The state of michigan generates a three-digit num-ber at random twice a day, seven days a week for its daily 3 game. the numbers are generated one digit at a time. consider the following set of 50 three-digit numbers as 150 one-digit integers that were generated at random: 169 938 506 757 594 656 444 809 321 545 732 146 713 448 861 612 881 782 209 752 571 701 852 924 766 633 696 023 601 789 137 098 534 826 642 750 827 689 979 000 933 451 945 464 876 866 236 617 418 988

let x denote the outcome when a single digit is generated.

(a). with true random numbers, what is the pmf of x? draw the probability histogram.

(b). for the 150 observations, determine the relative frequencies of 0,1,2,3,4,5,6,7,8, and 9, respectively.

(c). draw the relative frequency histogram of the observations on the same graph paper as that of the probability histogram. use a colored or dashed line for the relative frequency histogram

the answer is (4,3)

since the rule for r0, 90º is (-y,x) and it was already applied to form the image, all you have to do is reverse the answer using this formula.

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

answer: correct

step-by-step explanation: