Our circuit is familiar with appeals from convicted gang members of the Almighty Latin Kings Nation.1 This appeal is a consolidation of four cases of former Latin Kings gang members who were indicted, prosecuted, and sentenced in the Northern District of Indiana. The indictment included twenty-three defendants: one defendant went to trial, twenty-one pleaded guilty, and one was never apprehended. The group was part of a major drug trafficking ring and linked to nineteen homicides. After the twenty-two convictions, four defendants filed appeals.
I. BACKGROUND
A. Martin Anaya
Martin Anaya was the defendant who took his case to trial. He was charged with one count of conspiracy to participate in racketeering, one count of conspiracy to distribute a controlled substance, and two counts associated with the murder of Christina Campos, a member of the rival Latin Counts gang. Anaya faced a sentence of death or life imprisonment. See 18 U.S.C. §§ 924(c), 924(j).
It is undisputed that Anaya and three other Latin Kings (Brandon Clay, Jason Ortiz, and a juvenile nicknamed “DK”) were driving in Anaya’s van in the territory of their rival, the Latin Counts gang, after midnight on April 22, 2009. They saw three Latin Counts gang members on foot and picked a fight. The fight lasted from a few seconds to a couple minutes, at most, leaving Campos dead from a gunshot wound. The medical examiner concluded that Campos died of a gunshot
There were many versions of how Campos died that night. The three Latin Kings present with Anaya did not testify at trial but made several conflicting statements during the investigation. The three ultimately concluded that none of the Latin Kings were responsible for shooting Campos and suggested that someone from the Latin Counts, Campos’ own gang, acci-dently shot her. Other Latin Kings not present at the shooting testified at trial: they stated that the Latin Kings were not responsible for Campos’ murder. Isaac Wilhelm, one of the Latin Counts walking with Campos, identified Anaya in court as one of the people in the van, but Wilhelm ran before shots were fired and could not identify the shooter.
Mary Gonzalez, a nearby resident, also testified. She said that she was on her way out to walk her dog when she heard gunfire. She testified that she saw a man get out of the passenger side of the van, walk between two cars (the location where Campos was later found dead), lean over, fire a gun at the ground a couple times, and get back in the van before it drove away. She identified Anaya as the shooter in a live line-up at the police station three weeks later, but she was not asked to identify Anaya as the shooter during the trial.
*737The jury returned a verdict convicting Anaya of conspiring to participate in racketeering, a violation of 18 U.S.C. § 1962(d), and conspiring to distribute illicit drugs, a violation of 21 U.S.C. §§ 841(b)(1)(A), 846. The jury found Anaya not guilty of Campos’ murder.
The jury answered special interrogatories about Anaya’s racketeering conspiracy conviction; it found that the charge was not associated with Campos’ murder, the distribution of more than five kilograms of cocaine, nor the distribution of 1,000 kilograms or more of marijuana. The jury did find, however, that Anaya’s conviction for conspiring to traffic narcotics involved more than five kilograms of cocaine and 1,000 kilograms or more of marijuana. The district court sentenced Anaya to 360 months’ imprisonment for each count, to be served concurrently.
B.Oscar Gonzalez
Oscar Gonzalez was charged with one count of conspiracy to participate in racketeering and one count of conspiracy to distribute a controlled substance. The crime underlying the racketeering charge involved an incident in May 2008, when Gonzalez, accompanied by several Latin Kings gang members, fired guns into a tavern in East Chicago, Indiana, killing one person. In exchange for concessions from the government, Gonzalez agreed to plead guilty to both counts and expressly waived his right to appeal his conviction and sentence on any ground except a claim of “ineffective assistance of counsel relate^] directly to th[e] waiver or its negotiation.” The district court reviewed the plea agreement with Gonzalez, advised him of the rights he was giving up, and reinforced the permanence of that decision. The district court found that Gonzalez knowingly and voluntarily entered his plea of guilty, accepted the plea, and imposed a sentence of 240 months’ imprisonment.
C. Sisto Bernal
Sisto Bernal’s legal proceeding was similar to that of Gonzalez. Bernal was charged with one count of interfering with commerce by threats or violence, one count of conspiracy to participate in racketeering, and one count of conspiracy to distribute a controlled substance. In exchange for concessions from the government, Bernal agreed to plead guilty to both counts and expressly waived his right to appeal his conviction and sentence. The waiver signed by Bernal is verbatim to that signed by Gonzalez. A magistrate judge reviewed the plea agreement with Bernal, advised him of the rights he was giving up, found that he knowingly and voluntarily entered his guilty plea, and recommended that the district court accept the plea. The district court accepted the recommendation and imposed a sentence of 288 months’ imprisonment.
