Answer:
1. trabajen
2.come
3. salgan
4. ganen
5. vuelva
6. vayamos
7. recicles
8. juegan
9.<em> </em>estudia
10. venga
11. duerman
12. llame
13. oiga
14. ayuden
Explanation:
1. I doubt that they work.
The verb <em>dudar</em> in Spanish calls into question the phrase introduced by it. That is why we have to use the subjunctive mode, which illustrates this kind of <em>questioning</em>. The verb that should be put in the subjunctive mode is <em>trabajar</em> and in the subjunctive mode it gives: trabajEN.
2. It is true that he eats a lot.
This sentence is far from questioning: it expresses a fact. There is no personal opinion whatsoever. <em>It is </em><em>true.</em> So we choose the indicative mode. The verb <em>comer</em> belongs in the second -ER group and should be conjugated in the third person singular: comE.
3. It is not possible that they go out.
When we deny something, it calls for the subjunctive mode, because we are speaking of something that <em>is not</em>. Here we also have a <em>personal opinion</em>: it's the<em> speaker's attitude </em>that it is impossible! The verb <em>salir</em> uses the first person singular as base to create the subjunctive form: SALGan.
4. It is possible that you win.
Uncertainty and possibility are also characteristics of the subjunctive mode. Whatever isn't <u>fact</u> and isn't <u>objective</u> is - <em>subjective.</em> The subjunctive is also necessary when it comes to <em>subordinate</em> clauses with a subject different from that of the main clause. In this case the the verb <em>ganar </em>is used in its subjunctive form for <em>ustedes: </em>ganEN.
5. I don't think she will come back.
The negation of the verb <em>creer </em>is<em> </em>suggestestive. When affirmative this verb is followed by an indicative form, but when it's in its negative form, it demands a subjunctive form. The subjunctive of the verb <em>volver </em>gives here VUELVA.
6. It is possible that we go.
When we need to express uncertainty, something that is <em>possible </em>but not entirely true, in Spanish we express it through the subjunctive mode. It illustrates the gap between what is and what it isn't and it bears an entirely different meaning from the one communicated by the use of the indicative. The verb <em>ir </em>is here used in the first person plural: VAYAMOS.
7. We doubt that you recycle.
Expressing one's doubt is another way of rivaling the objective truth. Whenever something is not a fact, a non-debatable truth, think of the subjunctive mode. You will be right. The verb <em>reciclar </em>is from the -AR group and in the subjunctive changes its vowel: reciclES<em>.</em>
8. I think they play football.
The verb <em>creer </em>expresses our perception of the reality. That is why this verb demands the use of indicative - it represents an objective attitude. It is different from the expression of <em>feelings </em>because it is the rational part that expresses itself: I <em>think</em>. I <em>use my mind </em>to tell you this. <em>Jugar </em>is used in the third person plural: ellos JUEGAN.
9. I do not deny that you study.
Normally, <em>negar </em>would grammatically suggest the use of the subjunctive. But it is in its negative form. This way we can use both modes as we choose. But bare in mind: if I do not deny, I affirm. We can use the indicative mode here: estudiA. The use of the subjunctive mode adds a nuance of uncertainty (<em>It's not that I deny </em><em>whether or not you study.</em>).
10. It is possible that she doesn't return home.
Here we want to express <em>a possibility</em>, one of many alternatives that <u>cannot be all true</u>. That is why we use the subjunctive mode. The verb <em>volver </em>changes is ending vowel in order to obey to the subjunctive mode: vuelvA.
11. It is probable that Lucio and Carmen are asleep.
Again, a possibility is expressed. The speaker cannot know for sure, so he insists on this poly-valency of the reality using the subjunctive. The adverb that introduces the clause determines the mode to use. Here the adverb doesn't present us a fact. The verb <em>dormir </em>in the subjunctive mode gives: duermAN.
12. It is possible that my cousin Marta calls.
The use of the subjunctive mode helps give a <em>subjective </em>opinion or feeling. It <em>underlines</em> the speaker's uncertainty but <em>accentuates</em> their hopes and wishes: they could have said: <em>Es posible que no llame. </em>The verb <em>llamar </em>uses the vowel -E to form the subjunctive mode: llamE.
13. Maybe Juan can't hear us.
<em>Tal vez </em>means the same as <em>puede ser</em>. But <em>tal vez </em>introduces <u>both</u>, the subjunctive, as well as the indicative mode. Therefore we can put whatever mode we like. The verb oír uses the first person singular as base for the subjunctive mode: OIGA.
14. It is not true that Paco and Daniel help us.
We have already had the <em>es cierto que </em>and we've seen it introduces the indicative mode. But what happens when we deny it? The same as for the verb <em>creer. </em>This way it shows how even what we think of as <em>the truth</em>, might just be a <em>lie. </em>The subjunctive teaches us some important life lessons. Learn your subjunctives! The form we use for <em>ayudar </em>receives endings in -E: ayudEN.