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(Continued) Suppose instead that each customer may buy any number of pieces, including zero. If the gallery sells all the artwork, in how many different ways can the sales occur? Justify your reasoning.

Prove by induction that \[ 2 + 4 + 6 + \cdots + 2n = n(n + 1) \] for all integers \(n \geq 1\).

Find matchings of the bipartite graphs below, or explain why no matching exists.

Four customers visit a gallery with 10 unique pieces of artwork. Each customer buys exactly one piece of artwork. In how many different ways can this occur? Justify your reasoning.

Select all that apply:  A 55 year old woman comes to her annual health check up.  The client is postmenopausal (last menstrual period was 5 years ago). Has a family history of coronary artery disease.  She smokes a pack and a half of cigarettes a day and drinks alcohol occasionally (one glass of wine a few times a week). Her Body Mass Index (BMI) is 30 kg/m². (obese) Based on the information provided, select which health promotion activities should the nurse recommend  to reduce her risk of developing coronary artery disease.

Case Study: Patient Profile:Scenario: 25 year old female client. No significant history of chronic illnesses. No previous sexually transmitted diseases (STDs) or hospitalizations. Recently started a new sexual relationship. Presenting Complaint:Client visits the clinic complaining of painful urination, a change in vaginal discharge, and discomfort during intercourse. She also mentions feeling unusually tired. Symptoms Observed During Examination: Redness and irritation around the genital area Thin, yellowish vaginal discharge Slightly swollen lymph nodes in the groin area Painful urination The physician suspects an STD based on the client’s symptoms, and further tests are ordered. The client is diagnosed with chlamydia.  Which of the following is a common treatment for chlamydia? 

Patient:  52-year-old woman Chief Complaint: Hot flashes, night sweats, vaginal dryness, and mood swings History of Present Illness: The client has been experiencing hot flashes and night sweats for the past year. These episodes are characterized by sudden feelings of intense heat, often accompanied by sweating and flushing.   The client also complains of vaginal dryness, which has led to discomfort during intercourse. Additionally, she has noticed increased irritability and mood swings.  Past Medical History: Hypothyroidism Family History: Mother and sister experienced menopausal symptoms Physical Exam: Normal vital signs Dry vaginal mucosa No other significant findings Laboratory Results: FSH (Follicle-Stimulating Hormone): Elevated LH (Luteinizing Hormone): Elevated Estradiol (estrogen): Low  Select all that apply.  Which of the following medications would the health care provider prescribe to treat the client’s menopausal symptoms?

A woman is being treated in the hospital with chronic pelvic infection.   The physician order is Ampicillin 2 grams IV piggyback in 100 mL bag of 0.9 normal saline every 12 hours.  What rate would the nurse set the pump at to administer the medication over 60 minutes?

A client is 2 hours post operative double mastectomy secondary to breast cancer. Vital signs are:  110/60, pulse 88, respirations 18, pulse oximetry 94% on room air.  Rates pain 8 on 0-10 pain scale. Guarding abdomen. Abdominal dressing with scant amount of dried blood.   Client becomes emotional and tears up.  The nurse is anticipating that the priority intervention immediately postoperatively will be with this client:

The client is a 25-year-old woman who has been experiencing increasingly painful periods since her late teens. The pain starts a few days before her period and can last for several days, sometimes even interfering with her daily activities. She also notices heavy bleeding and fatigue during her menstrual cycle, discomfort with bowel movements, especially during her period.    The health care provider is suspecting endometriosis.  Which of the following complications listed below would the nurse need to educate the client on based on the diagnosis of endometriosis?