Prodavačica radi brzo, ali blagajnica izgleda umorno.

Because they are feminine nouns referring to professions.

• prodavačica = a female shop assistant / saleswoman
• blagajnica = a female cashier

In Croatian, profession words often change form depending on gender:

• prodavač = male shop assistant
• prodavačica = female shop assistant
• blagajnik = male cashier
• blagajnica = female cashier

So in this sentence, both workers are being referred to as women.

They are in the nominative singular, because they are the subjects of the sentence.

• Prodavačica radi brzo.
• Blagajnica izgleda umorno.

The nominative is the basic dictionary form, and it is normally used for the person or thing doing the action or being described.

Radi is the 3rd person singular present tense of raditi = to work.

So:

• ja radim = I work
• ti radiš = you work
• on/ona radi = he/she works

Here it matches prodavačica, which is a singular subject, so radi means works.

Izgleda is the 3rd person singular present tense of izgledati = to look / seem / appear.

Examples:

• On izgleda dobro. = He looks good.
• Ona izgleda umorno. = She looks tired.
• Blagajnica izgleda umorno. = The cashier looks tired.

Again, it is singular because blagajnica is singular.

Because brzo is an adverb, not an adjective.

It describes how she works:

• radi brzo = works quickly

Adverbs in Croatian do not agree with the noun in gender or number.

Compare:

• brza prodavačica = a fast shop assistant
  
  • here brza is an adjective describing the noun
• prodavačica radi brzo = the shop assistant works quickly
  
  • here brzo is an adverb describing the verb

This is a very common question. In izgleda umorno, umorno is used adverbially with izgledati.

So the idea is:

• blagajnica je umorna = the cashier is tired
  
  • umorna is an adjective agreeing with the feminine subject
• blagajnica izgleda umorno = the cashier looks tired
  
  • umorno is the usual form after izgledati in this kind of expression

For learners, it is often easiest to remember:

• biti + adjective: agreement is normal
  
  • Ona je umorna.
• izgledati + adverb-like form: often -o
  
  • Ona izgleda umorno.

Ali means but.

It connects two clauses that contrast with each other:

• Prodavačica radi brzo
• ali blagajnica izgleda umorno

The comma is used because Croatian, like English, normally puts a comma before ali when joining two clauses.

Croatian does not have articles like English a/an and the.

So:

• prodavačica can mean a shop assistant or the shop assistant
• blagajnica can mean a cashier or the cashier

You understand the exact meaning from context.

Not completely. Croatian word order is fairly flexible, although some orders sound more natural than others.

The given sentence:

• Prodavačica radi brzo, ali blagajnica izgleda umorno.

is neutral and natural.

You may also see different word orders for emphasis, for example:

• Brzo radi prodavačica, ali blagajnica izgleda umorno.

But that sounds more marked or stylistic. For everyday use, the original order is best.

Croatian often leaves out subject pronouns like ona because the verb form already shows the person and number.

But in this sentence, the nouns are important because we are contrasting two different people:

• Prodavačica radi brzo, ali blagajnica izgleda umorno.

If you removed the nouns, it would be unclear who is being compared.

Yes. Both verbs are in the present tense:

• radi = works / is working
• izgleda = looks / seems

Croatian present tense can often correspond to either simple present or present continuous in English, depending on context.

So radi brzo could be understood as:

• works quickly
• is working quickly

depending on the situation.

Most naturally, it describes the current situation or a visible impression:

• the shop assistant is working quickly
• the cashier looks tired

Croatian present tense can describe either general habits or what is happening now, and context tells you which is meant. In this sentence, izgleda umorno strongly suggests a present impression: she appears tired now.

This is an important meaning difference:

• Blagajnica je umorna. = The cashier is tired.
  
  • This states it more directly as a fact.
• Blagajnica izgleda umorno. = The cashier looks tired.
  
  • This is about appearance or impression.

So izgleda umorno is a little less direct and more observational.

Yes. It is a good example of how Croatian contrasts two ideas with ali:

• one person is doing something positively or efficiently: radi brzo
• the other seems to be in a less positive condition: izgleda umorno

This kind of pattern is very common:

• X ..., ali Y ...
• this is true, but that is different

So the sentence is useful not only for vocabulary, but also for learning how Croatian sets up contrast naturally.