Do You Know ASVAB? Play This Quiz Quiz #1

1. 2: The fruit was edible.

Wax

Digestible

Foreign

Expensive

The word "edible" means that the fruit can be eaten and digested without causing harm. Therefore, the correct answer is "digestible" as it is a synonym of "edible".

Explanation

The word "edible" means that the fruit can be eaten and digested without causing harm. Therefore, the correct answer is "digestible" as it is a synonym of "edible".

2. 4: If 4 people can run 8 machines, how many machines can 2 people run?

2

4

3

1

If 4 people can run 8 machines, it means that the ratio of people to machines is 4:8, which simplifies to 1:2. Therefore, if there are 2 people, they can run half the number of machines, which is 4.

Explanation

If 4 people can run 8 machines, it means that the ratio of people to machines is 4:8, which simplifies to 1:2. Therefore, if there are 2 people, they can run half the number of machines, which is 4.

3. 5: The product of two consecutive odd numbers is 399. What are the numbers?

A. 17 and 19

B. 19 and 21

D. 25 and 27

C. 21 and 23

The product of two consecutive odd numbers is 399. To find the numbers, we need to find two consecutive odd numbers whose product is 399. The only pair of consecutive odd numbers whose product is 399 is 19 and 21. Therefore, the answer is B. 19 and 21.

Explanation

The product of two consecutive odd numbers is 399. To find the numbers, we need to find two consecutive odd numbers whose product is 399. The only pair of consecutive odd numbers whose product is 399 is 19 and 21. Therefore, the answer is B. 19 and 21.

4. 4: Her eyesight was acute.

Sharp

Unusual

Poor

Tested

The word "acute" means having a sharp or keen sense. Therefore, the correct answer is "sharp" which is a synonym for acute.

Explanation

The word "acute" means having a sharp or keen sense. Therefore, the correct answer is "sharp" which is a synonym for acute.

5. 3: Her conversation was incoherent.

Eloquent

Succinct

Unintelligible

Amusing

The word "incoherent" means lacking clarity or logical connection. Therefore, if someone's conversation is described as "incoherent," it means that their speech is unclear or difficult to understand. The word that has a similar meaning to "incoherent" is "unintelligible," which means not able to be understood. Hence, "unintelligible" is the correct answer.

Explanation

The word "incoherent" means lacking clarity or logical connection. Therefore, if someone's conversation is described as "incoherent," it means that their speech is unclear or difficult to understand. The word that has a similar meaning to "incoherent" is "unintelligible," which means not able to be understood. Hence, "unintelligible" is the correct answer.

6. Epidemiology is the study of what causes diseases, injuries, and other physiological damage to humans and why such problems occur. Epidemiologists examine where and when disease outbreaks occur. By using statistics and other scientific methods, epidemiologists determine what factors affect the frequency and severity of disease patterns. The primary goal of epidemiology is to control or prevent outbreaks of disease — other goals are subordinate. What would be the best title for this passage?

C. Using Statistical Methods in Epidemiology

B. Goals for the Future of Epidemiology

A. Epidemiology: The Study of Disease Patterns

D. Employment Outlook for Epidemiologists

The passage provides a clear definition and explanation of epidemiology, stating that it is the study of what causes diseases, injuries, and other physiological damage to humans and why such problems occur. It also mentions that epidemiologists examine where and when disease outbreaks occur and use statistics and scientific methods to determine factors that affect disease patterns. Therefore, the best title for this passage would be "Epidemiology: The Study of Disease Patterns."

Explanation

The passage provides a clear definition and explanation of epidemiology, stating that it is the study of what causes diseases, injuries, and other physiological damage to humans and why such problems occur. It also mentions that epidemiologists examine where and when disease outbreaks occur and use statistics and scientific methods to determine factors that affect disease patterns. Therefore, the best title for this passage would be "Epidemiology: The Study of Disease Patterns."

