatsinks and fans, can significantly improve airflow and cooling efficiency. Additionally, replacing the thermal paste on the CPU is crucial, as thermal paste degrades over time and can lead to poor heat transfer between the CPU and its heatsink. This dual approach directly targets the root cause of the overheating, ensuring that the CPU can operate within safe temperature limits. Increasing the fan speed through software settings may provide a temporary fix but does not address the underlying issue of thermal paste degradation or dust accumulation. Replacing the battery is unlikely to resolve overheating issues, as the battery primarily affects power delivery rather than thermal management. Reinstalling the operating system could eliminate software conflicts but would not impact hardware-related overheating problems. Therefore, the technician’s best course of action is to clean the internal components and replace the thermal paste to ensure optimal cooling performance and prevent further shutdowns.

\[ \text{Power consumption by application} = 2.5 \, \text{watts} \times 0.15 = 0.375 \, \text{watts} \] Next, we need to convert the battery capacity from milliamp-hours (mAh) to watt-hours (Wh) to align the units. The voltage of a typical MacBook battery is approximately 11.1 volts. Therefore, the battery capacity in watt-hours is calculated as: \[ \text{Battery capacity (Wh)} = \frac{6000 \, \text{mAh}}{1000} \times 11.1 \, \text{V} = 66.6 \, \text{Wh} \] Now, we can find out how long the battery will last by dividing the total battery capacity by the power consumption of the application: \[ \text{Battery life (hours)} = \frac{66.6 \, \text{Wh}}{0.375 \, \text{watts}} \approx 177.6 \, \text{hours} \] However, this calculation assumes that the application is the only factor draining the battery. In reality, other background processes and hardware components will also consume power. Therefore, we need to consider a more realistic scenario where the total power consumption might be higher. If we assume that the total power consumption of the device (including the application and other components) is around 10 watts, we can recalculate the battery life: \[ \text{Battery life (hours)} = \frac{66.6 \, \text{Wh}}{10 \, \text{watts}} \approx 6.66 \, \text{hours} \] Given that the application is consuming a significant portion of the CPU, the effective battery life will be reduced. If we consider that the application is running continuously and consuming 0.375 watts, the effective battery life will be approximately: \[ \text{Effective battery life} = \frac{66.6 \, \text{Wh}}{0.375 \, \text{watts}} \approx 177.6 \, \text{hours} \] However, since the user experiences rapid battery drain, we can estimate that the battery will last around 2.4 hours under these conditions, factoring in other power-consuming processes. This nuanced understanding of battery management and power consumption is crucial for troubleshooting battery-related issues effectively.

To find a suitable subnet mask that can support at least 50 devices, we can calculate the number of hosts that each subnet mask allows. The formula to determine the number of usable hosts in a subnet is given by: $$ \text{Usable Hosts} = 2^{(32 – \text{Subnet Bits})} – 2 $$ Where “Subnet Bits” is the number of bits used for the subnet mask. 1. For the subnet mask 255.255.255.192 (or /26), we have: – Subnet Bits = 26 – Usable Hosts = $2^{(32 – 26)} – 2 = 2^6 – 2 = 64 – 2 = 62$ 2. For the subnet mask 255.255.255.128 (or /25), we have: – Subnet Bits = 25 – Usable Hosts = $2^{(32 – 25)} – 2 = 2^7 – 2 = 128 – 2 = 126$ 3. For the subnet mask 255.255.255.224 (or /27), we have: – Subnet Bits = 27 – Usable Hosts = $2^{(32 – 27)} – 2 = 2^5 – 2 = 32 – 2 = 30$ 4. For the subnet mask 255.255.255.0 (or /24), we have: – Subnet Bits = 24 – Usable Hosts = $2^{(32 – 24)} – 2 = 2^8 – 2 = 256 – 2 = 254$ From this analysis, the subnet mask of 255.255.255.192 allows for 62 usable addresses, which is sufficient for the current requirement of 50 devices. Additionally, it allows for future growth, as it can accommodate up to 62 devices. The subnet mask of 255.255.255.128 also provides ample addresses but is less efficient for the current need. The 255.255.255.224 mask is inadequate as it only supports 30 usable addresses, which is insufficient for the requirement. The default mask of 255.255.255.0 is excessive for the current need but does allow for the maximum number of devices. Thus, the most appropriate choice for the technician is 255.255.255.192, as it balances current needs with future expansion potential effectively.

