RESOLUTION TRUST CORP.

v.

ASSOCIATED INVESTMENT GROUP

KETHLEDGE, Circuit Judge.

A jury convicted Sandra Kincaid, Randy Kincaid, Dustin Morgan, and Wendi Henry of conspiring to distribute controlled substances in violation of 21 U.S.C. §§ 846 and 841(a)(1), and several related charges. The four defendants, in various combinations, challenge on appeal nearly every stage of this criminal proceeding, including allegations in the indictment, rulings on pre-trial motions, sufficiency of the trial evidence, and reasonableness of the sentences. We affirm.

I.

In July 2009, Sandra Kincaid and her husband Randy opened the Breakthrough Pain Therapy Center in Maryville, Tennessee. Sandra managed the daily operations while Randy handled the financial side of the business. Sandra’s two children, Dustin Morgan and Wendi Henry, worked at *279the clinic as well. Dustin started as a security guard but eventually collected payments and tracked accounts receivable. Wendi worked in the back office, maintaining patient records and occasionally helping customers. Dustin’s wife, Heather, worked at the reception desk. Wendi’s two daughters worked for the Center as well.

For a time the business was wildly successful. Just 17 months after it opened, however, federal agents raided the Center. Sandra, Randy, Dustin, and Wendi were arrested and charged with conspiring to distribute drugs. Randy and Sandra were charged with laundering the Center’s revenue, and Randy and Dustin were charged with possessing a firearm in furtherance of a drug conspiracy. Before trial, Sandra, Dustin, and Wendi challenged their indictments, and Dustin moved to exclude evidence that was seized from his house and safe-deposit box. The district court denied their motions.

At trial, the government presented evidence that the Center was actually a pill mill — a pain clinic known for freely distributing controlled substances. Witness after witness described each defendant’s contribution to the conspiracy: Sandra signed and handed out prescriptions before patients saw a doctor; Randy ensured that the Center’s banking practices avoided red flags; Dustin collected cash-only payments; and Wendi made sure that drug-seekers with forged MRIs still got their prescriptions. The jury convicted the defendants on all counts. The defendants then filed motions for acquittal or for a new trial. The district court denied the motions.

At sentencing, Sandra, Dustin, and Wendi challenged the methodology that federal agents used to calculate the quantity of drugs distributed by the Center. The district court denied the motions and sentenced Sandra to 470 months imprisonment, Dustin to 204 months, Wendi to 216 months, and Randy to 830 months. This appeal followed.

II.

A.

1,

Wendi and Sandra argue that the district court should have dismissed the indictment because it failed to charge an essential element of the crime. Specifically, they point out that “dispense” refers to when a medical practitioner, or someone acting under a practitioner’s authority, delivers controlled substances to a user. See 21 U.S.C. § 802(10), (11). Wendi and Sandra thus assert that an indictment may charge laypeople with conspiracy .to dispense narcotics only if the indictment also charges a medical practitioner in the conspiracy. The indictment here did not charge a medical practitioner. As an initial matter, our circuit has not adopted such a rule. See United States v. Johnson, 831 F. 2d 124, 128 n. 8 (6th Cir.1987). Moreover, Wendi and Sandra’s argument fails because the indictment charged them with conspiring to distribute a controlled substance — not dispense. 21 U.S.C. § 841(a)(1). Conspiring to distribute a controlled substance does not require a medical practitioner. See Johnson, 831 F. 2d at 127-28.

2.

Dustin and Sandra argue that the indictment lacks sufficient factual allegations for the conspiracy charge. An indictment must include “facts and circumstances” sufficient to “inform the accused of the specific offense” so the accused can prepare a defense and avoid double jeopardy. See United States v. Landham, 251 F. 3d *2801072, 1079 (6th Cir.2001) (internal quotation marks and emphasis omitted). An indictment sufficiently alleges the duration of a conspiracy by “fix[ing] the end of the conspiracy and provid[ing] an approximate start date[.]” See United States v. Vassar, 346 Fed.Appx. 17, 19-20 (6th Cir.2009).

Here, Sandra contends that the indictment failed both to make specific “allegations of time and place” and to describe how Sandra knew “that prescriptions were being issued outside the usual course of medical praetice[.]” But the indictment alleged that the conspiracy was located primarily at the Center, started “in or about May 2009, and continu[ed] through on or about December 14, 2010[.]” And the indictment alleged that Sandra—'who “is not a [medical] practitioner”—“personally examinefd] patients” at the Center and “fill[ed] out” and “sign[ed]” their “prescriptions for controlled substances.” The indictment did not need to specify that Sandra’s knowledge of the improper prescriptions came from observing her own actions. The indictment thus contained factual allegations sufficient to give Sandra notice of the charges.

