0 of 21 questions completed
Questions:
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
0 of 21 questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Use this information to answer questions 1 and 2. At some point, you have probably used paint or printed a document. Painters have a sense, through practice, of the ratios of different colors they should mix to form new colors. They also add different amounts of water or oil to their paints to control thickness and opacity. Very precise ratios are used by paint chemists to measure the ingredients in paints, inks, and coatings. Paint ingredients include pigment compounds for color:
They also include binders — such as linseed oil, acrylic, gum arabic, and egg yolk — that hold the molecules of pigment together. The pigment-to-binder ratio of a paint affects such qualities as saturation, gloss, and flexibility. Paints can include other components such as solvents and extenders that also affect how they behave.
You are mixing cobalt blue pigment, binder, and water to make an acrylic paint. If the ratio of cobalt blue pigment-to-binder to water in your mixture is 1:4:5, respectively, and there are no other substances in the mixture, what is the ratio of cobalt blue pigment to the mixture?
Mastery question: If the ratio of cobalt blue pigment to binder in an oil paint mixture is 7:18, and there are no other substances in the mixture, what percent of the mixture is cobalt blue pigment?
Use this information to answer question 3,4, and 5. What makes a drawing of a face look realistic? Not only are specific features important, but their size and arrangement relative to each other are, too. Take a look at this drawing of approximate proportions of an adult face. Note: No two people are the same, so there is no “exact” or “best” version of these relationships. These are rough similarities, not rules.
Because hairlines can make this difficult to see, some people are surprised to learn that an adult person’s eyes are roughly halfway between the top of their head (not hairline) and their chin. Generally, there is about one eye’s length of space between a person’s eye sockets, and the bottom of a person’s nose is usually about midway down the lower half of their face. Individual variations on these proportions make specific people recognizable and interesting!
Human bodies also have common overall proportions, allowing us to recognize simplified versions on walk signs, bathroom doors, and icons. Other animals — and plants, and all kinds of things — have recognizable proportions. If you change familiar proportions dramatically, you will get a cartoon.
What is the approximate ratio of the space above an adult person’s eyes (to the top of their head) to below their eyes?
What is the approximate ratio of the combined width taken up by a person’s eyes to the width between their eyes?
Mastery Question: In simplified form, what is the approximate ratio of the space below the center of a person’s mouth to above it?
Photo by Sarah Pflug
Use this information to answer question 6. Every time you scale up or down a recipe, you are using ratios. You can measure these precisely if you need to change something from the written recipe. Professional chefs have many commonly used ratios memorized, like that pie dough has a ratio of flour to butter to water of 3:2:1, allowing them to move and think quickly in the kitchen.
You are baking bread. Your recipe calls for \( \frac{1}{4} \) oz of active yeast to 2 \( \frac{1}{4} \) cups of warm water. If you decide to use all of the 1 \( \frac{1}{3} \) oz of yeast that you currently have, how many cups of water do you need?
Photo by Shopify Partners
Use this information to answer question 7. Converting between units isn’t just useful in technology; all sorts of fields and concepts use different kinds of units. You might use unit conversion when the units you’re working with get too big or small.
There are 3 ft in a yard. How many \( ft^{3} \) are there in 3 \( yd^{3} \)?
Use this information to answer questions 8-10. The average person sleeps for \( \frac{1}{3} \) of a day (8 hrs). If this person kept this same sleep ratio for their entire life, what fraction of their life would they have spent asleep?
Let’s say this same person lives to be 75 years of age exactly. How many total days would they have spent asleep? Assume each year has 365 days. (In the previous question, we figured out this person spends \( \frac{1}{3} \) of their life asleep.)
Mastery Question: How old would this person be when they reached their 1000th cumulative day slept, rounded down to the year? (Still assume each year is 365 days and this person spends \( \frac{1}{3} \) of their life asleep.)
Photo by Sarah Pflug
Use this information to answer questions 11 and 12. We all interact with architecture, and architects use ratios when they design and model the dimensions of a space in their plans. Architects draft their plans, or scale drawings, at a fraction of the construction’s actual size for ease of use. They often use common scales so that other architects have an intuitive sense of how big the space will be in real life when they look at the scale drawing.
Examples of scales in the imperial system of measurement (US, Liberia, and Myanmar):
\( \frac{1}{4} \) inch: 1 foot
\( \frac{1}{8} \) inch: 1 foot
Examples of scales in the metric system of measurement (…everyone else):
1 unit :100 units
1 unit : 500 units
Other professionals who use scale drawings include engineers, interior designers, model makers, and surveyors. The Golden Ratio is another ratio used in architecture and design.