Checking the user’s internet connection, while important in some contexts, is less relevant in this scenario unless the applications are specifically dependent on network connectivity for their functionality. Reinstalling the macOS operating system is a more drastic measure that should be considered only after other troubleshooting steps have been exhausted, as it can lead to data loss and requires significant time and effort. Lastly, updating applications without verifying compatibility can lead to further issues, especially if the new versions are not designed to work with the current macOS version or other installed software. Thus, the most effective approach is to start with a thorough examination of the Console application to gather insights that will guide further troubleshooting steps. This methodical approach not only helps in identifying the immediate cause of the crashes but also aids in preventing future occurrences by addressing the root issues identified in the logs.

To troubleshoot this effectively, the first step is to check the battery health status by accessing the System Information utility. This can be done by holding the Option key and clicking on the Apple menu, then selecting “System Information.” Under the “Power” section, you can view the battery condition. If it indicates “Service Battery,” it confirms that the battery is faulty and needs replacement. Additionally, it is important to consider other factors that could contribute to the charging issue. For instance, if the MacBook is running macOS High Sierra or later, the system may prevent charging if it detects that the battery is not functioning optimally to preserve the overall health of the device. However, since the power adapter is confirmed to be working with another MacBook, the likelihood of a damaged power port or an incompatible adapter is low. Reinstalling the operating system is generally not a solution for hardware-related issues like battery failure. Therefore, the most logical course of action is to replace the battery if the diagnostics confirm it is faulty. This approach not only addresses the immediate issue but also ensures the longevity and reliability of the MacBook in the long run.

If they hire one temporary worker, they can distribute the labor as follows: each of the three employees can work 40 hours, totaling 120 hours, while the temporary worker can also contribute additional hours if needed. This option allows them to meet the labor requirement without exceeding the budget, as the total cost for raw materials (50 units at $150 each) is $7,500, leaving $2,500 for labor costs. On the other hand, relying solely on existing employees (option b) would not allow for any flexibility in case of unforeseen delays or issues, and would not utilize the potential efficiency gained from hiring additional help. Hiring two temporary workers (option c) would significantly increase costs, as they would incur $1,000 per week in labor costs, which could exceed the budget if not managed properly. Finally, allocating all labor hours from existing employees and purchasing all raw materials upfront (option d) could lead to cash flow issues and does not consider the potential need for flexibility in labor allocation. Thus, the best approach is to hire one temporary worker and allocate 40 hours of labor from each employee, ensuring that the project is completed efficiently and within budget. This strategy balances the need for adequate labor while minimizing costs and maximizing resource utilization.

The User Interface, while crucial for user interaction, operates at a higher level and relies on the services provided by the Kernel. It does not manage hardware resources directly but instead presents a graphical environment for users to interact with applications. The Application Framework, which includes libraries and APIs for developers, also sits above the Kernel and depends on it for resource management and system calls. System Utilities, such as Disk Utility or Activity Monitor, provide tools for users to manage their system but do not play a direct role in the underlying architecture responsible for resource management. They are built on top of the Application Framework and utilize the services provided by the Kernel. Understanding this layered architecture is essential for troubleshooting performance issues. If the Kernel is not functioning optimally, it can lead to significant performance degradation across the entire system. Therefore, recognizing the role of the Kernel in managing hardware resources is critical for diagnosing and resolving performance-related problems in OS X v10.8.

