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Based on the chart below, if a patient can receive only blood types [tex]$O -, O +, B -$[/tex], and [tex]$B +$[/tex], which blood type does she have?

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline \multirow{2}{*}{\begin{tabular}{l} \end{tabular}} & \multicolumn{9}{|c|}{ Donor's Blood Type } \\
\hline & & [tex]$O -$[/tex] & [tex]$O +$[/tex] & [tex]$B -$[/tex] & [tex]$B +$[/tex] & [tex]$A-$[/tex] & [tex]$A+$[/tex] & [tex]$AB -$[/tex] & [tex]$AB +$[/tex] \\
\hline & [tex]$AB +$[/tex] & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] \\
\hline & [tex]$AB -$[/tex] & [tex]$\checkmark$[/tex] & & [tex]$\checkmark$[/tex] & & [tex]$\checkmark$[/tex] & & [tex]$\checkmark$[/tex] & \\
\hline & [tex]$A +$[/tex] & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] & & & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] & & \\
\hline & [tex]$A-$[/tex] & [tex]$\checkmark$[/tex] & & & & [tex]$\checkmark$[/tex] & & & \\
\hline & [tex]$B +$[/tex] & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] & & & & \\
\hline & [tex]$B -$[/tex] & [tex]$\checkmark$[/tex] & & [tex]$\checkmark$[/tex] & & & & & \\
\hline & [tex]$O +$[/tex] & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] & & & & & & \\
\hline & [tex]$O -$[/tex] & [tex]$\checkmark$[/tex] & & & & & & & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
In order to determine the patient's blood type based on the information given about which blood types they can receive, we need to identify the blood type that can accept donations from [tex]$O-, O+, B-$[/tex], and [tex]$B+$[/tex].

Let's analyze the chart row by row:

1. [tex]$AB+$[/tex]:
- Can receive [tex]$O-$[/tex], [tex]$O+$[/tex], [tex]$B-$[/tex], [tex]$B+$[/tex], [tex]$A-$[/tex], [tex]$A+$[/tex], [tex]$AB-$[/tex], [tex]$AB+$[/tex].
- This includes all types the patient can receive but also more, so the patient is probably not [tex]$AB+$[/tex].

2. [tex]$AB-$[/tex]:
- Can receive [tex]$O-$[/tex], [tex]$B-$[/tex], [tex]$A-$[/tex], [tex]$AB-$[/tex].
- This excludes [tex]$O+$[/tex] and [tex]$B+$[/tex], which the patient can receive, so the patient cannot be [tex]$AB-$[/tex].

3. [tex]$A+$[/tex]:
- Can receive [tex]$O-$[/tex], [tex]$O+$[/tex], [tex]$A-$[/tex], [tex]$A+$[/tex].
- This does not include [tex]$B-$[/tex] or [tex]$B+$[/tex], which the patient can receive, so the patient cannot be [tex]$A+$[/tex].

4. [tex]$A-$[/tex]:
- Can receive [tex]$O-$[/tex], [tex]$A-$[/tex].
- This does not include [tex]$O+$[/tex], [tex]$B-$[/tex], or [tex]$B+$[/tex], so the patient cannot be [tex]$A-$[/tex].

5. [tex]$B+$[/tex]:
- Can receive [tex]$O-$[/tex], [tex]$O+$[/tex], [tex]$B-$[/tex], [tex]$B+$[/tex].
- This matches exactly with the types the patient can receive.

6. [tex]$B-$[/tex]:
- Can receive [tex]$O-$[/tex], [tex]$B-$[/tex].
- This does not include [tex]$O+$[/tex] or [tex]$B+$[/tex], so the patient cannot be [tex]$B-$[/tex].

7. [tex]$O+$[/tex]:
- Can receive [tex]$O-$[/tex], [tex]$O+$[/tex].
- This does not include [tex]$B-$[/tex] or [tex]$B+$[/tex], so the patient cannot be [tex]$O+$[/tex].

8. [tex]$O-$[/tex]:
- Can receive only [tex]$O-$[/tex].
- This does not include [tex]$O+$[/tex], [tex]$B-$[/tex], or [tex]$B+$[/tex], so the patient cannot be [tex]$O-$[/tex].

Thus, the patient's blood type must be [tex]$B+$[/tex], as it is the only type that can receive from [tex]$O-, O+, B-, B+$[/tex] and does not require any other donations.

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