12. Venu and Tanuj are running along a circular track. They take 48 seconds and 56 seconds to

Response:

b

Detailed explanation:

The height of the missing rectangle measures 0.15. The image includes the mentioned histogram that outlines the relative frequencies for the categories [0,1], [1,2], [2,3], [4,5], and [5,6] for Silver in ppm. The rectangle for the class [3,4] is the only one that is missing. Each rectangle's height represents the relative frequency for its respective class. The total of the relative frequencies must sum to 1; this is determined by dividing the absolute class frequency by the total sample size. Therefore, by summing the known relative frequencies and subtracting from 1, we can find the missing relative frequency, which corresponds to the height of the absent rectangle. To find the known relative frequencies, we add: 0.2 + 0.3 + 0.15 + 0.1 + 0.1 = 0.85. The missing frequency turns out to be 1 - 0.85 = 0.15. Hence, the height of the missing rectangle is determined to be 0.15.

Response:

a)

b) 0.044

Step-by-step breakdown:

Part a)

A Sonet consists of 14 lines. Raymond Queneau published a collection of 10 sonnets, each placed on separate pages. This implies that every page contains a 14-line poem. We are to determine how many unique sonnets can be created from the 10 published sonnets.

As the first line of a new sonnet can be chosen from any of the 10 published sonnets, it offers 10 options for the selection of the first line. Likewise, the second line of the new sonnet can also be from any of the 10 sonnets, leading to another 10 choices for the second line, and this applies identically for all 14 lines, resulting in 10 options for each line.

According to the fundamental principle of counting, the total number of possible sonnets would equal the product of the options available for all 14 lines.

Thus,

the number of sonnets created from those in the book = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 =

sonnets

Therefore,

can be formed from the 10 in the book.

Part b)

Next, we will ascertain how many sonnets can be generated that utilize none of the lines from the first and last page. Given that there are 10 pages total, the exclusion of the 1st and last leaves us with 8 pages (8 sonnets).

Consequently, the number of options for each line of such a sonnet will be restricted to 8 choices. Applying the fundamental principle of counting, the total sonnets with no lines from either the first or last sonnet is calculated as

This shows the number of favorable outcomes that ensure the selection of a sonnet does not result in lines from the first or last sonnet in the collection.

Thus,

The probability that no lines are selected from either the first or the last sonnet =

Answer:r=1.104

Step-by-step explanation:

Starting value a_1=256

Also

can be expressed as

where r=common ratio

r=1.104

2/3 of 7/8
2/3×7/8=7/12