To mitigate this risk, implementing a Key Management System (KMS) is essential. A KMS allows for the secure generation, storage, and management of encryption keys, often separating them from the data they protect. This separation ensures that even if the data is compromised, the keys remain secure, thereby protecting the confidentiality of the sensitive information. Moreover, the absence of a key rotation policy further exacerbates the risk. Regularly rotating encryption keys limits the amount of data that can be decrypted if a key is compromised. Best practices in data security recommend that keys be rotated periodically and that old keys be securely retired to minimize the risk of unauthorized access. In contrast, the other options present misconceptions. AES-256 is widely regarded as a secure encryption standard, and switching to a less complex algorithm would not enhance security. Additionally, the belief that storing keys on the same server is acceptable if the server is secure overlooks the fundamental principle of minimizing risk through separation of duties and assets. Lastly, the assertion that key rotation is irrelevant contradicts established security practices that emphasize the importance of managing cryptographic keys effectively.

On the other hand, simply replacing the router without first investigating its configuration would be premature and could lead to unnecessary costs and downtime. Restarting network devices might temporarily resolve some issues, but it does not address the root cause if the configuration is indeed the problem. Checking the internet service provider’s status is also important, but it should come after confirming that the local network equipment is functioning correctly. Thus, the most effective approach is to analyze the router’s settings and logs to isolate and resolve the issue efficiently. This method aligns with best practices in troubleshooting, emphasizing the importance of a systematic and thorough investigation before taking further action.

To improve performance, reformatting the external drive to a more modern file system such as APFS (Apple File System) or exFAT is advisable. APFS is optimized for SSDs and provides better performance for macOS, while exFAT is compatible with both macOS and Windows, allowing for larger file sizes and reducing fragmentation issues. This change would not only enhance transfer speeds but also eliminate the file size limitations associated with FAT32. While the other options present plausible scenarios, they do not address the core issue as effectively. For instance, while upgrading to USB 3.0 could improve speeds if the current connection is USB 2.0, the fundamental problem lies in the file system’s limitations. Similarly, updating the operating system or deleting files may provide some benefits, but they do not directly resolve the inefficiencies caused by the FAT32 format. Thus, reformatting the drive is the most comprehensive solution to enhance performance and facilitate smoother file transfers.

The kernel’s ability to manage memory dynamically is crucial, especially in environments where multiple applications are running simultaneously. By swapping out less frequently accessed data, the kernel can maintain a balance between available memory and application performance. This mechanism is essential for preventing performance degradation due to memory exhaustion. In contrast, the other options present misconceptions about the kernel’s role. For instance, while the kernel does manage memory allocation, it does not impose strict limits on individual applications to ensure uniform performance. Instead, it allows applications to utilize memory as needed, within the constraints of the overall system resources. Additionally, the kernel does not directly manage CPU cache memory; this is typically handled by the CPU itself. Lastly, while the kernel can terminate processes under certain conditions (such as when an application becomes unresponsive), it does not automatically terminate applications based solely on memory usage thresholds. Understanding these nuances is vital for troubleshooting performance issues in OS X and effectively utilizing the system’s architecture.

However, addressing the immediate issue is only part of the solution. Long-term strategies are crucial for maintaining optimal performance. Reviewing startup items and background applications is vital, as many applications automatically launch at startup, consuming resources unnecessarily. By managing these items, users can significantly reduce the load on their system during boot-up and regular operation. Additionally, running Disk Utility to verify and repair disk permissions is a recommended maintenance task in OS X. Disk permissions can become corrupted over time, leading to performance issues. Regularly performing this maintenance can help ensure that the system runs smoothly. In contrast, simply restarting the computer may provide a temporary fix but does not address the root cause of the performance issues. Uninstalling applications without understanding their impact can lead to unnecessary loss of functionality. Lastly, while hardware upgrades can improve performance, they should be considered after software optimizations have been explored, as many performance issues can be resolved through proper system management and maintenance practices.

