1. Correct answer: trabaja mucho.
José Miguel está cansado porque trabaja mucho.
This sentence means José Miguel is tired because he works a lot. In this sentence there is an important Spanish verb (estar) conjugated for the third person singular because José Miguel can be replaced by the subject pronoun él (he). The tense we use here is the simple present tense. This tense is used to talk about habitual actions or routines. It is also used when describing things that happen now or in the near future. Moreover, the verb estar here stands for emotion, describing José Miguel is feeling.
2. Correct answer: va a pasar un huracán
Los viajeros están preocupados porque va a pasar un huracán
This sentence means Travelers are worried that a hurricane will hit. We also use a conjugation of the verb estar here. In fact, the verb estar is used in every item of this problem standing for the simple present tense. Then, we'll assume this in the other questions from now on. Since we can replace los viajeros by the subject pronoun ellos (they) that matches the third person plural, then the conjugation of the verb estar we must use here is están and here this verb also stands for emotions because the sentence tells us how travelers are felling because of the hurricane.
3. Correct answer: nieva mucho y no pueden salir
Maribel y Claudia están tristes porque nieva mucho y no pueden salir
This sentence means Maribel and Claudia are sad because it snows a lot and they can not go out. In this case, Maribel y Claudia can be replaced by ellas that also means they but it matches the feminine form because Maribel and Claudia are both women. As in the previous exercises, the verb estar is used here as emotion because the sentence tells us how Maribel and Claudia are feeling because of the snow.
4. Correct answer: su respuesta es incorrecta
Los estudiantes están equivocados porque su respuesta es incorrecta
This sentence means the students are wrong because their answer is incorrect. As in exercise 2, we can replace los estudiantes by ellos, so we need to use the conjugation that matches the third person plural, which is están. On the other hand, the verb estar is used here indicating condition because it's expressing a thing that can vary over several hours or days, that is, the students are wrong now but they can be right later.
5. Correct answer: su novio es simpático, inteligente y guapo
Laura está enamorada porque su novio es simpático, inteligente y guapo
This sentence means Laura is in love because her boyfriend is nice, intelligent and handsome. Since we can replaced Laura by ella (she), then we must use the verb estar conjugated for the third person singular, which is está. On the other hand, this sentence also uses the verb estar here as condition, because she's in love in the present, but we don't know whether she'll be in love in the future.
6. Correct answer: porque vamos a pasar el verano con ellos
Mis abuelos están felices porque vamos a pasar el verano con ellos
This sentence means my grandparents are happy because we're going to spend the summer with them. Sin mis abuelos can be replaced by ellos, then we have to use the conjugation están. Here the verb estar is also being used as emotion because the sentence tells us how the grandparent are feeling because of the coming of their grandchildren.