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business mathematics

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Mathematics

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Homework

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(1)
Convert the number to the numeral in the base indicated:
14 to base 2
2 14
2 7 0 Once place
2 3 1 Second place
2 1 1 fourth place
2 0 1 eigth place
Therefore, 14 to base 2 is
( )
2
14 1110=
(Or)
For base 2 the place values are 8,4,2,1
( ) ( ) ( ) ( )
14 1 8 1 4 1 2 0 1
1110 in base 2
= × + × + × + ×
=
(2)
Convert the number to the numeral in the base indicated:
73 to base 3
For base 3 the place values are 27,9,3,1
( ) ( ) ( ) ( )
73 2 27 2 9 0 3 1 1
2201 in base 3
= × + × + × + ×
=
(3)
Convert the given measure to the unit indicated.
0.034 ml to liters.
1 mL =
1
1000
litres
0.034 ml = 0.0000340000000000000 litres.
(4)
Arrange the quantities in order from smallest to largest.
Given that 514 hm, 62 km, 680 m
We have
1 km 10 hectometres 1000 meters
= =
Smallest to largest
680 m,514 hm,62km
(5)
Calcium tablets, sean takes two 25-mg chewable calcium tablets each day.
(a)
How many milligrams of calcium will sean take in a week.
Sean takes two 25-mg chewable calcium tablets each day
So Sean takes
25 2 50 milligrams per day× =
Sean take in a week
(6)
How many milligrams of calcium will sean take in a week.
1000 milligrams is equal to one gram.
1
1 milligram gram
1000
=
Sean take in a week
300
300 milligram gram
1000
3
gram
10
0.3gram
=
=
=
Sean take in a week
50 7 0.3grams× =
(7)
Choose the best answer to indicate the volume of the following.
Air in a balloon with a diameter on about 17 meters.
a)
3
2600m
b)
3
2600 mc
c)
3
2600 mk
So the volume of the air in a balloon is
3
2600m
Kim Martello has purchased a farm that is in the shape of a rectangle. The dimension of
the piece of land are 1.4 km by 3.75 km
(a)
How many square kilometers of land did she purchase?
A farm that is in the shape of a rectangle.
And the dimensions of the piece of land are
1.4 km
by
3.75 km
The area of the rectangle is
2
1.4 km 3.75 km 5.25 km× =
(b)
If
2
1km
equals 100 ha, determine the amount of land she purchased in hectares.
Given that
2
1 km
equals to
100 ha
So that
2
5.25 km
equals to
( )
5.25 100 ha 525 ha× =
(8)
A cylindrical shaped hot water heater has a diameter of 0.56 m and a height of 1.17 m. if
the hot water heater is filled, determine the volume of the water in the hot water heater in
a) Cubic meters b) liters
A cylindrical shaped hot-water heater has a diameter of 0.56 m and
a height of 1.17 m. If the hot-water heater is filled,

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Therefore, the volume of the water in the hot-water heater in cubic meters.
(9)
9 lb to kilograms
( )
1 lb 0.45359237 kilograms.
9 lb 0.45359237 9 kilograms
4.08233133 kilograms
=
= ×
=
(10)
1 km
is equivalent to
0.6214
miles.
Convert 105 mi on 5 gal of gasoline.
1.609 105 168.945
169 km
× =
(11)
(a)
The weight restriction on a road in Italy is 7.5 t.
One ton is equal to 2000 pounds.
So
7.5 tons
is equal to
( )
7.5 2000 pounds
×
( )
7.5 tons 7.5 2000 pounds
15000 pounds
= ×
=
(b)
There are
15000 pounds
(12)
(a)
Each tablespoon contains 236 mg of the active ingredient bismuth subsalicylate.
2 tablespoons is
( )
236 2 mg 472mg
× =
(b)
One fl oz is equals to 34125 milligrams.
So 8 fl oz is equals to
34125 8 273000
× =
milligrams.
(13)
Department of Agriculture's recommended daily allowance of potassium for adults is 350
mg.
One serving of Cheerios provides 95 mg of potassium.
The percent of the potassium is
95
100 27.14%
350
× =
(14)
In a study of US rivers, 693,905 miles of river were studied
it was found that 36% of the total miles of river studied had impaired water quality.
Mile of rivers had impaired water quality is,
693905 36
693905 36%
100
249805.8 miles
×
× =
=
(15)
In 1990, the population of the United States was about 249 million.
In 2010, the population was about 308 million
The difference of population is ,
308 249 59
0.2369477 0.2369477 100 23.7%
249 249
= = = × =
(16)
Let the original number of employees be
a
But
The Fastlock Company hired 57 new employees, which increased its staff by 30%
57
100 30
5700
30
5700
30
190
a
a
a
a
× =
÷
=
=
=
Therefore, the original number of employees are 190
(17)
6000, 3.5%, 3 timesp r n
= = =

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( )
( )
3
3
1
100
3.5
6000 1 2
100
6000 1.07
6000 1.225043
7350.258
n
R
A P
= +
÷
= + ×
÷
=
=
=
(18)
10000, 1.29%, 3 timesp r n
= = =
( )
3
3
1
100
1.29
6000 1 2
100
6000 1.0258
n
R
A P
= +
÷
= + ×
÷
=
( )
6000 1.079414093512
6476.48
=
=
(19)
Determine the effective annual yields for $1 invested for 1 year at 4.75% compounded
monthly.
( )
12
4.75
1 1
12
1.3958333
54.70194 1
53.7019
r
r
r
+ = +
÷
=
=
=
(20)
Tom angelo needs to borrow $1500 to expand his fram implement maintenance business.
He learns that the local bank will lend him the money for 2 years with a simple interest
this rate of 7% . How much money will Tom save by borrowing the money from his
grandfather?
Tom’s grandfather offers to lend him the money for 2 years with a simple interest rate of
7%.
The simple interest rate of
7%
on 1500
That is
7
1500 7% 1500
100
105
× = ×
=
Therefore, Tom save by borrowing the money from his grandfather
That is total amount:
(12)
Sadaf Din purchased a house selling for $215,000 . To obtain her mortgage
sadaf must make a 20% down payment. The current mortgage rate is 4.5%
(a)
Determine the amount of the required down payment.
20
215000 20% 215000
100
43000
× = ×
=
(b)
Determine the monthly principle and interest payment for a 25-year mortgage with a 20
% down payment.
43000 25.45
10083.5
100
×
=

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