
540 F.3d 506 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
Shawn MAYBERRY (06-2239); James Peoples (06-2413), Defendants-Appellants.
Nos. 06-2239, 06-2413.
United States Court of Appeals, Sixth Circuit.
Argued: July 22, 2008.
Decided and Filed: August 21, 2008.
*509 ARGUED: Michael A. Faraone, Lansing, Michigan, Jolene J. Weiner-Vatter, Law Offices, Grand Rapids, Michigan, for Appellants. Timothy P. VerHey, Assistant United States Attorney, Grand Rapids, Michigan, for Appellee. ON BRIEF: Michael A. Faraone, Lansing, Michigan, Jolene J. Weiner-Vatter, Law Offices, Grand Rapids, Michigan, for Appellants. Phillip J. Green, Christopher M. O'Connor, Assistant United States Attorneys, Grand Rapids, Michigan, for Appellee. James Carnell Peoples, Terre Haute, Indiana, pro se.
Before: BOGGS, Chief Judge; MOORE and CLAY, Circuit Judges.

OPINION
CLAY, Circuit Judge.
Defendant James Peoples appeals his conviction as a felon in possession of a firearm in violation of 18 U.S.C. § 922(g)(1), alleging that he was deprived of his Fifth Amendment rights when the prosecution introduced evidence demonstrating that he possessed firearms during multiple armed robberies, that insufficient evidence exists to support his conviction, and that he was denied his Sixth Amendment right to confront a witness. Defendant Shawn Mayberry appeals his 110-month *510 sentence on similar charges, claiming that the district judge unconstitutionally made findings of fact at sentencing, and that his sentence is unreasonable. As none of these claims have merit, we AFFIRM both Defendants' convictions and sentences.

BACKGROUND

A. The Robberies
Although Defendants James Peoples and Shawn Mayberry were charged only as felons in possession of a firearm, not with armed robbery, both Defendants allegedly participated in a string of such robberies prior to their December 24, 2005 arrest. On October 30, 2005, the night of the first robbery, three men wearing dark clothes and ski masks entered a D & W Food Store in Grand Rapids, Michigan at just before midnight. At least two of these men were armed, and both of the armed men were described by witnesses as African-American. Additionally, one of the armed robbers was carrying an assault rifle with a wooden stock and distinctive scratches in the wood. During the two minutes the robbers spent in the store, approximately $5000 was stolen.
On November 19, 2005, four armed men wearing masks entered a different D & W Food Store at just before midnight.[1] One of these men was carrying an assault rifle just like the one used in the first robbery. In addition to stealing money, the robber carrying the assault rifle attempted to steal several cartons of Newport and Kool brand cigarettes, but the cartons he grabbed were empty displays. After robbing the store, the men fled in a black, four-door pick-up truck which fit the description of a truck which had been rented by Defendant Peoples' cousin Lashenica Armstrong.
On December 1, 2005, Grand Rapids Police Officer Connie Moore was directed to meet with Laura Hammond and her boyfriend Mario Fagairo, who had previously contacted the police department regarding an assault rifle which he had found. Officer Moore met the couple in a public park, where she confiscated the weapon and learned that Mario had discovered it at the home of his sister Robin Defendant Peoples' girlfriend and the mother of Peoples' children. According to Mario, he and Hammond were visiting his sister's house when they discovered the gun leaning against a wall. Mario wrapped the gun in a jacket and immediately called the police to retrieve it.
On December 10, 2005, Officer Moore interviewed Robin Fagairo regarding the assault rifle which was reportedly found in her home. The next day, Peoples called Mario, admitted that the gun belonged to him, and expressed concern that police would discover his prints on it. Peoples also asked Mario to help him concoct an innocent explanation for why his prints would be on the firearm, but Mario refused to help Peoples fabricate such a story for the police.
A government weapons expert later identified the confiscated assault rifle as an AK-47, the same type of weapon used in the two grocery store robberies.