Dustin contends that the indictment alleged “no facts” related to his role in the conspiracy except that he “armed himself with a weapon.” But the indictment alleged that Dustin “conspire[d]” with the other defendants “to distribute, and to possess with intent to distribute” various controlled substances; that he and the other defendants “knowingly open[ed]” and “operate[d]” the Center “for the purpose of unlawfully distributing” controlled substances; and that Dustin “armed” himself with a “firearm” to protect the “large amounts of cash revenue” generated by the “cash-only” Center. These allegations provided Dustin with sufficient notice of the charges against him.

3.

Dustin also contends that the government presented facts at trial that varied from those alleged in the indictment. “A variance to the indictment occurs when the charging terms of the indictment are unchanged, but the evidence at trial proves facts materially different from those alleged in the indictment.” United States v. Caver, 470 F. 3d 220, 235 (6th Cir.2006).

Here, the indictment alleged that Dustin possessed a firearm to further the conspiracy to distribute drugs at the Center. At trial, the government presented evidence seized from Dustin’s home, including pill bottles that belonged to his wife and firearms legally possessed by Dustin. According to Dustin, this evidence “had nothing to do with the charged offenses.” But Heather got the prescription for these pills during the time that she and Dustin were both employed by the Center. And near the bottles investigators found the pharmacy contract—promising not to fill the prescription at multiple pharmacies. The contract bore his wife’s signature as the customer and Dustin’s signature as the Center representative. This evidence is relevant to Dustin’s knowledge of the conspiracy as charged in the indictment.

As for the firearms, the indictment alleged that Dustin possessed firearms in furtherance of the drug conspiracy—not that he possessed them illegally. Evidence that a firearm was found in Dustin’s home was not materially different from the evidence alleged in the indictment. Thus, this evidence did not vary impermissibly from the indictment’s allegations.

B.

Dustin also challenges the district court’s denial of his evidentiary motions in limine. We review for an abuse of discretion the district court’s evidentiary rulings. *281See United States v. Davis, 577 F. 3d 660, 666 (6th Cir.2009). Prior to Dustin’s trial, he moved to exclude, on relevance and prejudice grounds, the gun and pill bottles seized from his home and the cash seized from his safe-deposit box. The district court denied both motions and later admitted the evidence during trial. Evidence is relevant if “it has any tendency to make a fact more or less probable than it would be without the evidence” and “the fact is of consequence in determining the action.” Fed.R.Evid. 401. A district court “may exclude relevant evidence if the probative value is substantially outweighed by a danger” of “unfair prejudice.” Fed.R.Evid. 403.

Here, Dustin contends that the gun seized in his home “did not make any fact of consequence more probable” because the gun was not the one “used to support the [i]ndictment[.]” Dustin might well be right about that. But we do not see how this evidence caused much prejudice either and given the other evidence of Dustin’s guilt we think the evidence was harmless.

Dustin next argues that, because the pill bottles “belonged to his wife” and “were properly prescribed by a medical provider at” the Center, the bottles were irrelevant. But the rest of the record suggests otherwise. That Dustin signed the contract for his wife’s prescription— while she was also an employee of the Center—makes Dustin’s knowledge of the distribution conspiracy more likely.

Dustin also argues that the cash in his safe-deposit box was irrelevant because he shared the box with his wife. Whether the cash was the result of Dustin’s or his wife’s work for the Center does not determine its relevance. In either case, the presence of $23,000 in Dustin’s safe-deposit box makes more likely that Dustin knew about and agreed to join a conspiracy to distribute drugs for the purpose of making money.

Dustin further argues that, even if relevant, evidence of the cash was unfairly prejudicial because the jury could infer that the cash “was proceeds from illegal activity” at the Center. But Dustin never explained how the inference was unfair and we see no reason why it was. See In re Air Crash Disaster, 86 F. 3d 498, 538 (6th Cir.1996). Thus, the district court did not abuse its discretion by admitting evidence of the firearm and pill bottles found in Dustin’s home or the cash found in his safe-deposit box.

C.

Next, all four defendants contend that the evidence at trial was insufficient to sustain their convictions for conspiring to possess controlled substances with the intent to distribute. For all of these convictions, we ask merely if, “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. Wright, 774 F. 3d 1085, 1088 (6th Cir.2014). A drug conspiracy has three essential elements: “(1) an agreement to violate drug laws, (2) knowledge and intent to join the conspiracy, and (3) participation in the conspiracy.” United States v. Welch, 97 F. 3d 142, 148 (6th Cir.1996).