D. Dante Reyes
Again, Dante Reyes’ proceeding was just like his codefendants. He was charged with one count of conspiracy to participate in racketeering and one count of conspiracy to distribute a controlled substance. In exchange for concessions from the government, Reyes agreed to plead guilty to the one count of conspiracy to distribute illicit drugs and expressly waived his right to appeal his conviction and sentence. Reyes signed the same waiver as Gonzalez and Bernal. The district court reviewed the plea agreement with Reyes, advised him of the rights he was giving up, and reinforced the permanence of that decision. The district court found that Reyes knowingly and voluntarily entered his plea of guilty, accepted the *738plea, and imposed a sentence of 262 months’ imprisonment.
II. DISCUSSION
A. Martin Anaya
Anaya does not appeal his conviction but raises three substantive challenges to his sentence. First, Anaya argues that the district court erred when it enhanced his sentence based on a finding that Anaya killed Campos, conduct that he had been acquitted of; second, he attacks the drug quantity attributed to his conspiracy to traffic narcotics conviction; and last, he contends that his sentence is substantively unreasonable.
We review an appellant’s claims regarding the district court’s legal conclusion and sentencing procedures de novo. United States v. Annoreno, 713 F.3d 352, 356-57 (7th Cir.2013). We review a district court’s factual findings at sentencing for clear error and only reverse if we are “left with the definite and firm conviction that a mistake has been committed.” United States v. Claybrooks, 729 F.3d 699, 706 (7th Cir.2013) (internal quotation and citations omitted). “Likewise, we defer to a district court’s determination of witness credibility, which can virtually never be clear error.” United States v. Pulley, 601 F.3d 660, 664 (7th Cir.2010) (citing United States v. Acosta, 534 F.3d 574, 584 (7th Cir.2008)).
1. The District Court’s Use of Acquitted Conduct as a Sentencing Enhancement
It has long been established that “a sentencing court may consider conduct of which a defendant has been acquitted.” United States v. Watts, 519 U.S. 148, 154, 117 S.Ct. 633, 136 L.Ed.2d 554 (1997). We have since clarified that “[a]ll an acquittal means is that the trier of fact, whether judge or jury, did not think the government had proved its case beyond a reasonable doubt.” United States v. Horne, 474 F.3d 1004, 1006 (7th Cir.2007). The facts which a judge relies upon to determine the term of a defendant’s sentence “need be found only by a preponderance of the evidence, the normal civil standard.” Id. Given the difference in standards of proof, there was no error in the district court’s legal conclusion that it could consider Ana-ya’s culpability for Campos’ death at the sentencing hearing.
Turning to the district court’s factual findings at sentencing, it appears that the district court relied heavily on the credibility of the witnesses. It found the testimony of the Latin Kings to be “questionable,” whereas, it found Wilhelm’s and Mary Gonzalez’s testimony to be “credible” and “consistent.” We find no error in the district court’s reliance on the testimony from one of the survivors of the Latin Kings’ attack, supported by the statements of an uninterested bystander. We defer to the district court’s determination of credibility, and this evidence easily supported its finding that Anaya was responsible for Campos’ murder by a preponderance.
2. The District Court’s Drug Quantity Finding
Next, we turn to Anaya’s drug conviction. The jury found Anaya guilty of a drug trafficking conspiracy and explicitly found over five kilograms of cocaine and 1,000 kilograms of marijuana were distributed over the course of the conspiracy. At sentencing, the district court found that a preponderance of the evidence supported that Anaya and his co-conspirators distributed over 150 kilograms of cocaine and 1,000 kilograms of marijuana. Anaya wants the precise drug amount proven to a jury, but this is not what the law requires.
*739The Sixth Amendment, in conjunction with Due Process, requires that “any fact that increases the mandatory minimum” or the statutory maximum sentence be proved to a jury beyond a reasonable doubt. United States v. Alleyne, — U.S. —, 138 S.Ct. 2151, 2155, 186 L.Ed.2d 314 (2013); see also Apprendi v. New Jersey, 530 U.S. 466, 490, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000). A conviction for trafficking more than five kilograms of cocaine or more than 1,000 kilograms of marijuana carries a statutory minimum sentence of ten years and a maximum of life. See 21 U.S.C. § 841(b)(1)(A). As long as the court stays within the statutory sentencing minimum and maximum, in this case ten years to life, it has the discretion to impose a sentence based on the precise drug quantity attributable to the defendants’ conspiracy by a preponderance of the evidence. United States v. Medina, 728 F.3d 701, 705 (7th Cir.2013); see also U.S.S.G. § 2Dl.l(c).
We turn again to the district court’s factual findings, particularly the finding that 150 kilograms of cocaine could be attributed to Anaya. For a conviction of conspiring to traffic narcotics, a sentencing court can include not only the drugs the defendant directly sold or knew about, but can also include the “reasonably foreseeable quantity of drugs sold by his or her coconspirators” in its calculation of drug quantity attributable to the defendant. United States v. Seymour, 519 F.3d 700, 710-11 (7th Cir.2008). A defendant’s long tenure and critical role in an organization support the finding that the defendant can be held accountable for the aggregate amount of drugs attributable to all the conspirators. Id. at 711.
