Agovernment agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages. in standard english text, a particular letter is used at a rate of 6.8%.
a. find the mean and standard deviation for the number of times this letter will be found on a typical page of 3000 characters.

let n be the number of times letter be found (1800), p be the success rate (0.068), and q be the failure rate (1 - 0.068 = 0.932)  

mean = np = 1800 x 0.068 = 122.4  

standard deviation = √(npq) = √(1800 x 0.068 x 0.932) = 10.6807414

you would have to sell 24 bracelets.

step-by-step explanation:

84/3.5 = 24

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .