Answer to Question #196165 in Math for Ichigo

Question

True and False with explanation

1.Total 5³ simple random samples of size 3 can be drawn without replacement from a 

population of size 5. 

2.f(x)=x+(1/x ) 0<x<=1

3.The best measure of tendency for the data 10,8,6,4,2 98, ,100 is its mean. 

4.|axb| is max when a nad b are parallel.

Answer 1

1. False.

$$\dbinom{5}{3}=\dfrac{5!}{3!(5-3)!}=\dfrac{5(4)}{1(2)}=10$$

Total 10 simple random samples of size 3 can be drawn without replacement from a population of size 5. 

2. $f(x)=x+\dfrac{1}{x}, 0<x\leq1$

$$f'(x)=(x+\dfrac{1}{x})'=1-\dfrac{1}{x^2}$$

Find the critical numbers

$$f'(x)=0=>1-\dfrac{1}{x^2}=0$$

$$\dfrac{x^2-1}{x^2}=0$$

Since $0<x\leq1,$ we take $x=1$

The function $f(x)$  decreases for $0<x\leq1$

$$f(1)=1+\dfrac{1}{1}=2$$

$$f(x)\to\infin \text{ as} \ x\to0^+$$

$f(x)\geq2$ for $0<x\leq1.$

3. False.

$$2, 4, 6, 8, 10, 98, 100$$

$$mean=\dfrac{10+8+6+4+2+98+100}{7}=\dfrac{228}{7}$$

$$median=8$$

The mean of $\dfrac{228}{7}$ is higher than every score but two, so it doesn't represent the scores very well. There are two high outliers.

The best measure of tendency for the data 10,8,6,4,2 98 ,100 is its median. 

4.

False

$$|\vec a\times\vec b|=|\vec a||\vec b|\sin(\vec a, \vec b)$$

$$0\leq \sin(\vec a, \vec b)\leq1$$

$|\vec a\times\vec b|$ is max when $\vec a$ and $\vec b$ are perpendicular.