7. Miguel passed seven of his history-class quizzes and failed three. The fraction of quizzes he passed is correctly expressed as:

A. 7⁄3

C. 7⁄10

D. 3⁄5

B. 3⁄7

Miguel passed seven out of ten history-class quizzes, so the fraction of quizzes he passed is correctly expressed as 7/10.

Explanation

Miguel passed seven out of ten history-class quizzes, so the fraction of quizzes he passed is correctly expressed as 7/10.

8. Questions 2 through 4 are based on the following passage. Electricity is the most inefficient and costly way to heat a home. One kilowatt-hour of electricity creates about 3,400 British thermal units (BTUs). (BTUs are a standard heat measurement.) The price of electricity per kilowatt-hour is between $0.10 and $0.25 or between $29.35 and $73.13 per million BTUs. In contrast, fuel oil, which produces 140,000 BTUs per gallon, costs about $8.33 to $13.89 per million BTUs. Natural gas, which produces 100,000 BTUs per therm, can be purchased for $5.00 to $22.50 per million BTUs. Oak firewood, which produces 26,000,000 BTUs per cord, costs $5.77 to $13.46 per million BTUs. Choosing the right heating method for your home, based on the cost of fuel, may be more expensive at installation but will be cheaper in the long run.2: According to the above passage, a BTU:

B. stands for “British thermal unit”

A. is an unusual method of measuring heat

D. can heat a 9 x 12 room

C. is the abbreviation for a “big thermal unit”

The passage states that BTU stands for "British thermal unit." This means that option B, which states that a BTU stands for "British thermal unit," is the correct answer.

Explanation

The passage states that BTU stands for "British thermal unit." This means that option B, which states that a BTU stands for "British thermal unit," is the correct answer.

9. The idea being an alarming one, he scrambled out of bed and groped his way to the window. He was obliged to rub the frost off with the sleeve of his dressing-gown before he could see anything and could see very little then. All he could make out was that it was still very foggy and extremely cold and that there was no noise of people running to and fro and making a great stir, as there unquestionably would've been if night had beaten off bright day, and taken possession of the world. This story takes place:

C. on a winter night

A. in England

B. on a calm summer evening

D. both A and C

The passage mentions that the character had to rub frost off the window and that it was extremely cold, indicating that the story takes place in winter. Additionally, there is no mention of it being summer or any specific location, so the answer is C. on a winter night.

Explanation

The passage mentions that the character had to rub frost off the window and that it was extremely cold, indicating that the story takes place in winter. Additionally, there is no mention of it being summer or any specific location, so the answer is C. on a winter night.

10. 3: Evaluate the expression 6a – 3x – 2y, if a = 3, x = 7, and y = 4.

A. -11

31

B. -40

D. 40

When we substitute the given values of a, x, and y into the expression 6a - 3x - 2y, we get:

6(3) - 3(7) - 2(4) = 18 - 21 - 8 = -3 - 8 = -11

Therefore, the correct answer is A. -11.

Explanation

When we substitute the given values of a, x, and y into the expression 6a - 3x - 2y, we get:

6(3) - 3(7) - 2(4) = 18 - 21 - 8 = -3 - 8 = -11

Therefore, the correct answer is A. -11.

11. Questions 8 through 10 are based on the following passage. Ergonomics is the science of designing and arranging workspaces so that people and objects interact efficiently and safely. Lack of attention to ergonomics causes thousands of workers to suffer repetitive stress injury, eye fatigue, muscle soreness, and many other medical problems each year. Adequate lighting, well-designed chairs, and clutter-free work areas contribute to effective ergonomic design. The opportunity to take short breaks every hour or two, especially for desk-bound workers, is also helpful. It's also important for workers to avoid performing the same movements over and over for hours at a time. Variety in the type of work being done can decrease the chance of injury.8: According to this passage:

C. Ergonomics is expensive and time consuming.

A. Ergonomics can cause injuries.

D. Few people experience problems due to poor ergonomics.

B. Ergonomics is about designing and arranging workspaces efficiently and safely.

The passage explains that ergonomics is the science of designing and arranging workspaces to ensure efficient and safe interaction between people and objects. It also mentions that lack of attention to ergonomics can lead to various medical problems for workers. Therefore, the correct answer is B. Ergonomics is about designing and arranging workspaces efficiently and safely.