The district court sentenced Anaya based on the quantity of drugs distributed by his entire group of co-conspirators because Latin Kings gang members testified that it was “no secret” that Anaya’s region distributed large amounts of cocaine and marijuana. Anaya was a member of the Latin Kings for roughly twenty-one years. Although he spent a number of those years in prison, he never withdrew from the conspiracy. He was an “Inca,” the leader of his chapter, at one point and also held a position as an “Enforcer.” Anaya attended meetings, at which drug distribution was often a topic, arid he personally sold drugs anytime he had the opportunity. The district court found that as a leader and long-term gang member, Anaya knew and benefitted from the large amount of drugs the gang sold. We see no error in the district court’s decision to attribute the amount of drugs distributed by Anaya’s co-conspirators to set his Sentencing Guidelines range.
3. The Substantive Reasonableness of Anaya’s Sentence
Anaya’s final argument is that his 360-month sentence is substantively unreasonable because none of his co-defendants received a sentence longer than he did. Anaya thus claims that his sentence created an unwarranted disparity with his codefendants’ sentences. His argument fails for a couple reasons.
When deciding the length of a defendant’s sentence, the court considers a multitude of factors, one being the “need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct.” 18 U.S.C. § 3553(a)(6). Unwarranted disparities result when the court relies on things like alienage, race, and sex to differentiate sentence terms. United States v. Boscarino, 437 F.3d 634, 638 (7th Cir.2006). However, a defendant’s cooperation should be rewarded and is a warranted disparity in sentencing. Id. The Bos-carino court reasoned that “[t]here would *740be considerably less cooperation — and thus more crime — if those who assist prosecutors could not receive lower sentences compared to those who fight to the last.” Id. Anaya was the only one of twenty — two defendants that refused to cooperate with the government and the difference in his sentence is warranted.
Secondly, the main goal of the Sentencing Reform Act was to “treat similar offenders similarly,” so a sentence within a properly constructed Sentencing Guidelines range is presumptively reasonable and “cannot be treated as unreasonable by reference to § 3553(a)(6).” Id. Likewise, a sentence below the applicable Sentencing Guidelines range cannot be an unwarranted disparity. United States v. Pape, 601 F.3d 743, 750 (7th Cir.2010); United States v. Nania, 724 F.3d 824, 840 (7th Cir.2013). The recommended sentence for Anaya pursuant to the Sentencing Guidelines was life, and he received 360 months; Anaya’s substantive challenge is foreclosed.
4. The Government’s Concession of Error
On the eve of the oral argument, the government discovered a technical error in Anaya’s sentence. On page two of Anaya’s Judgment, the district court described the terms of the racketeering conspiracy and the drug distribution conspiracy convictions as 360 months each, to be served concurrently; however, the maximum sentence for a general racketeering conviction is twenty years. See 18 U.S.C. § 1963(a).
Recall, any fact that increases the statutory maximum sentence must be proved to a jury beyond a reasonable doubt. Apprendi 530 U.S. at 490,120 S.Ct. 2348. In this case, the jury found Anaya guilty of conspiring to participate in racketeering, but it also found the government did not prove beyond a reasonable doubt that Ana-ya’s racketeering activities involved Campos’ murder, the distribution of more than five kilograms of cocaine, or the distribution of 1,000 kilograms of marijuana. Without the jury’s finding of a fact (murder) that increases the maximum sentence for racketeering beyond twenty years, see, e.g., 18 U.S.C. § 1959(a)(1), the district court’s statement that the term of Anaya’s racketeering conviction is 360 months is clearly an error.
Accordingly, we remand Anaya’s case to allow the district court to correct Anaya’s Judgment to reflect that his racketeering conviction can only be for a maximum of twenty years. We affirm all other aspects of his sentence.
B. Oscar Gonzalez, Sisto Bernal, and Dante Reyes
In exchange for concessions from the government, Oscar Gonzalez, Sisto Bernal, and Dante Reyes pleaded guilty. They agreed to waive their rights to appeal their convictions and sentences on all grounds except for a claim of “ineffective assistance of counsel relate[d] directly to th[e] waiver or its negotiation.” After they were sentenced, they each separately notified the district court of their intent to file a direct appeal. This court appointed counsel for all three appellants. Counsel for Gonzalez and Bernal concluded that the appeal would be frivolous and moved to withdraw under Anders v. California, 386 U.S. 738, 744, 87 S.Ct. 1396, 18 L.Ed.2d 493 (1967).