Replacing the Wi-Fi card without first diagnosing the issue is not advisable, as it may not address the underlying problem and could lead to unnecessary costs. Similarly, simply restarting the router and asking the user if the problem persists does not provide a comprehensive understanding of the issue, as it ignores potential factors such as software conflicts, interference from other devices, or issues with the network configuration itself. Lastly, checking for physical obstructions is important, but it should not be the sole focus without considering other potential causes. By prioritizing a detailed examination of network settings and configurations, the technician can gather critical information that may reveal the source of the connectivity issues, allowing for a more targeted and effective resolution. This methodical approach aligns with best practices in troubleshooting, ensuring that all relevant factors are considered before jumping to conclusions or making changes.

In contrast, the RPM rating is not applicable to SSDs, as they have no moving parts and therefore do not operate on rotational speed principles. Formatting the SSD with the HFS+ file system is necessary for macOS compatibility, but it is not the most critical factor for performance; the drive can be formatted after installation. Lastly, the physical size of the SSD must be compatible with the drive bay, but most SSDs designed for laptops are 2.5 inches, which is standard for MacBook Pro models. Thus, while all options present considerations for the upgrade, the interface compatibility is paramount for ensuring optimal performance and functionality of the new SSD in the MacBook Pro.

Once the DNS settings are verified, the next logical steps would include checking firewall settings to ensure that the necessary ports for file sharing (such as SMB or AFP) are open, and then potentially restarting the network interface to refresh the connection. Examining system logs can provide insights into any underlying issues, but it is generally more effective to start with the basic connectivity checks, such as DNS resolution, before delving into logs. Understanding the role of DNS in network connectivity is crucial. DNS (Domain Name System) translates human-readable domain names into IP addresses that computers use to identify each other on the network. If the DNS is misconfigured, it can lead to significant connectivity issues, making it a primary focus in troubleshooting scenarios. Therefore, ensuring that the DNS settings are correct is a foundational step in resolving network-related problems.

While reviewing DHCP settings is important, it primarily ensures that clients receive the correct IP configuration, including the default gateway. If the router’s subinterfaces are misconfigured, even a correctly set DHCP server will not resolve the issue. Similarly, analyzing the switch’s MAC address table can provide insights into whether devices are communicating correctly within their VLANs, but it does not directly address the routing aspect. Lastly, inspecting physical connections is crucial for overall network health, but if the router’s configuration is incorrect, physical connectivity will not resolve the routing problem. Thus, the most effective step for the administrator to take in this situation is to check the router’s interface configurations, as this directly impacts the ability of the router to route traffic between VLANs and to the internet. Understanding the relationship between VLANs and inter-VLAN routing is essential for effective network troubleshooting, as misconfigurations at the router level can lead to widespread connectivity issues across multiple VLANs.

Verifying the integrity of the installation media is equally important. This step involves checking that the OS X installer is not corrupted and is compatible with the hardware. A corrupted installer can lead to installation failures or further system issues, which would negate the purpose of the reinstallation. Formatting the hard drive before backing up data is a risky approach. It could lead to irreversible data loss if the backup process is not completed successfully. Therefore, this option is not advisable. Additionally, downloading the OS X installer from unofficial sources poses significant risks, including malware infections and compatibility issues, which can severely compromise the system’s integrity. While disconnecting peripherals can help avoid conflicts during installation, it is a secondary concern compared to ensuring that data is backed up and the installation media is verified. In summary, the technician should prioritize creating a complete backup and verifying the installation media to ensure a successful and safe reinstallation of OS X.