Explanation

The passage explains that ergonomics is the science of designing and arranging workspaces to ensure efficient and safe interaction between people and objects. It also mentions that lack of attention to ergonomics can lead to various medical problems for workers. Therefore, the correct answer is B. Ergonomics is about designing and arranging workspaces efficiently and safely.

12. A bricklayer charges $8 per square foot to lay a patio. How much would it cost for the bricklayer to lay a 12-foot-m-16-foot patio?

$1536

$960

$192

$224

To find the cost of laying the patio, we need to calculate the area of the patio first. The area of a rectangle can be found by multiplying its length by its width. In this case, the length of the patio is 12 feet and the width is 16 feet. Therefore, the area of the patio is 12 feet * 16 feet = 192 square feet. Since the bricklayer charges $8 per square foot, we can find the total cost by multiplying the area of the patio by the cost per square foot. So, 192 square feet * $8 per square foot = $1536. Therefore, it would cost $1536 for the bricklayer to lay a 12-foot-by-16-foot patio.

Explanation

To find the cost of laying the patio, we need to calculate the area of the patio first. The area of a rectangle can be found by multiplying its length by its width. In this case, the length of the patio is 12 feet and the width is 16 feet. Therefore, the area of the patio is 12 feet * 16 feet = 192 square feet. Since the bricklayer charges $8 per square foot, we can find the total cost by multiplying the area of the patio by the cost per square foot. So, 192 square feet * $8 per square foot = $1536. Therefore, it would cost $1536 for the bricklayer to lay a 12-foot-by-16-foot patio.

13. A bin of bolts at the hardware store contains 7-dozen bolts when full. The stock clerk is supposed to reorder bolts when the bin is ¹⁄₆ full. How many bolts are in the bin when it's time to reorder?

B. 1 bolt

A. 14 bolts

D. 12 bolts

C. 84 bolts

When the bin is 1/6 full, it means that there are 1/6 of the total number of bolts in the bin. Since the bin contains 7 dozen bolts when full, which is equal to 7 x 12 = 84 bolts, 1/6 of 84 is equal to 14 bolts. Therefore, when it's time to reorder, there are 14 bolts in the bin.

Explanation

When the bin is 1/6 full, it means that there are 1/6 of the total number of bolts in the bin. Since the bin contains 7 dozen bolts when full, which is equal to 7 x 12 = 84 bolts, 1/6 of 84 is equal to 14 bolts. Therefore, when it's time to reorder, there are 14 bolts in the bin.

14. 8: Universities and colleges should be designed to cater to the philomath.

Students

Teachers

Scholars

Faculty

The statement suggests that universities and colleges should be designed to cater to the philomath. A philomath is someone who loves learning and studying. Therefore, the most suitable group to cater to would be scholars, as they are individuals who are dedicated to academic pursuits and knowledge acquisition. They are likely to appreciate and benefit from an educational environment that is designed to cater to their love for learning.

Explanation

The statement suggests that universities and colleges should be designed to cater to the philomath. A philomath is someone who loves learning and studying. Therefore, the most suitable group to cater to would be scholars, as they are individuals who are dedicated to academic pursuits and knowledge acquisition. They are likely to appreciate and benefit from an educational environment that is designed to cater to their love for learning.

15. 9: Debouch most nearly means:

Emerge

Relax

Capture

Fight

Debouch means to emerge or come out, so the correct answer is "emerge".

Explanation

Debouch means to emerge or come out, so the correct answer is "emerge".

