# Tutor profile: Bhawna C.

## Questions

### Subject: Linear Algebra

Can you just look at the equations and know at a glance how many solutions will they have? $$x+y+z=6......(eqn1)$$ $$3x+3y+3z=18........(eqn2)$$ $$x+2y-z=4.......(eqn3)$$

Notice that eqn 1 and 2 give the same information about the relationship between x,y and z. When we know that $$x+y+z=6$$, it is obvious that $$3(x+y+z)=3(6)$$ i.e. $$3x+3y+3z=18$$ These equations are linearly dependent i.e. $$constant\cdot(eqn1)=eqn2$$ Therefore, we only have 2 meaningful equations 1 and 3, $$x+y+z=6$$ $$x+2y-z=4$$ Add eqn 1 and eqn 3 to eliminate z, We get, $$2x+3y=10$$ This is a straight line which has infinite values of x and y that satisfy the condition.

### Subject: Trigonometry

Given $$\sum_{n=1}^{\infty} (2sinAcosA)^{n} = 1$$ What is the value of A?

We know that sin2A = 2sinAcosA Therefore, the sum becomes, $$\sum_{n=1}^{\infty} (sin2A)^{n} $$ Notice this is a geometric progression, $$\sin2A + sin^{2}2A + sin^{3}2A+...$$ Sum of an infinite geometric progression of the form $$a + ar + ar^{2}+ar^{3}+...= \frac{a}{1-r}$$ Here, a=sin2A, r = sin2A Therefore, $$ \frac{sin2A}{1-sin2A}=1$$ $$sin2A = 1 -sin2A$$ $$sin2A = \frac{1}{2}$$ $$2A = sin^{-1} \frac{1}{2}$$ $$2A = 30^{\circ}$$ $$A= 15^{\circ}$$

### Subject: Statistics

A survey was done asking people if tiktok should be banned in India. Poll surveyed 518 adults and 233, or 0.45 of them answered yes. Could we conlcude that only a minority if the people want tiktok to be banned?

Null hypothesis: the proportions who would answer yes or no are each 0.50. Alternative hypothesis: Fewer than 0.50, or 50%, of the population would answer yes to this question. The majority do not think that tiktok should be banned. Sample proportion is: $$\frac{233}{518} = 0.45$$ The standard deviation: $$ \sqrt{\frac{050(1-0.50)}{518}}$$ Test statistic: $$z = (0.45 – 0.50)/0.022 = –2.27 $$ Now we determine the p-value, Recall the alternative hypothesis was one-sided. p-value = proportion of bell-shaped curve below –2.27 Exact p-value = 0.0116 The p-value of 0.0116 is less than 0.05, so we conclude that the proportion of Indians who want the tiktok ban was significantly less than a majority.

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