Alfred is opening a new office and needs to decorate and furnish it. He has 3 sources for wallpaper, 5 sources for carpet, 4 sources for drapes, 8 sources for furniture, and 2 sources for pictures. How many ways can he select one of each?

960 ways

Step-by-step explanation:

Given Data:

Wallpaper sources = 3

Carpet  sources     = 5

Drape  sources       = 4

Furniture sources   = 8

Pictures sources     = 2

No of ways Alfred can select one of each = ³C₁*⁵C₁*⁴C₁*⁸C₁*²C₁

                                                                     = 960

There are 960 ways Alfred can select each of these.

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)