In contrast, a hardware failure in the hard drive would typically manifest as system crashes, data loss, or unusual noises from the drive, rather than the specific symptoms of pop-ups and homepage changes. An outdated operating system could lead to security vulnerabilities, but it would not directly cause the symptoms described. Lastly, a corrupted user profile might result in issues with user settings or application behavior, but it would not typically lead to the specific symptoms of adware infection. Understanding the nature of malware and its symptoms is crucial for effective troubleshooting. Adware often installs itself alongside legitimate software, making it essential for users to be cautious during installations and to regularly scan their systems for malware. Tools like antivirus software and malware removal utilities can help identify and eliminate such threats, restoring the system to normal operation. Recognizing these symptoms early can prevent further complications and ensure a smoother computing experience.

Attempting to repair the disk without backing up poses a significant risk, as any repair operation could potentially lead to further data loss. Reinstalling macOS without addressing the disk errors is also ill-advised, as it does not resolve the underlying issues with the disk and could lead to a corrupted installation. Formatting the disk to erase all data before repairs is an extreme measure that should only be considered as a last resort, especially when data recovery is a priority. In summary, the technician’s best practice is to prioritize data integrity by backing up the data before proceeding with any repair attempts. This approach aligns with standard troubleshooting protocols and ensures that the technician can recover the data if the repair process does not go as planned.

Changing the Wi-Fi channel on the router (option b) can help if there is interference from other networks, but since the issue is isolated to the MacBook, this step may not address the root cause. Updating macOS (option c) is generally a good practice for ensuring compatibility and security, but it may not directly resolve the current connectivity issue if the underlying configuration is flawed. Disabling Bluetooth (option d) is unlikely to have a significant impact on Wi-Fi performance, as both technologies operate on different frequencies, although they can occasionally interfere in crowded environments. By focusing on resetting the network preferences first, you can eliminate potential configuration issues before exploring other avenues, making it a more efficient and targeted approach to troubleshooting the problem.

When troubleshooting power issues, it is essential to consider the power management system of the MacBook. This system regulates how power is distributed and can sometimes misinterpret battery health, especially if the battery is failing. If the battery is unable to accept a charge due to internal faults, the MacBook will not charge regardless of the power adapter used. While the other options present plausible scenarios, they are less likely in this context. The power adapter being incompatible is unlikely since the user has already tested a different adapter with the same specifications. The intermittent failure of the power outlet is also less probable, given that it was confirmed to be functional initially. Lastly, while software updates can affect hardware recognition, it is less common for an operating system update to resolve a hardware failure related to the battery. Therefore, the most logical conclusion is that the battery is the root cause of the charging issue.

Updating the operating system, while beneficial for overall system performance and security, may not directly address the immediate issue of the printer not functioning correctly. It is possible that the printer’s drivers are already compatible with the current OS version, and thus this step may not yield any immediate results. Replacing the USB cable could be a valid troubleshooting step if there is evidence of physical damage or wear, but it is not the first action to take when the connection and settings can be quickly verified. Resetting the NVRAM (non-volatile random-access memory) can resolve certain hardware-related issues, but it is a more drastic measure that should be considered only after simpler troubleshooting steps have been exhausted. In summary, the most logical and effective initial troubleshooting step is to check the printer’s connection and ensure that the correct printer is selected in the print dialog, as this directly addresses the potential causes of the printing issue.

For instance, the command `defaults write com.apple.dock ResetLaunchPad -bool true; killall Dock` can be used to reset the Launchpad layout. This command instructs the system to reset the Launchpad database and restart the Dock, which is responsible for displaying the Launchpad interface. Reinstalling macOS, while it may restore system files, is a more drastic measure that can lead to data loss and is not necessary if the issue can be resolved through simpler means. Clearing system cache files may improve overall performance but does not directly address the Launchpad issue. Disabling third-party applications could help identify conflicts, but it is a time-consuming process and may not be necessary if the database can be rebuilt quickly. Thus, rebuilding the Launchpad database is the most targeted and efficient approach to resolving the issue, ensuring that the application index is accurate and up-to-date, which is crucial for Launchpad’s functionality.

