Avacuum cleaner costs $68, and the full-replacement extended warranty costs $22. if the manufacturer sells 360,920 vacuum cleaners under warranty and must replace 15% of them to honor the warranties, how much will the replacement costs be?

$3,681,384.

Step-by-step explanation:

A vacuum cleaner costs = $68

and replacement extended warranty costs = $22

Total sale of vacuum cleaners under warranty = 360,920

Vacuum cleaners must replace = 15%

First we calculate the number of vacuum cleaners that need to be replace

15% × 360,920

= 0.15 × 360,920

= 54,138

Since these vacuum cleaners need to be replaced free of cost to the consumers, the cost to the company will be selling price of the units.

Therefore, cost of replacement = 54,138 × 68 = $3,681,384

The cost of replacement would be $3,681,384.

The formula used will be:

tan 42° = y/115

Step-by-step explanation:

Lets simplify the the question.

We have a boat which is situated at 115 meters away from a light house. It forms the base of the right angled triangle.

We need to find the distance from the bottom of the light house to the top of the light house. This distance is the height of the lighthouse, which forms the perpendicular side of the right angled triangle.

The distance between boat and top of the lighthouse is unknown, it forms the hypotenuse.

The angle of elevation, which is the angle between base and hypotenuse, is given as 42°.

The right angled formed is shown below.

We know that

tanθ = Perpendicular / Base

tan42 = height / 115

If height= y

tan 42° = y/115

Solve for y.

y = 103.55 meters