Tutoring IB Higher Level mathematics
If $f(x)=x+\sqrt{2-x}$ and $g(u)=u+\sqrt{2-u},$ is it true that $f=g ?$
In Exercises 59-66, find all real values of $x$ such that $f(x)=0$.
$f(x) = x^3-x$
Find a vector equation and parametric equations for the line.The line through the point $(2,2.4,3.5)$ and parallel to the vector $3 \mathbf{i}+2 \mathbf{j}-\mathbf{k}$
Find parametric equations and symmetric equations for the line.The line through the origin and the point $(1,2,3)$
Find parametric equations and symmetric equations for the line.The line through the points $(1,3,2)$ and $(-4,3,0)$
You are driving south along the shore of the Mississippi River. At this point it is flowing due South. You notice a prominent radio tower right on the far shore, at a bearing of 115 degrees. You drive on for 2 miles and notice that now the radio tower appears at a bearing of 55 degrees. You figure that at this point the Mississippi river is. miles wide. round to 2 decimal places
1. Three cards are dealt. What is the probability that the first is a king, the second is a diamond, and the third is a diamond?2. You are given that Event A = owning a car and that Event B = owning a bike. P(A) = 0.20, P(B) = 0.30, and P(A and B) = 0.12. What is the P(A|B)? Are the events independent? Explain how you know. [Just in case someone's computer is having trouble with symbols, the question is, "What is the probability of A given B?"]3. Bob goes to the bakery and purchases one dozen doughnuts. He gets six chocolate, four glazed, and two plain doughnuts. Paul (Bob’s co-worker) reaches into the box and randomly picks two doughnuts. What is the probability that both of these first two doughnuts are not glazed?
1. A combination lock will open when you select the right choice of four numbers (from 1 to 40, inclusive). How many different lock combinations are possible? 2. In how many orders can five girls and three boys walk through a doorway single file for each of the following? a) There are no restrictions b) The boys walk before the girls 3. From a pool of 16 candidates, the offices of president, vice-president, secretary, and treasurer need to be filled. In how many different ways can the offices be filled?
On average, a student takes 90 words/minute midway through anadvanced court reporting course at the American Institute of CourtReporting. Assuming that the dictation speeds of the students arenormally distributed and that the standard deviation is 10words/minute, find the probability that a student randomly selectedfrom the course can take dictation at the following speeds. (Roundyour answers to four decimal places.)(a) more than 120 words/minute(b) between 60 and 120 words/minute(c) less than 60 words/minute
excel: In a large university, 55% of the students are male. If arandom sample of twenty students is selected,a. what is the probability that the sample contains exactly fourmale students?b. what is the probability that the sample will contain morethan nine male students?c. what is the probability that the sample will contain fewerthan five male students?d. what is the expected number of male students?
Tom has to make a code for his bike lockHe buys a lock that consists of four locking wheels, where each ofthe locking wheels shows 0, 1, 2, 3, 4 or 5.a) How many different lock codes can Tom make on his bicyclelock?b) Tom's wife wants to guess what his code is. She tips 1513.What's the probability that Tom's wife is typing the correct lockcode?c) Tom decides that the lock code should consist of four differentdigits.How many different lock codes can Tom now create?d) Tom's wife will guess at this new code, and guess 0125.What is the probability that Tom's wife does not type the correctlock code?