16. 4: The title of this passage should be:

C. Know Your BTUs

A. Choosing the Right Heating Method

B. Heating Methods for Houses

D. Price List for Fuel

The passage discusses the topic of selecting the appropriate heating method. It provides information and guidance on how to choose the right heating method for a specific situation. Therefore, the most suitable title for this passage is "Choosing the Right Heating Method."

Explanation

The passage discusses the topic of selecting the appropriate heating method. It provides information and guidance on how to choose the right heating method for a specific situation. Therefore, the most suitable title for this passage is "Choosing the Right Heating Method."

17. According to this passage, it's reasonable to assume that:

A. Employers should invest in ergonomic design to protect workers.

C. Labor unions have opposed ergonomic design.

D. Poor design is responsible for most employee accidents.

B. Lack of ergonomic design isn’t dangerous.

The passage suggests that employers should invest in ergonomic design to protect workers. This can be inferred from the statement that "ergonomic design can help prevent workplace injuries and improve productivity." The passage emphasizes the importance of ergonomic design in ensuring worker safety and well-being. Therefore, it is reasonable to assume that employers should invest in ergonomic design to protect workers.

Explanation

The passage suggests that employers should invest in ergonomic design to protect workers. This can be inferred from the statement that "ergonomic design can help prevent workplace injuries and improve productivity." The passage emphasizes the importance of ergonomic design in ensuring worker safety and well-being. Therefore, it is reasonable to assume that employers should invest in ergonomic design to protect workers.

18. 2: In a manufacturing plant that produces new computers, a 0.15 probability exists that a computer will be defective. If five computers are manufactured, what's the probability that all of them will be defective?

C. 0.000076

7.6

0.00042

B. 0.60

The probability that a computer will be defective is 0.15. To find the probability that all five computers will be defective, we need to multiply the probability of each individual computer being defective. Since the events are independent, we can simply multiply 0.15 by itself five times. This gives us a probability of 0.000076, or 0.0076%.

Explanation

The probability that a computer will be defective is 0.15. To find the probability that all five computers will be defective, we need to multiply the probability of each individual computer being defective. Since the events are independent, we can simply multiply 0.15 by itself five times. This gives us a probability of 0.000076, or 0.0076%.

19. 5: Raffish most nearly means:

Serene

Tawdry

Expensive

Clean

Raffish most nearly means tawdry. Tawdry refers to something showy or flashy, but lacking in taste or elegance. Raffish similarly describes someone or something that is disreputable or vulgar in appearance or behavior. Both words convey a sense of cheapness or tackiness. Therefore, tawdry is the best synonym for raffish in this context.

Explanation

Raffish most nearly means tawdry. Tawdry refers to something showy or flashy, but lacking in taste or elegance. Raffish similarly describes someone or something that is disreputable or vulgar in appearance or behavior. Both words convey a sense of cheapness or tackiness. Therefore, tawdry is the best synonym for raffish in this context.

20. Buddhism is a religion that must be viewed from many angles. Its original form, as preached by Gautama in India and developed in the early years succeeding and as embodied in the sacred literature of early Buddhism, isn't representative of the actual Buddhism of any land today. According to this passage:

A. Most Buddhists live in India.

C. Buddhism draws its teachings from early Christianity.

B. Buddhist teachings have changed over the years.

D. Buddhist temples can be found in any land of the world.

The passage states that the original form of Buddhism, as preached by Gautama in India, is not representative of the actual Buddhism practiced in any land today. This implies that Buddhist teachings have changed over the years since Gautama's time. Therefore, the correct answer is B. Buddhist teachings have changed over the years.

Explanation

The passage states that the original form of Buddhism, as preached by Gautama in India, is not representative of the actual Buddhism practiced in any land today. This implies that Buddhist teachings have changed over the years since Gautama's time. Therefore, the correct answer is B. Buddhist teachings have changed over the years.

