Contemporary Mathematics

# Chapter Review

## Section 13.1 Math and Art

1 .
A person’s length from their belly button to the floor is 25 in. What is the person’s approximate height rounded to the nearest inch?
2 .
The spiral seeds on a fruit mirror the Fibonacci sequence. If a row of the spiral contains 34 leaves, how many leaves would be found on the next larger spiral of seeds?
3 .
The seeds on a sunflower mirror the Fibonacci sequence. If a circular layer on the sunflower contains 89 seeds, approximately how many seeds would be found on the next larger circular layer?
4 .
A term of the Fibonacci sequence is 17,711 and the previous term is 10,946. What is the following term of the sequence?
5 .
The 35th term of the Fibonacci sequence is 9,227,465. Use the approximate value of $\mathit{ϕ}$ of 1.618 to estimate the 34th term. Round your answer to the nearest whole number.
6 .
A frame has dimensions of 16 in by 24 in. Calculate the ratio of the sides rounded to the nearest tenth and determine if the size approximates a golden rectangle.

## Section 13.2 Math and the Environment

7 .
An average toilet uses 5 gal of water per flush. A high-efficiency toilet uses about 1.25 gal per flush. How much water would a household save in a month (30 days) if the toilet was flushed 6 times a day?
8 .
When washing dishes, leaving the faucet running utilizes about 15 gal every 5 minutes, whereas filling the sink and turning the faucet off except to rinse the dishes uses about 6 gal for washing a dishpan-sized load of dishes. How much water is saved by not leaving the faucet running if it takes 10 minutes to wash a dishpan-sized load of dishes each day for a year containing 30 days in each month?
9 .
Leaving the water running when washing your hands consumes about 4 gal of water, whereas turning the water off when lathering reduces the water used to 1 gal. How much water is saved in an apartment of 4 people in 6 months (180 days) if each person averages washing their hands twice a day?
10 .
How long would it take for an energy-saving light bulb to consume 1 kW of power if the bulb is rated at 2.5 W? Round your answer to the nearest hour.
11 .
How long would it take for a 60 W light bulb to consume 1 kW of power? Round your answer to the nearest hour.
12 .
A portable fan uses about 40 W. How many kilowatt-hours are needed to run the fan during a 10-day trip if the fan is run for an average of 3.5 hours a day?

## Section 13.3 Math and Medicine

13 .
In a 2% solution of lidocaine, how many milligrams are there per milliliter?
14 .
You are prescribed a nebulizer solution to aid with asthma. If the solution is 0.7% w/v, what volume is needed to deliver a 7 mg dose?
15 .
A prescription calls for a patient to receive 17 mg of a drug to be taken in oral form. If the pills are available in 3.4 mg, how many pills will the patient need daily?
16 .
A prescription calls for a patient to receive 9 mg daily of a drug to be taken daily for 10 days. If the pills are available in 2.25 mg, how many pills are needed to fill the prescription?
17 .
A patient is prescribed 2 mg/kg of a drug to be delivered daily intramuscularly, divided into three doses. If the patient weighs 30 kg, how many milligrams of the drug is needed for each dose?
18 .
A patient is prescribed 0.75 mg/kg of a drug to be delivered intramuscularly once per day. If the drug is available in 2.5 mg/mL and the patient weighs 63 kg, how many milliliters of the drug should be given per day?

## Section 13.4 Math and Music

19 .
Select the most representative sound registering 50 dB: airport gate noise, light rain on a car, dirt bike racing.
20 .
Select the most representative sound registering 100 dB: city traffic when in a car with windows rolled up, children playing on a school playground, professional sporting event such as football.
21 .
What frequency range can teenagers typically hear but adults over 20 are often not able to hear?
22 .
What is three whole steps up from G#?
23 .
What is one half-step down from F?
24 .
What is an octave above D3?
25 .
Given that the frequency of ${{\rm{A}}_4} = 440\,{\rm{Hz}}$, what is the frequency of A6?

## Section 13.5 Math and Sports

For the following exercises, compute how many games would be played in the style of tournament and number of teams given in each question. Assume all tournaments are single round-round or single-elimination.
26 .
How many games would be played with 10 teams using a round-robin tournament?
27 .
How many games would be played with 25 teams using a round-robin tournament?
28 .
How many games would be played with 12 teams using a round-robin tournament?
29 .
How many games would be played with 4 teams using a single-elimination tournament?
30 .
How many games would be played with 9 teams using a single-elimination tournament?
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