You are renovating a building with a length from the two outermost walls of 50 ft. How long will the house be on your scale drawing if your drawing is \( \frac{1}{4} \) of an inch for every 1 foot of actual building?
Mastery Question: A living room of a house you are building will be shown on two different architectural plans: a floor plan with the scale 1 cm on the drawing : 100 cm of actual building and a site plan with the scale 1 cm on the drawing : 500 cm of actual building. Which scale will produce the plan where the living room is drawn larger? (Write the scale as your answer.)
Photo by Matthew Henry
Use this information to answer questions 13-16. Have you ever started to download a large file and wondered low long it would take? Unit prefixes allow for quick and clean representations of small and large numbers. Being able to understand and convert between these prefixes is very useful, especially in a field like technology that uses quite a lot of them.
You want to download a new video game that is 10 Gigabytes large (1 Gb = \(10^{9}\) bytes). How large is this game in bits given the ratio of bits per byte is \(8:1\)?
Your internet download speed is 100 Mb/s (1Mb = \(10^{6}\) bytes). How many seconds will it take to download the same 10 Gb game?
How many minutes is your answer to number 10?
Mastery Question: Say you want to upgrade your internet’s download speed such that the same 10 Gb game takes under one minute to download. Which of the following is the cheapest internet package your Internet Service Provider offers that still achieves this goal?
Photo by Shopify Partners
Use this information for question 17. Medicine is a field where being sure of your ratios and units is critical. Giving your patients the correct dose of medicine can mean the difference between curing their disease or making them sicker!
You are on a flight from New York to Memphis when a 10 kilogram child sitting next to you starts to have an allergic reaction. You notify the flight attendant, who promptly brings you a case containing 4 Epi-Pens of various dosages:
A. 0.05 mL
B. 0.1 mL
C. 0.15mL
D. 0.3mL
with each at a 1:1000 concentration of Epinephrine to solution (1mg/mL). An instructional insert gives a dose radio of 0.01 mg Epinephrine per kilogram the patient weighs. Which of the epi-pens should you administer to the child?
Photo by Matthew Henry
Use the following information to answer questions 18 and 19. Human ears distinguish between pitches of sounds based on their frequency. The unit of frequency is Hertz (Hz = \( \frac{1}{s} \) ), and the frequency of a wave is given as a ratio of the wave’s velocity over its wavelength. Musicians define the frequency of 440 Hz as A. If the frequency of a note is doubled (say from 440 Hz to 880 Hz), then our ears perceive it as identical to the original, only higher pitched. We call this range an octave because it is customary to introduce 6 other notes on the way from one A to another (B, C, D, E, F, and G). If we include both A’s, then we have a total of 8 notes (octave being the Latin word for eighth).
The frequencies of the notes from the 440Hz A to the 880Hz A are generally given as:
A= 440 A=880
B= 247.5 B=
C= 264 C=
D= 297 D=
E= 330 E=
F= 352 F=
G= 396 G=
Given the table above, what is the frequency of the C one octave above the C at 264 Hz?
The frequencies of the notes from the 440Hz A to the 880Hz A are generally given as:
A= 220 A=880
B= 247.5 B=
C= 264 C=
D= 297 D=
E= 330 E=
F= 352 F=
G= 396 G=
A C-Major chord consists of three notes, C, E, and G. Given the table above, what is the ratio of the frequencies of these notes in reduced form?
Photo by Brodie Vissers
Use the following information to answer questions 20 and 21. Pi (π) is simply the constant ratio between a circle’s circumference and its diameter. π can be found in countless areas of study: generally, anything that curves will have π associated with its mechanics.
NASA uses π all the time, especially because satellites often are put in perfectly circular orbits around planets and moons. NASA’s “Dawn” spacecraft, for example, was placed in a circular orbit around the dwarf planet Ceres to take pictures of its surface. If Ceres has an average radius of 475 km, what is its approximate surface area, rounded to the nearest thousand square kilometer (Surface area of a sphere = 4π \( r^2 \) )?
The Dawn spacecraft’s orbit was at an altitude of 385 km. From this altitude, the biggest picture it could take covered a square on Ceres’ surface about 26 km long on each side (area = length x width). If we assume that there is no overlap between photographs, how many photos would it take for Dawn to fully map Ceres’ surface? (Use your rounded answer to previous problem as the surface area.)