Unlike Gonzalez’s and Bernal’s attorneys, Reyes’ counsel concluded that a direct appeal was not frivolous. Counsel argues that the district court failed to have a sufficient colloquy with Reyes before accepting his guilty plea. Counsel contends that the district court should have asked Reyes to explain his own understanding of *741what the consequences would have been if he changed his plea to guilty. Counsel relies on United States v. Frye, 738 F.2d 196, 201 (7th Cir.1984), to support his proposition that Reyes’ predominantly “yes” and “no” responses to the court’s questions inadequately tested Reyes’ understanding of the charges against him. We first address the argument made by Reyes’ counsel.
It is without question that a defendant’s guilty plea must be knowing and voluntary. Henderson v. Morgan, 426 U.S. 637, 647, 96 S.Ct. 2253, 49 L.Ed.2d 108 (1976); United States v. Adams, 746 F.3d 734 (7th Cir.2014); United States v. Walker, 721 F.3d 828, 842 (7th Cir.2013). To ensure that a plea of guilty is entered knowingly and voluntarily, Fed.R.Crim.P. 11(b) prescribes a set of questions to guide federal courts’ colloquies with defendants. We rely on the record of the colloquy because it is conducted under oath and has a “presumption of verity.” United States v. Adams, 746 F.3d 734, 746 (7th Cir.2014) (quotations and citations omitted). The Frye court recognized that “[wjhether a colloquy is sufficient in a particular case will depend on the facts of that case.” 738 F.2d at 201 (co-defendants were represented by the same counsel and the district court did not adequately test the conflict of interest before accepting a guilty plea). However, the lone fact that a defendant responds to the court’s questions with only “yes” or “no” answers does not defeat the presumption that his answers were truthful and that he actually understood the consequences of changing his plea to guilty. United States v. Alcala, 678 F.3d 574, 579 (7th Cir.2012).
The Alcala court held that the guilty plea of a native Spanish-speaking defendant was knowing and voluntary even though he had an eighth grade education and predominantly answered “yes” or “no.” Id. Here, Reyes has a master’s degree and speaks fluent English, so it seems apparent that he could understand the district court’s questions and knowingly plead guilty when he answered “yes” and “no” during the Rule 11 colloquy. Without more, counsel’s proposition that Reyes must engage in a verbose colloquy with the district court before it can accept his guilty plea is more than Rule 11 or Frye require.
Now we turn to the Anders briefs filed by Gonzalez’s and Bernal’s counsel. Because of the briefs’ non-advocacy nature, we “ ‘limit our review to the subjects that counsel has discussed, plus any additional issues that the defendant, disagreeing with counsel, believes have merit.’” United States v. Bey, 748 F.3d 774, 776 (7th Cir.2014) (quoting United States v. Wagner, 103 F.3d 551, 553 (7th Cir.1996)). We invited Gonzalez and Bernal to respond to their attorneys’ motions to withdraw; but they did not. See Cir. R. 51(b). The briefs filed by Gonzalez’s and Bernal’s counsel appear to be thorough and address the types of issues congruent with appeals of this nature, so we limit our review to the subjects that counsel addressed.
A defendant’s plea agreement often contains a provision waiving his right to appeal and that appeal waiver stands or falls with the guilty plea. United States v. Zitt, 714 F.3d 511, 515 (7th Cir.2013). Here, Gonzalez’s and Bernal’s appellate counsel believe that their clients knowingly and voluntarily pleaded guilty, and their appeal is frivolous because they forfeited their right to appeal in their plea agreements. We agree. Gonzalez and Bernal engaged in proper Rule 11 colloquies, substantially similar to Reyes, “and that means [their] waiver[s] [are] enforceable.” Id.
*742With the indictment of twenty-three defendants and plea bargains negotiated for twenty-one of them, this case exemplifies Justice Burger’s sentiment that, “‘plea bargaining,’ is an essential component of the administration of justice. Properly administered, it is to be encouraged.” Santobello v. New York, 404 U.S. 257, 260, 92 S.Ct. 495, 30 L.Ed.2d 427 (1971). The plea bargains for appellants Gonzalez, Bernal, and Reyes were properly administered (ie., the prosecutors did not break any promises, the district court followed Rule 11, and the defendants knowingly and voluntarily waived their right to appeal). Furthermore, no exceptions to their waivers exist because the district court did not rely on any constitutionally impermissible factor when it imposed their sentences and the sentences do not exceed the statutory maximum of life in prison. Jones v. United States, 167 F.3d 1142, 1144 (7th Cir.1999); see also 21 U.S.C. § 841(b)(1)(A). The appeal waivers in the defendants’ plea agreements preclude our review of these three appeals.
III. CONCLUSION
We AFFIRM Anaya’s sentence in part and REMAND for the LIMITED PURPOSE of correcting the Judgment. We DISMISS the appeals of Gonzalez, Bernal, and Reyes. Accordingly, we GRANT the motions filed by counsel for Gonzalez and Bernal.