B. Defendants' Arrest
On December 14, 2005, an informant named Jon Bowman contacted the Grand Rapids police and informed them that Peoples and Mayberry were involved in the two grocery store robberies. According to Bowman, Peoples and Mayberry approached him around "Christmas time" 2005 and asked if he would like to participate in their next robbery. (Peoples J.A. *511 40)[2] Peoples also told Bowman that he had used his AK-47 during a third, aborted robbery attempt, and that potential future victims included a person named "T.C." who was involved in check forging and drug dealing. (Peoples J.A. 220) Police learned from Bowman that the only thing preventing Peoples and Mayberry from committing another robbery was the fact that they liked to use rental cars as get-away vehicles, and they did not yet have the money to rent another car. As a result, the police provided Bowman with the money to allow Peoples and Mayberry to rent another car, and set up surveillance at the local Enterprise car rental station.
On December 23, 2005, police observed Peoples' cousin Lashenica Armstrong arriving at the Enterprise rental station in a white car along with Mayberry. The two rented a grey Nissan Altima, and they left together with both vehicles, eventually both stopping at the same apartment complex, placing a large white bag in the rental car, and entering one of the apartments. At some point while the vehicle was parked at this apartment complex, police secretly placed a GPS tracking device on the rental car.
Around midnight, Mayberry left in the rental car and drove to a nearby house, where an officer observed Peoples climbing into the passenger side of the vehicle. After stopping briefly at a nearby Meijer store, Mayberry and Peoples drove to Bowman's home, and Bowman joined the two of them in the rental car. The vehicle then proceeded toward the home of "T.C.," the check forger and potential victim. Fearing that Defendants were about to rob T.C., police decided to stop the vehicle and arrest the occupants. In a search of the vehicle made incident to this arrest, police found several dark-colored knit caps, and two handguns in the trunk of the car.
Subsequent to his arrest, Peoples was interrogated by police. Although he admitted to touching the AK-47 which police had previously confiscated, he initially claimed that he thought that the gun was a toy, and had picked it up and moved it aside when he was visiting his girlfriend Robin. Later, however, Peoples contradicted this claim, stating that he recognized the gun as one that "had been used in some armed robberies," but he claimed that the gun had been used by Shawn Mayberry. (Peoples J.A. 226) Despite also claiming that he did not participate in any of the previous robberies, Peoples did identify Mayberry in photographs of the masked participants in the grocery store robberies. He claimed that the other three robbers went by the names "O," "Meth" and "Black." (Peoples J.A. 231) Peoples also admitted that he smokes Newport cigarettes, the same brand of cigarettes which one of the robbers attempted to steal during the November 19, 2005 robbery.
After the interrogation, police briefly left Peoples alone in the interrogation room, but kept a tape recorder running. During this time, Peoples muttered under his breath "I'm hit." (Peoples J.A. 233)

C. Peoples' Trial
Despite his alleged involvement in multiple armed robberies, Peoples was only charged with two counts of being a felon in possession of a firearm; the first concerning the two handguns found in the trunk of the rental car at the time of his arrest, and the second concerning his possession of the *512 confiscated AK-47. Peoples pled not guilty to both charges.
During Peoples' trial, the government presented significant evidence linking Peoples to the armed robberies in order to show that he possessed a firearm during his participation in these robberies. Peoples did not object to this evidence, but did request that a limiting instruction be given to the jury. During final instructions, the judge did, in fact, give the following instruction:
You heard testimony during this trial that the defendant may have committed other crimes than the ones charged in the indictment. If you found and if you find that he did commit earlier crimes, you may consider this only as it relates to the government's contention that this defendant intended to carry the firearms that are at issue in Counts 1 and 2 of the indictment. You may not consider this evidence for any other purpose, remembering that this defendant is on trial only for being a felon in possession of firearms and not for any other acts. Do not return a guilty verdict unless the government proves those crimes beyond a reasonable doubt.
(Peoples J.A. 283-84)
Also during Peoples' trial, the prosecution called Bowman to testify. Although Bowman had previously testified to a grand jury regarding Peoples and Mayberry's plans to conduct additional robberies, he claimed that he was unable to remember numerous facts which he had recently revealed to the grand jury. As a result, the prosecution read excerpts of Bowman's prior sworn statements to the grand jury, and asked Bowman if he remembered making those statements, but Bowman continued to claim poor recollection. Despite counsel's objection to the introduction of these prior, sworn statements, the judge overruled the objection, and allowed the statements to be admitted as substantive evidence.

D. Mayberry's Hearing
Unlike Peoples, Mayberry was charged with just one count of being a felon in possession of a firearm. He pled guilty to this charge. At sentencing, the judge found by a preponderance of the evidence that Mayberry had been involved in at least one armed robbery, and eventually sentenced him to 110 months imprisonment.

