Beginners: Which is correct: Estoy una estudiante, y soy muy cansada OR Soy una estudiante, y estoy muy cansada? Intermediate/Advanced: ¿Cuándo se usa la forma imperfecto, y cuándo se usa el pretérito perfecto (aka pretérito del pasado)?
Beginners: The latter is correct. There are two verbs which translate to "to be" in English; ser and estar. The "yo" form of ser is "soy", while estar conjugates to "estoy". Ser is generally used to describe a trait, or something that doesn't change. "Soy una estudiante" is correct, because it is a position I am in. To say "soy cansada", however, would mean that I am always tired, and that it is one of my attributes. The correct way to "I am tired" is "estoy cansada", because it is how I am feeling, not something that describes me as a person. Don't worry if you are having a hard time differentiating the two right now; in the Spanish classes I took, it seemed like we reviewed this every year (for five years), but still I would learn new ways these two verbs are used. You will probably find exceptions to the "rules" I listed about the verbs, but this is a starting point. Intermediate/Advanced: The "pretérito" is a past tense verb form that generally describes a sudden or one-time event. For example, "el teléfono sonó" or "the phone rang". The "imperfecto" is a little more difficult to master. It can describe something that is continuous, or a characteristic, or how the weather was, all in the past. To say "it was two o'clock", you would say "eran las dos" rather than the pretérito "fueron los dos"; to say "it was sunny" you would say the imperfecto "hacía sol" rather than the pretérito "hizo sol". ¡Espero que esto te ayude!
Iodine-131 is a radioactive isotope of iodine used in thyroid treatment. How many protons, electrons, and neutrons are in a neutral atom of iodine-131? (Hint: you need to look at the periodic table for this one)
Isotopes are "versions" of elements with varying numbers of neutrons. There is a way to write Iodine-131 this in symbolic form, but unfortunately, it does not show up on this page. I recommend googling "Iodine-131 symbol" and you will find that the 131 is in the top left of Iodine's symbol - a capital "I" . The 131 in Iodine-131 tells us that this isotope has a mass of 131. To find out how many protons it has, we first need to check the periodic table. Because iodine has an atomic number of 53, we know that it has 53 protons. How many electrons? We are told that the atoms is neutral, so the number of protons must be equal to the number of electrons. So, 53 electrons, 53 protons. How many neutrons? The mass of a proton is measured as 1 amu (atomic mass unit). The same is true for neutrons; 1 neutron = 1 amu. Electrons have next to no mass, so their mass is called "negligible". So the protons and the neutrons account for the entire mass of one atom. The mass of one Iodine-131 atom is given to us in its name; one atom weighs 131 amu. So, knowing that 53 amu are coming from the 53 protons, and the electrons don't contribute to the mass, we can subtract 53 from the mass number to get the number of neutrons: 131 - 53 = 78 neutrons.
A pre-algebra class now has 15 students, because 25% of the students didn't get tutoring, and dropped out. How many students were originally enrolled at the beginning of the semester?
What we know: because 25% of the students dropped out, the number we are given - 15- equals 75% of the original class size. So if we make x equal to the number of students who were enrolled in class at the beginning, we could write the following equation: .75x = 15 Why did we use 75 as a decimal? Because 75% is the same as writing 75/100. Written as a decimal, that is .75. In order to get x by itself, we need to divide both sides of the equation by .75: (.75x)/.75 = (15)/.75 Then you could either put those numbers in the calculator, or practice your division skills to find the value of x. If you are a fraction person, you could write it like this: (3/4x) / (3/4) = (15) / (3/4) Does dividing by a fraction freak you out? See the bonus tip I include at the bottom of the page! Using either method - decimals or fractions - we get the answer x=20. Are we done? Almost! Remember, you need to write your answer in terms of what the word problem was asking, like so: ANSWER: 20 students were enrolled at the beginning of the semester. Voila! Now, for the bonus tip: I know that in my experience, some people get lost in the fraction stage of learning, and end up always relying on decimals to solve their problems. But they're always just a fraction away from getting this concept! (Sorry... I'm a pun person). To divide fractions, I always multiply by the reciprocal. What's a reciprocal? It's simply switching the numerator and the denominator, AKA flipping the fraction upside down - the reciprocal of 2/3 is 3/2, reciprocal of 3/5 is 5/3, etc. Then you MULTIPLY instead of divide! In our practice problem, it looks like this: (3/4x) / (3/4) = (15) / (3/4) Written as multiplying by the reciprocal: (3/4x) X (4/3) = (15) X (4/3) In the left side of the equation, we know that since there are equal numbers of threes and fours on the top and bottom, everything cancels to one. In the right side, some people can get confused as to what they are multiplying the 15 by. Think of 15 as the fraction 15/1 (dividing by a one does not change the value of a number). So if we multiply across on the top, we have 15 X 4 = 60, and on the bottom, 1 X 3 = 3. This gives us the fraction 60/3. This can be reduced (or divided) to equal 20. I hope these hints help!