AMDM UNIT 1 Review

AMDM UNIT 1 Review

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Estimating Large Numbers

• Fermi Problems

• Fundamental Counting Principal

• Scan the QR Code to the Right for a video tutorial

• Or click this link to watch the video https://youtu.be/SEYFyHqLwTg​

Fermi Problems

Fermi Problems help us to estimate large quantities by allowing us to use estimates to make an educated guess.

What assumptions can you make? or have been made? Use those values to multiply or divide as required.

Open Ended

How does estimation help to solve Fermi Problems?

Fill in the Blanks

Use a Fermi Estimate to approximate the answer to the question below using the provided assumptions.

How much air does someone breath in each day?

-It takes 5 breaths to breath 1 liter of air

-We breath on average 12 times per minute

Fill in the Blanks

Estimate the size of a crowd that is on both sides of a parade route 5 miles long and 4 feet deep, if each person occupies 2.2 square feet.

(Remember that 1 mile = 5,280 feet)

Fundamental Counting Principal

We use this to estimate large quantities by determining how many options we have for each letter or number in our identification value.

Count the number of options for each spot. Multiply the options together. This value is the total.

Fill in the Blanks

The Social Security number contains nine digits, if the form of 000-00-0000. How many different Social Security numbers can be formed using any numerals from 0 to 9?

Fill in the Blanks

Ten digit telephone number has a form (XYZ) - ABC-DEFG. In the particular state there are 4 possible area codes (404, 470, 678, and 607). The digit A is restricted to a number 2 through 8. The digits B and C can be any number but they cannot repeat. D,E,F, G have no restrictions. How many phone numbers are possible with these restrictions?

Weighted Averages

Weighted Averages are used to find an average when one category may be of more value than a number. We have used these in 3 ways analyzing grades, quarterback rankings, and batting averages.

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https://youtu.be/bnG4wrBp0ao?t=328

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Analyzing Grades

• Turn the percentage for each category into an expression. EX: Tests - 40% -> .4t

• Add all the variables to set up an equation.

• Substitute values from the problem and solve.

Fill in the Blanks

Tests - 30%

Quizzes - 20%

Classwork - 20%

Final Exam - 30%

Stan's test average is 72 and his quiz average is 80. If his classwork average is 86, then what will his grade in the class be if he gets a 70 on the final exam?

Fill in the Blanks

James worked for 12 consecutive days, earning an average wage of $160 per day as a contractor. During the first 6 days, James averaged $140 per day and his average wage for the next 5 days was $175. How much did he earn on the last day?

Quarterback Ratings/Batting Averages

• Write down the formula.

• Substitute all missing variables.

• Solve.

Multiple Choice

an average resulting from the multiplication of each component by a factor reflecting its importance.

• alarm clocks modulus

• weighted average

• letterbox

• pillarbox

Multiple Choice

A baseball players slugging average is a calculated by finding the weighted sum of the players at-bats. Singles are weighted 1, doubles are weighted 2, triples are 3, home runs are weighted 4 and all other outcomes are weighted 0. The weighted sum is then divided by the total number of at-bats.

Calculate this players slugging average:

8 singles

5 doubles

0 triples

2 home runs

40 at-bats

• 0.58

• 0.61

• 0.65

• 0.72

Fill in the Blanks

Calculate the Quarter back rating for Brett Farve

Attempts = 800

Completions = 400

TD = 59

INT = 8

Yards = 2500

Tire Ratios

We use tire ratios to determine how changing the size of our tires may affect the car's speedometer, odometer and gas mileage.

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https://youtu.be/lwaM5KwnpwA

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TIre Ratios

• Determine the section width (w), the aspect ratio (a) and the rim height (r).

• Formula for height: h=.04a(w)

• Formula for diameter: d=2h+r

• Formula for circumference.

Multiple Choice

P175/65R 15 (factory-installed)
Width 

• 175
• 65
• 15
• 1st Block runs on Jamaican time. 

Multiple Choice

P175/65R 15 (factory-installed)
Aspect Ratio

• 175
• 65
• 15
• Kyle is struggling with baseball conditioning, especially his legs...

Multiple Choice

P175/65R 15 (factory-installed)
height (in)

• 175
• 65
• 4.48
• Lexi and Lani are awesome FCA leaders. 

Multiple Choice

P175/65R 15 (factory-installed)
Diameter (in)

• 23.96
• 27.22
• 30.26
• Misty is going to come to school one full week. Hopefully. 

Multiple Choice

P175/65R 15 (factory-installed)
Circumference 

• 60.22
• 70.36
• 75.27
• Ben is going to start completing his class work without Mrs. Moxley nagging him. 

Multiple Choice

Suppose you install new tires that are 1.12 times larger in circumference than the factory tires. When your speedometer reads 65mph, how fast are you actually going?

• 78 mph

• 58 mph

• 73 mph

• 65 mph

Multiple Choice

The relationship of tire height to its width is called its ____.

• aspect ratio
• sidewall/tread ratio
• width percentage
• cross-sectional mass