DISCUSSION

I. PEOPLES' SUFFICIENCY OF THE EVIDENCE CLAIM

Standard of Review
Peoples argues, for the first time on appeal, that the district court constructively amended his indictment when it instructed the jury that it may consider evidence showing that Peoples committed armed robbery. "Generally, an appellant cannot raise a claim before the appellate court that was not raised below." United States v. Cline, 362 F.3d 343, 348 (6th Cir.2004). When an appellant does fail to raise an issue in the court below, this court reviews the decision of the district court for plain error. Id. To establish plain error, Peoples must demonstrate that "(1) an error occurred; (2) the error was obvious or clear; (3) the error affected his substantial rights; and (4) the error seriously affected the fairness, integrity, or public reputation of the judicial proceedings." Id.
Because he believes that the evidence linking him to the armed robberies should not have been considered at trial, Peoples also claims that insufficient evidence exists to support his conviction. "In reviewing a district court's denial of a motion for judgment of acquittal on a claim of *513 insufficient evidence, the pertinent inquiry is `whether after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.'" United States v. Coffee, 434 F.3d 887, 895 (6th Cir.2006) (quoting United States v. Lloyd, 10 F.3d 1197, 1210 (6th Cir.1993)). A judgment of conviction will be reversed on insufficiency of the evidence only if the evidence "is such that a rational factfinder must conclude that a reasonable doubt is raised." Id. The district court's findings of fact are reviewed for clear error, and all reasonable inferences must be drawn in the government's favor. Id.

Analysis

A. Constructive Amendment
Peoples argues that by instructing the jury that it may consider evidence suggesting that Peoples may have committed armed robbery "only as it relates to the government's contention that this defendant intended to carry the firearms that are at issue in Counts 1 and 2 of the indictment," the district court "constructively amended the indictment by instructing the jury that they may consider and find whether defendant Peoples committed the earlier crimes not charged in the indictment." (Peoples Br. at 17) In a related vein, Peoples also claims that, given the large amount of evidence presented to the jury suggesting that Peoples committed armed robbery, "it is impossible to determine if the jury convicted defendant Peoples on the charges of armed robbery, because defendant Peoples was simply a `bad guy' or for the indicted conduct of felon in possession of a firearm." (Id. at 20) Peoples' arguments are wholly without merit.
A constructive amendment of an indictment occurs when "an indictment's terms are effectively altered by the presentation of evidence and jury instructions that so modify essential elements of the offense charged that there is a substantial likelihood the defendant [was] convicted of an offense other than that charged in the indictment." United States v. Hynes, 467 F.3d 951, 961-62 (6th Cir.2006) (quoting United States v. Combs, 369 F.3d 925, 936 (6th Cir.2004)) (alteration in original). Although a constructive amendment is a per se violation of the Fifth Amendment, the burden of proving a constructive amendment rests with the defendant, and this burden can only be met "by pointing to a combination of evidence and jury instructions that effectively alters the terms of the indictment and modifies the essential elements of the charged offense to the extent that the defendant may well have been convicted of a crime other than the one set forth in the indictment." Id. at 962. Peoples, however, has not identified a jury instruction which constructively amended his indictment.
Although Peoples claims that the judge's limiting instruction to the jury regarding the use of evidence proving other crimes somehow encouraged the jury to convict Peoples on charges not contained in the indictment, the plain language of the limiting instruction carries the opposite meaning. The instruction clearly stated that the jury may consider evidence proving other crimes "only as it relates to the government's contention that this defendant intended to carry the firearms that are at issue in Counts 1 and 2 of the indictment," and expressly forbade the jury from considering such evidence "for any other purpose." (Peoples J.A. 283-84) The instruction informed the jury that "this defendant is on trial only for being a felon in possession of firearms and not for any other acts," and told them in no uncertain terms to "not return a guilty verdict *514 unless the government proves those crimes beyond a reasonable doubt." (Peoples J.A. 284) The instruction cannot reasonably be read to permit the jury to convict Peoples of any crime other than being a felon in possession of firearms.
Furthermore, in arguing that his indictment was constructively amended by the prosecutor's mere act of presenting evidence that suggests he may have committed other crimes, Peoples treads too far on the general rule that "the prosecution is entitled to prove its case by evidence of its own choice." See Old Chief v. United States, 519 U.S. 172, 186, 117 S.Ct. 644, 136 L.Ed.2d 574 (1997). Generally speaking, a prosecutor may present background evidence which "has a causal, temporal or spatial connection with the charged offense." United States v. Wesley, 417 F.3d 612, 621 (6th Cir.2005) (quoting United States v. Hardy, 228 F.3d 745, 748 (6th Cir.2000)). Were the Court to adopt the rule Peoples suggests, however, prosecutors would be placed in the impossible position of having to ignore highly probative background evidence merely because that evidence also would support a conviction on an uncharged offense; yet Peoples cites no case law which suggests that a conviction is invalid merely because a prosecutor failed to charge other crimes which could have been supported by the underlying facts.
Because Peoples has not met his burden of demonstrating that his indictment was constructively amended by the introduction of evidence which might support conviction on an uncharged crime, the evidence suggesting that he committed armed robbery was properly admitted at his trial.

