# 7.8 Exercise supplement

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter "Ratios and Rates" and contains many exercise problems. Odd problems are accompanied by solutions.

## Ratios and rates ( [link] )

Compare 250 watts to 100 watts by subtraction.

250 watts are 150 watts more than 100 watts

Compare 126 and 48 by subtraction.

Compare 144 to 9 by division.

Compare 100 tents to 5 tents by division.

100 tents are 20 times as many tents as 5 tents

Compare 28 feet to 7 feet by division.

Comparison, by division, of two pure numbers or two like denominate numbers is called a .

ratio

A comparison, by division, of two unlike denominate numbers is called a .

For problems 9-12, express each ratio or rate as a fraction.

15 to 5

$\frac{3}{1}$

72 to 12

8 millimeters to 5 milliliters

$\frac{8\text{ml}}{5\text{ml}}$

106 tablets to 52 tablets

For problems 13-16, write each ratio in the form " $a$ to $b$ ".

$\frac{9}{16}$

9 to 16

$\frac{5}{11}$

1 diskette to 8 diskettes

For problems 17-21, write each ratio or rate using words.

$\frac{9}{16}=\frac{18}{32}$

9 is to 16 as 18 is to 32

$\frac{1}{4}=\frac{12}{48}$

8 items are to 4 dollars as 2 items are to 1 dollar

150 milligrams of niacin is to 2 tablets as 300 milligrams of niacin is to 4 tablets.

20 people is to 4 seats as 5 people is to 1 seat.

$\frac{20}{4}=\frac{5}{1}$
20 people are to 4 seats as 5 people are to 1 seat

For problems 22-27, determine the missing number in each proportion.

$\frac{x}{3}=\frac{24}{9}$

$\frac{15}{7}=\frac{60}{x}$

28

$\frac{1}{1}=\frac{x}{44}$

$\frac{3}{x}=\frac{15}{50}$

10

406

## Applications of proportions ( [link] )

On a map, 3 inches represents 20 miles. How many miles does 27 inches represent?

A salt solution is composed of 8 parts of salt to 5 parts of water. How many parts of salt are there in a solution that contains 50 parts of water?

80

A model is built to $\frac{4}{15}$ scale. If a particular part of the model measures 8 inches in length, how long is the actual structure?

The ratio of ammonia to air in a container is $\frac{3}{40}$ How many milliliters of air should be in a container that contains 8 milliliters of ammonia?

$\frac{320}{3}$ or 106 $\frac{2}{3}$

A 4-foot girl casts a 9-foot shadow at a particular time of the day. How tall is a pole that casts a 144-foot shadow at the same time of the day?

The odds that a particular event will occur are 11 to 2. If this event occurs 55 times, how many times would you predict it does not occur?

10

Every 1 $\frac{3}{4}$ teaspoon of a multiple vitamin, in granular form, contains 0.85 the minimum daily requirement of vitamin A. How many teaspoons of this vitamin are required to supply 2.25 the minimum daily requirement?

## Percent and fractions of one percent ( [link] , [link] )

For problems 35-39, convert each decimal to a percent.

0.16

16%

0.818

5.3536

535.36%

0.50

3

300%

For problems 40-48, convert each percent to a decimal.

62%

1.58%

0.0158

9.15%

0.06%

0.0006

0.003%

$5\frac{3}{11}$ % to a three-place decimal

0.053

$\frac{9}{13}$ % to a three-place decimal

82 $\frac{25}{29}$ % to a four-place decimal

0.8286

$18\frac{1}{7}$ % to a four-place decimal

For problems 49-55, convert each fraction or mixed number to a percent.

$\frac{3}{5}$

60%

$\frac{2}{10}$

$\frac{5}{16}$

31.25%

$\frac{35}{8}$

$\frac{105}{16}$

656.25%

45 $\frac{1}{11}$

6 $\frac{278}{9}$

$3688.\stackrel{_}{8}%$

For problems 56-64, convert each percent to a fraction or mixed number.

95%

12%

$\frac{3}{25}$

83%

38.125%

$\frac{61}{160}$

$61.\stackrel{_}{2}%$

$\frac{5}{8}%$

$\frac{1}{160}$

$6\frac{9}{20}%$

$15\frac{3}{22}$ %

$\frac{2977}{19800}$

$106\frac{19}{45}%$

## Applications of percents ( [link] )

For problems 65-72, find each solution.

What is 16% of 40?

6.4

29.4 is what percent of 105?

$3\frac{21}{50}$ is 547.2% of what number?

0.625 or $\frac{5}{8}$

0.09378 is what percent of 52.1?

What is 680% of 1.41?

9.588

A kitchen knife is on sale for 15% off the marked price. If the marked price is $39.50, what is the sale price? On an 80 question geology exam, a student gets 68 correct. What percent is correct? 85 A salesperson makes a commission of 18% of her monthly sales total. She also receives a monthly salary of$1,600.00. If, in a particular month, she sells \$4,000.00 worth of merchandise, how much will she make that month?

find the 15th term of the geometric sequince whose first is 18 and last term of 387
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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