Homework Assignment - Chapter P

Solutions (according to Karl)

Problem 2

The pet owner problem....

65% of US households have at least one pet
42% of that 65% have at least two pets

How many households owned at least two pets if there are 117 million households?

117*0.65

There are 76.05 million households that have at least one pet.  If we take 42% of that, we will get our answer!

76.05*0.42

There are 31.94 million households with at least two pets.

Problem 3

The billion dollar question...

each dollar bill is 0.0043 inches  how tall is a stack of a billion dollars?

0.0043*1000000000

So this is the answer in inches... we need to divide by 12*5280 to get the answer in miles

%/(12*5280.0)

This would be 67.9 miles worth of dollar bills if they are all stacked up.

Problem 6

A good investment....

Our original investment of $850 has increased in value by 13%, what is the current investment value?

We take $850 and want 113% of it, which would be multiplying it by 1.13.

850*1.13

So the result is $960.50.

Problem 8

Investment time again!

We start with $1300 two years ago, after year one we had a 12% increase:

1300*1.12

This comes to $1456.  Now, we take that, and we loose 12% of this, i.e. we retain 88% of this amount:

%*0.88

This leaves us with $1281.28, which means we lost money.  How much?

1300-%

We lost $18.72 over the two years.

Problem 9

We have a pay raise from $9.25 to $9.50, what percentage increase in pay does this represent?

The raise in pay is $0.25, so we can take this value, divide it by current pay:

0.25/9.25

As a percentage, this is 2.70% increase in pay.

Problem 18

The radius problem...

Part a.

A rope is wrapped around a wheel with radius 2 ft.  Now we increase the radius by 1 ft to 3 ft.  How much does the rope need to be lengthened?

We simply take the difference of the radii.  Remember the circumference of a circle is C = 2π r.

2*π*3-2*π*2

N[%]

So the rope needs to be lengthened by 2π feet.

Part b.

Now we wrap a rope around the equator of the Earth!  The radius of the Earth is approximately 4000 miles, which is equivalent  to 21120000 feet.  The circumference is: 2*π *21120000.  Now, if we raise the rope 1 foot above the equator, the new radius is 21120001, thus the new circumference is 2*π *21120001.  The difference is:

2π*21120001-2π*21120000

The result is still 2π for the amount the length the rope needs to be lengthened!