B. Sufficiency of the Evidence
Having determined that the evidence linking Peoples to the armed robberies was properly admitted, there is no question that, based on the evidence introduced at trial, a reasonable jury could have convicted Peoples of both counts of being a felon in possession of a firearm. See Coffee, 434 F.3d at 895. The elements of the crime of being a felon in possession of a firearm are: 1) a prior felony conviction; 2) knowing possession of a firearm; and 3) the firearm must have traveled in interstate commerce. 18 U.S.C. § 922(g)(1). Peoples stipulated at trial that he had a prior felony conviction, and the government introduced expert testimony showing that all three of the firearms at issue in this case were manufactured outside of the state of Michigan, where the events underlying this case took place. Accordingly, so long as a reasonable juror could have found, beyond a reasonable doubt, that Peoples possessed the firearms at issue in this case, his conviction should be affirmed. Coffee, 434 F.3d at 895. Moreover, possession can be shown if Peoples had constructive possession of the firearmsthat is, if he did not "have actual possession but instead knowingly ha[d] the power and the intention at a given time to exercise dominion and control" over the firearms. Id. (quoting United States v. Craven, 478 F.2d 1329, 1333 (6th Cir.1973)). Although "mere proximity" to a gun is not alone sufficient to establish constructive possession, "evidence of some other factorincluding connection with a gun, proof of motive, a gesture implying control, evasive conduct, or a statement indicating involvement in an enterprisecoupled with proximity may suffice." United States v. Alexander, 331 F.3d 116, 127 (D.C.Cir.2003) (internal quotation marks omitted).[3]
*515 Peoples does not challenge his conviction for possessing the AK-47, and even if he had, Peoples' admission that he touched the gun, his conflicting explanations regarding his reasons for doing so, and the fact that he tried to induce Mario Fagairo to lie on his behalf regarding whether he had possessed the firearm provide sufficient grounds to allow a reasonable jury to convict Peoples, even absent the evidence that he used the weapon in two armed robberies.
Similarly, after hearing testimony from multiple witnesses linking Peoples to the armed robberies, the jury also heard the prior sworn statement of police informant Bowman, to whom Peoples admitted that he participated in the two prior robberies, and who Peoples invited to participate in a third robbery on the day of his arrest. Bowman informed police that Peoples and Mayberry would rent a car, and potentially drive it to the home of "T.C.," where they would use firearms to rob that home. Moreover, when Peoples was arrested, he was indeed found in a rental car, with Mayberry, by T.C.'s home, and with two firearms in the rental car's trunk.
Based solely on this evidence, a reasonable jury could have concluded, beyond a reasonable doubt, that Peoples had "the power and the intention" at the time of his arrest "to exercise dominion and control" over the firearms in the trunk by using them in a robbery. Coffee, 434 F.3d at 895. Although Peoples did not have physical possession of the firearms at the time of his arrest, they were discovered in close proximity to Peoples, and Peoples' participation in prior robberies and his statements to informant Bowman outlining his plan for an additional robbery are sufficient to establish both that Peoples had a motive to use the guns, and that he was engaged in a criminal enterprise in which he commonly used firearms. Accordingly, we hold that sufficient evidence was introduced at trial to allow a jury to find that Peoples had constructive possession of a firearm at the time of his arrest. See Alexander, 331 F.3d at 127.

