
    Raul CARRILLO, Petitioner-Appellant, v. SECRETARY, FLORIDA DEPARTMENT OF CORRECTIONS, Respondent-Appellee.
    No. 10-14732
    Non-Argument Calendar.
    United States Court of Appeals, Eleventh Circuit.
    April 25, 2012.
    
      Erica J. Hashimoto, University of Georgia School of Law, Athens, GA, for Petitioner-Appellant.
    Raul Carrillo, Miami, FL, pro se.
    Linda S. Katz, Pam Bondi, Michael C. Greenberg, Richard L. Polin, Office of the Attorney General, Miami, FL, for Respondent-Appellee.
    Before EDMONDSON, MARTIN, and ANDERSON, Circuit Judges.
   PER CURIAM:

Raul Carrillo, a Florida prisoner proceeding with the assistance of appointed counsel, appeals the district court’s dismissal of his pro se 28 U.S.C. § 2254 habe-as corpus petition challenging his convictions and life sentence for first-degree murder and aggravated stalking with a firearm. No reversible error has been shown; we affirm.

As an initial matter — because the timely filing of a notice of appeal is a mandatory prerequisite for the exercise of appellate jurisdiction — we must address whether Carrillo’s notice of appeal was timely filed. See Rinaldo v. Corbett, 256 F.3d 1276, 1278 (11th Cir.2001). Carrillo was required to file a notice of appeal “within 30 days after the judgment or order appealed from [was] entered.” See Fed.R.App.P. 4(a)(1)(A). Although the district court entered an order denying Carrillo’s petition on 23 July 2010, it failed to set forth its judgment in a separate document, as required by Fed.R.Civ.P. 58(a). See Jackson v. Crosby, 375 F.3d 1291, 1293 n. 5 (11th Cir.2004) (noting that Rule 58(a)(1) requires a district court to set out its judgment in a separate document when denying a petition for habeas corpus). As a result, the court’s judgment was not deemed “entered” for purposes of Rule 4(a) until 150 days later — on 20 December 2010. See Fed.R.App. P. 4(a)(7)(A)(ii). Because Carrillo’s notice of appeal was filed before the judgment was entered, we treat it as having been filed on the date of entry. See Fed.R.App.P. 4(a)(2). Thus, Carrillo’s notice of appeal was timely and we have jurisdiction to consider his appeal.

In his section 2254 petition, Carrillo argued that the trial court erred in denying his Batson challenge to the government’s use of a peremptory strike against a male venire member, Paul Soule. In response to Carrillo’s Batson challenge, the trial court stated that males were not a suspect class requiring a Batson-type inquiry. Despite this error, the prosecutor set forth neutral explanations for the strike, stating that Soule had asked why the state was not seeking the death penalty and had expressed doubt about the credibility of witnesses who were convicted felons. After some discussion about Soule’s responses, the trial court granted the strike over Carrillo’s objection.

On direct appeal, the state appellate court affirmed Carrillo’s conviction. In doing so, it concluded that — “[bjecause the trial court heard the state’s gender-neutral explanation, allowed defense counsel to argue its position, and then granted the peremptory strike” — the court “implicitly underwent a genuineness inquiry.”' The court also determined that the strike was proper because the state’s gender-neutral reasons were supported by the record.

Carrillo raised his Batson claim again in his section 2254 petition, and the district court denied it. But the court granted Carrillo a certificate of appealability on “whether the state appellate court unreasonably applied federal law in (1) its determination that the trial court implicitly performed the third step under Batson ... and (2) its determination that no violation of Batson and its progeny occurred, in affirming Petitioner’s conviction.”

To obtain habeas relief, Carrillo must demonstrate that the state appellate court’s ruling was (1) “contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court,” or (2) “based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” 28 U.S.C. § 2254(d)(1), (2). A state court’s decision is “contrary to” federal law if “the state court arrives at a conclusion opposite to that reached by [the Supreme Court] on a question of law or if the state court decides a case differently than th[e] Court has on a set of materially indistinguishable facts.” Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 1523, 146 L.Ed.2d 389 (2000). We may not grant habeas relief based solely on our conclusion that the state court “applied clearly established federal law erroneously or incorrectly.” Id. at 1522. Instead, the state court’s application of federal law “must also be unreasonable.” Id. We review de novo the district court’s decision about whether the state court’s ruling was contrary to federal law, involved an unreasonable application of federal law, or was based on an unreasonable determination of the facts. Smith v. Sec’y, Dep’t of Corr., 572 F.3d 1327, 1332 (11th Cir.2009).

