or the compound:

carbon in the middle with 3 bonds
-double bond to oxygen
-bond to Mn(CO)5
-bond to CH3 group

is the oxidation state of the metal +1?
d count 6?
total electron count 20?
coordination number 7?

To determine the oxidation state of the metal in the compound you described, we need to calculate the formal charges on each atom and determine the overall charge of the compound.

First, let's assign oxidation states to each atom based on common rules:

- The oxidation state of carbon in an organic compound is usually -4, but since it has double bonds to both oxygen and manganese (Mn), it will have a lower oxidation state.
- The oxidation state of oxygen in most compounds is -2.
- The oxidation state of hydrogen (H) is +1.
- The oxidation state of Mn is usually +2 or +3.

Now let's count the formal charges on each atom:

1. Carbon (C): Since it has three bonds in this compound, it will have a +1 formal charge [(6 valence electrons) - (3 bonds + 1 non-bonded electron)].
2. Oxygen (O): Since it has a double bond and no formal charge, it will have a -1 formal charge [(6 valence electrons) - (2 bonds + 4 non-bonded electrons)].
3. Mn(CO)5: The Mn atom will have a formal charge of +1 [(7 valence electrons) - (3 bonds + 4 non-bonded electrons)].
4. CH3: The carbon atom in the CH3 group will have a neutral formal charge since it has four bonds and no non-bonded electrons.

Based on the above calculations, we can see that the overall charge of the compound is 0 since all the formal charges cancel out. Therefore, the oxidation state of the Mn atom is +1 in this compound.

Now let's move on to assessing the d count, total electron count, and coordination number:

1. d count: The d count corresponds to the number of d electrons in the central metal atom/ion. Since Mn is in the +1 oxidation state, it loses one electron from its d orbital. Therefore, the d count for Mn in this compound is 5.

2. Total electron count: To calculate the total electron count (TEC), we sum up the valence electrons of each atom in the compound.
- Carbon (C): 4 valence electrons (VE)
- Oxygen (O): 6 VE
- Mn: 7 VE
- Hydrogen (H): 1 VE
- Total = 4(1) + 6(1) + 7(1) + 1(3) = 20 electrons

3. Coordination number: The coordination number (CN) is the number of bonds formed by the central metal atom/ion. In this compound, the Mn atom is bonded to one carbon atom, one oxygen atom, and one CH3 group. So the CN is 3.

To summarize:
- The oxidation state of the metal (Mn) in this compound is +1.
- The d count is 5.
- The total electron count is 20.
- The coordination number is 3.