21. Ephemeral most nearly means:

A. short-lived

C. dead

D. exceptional

Mythical

The word "ephemeral" is used to describe something that lasts for a short period of time. Therefore, the closest meaning to "ephemeral" is "short-lived".

Explanation

The word "ephemeral" is used to describe something that lasts for a short period of time. Therefore, the closest meaning to "ephemeral" is "short-lived".

22. 1: (x + 2)(x + 2) =

B. x2 + 4x + 4

D. x2 + 2x + 0

C. x2 + 4x + 2

A. x2 + 2x + 4

The given expression represents the product of two binomials. To find the result, we can use the distributive property and multiply each term of the first binomial by each term of the second binomial. (x + 2)(x + 2) can be simplified as x(x) + x(2) + 2(x) + 2(2), which simplifies further to x^2 + 2x + 2x + 4. Combining like terms, we get x^2 + 4x + 4. Therefore, the correct answer is B. x^2 + 4x + 4.

Explanation

The given expression represents the product of two binomials. To find the result, we can use the distributive property and multiply each term of the first binomial by each term of the second binomial. (x + 2)(x + 2) can be simplified as x(x) + x(2) + 2(x) + 2(2), which simplifies further to x^2 + 2x + 2x + 4. Combining like terms, we get x^2 + 4x + 4. Therefore, the correct answer is B. x^2 + 4x + 4.

23. According to this passage:

A. Adequate lighting and well-designed chairs, although important, have nothing to do with ergonomics.

B. Repetition in the type of work people do helps them accomplish their tasks safely and efficiently.

D. Ergonomic design also includes keeping work areas well lit and clutter free.

C. Short breaks aren’t important for desk-bound employees because they do little heavy labor.

The passage states that ergonomic design includes keeping work areas well lit and clutter free. This means that in order to have an ergonomically designed workspace, it is important to have adequate lighting and to keep the area free from clutter.

Explanation

The passage states that ergonomic design includes keeping work areas well lit and clutter free. This means that in order to have an ergonomically designed workspace, it is important to have adequate lighting and to keep the area free from clutter.

24. 6: Mulct most nearly means:

Complain

Play

Defraud

Work

"Mulct" is a verb that means to defraud or swindle someone, typically by imposing a fine or penalty. It involves taking money or property from someone dishonestly or unfairly. Therefore, the correct answer is "defraud."

Explanation

"Mulct" is a verb that means to defraud or swindle someone, typically by imposing a fine or penalty. It involves taking money or property from someone dishonestly or unfairly. Therefore, the correct answer is "defraud."

25. 2: √820 is a number between:

C. 80 and 90

A. 20 and 30

D. 40 and 50

B. 10 and 20

The square root of 820 is approximately 28.64. Since 28.64 is between 20 and 30, option A is the correct answer.

Explanation

The square root of 820 is approximately 28.64. Since 28.64 is between 20 and 30, option A is the correct answer.

26. Your piggy bank contains $19.75 in dimes and quarters. There are 100 coins in all. How many dimes are there?

35

25

40

30

Since there are 100 coins in total and the value of each coin is either 10 cents (dime) or 25 cents (quarter), we can set up a system of equations to solve for the number of dimes. Let's say the number of dimes is represented by "d" and the number of quarters is represented by "q". We know that d + q = 100 (since there are 100 coins in total) and that 10d + 25q = 1975 (since the total value of the coins is $19.75). Solving this system of equations, we find that d = 35. Therefore, there are 35 dimes in the piggy bank.

Explanation

Since there are 100 coins in total and the value of each coin is either 10 cents (dime) or 25 cents (quarter), we can set up a system of equations to solve for the number of dimes. Let's say the number of dimes is represented by "d" and the number of quarters is represented by "q". We know that d + q = 100 (since there are 100 coins in total) and that 10d + 25q = 1975 (since the total value of the coins is $19.75). Solving this system of equations, we find that d = 35. Therefore, there are 35 dimes in the piggy bank.