II. ADMISSIBILITY OF BOWMAN'S PRIOR STATEMENTS

Standard of Review
Generally speaking, a district court's evidentiary decisions are reviewed for abuse of discretion. Gibson v. Moskowitz, 523 F.3d 657, 665 (6th Cir.2008). However, claims alleging that the admission of certain evidence violates the Confrontation Clause are reviewed de novo. United States v. Vasilakos, 508 F.3d 401, 406 (6th Cir.2007).

Analysis
A witness' prior inconsistent statement may be admitted as substantive evidence if "[t]he declarant testifies at the trial or hearing and is subject to cross-examination concerning the statement, and the statement ... was given under oath subject to the penalty of perjury at a trial, hearing, or other proceeding, or in a deposition." Fed.R.Evid. 801(d)(1). Nevertheless, Peoples argues that the district court abused its discretion by permitting police informant Bowman's prior, sworn statements, made during his grand jury testimony, to be admitted as substantive evidence once Bowman claimed he did not remember having conversations with Peoples that implicated Peoples in the grocery store robberies.
*516 It is well established that a witness "limited and vague recall of events, equivocation, and claims of memory loss" can constitute prior inconsistent statements under Fed.R.Evid. 801(d)(1), and thus such statements allow the witness' prior inconsistent grand jury testimony to be admitted as substantive evidence. United States v. Hadley, 431 F.3d 484, 511-12 (6th Cir.2005). This is exactly what occurred in the instant case. Bowman testified to a grand jury regarding incriminating statements made by Peoples. These statements were made under oath. Later, he testified at Peoples' trial, claimed a loss of memory, and was later available for cross-examination by Peoples' counsel. Such events fall exactly within the scope of Rule 801(d)(1), and thus Peoples' testimony to the grand jury was properly admitted as substantive evidence. See Hadley, 431 F.3d at 511-12.
Peoples also argues, however, that the district court violated his rights under the Confrontation Clause by allowing Bowman's grand jury testimony to be admitted into evidence. As the Supreme Court held in Crawford v. Washington, 541 U.S. 36, 124 S.Ct. 1354, 158 L.Ed.2d 177 (2004), however, "when the declarant appears for cross-examination at trial, the Confrontation Clause places no constraints at all on the use of his prior testimonial statements." Id. at 59 n. 9, 124 S.Ct. 1354. Because Bowman appeared for cross-examination at trial, Peoples' claim that the Confrontation Clause prevents admission of Bowman's prior statements is without merit.
The district court neither violated Peoples' rights under the Confrontation Clause nor abused its discretion in admitting Bowman's statements under Fed. R.Evid. 801(d)(1). As Peoples raises no other meritorious claims, his conviction is affirmed.

III. JUDICIAL FACT-FINDING

Standard of Review
Mayberry argues, for the first time on appeal, that the district judge violated the Fifth and Sixth Amendments by making findings of fact under a preponderance of the evidence standard at sentencing. Because this argument was not raised in the court below, it is reviewed on appeal for plain error. See United States v. Vonner, 516 F.3d 382, 385 (2008) (en banc).

