Tutor profile: Arielle L.
Which of the following is equivalent to (7^16)? A) (7^19) / (7^3) B) (3^16) + (4^16) C) (7^8) * (7^8) D) (7^8) + (7^8) E) (7^8)^8
The answer to this question would be A) and C). Explanations are below. A) One of the important exponent rules to know is that (X^a) / (X^b) = X^(a-b). This means that (7^19) / (7^3) is equal to 7^(19-3) which is equal to 7^16. B) This option would not be equivalent to 7^16. We can combine terms with the same base, and combine their exponents. However, when we have two bases that are different, with exponents that are the same, we cannot combine these terms. C) Another important exponent rule is that (X^a) * (X^b) = X^(a+b). This means that (7^8) * (7^8) is equal to 7^(8+8) which is equal to 7^16. D) Knowing that C is correct tips us off a bit to the fact that this option would not be correct. Make sure you remember that MULTIPLYING terms means ADDING exponents and not the other way around. When adding terms we can't combine the exponents. Also, note that (7^8) + (7^8) is equivalent to 2*(7^8). E) This option would also be incorrect. When we have a term with an exponent raised to a certain power (another exponent), we MULTIPLY the two exponents. It is easy to get confused and instead think you would add the two exponents to get 8 + 8 = 16. However, this would be the case if we had (7^8) * (7^8) like in option C. For (7^8)^8 we would multiply the two exponents to get 8 * 8 = 64 and our simplified result would be (7^64), which is not what we are looking for.
How do SSRIs treat depression?
SSRIs are a category of antidepressants; their full name is Selective Serotonin Reuptake Inhibitors. Just like this name implies, SSRIs selectively inhibit the reuptake of serotonin from synapses. Normally, when neurotransmitters are released by a cell, they remain in the synapse for a short period of time (where they can bind with the postsynaptic cell), and then the neurotransmitters are "taken back" by the presynaptic cell through a process called reuptake. SSRIs inhibit reuptake of serotonin so that once it is released by presynaptic cells it remains in the synapses and can continue to bind to postsynaptic neurons. This can help improve mood because more serotonin is left in the synapses to bind with neurons.
What does the p-value of a hypothesis test really tell you?
In simple, practical terms, the p-value of a test tells you whether or not to reject the null hypothesis of the test. However, it can be beneficial to understand WHY our p-value allows us to do this, and what it actually tells us at a deeper level. The p-value of a test gives the probability of finding those experimental results assuming that the null hypothesis is true. Essentially, if we have a p-value of 0.21, this means that there is a 21% probability that we would find our results assuming that the null hypothesis is true. We reject the null hypothesis of a test when our p-value is less than our alpha level. A common alpha level is 0.05, and we often reject the null hypothesis if our alpha level is less than this. The reason for this is that an alpha of 0.05 represents a 5% chance of finding those results if the null hypothesis is true, and anything below a 5% chance is quite small. When our p-value is less than 0.05, we say "if the null hypothesis is true, there is less than a 5% probability of getting these results. Therefore, since the chance of getting these results is so small if the null hypothesis is true, it's likely that the null hypothesis is not true, and that these results came from the alternative hypothesis being true."
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