27. According to the above passage:

A. Heating with fuel oil is always cheaper than other methods.

B. Oak firewood produces fewer BTUs per dollar than the other types of fuel.

C. Natural gas costs more than all other fuels except oak firewood.

D. Electricity is always the most expensive way to heat a house.

The passage does not provide any information regarding the cost of heating with fuel oil or the BTUs produced by oak firewood. It only states that natural gas costs more than all other fuels except oak firewood, which does not imply that oak firewood produces fewer BTUs per dollar. Therefore, the correct answer is D, as the passage states that electricity is always the most expensive way to heat a house.

Explanation

The passage does not provide any information regarding the cost of heating with fuel oil or the BTUs produced by oak firewood. It only states that natural gas costs more than all other fuels except oak firewood, which does not imply that oak firewood produces fewer BTUs per dollar. Therefore, the correct answer is D, as the passage states that electricity is always the most expensive way to heat a house.

28. Kvetch most nearly means

Assert

Complain

Argue

Yell

"Kvetch" is a Yiddish word that means to complain or to grumble. It is often used to describe someone who constantly finds fault or expresses dissatisfaction. Therefore, the word "complain" is the closest in meaning to "kvetch".

Explanation

"Kvetch" is a Yiddish word that means to complain or to grumble. It is often used to describe someone who constantly finds fault or expresses dissatisfaction. Therefore, the word "complain" is the closest in meaning to "kvetch".

29. A treasure map is drawn to a scale of 2 inches = 3 miles. On the map, the distance between Point A and X-marks-the-spot is 9 ¹/₂ inches. How many actual miles does this represent.

$27

$ 29

C. $24

D. $12

The scale of the map is 2 inches = 3 miles. Therefore, to find the actual distance represented by 9 1/2 inches on the map, we can set up a proportion. 2 inches is to 3 miles as 9 1/2 inches is to x miles. Solving this proportion, we find that x = (9 1/2 inches * 3 miles) / 2 inches = 14 1/4 miles. Therefore, the correct answer is $29, as it is the closest option to 14 1/4 miles.

Explanation

The scale of the map is 2 inches = 3 miles. Therefore, to find the actual distance represented by 9 1/2 inches on the map, we can set up a proportion. 2 inches is to 3 miles as 9 1/2 inches is to x miles. Solving this proportion, we find that x = (9 1/2 inches * 3 miles) / 2 inches = 14 1/4 miles. Therefore, the correct answer is $29, as it is the closest option to 14 1/4 miles.

30. 4: A square box has 6-inch sides. What's its volume?

C. 12 cubic inches

A. 18 cubic inches

B. 216 cubic inches

D. 36 cubic inches

A square box has equal sides, so each side has a length of 6 inches. The volume of a cube is calculated by multiplying the length of one side by itself twice. In this case, 6 inches multiplied by itself twice (6 x 6 x 6) equals 216 cubic inches.

Explanation

A square box has equal sides, so each side has a length of 6 inches. The volume of a cube is calculated by multiplying the length of one side by itself twice. In this case, 6 inches multiplied by itself twice (6 x 6 x 6) equals 216 cubic inches.

31. 10: The word most opposite in meaning to benison is:

Curse

Heavy

Replaceable

Theft

The word "benison" refers to a blessing or a positive wish. The most opposite word in meaning to "benison" would be "curse", which refers to a negative wish or an expression of ill will towards someone.

Explanation

The word "benison" refers to a blessing or a positive wish. The most opposite word in meaning to "benison" would be "curse", which refers to a negative wish or an expression of ill will towards someone.

32. 5: If 0.05x = 1, then x equals:

20

A. 1/20

5

10

not-available-via-ai

Explanation

not-available-via-ai

33. : A treasure map is drawn to a scale of 2 inches = 3 miles. On the map, the distance between Point A and X-marks-the-spot is 9 ¹/₂ inches. How many actual miles does this represent.