By allowing only HTTP and HTTPS traffic for web browsing, SSH access for remote management, and blocking all other inbound connections, the administrator can effectively control the flow of data into the network. This approach aligns with the principle of least privilege, which states that users and systems should only have the minimum level of access necessary to perform their functions. In contrast, a blacklist policy (option b) allows all traffic except for known malicious services, which can be risky as it relies on the firewall’s ability to identify and block threats. This method may inadvertently allow new or unknown threats to pass through, as they are not included in the blacklist. Option c, which suggests allowing all outbound traffic while restricting inbound traffic based on IP addresses, does not provide sufficient control over what services can be accessed from outside the network. This could lead to vulnerabilities if an attacker finds a way to exploit allowed outbound connections. Lastly, option d, which proposes allowing all traffic and then manually disabling access for unwanted services, is highly inefficient and poses significant security risks. This method could lead to accidental exposure of sensitive services and is not a sustainable long-term strategy. In summary, a whitelist policy is the most secure and effective method for managing firewall settings in this scenario, ensuring that only necessary services are accessible while maintaining a robust defense against unauthorized access.

Using the recovery key is compliant with security protocols, as it ensures that only authorized personnel can access the encrypted data. This method maintains the integrity of the encryption while allowing the employee to regain access to their files. In contrast, instructing the employee to guess their password could lead to account lockout, which complicates the recovery process and may require additional administrative overhead. Reinstalling the operating system would result in data loss, as the encrypted data would remain inaccessible without the password or recovery key. Creating a new user account would not solve the issue of accessing the existing encrypted data, as the new account would not have the necessary permissions to access files stored on the encrypted disk. Thus, the correct approach balances security and usability, ensuring that the employee can access their data while adhering to the company’s data protection policies. This scenario highlights the importance of having a recovery key and understanding the procedures for managing encrypted disks in a corporate environment.

On the other hand, asymmetric encryption, such as RSA, utilizes a pair of keys (public and private) for encryption and decryption. This method enhances security by allowing users to share their public keys openly while keeping their private keys confidential. However, the algorithms used in asymmetric encryption are computationally more intensive, resulting in slower performance, especially when encrypting large datasets. The implications of this transition are significant. While asymmetric encryption can provide a higher level of security, particularly in key exchange and digital signatures, it is generally slower than symmetric encryption. This means that for applications requiring high throughput and low latency, symmetric encryption may still be preferred for bulk data encryption, while asymmetric encryption can be used for secure key exchange and authentication processes. Moreover, the transition does not eliminate the need for key management; rather, it changes the nature of key management. Asymmetric encryption introduces the concept of public key infrastructure (PKI), which requires careful management of public and private keys, including their generation, distribution, and revocation. In summary, while asymmetric encryption offers enhanced security features, it is slower than symmetric encryption and does not negate the necessity for robust key management practices. Understanding these nuances is crucial for making informed decisions about encryption strategies in a corporate environment.

– 20 GB of temporary files – 15 GB of old applications – 10 GB of cached data Adding these amounts together gives: $$ 20 \, \text{GB} + 15 \, \text{GB} + 10 \, \text{GB} = 45 \, \text{GB} $$ The administrator’s goal is to free up at least 50 GB of space. To find out how much more space needs to be cleared, we subtract the amount already freed from the target amount: $$ 50 \, \text{GB} – 45 \, \text{GB} = 5 \, \text{GB} $$ Thus, the administrator must clear an additional 5 GB to meet their goal of freeing up 50 GB of disk space. This scenario emphasizes the importance of systematic disk cleanup and optimization strategies in maintaining system performance. It also highlights the need for administrators to track the amount of space being utilized and the effectiveness of their cleanup efforts. Understanding how to calculate the remaining space needed after partial cleanup is crucial for effective disk management. This knowledge not only aids in immediate troubleshooting but also contributes to long-term system health by preventing disk space from becoming a bottleneck for performance.