Question

in exercises 5–8, determine whether each statement is true or false. if the statement is false, make the necessary change(s) to produce a true statement. 5) there is no variation in hand length among adult males. 6) a person’s stride length is about three - fourths of that person’s height. 7) the size of the eggs used in cookie dough can affect the texture of the cookies. 8) a u.s. quarter is a good non - standard unit of measure because its diameter is exactly one inch. critical thinking exercises 9) describe a situation where non - standard units are useful despite the variation in the units. 10) give an example of a situation where the consequences of poor measurement would be so severe that you would not want to rely on non - standard units of measure. 11) suppose the estimated length and width of a room have an error of 5.19%. will the area of the room calculated from this length and width also have an error of 5.19%? explain. make sense? in exercises 46–49, determine whether each statement makes sense or does not make sense, and explain your reasoning. 12) my friend is 6 feet tall and the height of the room seems to be about one and a half times the height of my friend, so i estimate the height of the room to be 9 feet. 13) my other friend is 5 foot 5 inches tall. i estimate this friend’s stride length to be 36 inches. 14) if i know the length of my smartphone in centimeters or inches, i can use my smartphone to estimate the height of my desk in centimeters or inches.

Explanation:

Step1: Evaluate statement 5

False. Adult males have varying hand lengths.
Corrected: There is variation in hand length among adult males.

Step2: Evaluate statement 6

True. A person's stride length is roughly $\frac{3}{4}$ of their height.

Step3: Evaluate statement 7

True. Larger eggs add more moisture, altering cookie texture.

Step4: Evaluate statement 8

False. A U.S. quarter has a fixed diameter, so it is a standard non-custom unit.
Corrected: A U.S. quarter is a good standard non-custom unit of measure because its diameter is exactly one inch.

Step5: Answer exercise 9

Non-standard units (like hand spans) are useful for quick, approximate measurements when a standard tool is unavailable, e.g., estimating the width of a bookshelf using your hand span when you don’t have a ruler.

Step6: Answer exercise 10

When measuring medication dosages for a patient: poor measurement could lead to overdose or underdose, causing severe harm or death, so non-standard units (like "a handful") are unsafe and unreliable.

Step7: Evaluate exercise 11

Let the actual length be $L$ and width be $W$. The estimated length is $L(1\pm0.054)$ and estimated width is $W(1\pm0.054)$.
Actual area: $A = L \times W$
Estimated area: $A_{est} = L(1\pm0.054) \times W(1\pm0.054) = LW(1\pm0.054)^2 = A(1\pm0.108 + 0.002916)$
The maximum error is ~10.8%, not 5.4%. So no, the area error is larger.

Step8: Evaluate statement 12

Makes sense. Calculate $6 \times 1.5 = 9$ feet, which is a valid estimation using a known reference.

Step9: Evaluate statement 13

Makes sense. A 5'5" person (65 inches) has an expected stride length of ~$\frac{3}{4} \times 65 = 48.75$ inches; 50 inches is a reasonable close estimate.

Step10: Evaluate statement 14

Makes sense. If you know your smartphone's fixed length, you can use it as a non-standard measuring tool to count how many times it fits against the desk height, then calculate the total height.

Answer:

1. False. Corrected: There is variation in hand length among adult males.
2. True
3. True
4. False. Corrected: A U.S. quarter is a good standard non-custom unit of measure because its diameter is exactly one inch.
5. Example: Estimating the width of a window using your hand span when you don't have a ruler.
6. Example: Measuring the dosage of a critical, narrow-range medication for a patient.
7. No, the area will not have a 5.4% error. The area error is approximately 10.8% because errors in length and width compound when multiplied.
8. Makes sense. The estimation uses a known height reference and simple multiplication.
9. Makes sense. The estimate is close to the expected stride length (3/4 of height).
10. Makes sense. The smartphone's known length acts as a portable measuring reference.