1.

Sandra contends that the government “failed to prove the existence of an agreement to violate federal drug laws.” But the government need not prove a formal agreement between the members of a conspiracy; a tacit understanding will suffice. United States v. Deitz, 577 F. 3d 672, 677 (6th Cir.2009). This understanding “may be inferred from circumstantial evi*282dénce [that] may reasonably be interpreted as participation in a common plan.” United States v. Hughes, 505 F. 3d 578, 593 (6th Cir.2007).

Sandra argues that her actions were consistent with lawful employment at the center and thus fail to suggest participation in a common plan to’ distribute drugs. Specifically, she contends that the government lacked sufficient evidence that she signed prescriptions, examined patients, or exchanged medication without a valid prescription. But the testimony of numerous patients shows otherwise. Tonya Overholt, for example, testified that on one visit she paid the cash fee to Dustin and filled out paperwork describing her pain symptoms. Sandra then sat down with Overholt, reviewed the paperwork, “went over all the pain problems” that Overholt had listed, and suggested a medication. Sandra then filled out and signed multiple prescriptions for Overholt. - At no point during this visit did either Overholt or Sandra consult with a medical professional.

Similarly, Shawn Crawford testified that Sandra would come into the waiting room and ask if he “was okay with [his] script.” When Crawford answered “yes,” Sandra “would sign my script and I would be gone.” Another patient, Robin O’Gorman, said that Sandra would come into the waiting room and ask the patients to raise their hand if they wanted to see a doctor. Sandra would then go back to her office— not to see a doctor — and return with prescriptions for all the patients who did not raise their hand. On one occasion, when O’Gorman ran out of pills early due to her increasing tolerance, she came into the Center for a new prescription. Sandra put two pills directly in O’Gorman’s mouth when she saw that O’Gorman was suffering from withdrawal. Douglas Thacker testified that Sandra gave him a new prescription when he claimed one had been stolen. And Keith Atkins testified that he failed every drug test at the Center because he had cocaine in his system — but Sandra told him “that was not a problem.”

Nor did Sandra act in isolation, without a “tacit understanding” of a common plan. She and Randy shared an office at the Center. While Sandra handled the daily medical operations, Randy handled most of the finances — but not all. Sandra set up two different safe-deposit boxes at the Center’s bank. Together, Sandra and Randy regularly visited the bank to make deposits. As a result of their combined efforts, they made over $2 million. A rational trier of fact could have thus found beyond a reasonable doubt that Sandra formed at least a tacit understanding to participate in a common plan to violate drug laws.

Sandra also contends that the money-laundering charge fails because insufficient evidence supported the underlying conspiracy charge and because investigators raided the Center before its 2010 tax returns were due. But a money-laundering conspiracy requires only that a defendant knowingly and voluntarily joins at least one other person in a conspiracy to launder money. United States v. Prince, 618 F. 3d 551, 553-54 (6th Cir.2010). The Center’s 2010 tax returns were not necessary to the government’s ease. And as discussed above, sufficient evidence supported Sandra’s conviction of a conspiracy to distribute drugs.

2.

Randy contends that no evidence at trial proved that he knew the essential object of the conspiracy or that he agreed with anyone to distribute drugs. A defendant’s “knowledge of and participation in a conspiracy may be inferred from his conduct and established by circumstantial evi*283dence.” United States v. Conatser, 514 F. 3d 508, 518 (6th Cir.2008).

Here, Randy asserts that he founded a legitimate business and that the government failed to show that-he knew anything about the Center’s prescription practices. But Randy shared an office with Sandra—the same office where Sandra filled out prescriptions for patients who had not seen a doctor. O’Gorman testified that Randy was present in that office when Sandra put two pills directly in O’Gorman’s mouth. Randy himself exchanged pills for sexual favors in that office with two of the Center’s patients. And according to a bank employee, Randy retrieved prescription pads from a safe-deposit box almost every day. When federal agents raided the Center, they found an assortment of controlled substances in Randy’s desk. In the filing cabinet behind his desk, the agents found pill bottles that contained oxycodone and morphine and were labeled with other people’s names. Nevertheless, Randy accompanied Sandra to a local pharmacy to assure the pharmacist that the Center used all the proper safeguards before prescribing controlled substances.

The evidence also showed that Randy designed his financial practices to conceal the conspiracy. The Center accepted only cash from its customers. A bank employee testified that Randy asked how much cash he could deposit at a time without triggering the scrutiny of law enforcement. Randy’s cash deposits were almost always below the $10,000 threshold for that scrutiny. The record as a whole thus allowed the jury to convict Randy of conspiracy.