Hi

If a bag contains 2 red marbles, 3 white marbles and 3 blue marbles. Total

with replacement

P(1st is blue and 2nd is red) = 

without replacement

P(1st is blue and 2nd is red) = 

 

Hi, Re TY, note typo

A field is the form of a circle.  

The cost of ploughing the field at Rs. 1.50 per m^2 is Rs.5775. 

 $1.50· A(in m^2) = Rs.5775 or  

 and r  =    

 C = 2pi*r =  

cost of fencing the field at Rs.8.50 per metre = 8.50· C = 8.50· 

Using Calculator:  Using the keyboard  or   

 8.50·= Rounded to nearest whole number.

 

Hi,

perfect square in the form of 4abc9 is among 203^2 thru 223^2

 223 ,  49729    |a > b > c   and a + b + c = 18



 203 ,  41209

 207 ,  42849

 213 ,  45369 

 217 ,  47089 

 223 ,  49729

 

Hi,

The smaller of two numbers is 4 less than the larger.

Question states*** sum of their squares is 58

 x^2 + (x-4)^2 = 58

 x^2 + x^2 - 8x + 16 = 58   

2x^2 -8x -42 = 0

 x^2 - 4x - 21 = 0

solve by factoring: 

 

Hi,

cost C of renting a car for one day as a function of the number of miles driven x is C(x) = 0.11x + 36.

What is the rental cost for one day if 200 miles are driven?

C   = .11(200) + 36

 

Hi,

cost C of renting a car for one day as a function of the number of miles driven x is C(x) = 0.07x + 50.

How many miles were driven if the rental cost for one day is $75.90?



 $75.90 = .07x + 50

  25.90/.07 = x, miles driven

 

Hi, Re TY, Yes!  Good work! Two-tailed. 

How many people would need to be surveyed on health care to estimate the mean of an entire population to within 2 units 

if the standard deviation was 12 and we wanted a 92% confidence level?

92% confidence level ⇒ z = 

ME =  

    

        a	a/2	crtical regions

80%	0.2	10%	z <-1.28155	z >+1.28155

90%	0.1	5%	z <-1.645	          z >+1.645

92%	0.8	4%	z <-1.751	          z >+1.751

95%	0.05	2.50%	z <-1.96	          z >+1.96

98%	0.02	1%	z <-2.326	          z >+2.326

99%	0.01	0.50%	z<-2.576	          z >+2.576

 

Hi,

30% of California residents have adequate earthquake supplies...survey 11 of them

P(x ≥ 8) = 11C8(.3)^8(.7)^3 + 11C9(.3)^9(.7)^2 + 11C10(.3)^10(.7)^1 + 11C11(.3)^11

Stattrek.com Bionomial Calculator gives  P(x ≥ 8) = .0043

e. Is it more likely that none or that all of the residents surveyed will have adequate earthquakesupplies? Why?

 None (only 30% have them)and ...  P(0)= .02 > P(11)= .0000018

 

Hi,

The odds against Lounging Larry winning the horse race are 5:12. (5 Ls for every 12 Ws)

P(W) = 12/17

 

Hi,

In a pie chart there are 2 yellow slices, 2 green slices, 4 red slices: Total

P(yellow) = 2/8 = 1/4

 

Hi,

half of the pie at $2, 1/4 at $10 and 1/4 at $15... It costs $8 to play the game

 

Expected "winnings" =  = -.75˘

The fair price to play the game: = 0

 = 0 |Multiplying thru by 4 so as all denominators = 1

    4 - 2x + 10 - x + 15 - x = 0

               29 = 4x

                x = 29/4 = $7.25 

 

Hi,

mean of 4000 and a standard deviation of 500

Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and 50%  to the right



This curve alone does  not give exact percentages with the exception of P(z=0) = .50 or 50%

A Pictorial where 'some' of the % have been added for helps more...  

However, most often one needs to use a table, calculator, or an Excel function ect to find exact Percentage, 

after finding z: 


P(x < 3500) = P(z = (3500-4000)/500) = P(z = -1) = 1 - () = 1 - (.5 +.341) = 1-.841 = .159 or 15.9% |using above pictorial 

P(x > 4000) = P(z = 0) =  .50  or 50 % |using above pictorial 

P(3700< x < 4300) = P( -  z =) = P( - ) 

Using Calulator etc:  Here, am using the Excel NORMSDIST function to find the Percenatges:

P( - ) =  .7257 - .2742 =.4515 or 45.15%

 

Hi,

Determine whether ordered pair(x,y): (-2,3) is the solution of both the equations 

y-2x=7  Sustituting x and y:  - 2·=7  

2x+y=1  Sustituting x and y: 2·+=1

 

Hi,

 

1. Solve this equation for d = 

2. By looking at the equation  , would you expect tsunamis to travel faster or slower 

as they get closer to the shore (in shallower water)? slower



 3. Find the speed of a tsunami in a depth of 500 m 



 4. Find the speed of a tsunami in a depth of 100 m 

5. Do the answers to problems 3 and 4 confirm your expectation from problem 2? Yes

 Do Tsunami’s travel faster or slower in shallow water? 