Analysis
It is well-established in the Sixth Circuit that no Fifth or Sixth Amendment violation occurs when a judge makes findings of facts at sentencing under the preponderance of the evidence standard. United States v. Gates, 461 F.3d 703, 708 (6th Cir.2006). Nevertheless, Mayberry claims that, in light of Cunningham v. California, 549 U.S. 270, 127 S.Ct. 856, 166 L.Ed.2d 856 (2007), this well-established rule should be reconsidered.
In Cunningham, the Supreme Court considered a California sentencing scheme which required a sentencing judge to determine a "lower term," "middle term" and "upper term" sentence before selecting which sentence to apply to a convicted defendant. Id. at 868. Under this scheme, however, a court may only impose an upper term sentence if the judge first made a finding of fact that an aggravating circumstance justified such an enhanced sentence. Id. In holding this scheme unconstitutional, the Court reaffirmed Apprendi v. New Jersey's holding that "any fact that increases the penalty for a crime beyond the prescribed statutory maximum must be submitted to a jury, and proved beyond a reasonable doubt." Id. (quoting Apprendi v. New Jersey, 530 U.S. 466, 490, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000)). According to the Supreme Court, "the *517 `statutory maximum' for Apprendi purposes is the maximum sentence a judge may impose solely on the basis of the facts reflected in the jury verdict or admitted by the defendant." Id. (quoting Blakely v. Washington, 542 U.S. 296, 303, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004) (emphasis in original)). Because the California system permitted an enhanced, upper term sentence to be imposed based solely on facts found by the judge, the Supreme Court concluded that the California system violated Apprendi. Id.
The instant case, however, is distinguishable. The statutory maximum sentence for a felon in possession of a firearm is ten years, or 120 months. 18 U.S.C. § 924(a)(2). Mayberry received 110 months, less than the statutory maximum. Although the district judge made findings by a preponderance of the evidence to inform his decision to impose a sentence close to the maximum sentence allowed under statute, the judge did not rely on such findings to increase the statutory maximum, which Cunningham forbids. 127 S.Ct. at 868. By statute, the district judge was authorized to impose a sentence up to 120 months based on the facts proven to a jury at Mayberry's trial. § 924(a)(2). Because the judge did not exceed this statutory maximum, no Apprendi violation occurred. See Blakely, 542 U.S. at 303, 124 S.Ct. 2531.
Indeed, this Court has already considered whether Cunningham prevents sentencing judges from informing their sentencing by finding facts by a preponderance of the evidence, and has already rejected the argument that such fact-finding is inappropriate, so long as the sentence does not exceed the statutory maximum. See United States v. Conatser, 514 F.3d 508, 527-28 (6th Cir. 2008) ("Booker did not eliminate judicial factfinding. Nor are we persuaded that the Supreme Court's application of Blakely and Booker to California's determinate sentencing law in Cunningham v. California, requires a contrary conclusion.") (citations omitted). Accordingly, the district judge did not err by making findings of fact by a preponderance of the evidence at sentencing.

IV. THE REASONABLENESS OF MAYBERRY'S SENTENCE

Standard of Review
Mayberry also argues, for the first time on appeal, that his sentence was procedurally unreasonable. Because Mayberry raised no challenge to the adequacy of the court's explanation for his sentence in the court below, his procedural unreasonableness claim is reviewed for plain error. Vonner, 516 F.3d at 385-86. Mayberry did, however, raise substantive arguments at sentencing in favor of a lower sentence than the one he eventually received, and plain error review is inappropriate with respect to issues already raised by Mayberry in the court below. Id. at 386. Accordingly, Mayberry's substantive reasonableness claim should be reviewed under a "deferential abuse-of-discretion standard." Gall v. United States, ___ U.S. ___, 128 S.Ct. 586, 591, 169 L.Ed.2d 445 (2007).

