In the country abcd there are 17 roads from city a to city b. from city b to c −5 roads, from a to d −4 roads and from d to c −8 roads. how many ways can you drive from city a to city c?

117.

Step-by-step explanation:

In the country, ABCD are 4 cities.

Roads from city A to city B = 17

Roads from city B to city C = 5

Roads from city A to city D = 4

Roads from city D to city C = 8

We need to find the number of ways from city A to city C.

Route 1 : A-B-C

Total number of ways from A to B = C(17,1) = 17

Total number of ways from B to C = C(5,1) = 5

Total possible number of ways from A to C by route 1 is

A-B-C = 17 × 5 = 85

Route 2: A-D-C

Total number of ways from A to D = C(4,1) = 4

Total number of ways from D to C = C(8,1) = 8

Total possible number of ways from A to C by route 2 is

A-D-C = 4 × 8 = 32

Total ways to drive from city A to city C is

Therefore, the required number of ways is 117.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.