 

Hi,

Geometric Sequence: {16,-8,4,-2,1...}  r = -1/2

 

Hi,

P(x ≥ 98) = 1 - P(x≤ 97.5) = 1-.0025 = .9975   |Using 97.5 as a lower limit

*Note: P(x ≤ 97.5) = P(t = 

 with df = 35, P( t ≤ -3) = .0025  (stattrek.com  T Distribution Calculator)

 

Hi,

 Standard Form of an Equation of an Ellipse is  

where Pt(h,k) is the center. (a variable positioned to correspond with major axis)

 a and b  are the respective vertices distances from center

 and ±are the foci distances from center: a > b

   C(0,0) and 

 foci are (0, ±)

 

Hi, Re TY, sry on the typo, NORMSDIST(-1.2) = .1151, NORMSDIST is the Excel fucntion used here to detemine the Probability.  

ONe may use a Calculator or z - table to find the Accumulative Probabilities to the left of a particular z-score

the length of pregnancies of humans are normally distributed with a = 268 days and  = 15 days.

*Note: 

 P (x < 250) = P ( = -1.2)   Excel function: NORMSDIST(-1.2) = .1151

 

 

 

Hi,



Using Excel function CORREL, r = .7264, strong positive correlation 

 

Hi,

Miles Traveled, x: 2,  3,10,7, 8, 15,3, 1, 11  mean = 6.67 

         Sales, y: 31,33,78,62,65,61,48,55,120 mean = 61.4

Re:   www.alcula.com/calculators/statistics/linear-regression/

Regression line equation:  

a =   and  

y = 3.53x + 37.9

 when x = 8   ⇒ y = 66.15

 when x = 11  ⇒ y = 76.74

 

Hi,

 only 9 test scores listed

 

Hi,

log5(30) = log (30)/log(5) = 2.1133   || Using Calculator.  Note: log is base ten

 

Hi,

 1- 3 Bionimal Distribution Problems

Note: The probability of x successes in n trials is: 

P = nCx*  where p and q are the probabilities of success and failure respectively. 

In this case p = .20(uninsured & q = .80(insured)

nCx = 

1. P(x= 2) = 8C2 (.20)^2(.80)^6 = .2936

2. P(x=6) = 8C6(.20)^6(.80)^2   = .0011

3. P(x<1) = P(x=0) + P(x=1) = .1678 + .3355 = .5033

Using Normal distribution for #4 with SD = 1, therefore z = 1.3 and P(>3) = 1 - P(z=1.3) find 1 - NORMSDIST(1.3)

Using Poison Distribution for #5, Use stattrek.com Poison Distribution Calculator (WED and WED <3) = 

Using Normal distribution for #4 with mean of 19.2 and standard deviation of 2.5

P(x>24) = 1 - P(z = (24-19.2)/2.5) find 1 - NORMSDIST(1.92)

 

Hi,

odds against winning 5:12   |m:n odds against:  event will not occur m times for every n times it does occur.



P(winning) = 12/17

 

Hi,

circle is 1/2 green, 1/4 red, and 1/4 yellow.

probability that the spinner lands on 

P(red)  = 1/4

P(green)=  1/2

P(yellow) = 1/4

P(blue) = 0

 

Hi,

 A 45

 B 180

 C 210

 D 95

 F 65

 I 5 

  595

 P(at least a B)= 225/595

 

 

Hi,

I. find Mean and SD for each sample. 

Sample 1: m = 589, SD = 42.615

Sample 2: m = 684.9,  SD = 82.225

II.  Find the t-value

t =

Which is significant at the 99% Level(degree of Freedom 18):  3.2745 > 2.88 				

DF	0.1	0.05	0.01	0.001

18	1.73	2.1		3.92

b)What is the difference between the mean of the two groups? 684.9-589

What is the difference is standard deviation? 82.25-42.615

c)What is the null and alternative hypothesis? 

: m for over weight people ≤ 589

: m for over weight people > 589 

As 3.2745 > 2.88, we reject the null hypothesis

overweight people do eat faster according to this study



Note: www.chem.uoa.gr  is an interesting site

 

Hi,

Note:     |



    |

 

Hi

  

 || Keep going...More common factors of "p"

 

Hi

f(x)=x^3-5x^2+9x-5    | x = 1 is a solution

Using synthetic division

1	1	-5	9	-5

 	 	 1	-4	5

 	1	-4	5	0

 f(x) = (x-1)(x^2 - 4x + 5} 

x^2 - 4x + 5