Hun håber at blive ansat i firmaet.

Here, at is the infinitive marker, so it means to.

So:

• at blive ansat = to be hired / to become employed

Danish at can also mean that in other sentences, so this is a very common point of confusion for learners. In this sentence, it is definitely the to-type at, not the that-type.

Because Danish normally uses at before an infinitive.

After håber, you normally say:

• håber at blive
• not håber blive

English sometimes drops to in certain structures, but Danish usually keeps at unless the verb is a modal verb such as kan, vil, skal, må.

So:

• Hun håber at blive ansat = correct
• Hun håber blive ansat = not standard Danish

This is a very common Danish way to express a passive idea.

• blive literally means become
• ansat is the past participle of ansætte = hire/employ

Together, blive ansat means be hired or get hired.

It is similar to English:

• She hopes to be hired
• She hopes to get hired

Danish often uses blive + past participle to describe something happening to someone.

Ansat is the past participle of ansætte.

You can think of the parts like this:

• ansætte = to hire / employ
• ansat = hired / employed

In blive ansat, the word ansat is part of a passive construction:

• Firmaet ansætter hende = The company hires her
• Hun bliver ansat = She is getting hired / She gets hired

So ansat is not a separate full verb here; it works with blive.

Yes, that is also correct.

There are two common patterns here:

• Hun håber at blive ansat i firmaet
• Hun håber at hun bliver ansat i firmaet

The first one is more compact and often more natural when the subject is the same in both parts. The understood subject of blive is still hun.

The second one is more explicit because it repeats hun.

A useful rule of thumb:

• If the same person is doing or experiencing both actions, Danish often uses at + infinitive
• If you want a full clause, you can repeat the subject

Because the subject is understood from the first part of the sentence.

In:

• Hun håber at blive ansat

the person who håber is also the person who will blive ansat. So Danish does not need to repeat hun before blive.

This is very similar to English:

• She hopes to be hired

You do not say:

• She hopes she to be hired

So Danish works the same way here.

Because firmaet is the definite form, meaning the company.

Danish usually adds the definite article to the end of the noun:

• et firma = a company
• firmaet = the company

So the ending -et is doing the job of English the.

That also tells you that firma is a neuter noun, since its indefinite article is et.

I usually means in, and here it means something like in the company or at the company.

With workplaces and organizations, Danish often uses i to talk about being part of an organization or employed within it.

So:

• ansat i firmaet = employed in/by the company

In some contexts, learners may also hear på with workplaces, but i firmaet is a very natural and standard choice here.

The sentence is built like this:

• Hun = subject
• håber = finite verb
• at blive ansat = infinitive phrase
• i firmaet = prepositional phrase

So the structure is:

Subject + verb + infinitive phrase + prepositional phrase

This follows normal Danish main-clause word order, where the finite verb comes early in the sentence. The whole sentence is very straightforward and natural Danish.