A static entry is the best option to restore communication for the new machine in a small branch office that does not have a DHCP server. A static entry means manually configuring the IP address, subnet mask, default gateway, and DNS server for the network adapter of the machine. A static entry ensures that the machine has a valid and unique IP address that matches the network configuration and can communicate with the rest of the network.
The new machine automatically receives the IP address of 169.254.0.2 because it uses APIPA (Automatic Private IP Addressing), which is a feature that enables computers to self-assign an IP address when a DHCP server is not available. However, APIPA only works for local communication within the same subnet, and does not provide a default gateway or a DNS server. Therefore, the new machine is unable to communicate with the rest of the network, which may be on a different subnet or require a gateway or a DNS server to access.
The other options are not related to restoring communication for the new machine. ARP table is a cache that stores the mapping between IP addresses and MAC addresses for the devices on the network. NTP specification is a protocol that synchronizes the clocks of the devices on the network.
[References:, CompTIA A+ Certification Exam Core 2 Objectives1, CompTIA A+ Core 2 (220-1102) Certification Study Guide2, What is APIPA (Automatic Private IP Addressing)? - Study-CCNA3, How to Configure a Static IP Address in Windows and OS X4, , , , ]
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