Batson requires courts to use a three-part test to analyze equal protection challenges to the prosecutor’s use of peremptory challenges. Batson, 106 S.Ct. at 1723-24. First, the defendant must make a prima facie showing of purposeful discrimination based on a prohibited ground. Id. at 1723. The burden then shifts to the prosecutor to articulate a neutral explanation for the challenge. Id. Third, the trial court has the duty to determine whether the defendant has established purposeful discrimination. Id. at 1724. At this stage, “the defendant bears the burden of convincing the ... court that the proffered reasons are pretextual by introducing evidence of comparability.” Atwater v. Crosby, 451 F.3d 799, 807 (11th Cir.2006). “[T]he ultimate burden of persuasion regarding [discriminatory] motivation rests with, and never shifts from, the opponent of the strike.” Id. at 806.

Based on our review of the record, we cannot conclude that the state appellate court applied Batson unreasonably in this case. That the trial court erred in stating that men were not a protected class is undisputed. But that alone is not enough to warrant relief. See Williams, 120 S.Ct. at 1522. Moreover, the exchange between the court and the parties did not end there. Instead, the prosecutor proffered that she struck Soule based on his questions about the death penalty and his response about the credibility of convicted felons. Although brief, the trial court and the parties engaged in some discussion of the substance of Soule’s voir dire responses during which defense counsel attempted to rebut the prosecutor’s proffered reasons. After considering the parties’ arguments, the trial court granted the strike. We conclude that the trial court indeed touched on the third step of Batson and, thus, that the state appellate court’s application of Batson was reasonable. See Atwater, 451 F.3d at 807 (concluding that the trial court’s application of Batson was reasonable where the trial court “touched” on Batson’s third step by agreeing with the prosecutor’s characterization of a juror’s voir dire response).

We also are unconvinced that the state appellate court erred in concluding that the prosecutor’s peremptory strike was not the product of intentional discrimination. “The evaluation of a prosecutor’s [gender]-neutral explanations under Bat-son is a ‘pure issue of fact ... peculiarly within a trial judge’s province.’ ” McGahee v. Ala. Dep’t of Corr., 560 F.3d 1252, 1255 (11th Cir.2009). Thus, we will grant habe-as relief on a Batson claim only “if it was unreasonable to credit the prosecutor’s [genderj-neutral explanations.” Id. at 1256. Soule was the only juror to question the trial court about the death penalty and it was not unreasonable for the trial court to credit the prosecutor’s concern about a juror’s focus on the death penalty in a non-capital case. Carrillo also failed to compare Soule’s responses to the responses of other venire members and, thus, failed to satisfy his burden of demonstrating that the prosecutor’s proffered reasons were pretextual. See Atwater, 451 F.3d at 807.

AFFIRMED. 
      
      . Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986).
     
      
      . On appeal, the state argues that Carrillo’s section 2254 petition should be dismissed for failure to exhaust his state administrative remedies. In the district court, however, the state represented that Carrillo had "exhausted all of his claims in state court.” Because we conclude that the state explicitly waived its exhaustion defense in the district court, we will not consider this defense on appeal. See Dorsey v. Chapman, 262 F.3d 1181, 1186-87 (11th Cir.2001) (determining that the state waived its exhaustion defense when it expressly declined to raise it in its answer to a habeas petition).
     
      
      . Although the trial court did not address Batson itself, it referred to a Neil/Slappy Melbourne inquiry, which is Florida’s equivalent of an inquiry under Batson. See Melbourne v. State, 679 So.2d 759 (Fla.1996); State v. Slappy, 522 So.2d 18 (Fla.1988); State v. Neil, 457 So.2d 481 (Fla.1984).
     
      
      . When Carrillo’s case was tried in 2005, it was well-established that "the Equal Protection Clause prohibits discrimination in jury selection on the basis of gender.” See J.E.B. v. Ala. ex rel. T.B., 511 U.S. 127, 114 S.Ct. 1419, 1430, 128 L.Ed.2d 89 (1994).
     