Analysis

A. Procedural Reasonableness
When reviewing a sentence for procedural reasonableness, this Court's task is to "ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, failing to consider the § 3553(a) factors, selecting a sentence based on clearly erroneous facts, or failing to adequately explain the chosen sentence." Gall, 128 S.Ct. at 597. A sentence *518 is procedurally unreasonable if the district court "fails to `consider' the applicable Guidelines range or neglects to `consider' the other factors listed in 18 U.S.C. § 3553(a), and instead simply selects what the judge deems an appropriate sentence without such required consideration." United States v. Jones, 489 F.3d 243, 250-51 (6th Cir.2007). Furthermore, while a district court need not engage in a "ritualistic incantation" of the § 3553(a) factors, its reasoning must be "sufficiently detailed to reflect the considerations listed in § 3553(a)" and to allow for meaningful appellate review. United States v. Moon, 513 F.3d 527, 539 (6th Cir.2008) (quoting United States v. McBride, 434 F.3d 470, 474 (6th Cir.2006)). The district court must also "provide some indication that the court considered the defendant's arguments in favor of a lower sentence and the basis for rejecting such arguments." Id.
Mayberry alleges that his sentence was procedurally unreasonable in three ways. First, he argues that, by determining under a preponderance of the evidence standard that Mayberry was involved in armed robberies, and by using this determination in his Guidelines calculation, the judge improperly calculated Mayberry's proper Guidelines range. For the reasons already discussed in Part III of this opinion, however, a judge is permitted to make factual determinations under the preponderance of the evidence standard so long as the ultimate sentence does not exceed the statutory maximum for the crime of conviction. See Conatser, 514 F.3d at 527-28. Accordingly, Mayberry's first procedural unreasonableness claim lacks merit.
Mayberry's two remaining procedural reasonableness claims are equally unavailing. According to Mayberry, the district judge failed to consider the § 3553(a) factors at sentencing and he improperly treated the Guidelines as mandatory. Neither of these claims, however, are borne out by the record.
Under § 3553(a), a judge should consider a myriad of factors, including the nature and circumstances of the offense and the history and characteristics of the defendant; the need for the sentence to reflect the seriousness of the offense, to promote respect for the law, to provide just punishment for the offense, to afford adequate deterrence to criminal conduct, to protect the public from further crimes of the defendant, and to provide the defendant with needed educational or vocational training, medical care, or other correctional treatment in the most effective manner; the kinds of sentences available; the Guidelines sentencing range; any pertinent policy statement by the Sentencing Commission; the need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct; and the need to provide restitution to any victims of the offense. § 3553(a). A judge is not required, however, to expressly state each of these factors at sentencing, so long as his or her opinion reflects a consideration of these factors. See Moon, 513 F.3d at 539.
In the instant case, the district judge did expressly state that his duty at sentencing is to "impose a sentence sufficient, but not greater than necessary to comply with the federal statute 3553(a)...." (Mayberry J.A. 139) Moreover, the judge cited Mayberry's history of criminal activity, his poor disciplinary record when previously incarcerated, and the fact that he was involved in armed robberies as part of his history and characteristics, as a part of the circumstances underlying his offense, as signs he was unlikely to be deterred from future criminal activity, and as evidence that a long incarceration might be necessary to protect the public from future crimes. Accordingly, *519 Mayberry's sentence of 110 months was not procedurally unreasonable.

B. Substantive Unreasonableness
Because "[t]he sentencing judge is in a superior position to find facts and judge their import under § 3553(a)," this Court applies a great deal of deference to a district court's determination that a particular sentence is appropriate. See Gall, 128 S.Ct. at 597. A district court "has access to, and greater familiarity with, the individual case and the individual defendant" than a court of appeals, and it is more adept at sentencing, as a district judge hears far more sentencing cases than the members of an appellate panel. Id. at 597-98 (quoting Rita v. United States, ___ U.S. ___, 127 S.Ct. 2456, 2469, 168 L.Ed.2d 203 (2007)).
In the instant case, the district court determined that Mayberry is a recidivist offender who had a poor disciplinary record while incarcerated, and who possessed a firearm during a series of armed robberies and attempted armed robberies. Nevertheless, the district court determined that a sentence at the bottom of the applicable Guidelines range  110 months  was appropriate. Moreover, Mayberry provides little argumentation in his brief explaining why a 110-month sentence was unreasonable. Instead, Mayberry simply asserts that the district court relied too heavily on its finding that Mayberry was a serial armed robber. Mayberry does not, however, offer any evidence which sets his case aside from the "mine run of cases" in which the Sentencing Commission has determined that a 110-month sentence is within the acceptable range for a felon who possesses a firearm under the circumstances present in this case. See Rita, 127 S.Ct. at 2465. Accordingly, the district court did not abuse its discretion in sentencing Mayberry.

CONCLUSION
The district court properly admitted evidence that Peoples was involved in armed robberies, and the evidence introduced against Peoples was sufficient to sustain a conviction. Moreover, the district court neither erred in its evidentiary rulings nor abused its discretion at sentencing. Accordingly, Peoples' and Mayberry's convictions and sentences are AFFIRMED.
NOTES
[1]  According to a cashier at the second robbed grocery store, that store closes at midnight.
[2]  Because this case presents two consolidated appeals, and each defendant is represented by separate counsel, the case file contains two separate joint appendices. These appendices will be referred to in citation as the "Peoples J.A." and the "Mayberry J.A."
[3]  Although the Sixth Circuit has never expressly adopted the D.C. Circuit's holding in Alexander as its own, our cases have cited with approval Alexander's description of what evidence may suffice to prove constructive possession of a firearm. See, e.g., Parker v. Renico, 506 F.3d 444, 450 n. 4 (6th Cir.2007); United States v. Newsom, 452 F.3d 593, 610 (6th Cir.2006).