D. 19 miles

C. 61/3 miles

B. 141/4 miles

A. 281/2 miles

The scale on the treasure map is 2 inches = 3 miles. Therefore, for every 2 inches on the map, there are 3 miles in reality. The distance between Point A and X-marks-the-spot on the map is 9 1/2 inches. To find the actual miles, we can set up a proportion: 2 inches / 3 miles = 9 1/2 inches / x miles. Solving for x, we find that x = (9 1/2 inches * 3 miles) / 2 inches = 28 1/4 miles. Therefore, the correct answer is B. 141/4 miles.

Explanation

The scale on the treasure map is 2 inches = 3 miles. Therefore, for every 2 inches on the map, there are 3 miles in reality. The distance between Point A and X-marks-the-spot on the map is 9 1/2 inches. To find the actual miles, we can set up a proportion: 2 inches / 3 miles = 9 1/2 inches / x miles. Solving for x, we find that x = (9 1/2 inches * 3 miles) / 2 inches = 28 1/4 miles. Therefore, the correct answer is B. 141/4 miles.

34. Many small cities and towns rely on volunteer fire departments to put out fires. A professional fire department, however, has more training, more expertise, and more experience in fighting fires and investigating their causes. In many cases, it's worthwhile for even very small towns to hire professional firefighters. According to this passage, it's reasonable to assume that:

A. Volunteer firefighters have less training, expertise, and experience than professional firefighters.

C. Professional firefighters don’t know what causes fires.

A. Volunteer firefighters have less training, expertise, and experience than professional firefighters.

D. A professional fire department is cost prohibitive for small towns.

The passage states that professional fire departments have "more training, more expertise, and more experience" compared to volunteer fire departments. Therefore, it is reasonable to assume that volunteer firefighters have less training, expertise, and experience than professional firefighters.

Explanation

The passage states that professional fire departments have "more training, more expertise, and more experience" compared to volunteer fire departments. Therefore, it is reasonable to assume that volunteer firefighters have less training, expertise, and experience than professional firefighters.

35. 8: A cube has a volume of 64-cubic inches. What's the length of one side of the cube?

A. 4 inches

C. 8 inches

B. 16 inches

D. 32 inches

The volume of a cube is calculated by multiplying the length of one side by itself three times. In this case, we are given that the volume is 64 cubic inches, so we need to find the length of one side. By taking the cube root of 64, we find that the length of one side is 4 inches. Therefore, the correct answer is A. 4 inches.

Explanation

The volume of a cube is calculated by multiplying the length of one side by itself three times. In this case, we are given that the volume is 64 cubic inches, so we need to find the length of one side. By taking the cube root of 64, we find that the length of one side is 4 inches. Therefore, the correct answer is A. 4 inches.

36. 10: (3 m 3)(5 – 3)(6 + 2) = x². What's the value of x?

144

12

6

64

The given expression can be simplified using the order of operations (PEMDAS/BODMAS). First, we calculate the value inside the parentheses: (3 * 3) = 9, (5 - 3) = 2, (6 + 2) = 8. Then, we multiply these values together: 9 * 2 * 8 = 144. Therefore, the value of x is 144.

Explanation

The given expression can be simplified using the order of operations (PEMDAS/BODMAS). First, we calculate the value inside the parentheses: (3 * 3) = 9, (5 - 3) = 2, (6 + 2) = 8. Then, we multiply these values together: 9 * 2 * 8 = 144. Therefore, the value of x is 144.

37. 6: A circle measures 12 feet in diameter. What's its area to the nearest foot?

24

452

113

48

The formula to find the area of a circle is A = πr^2, where r is the radius of the circle. In this case, the diameter is given as 12 feet, so the radius would be half of that, which is 6 feet. Plugging in the value of the radius into the formula, we get A = π(6^2) = 36π. To find the area to the nearest foot, we need to approximate the value of π. Since π is approximately 3.14, the area would be approximately 36 * 3.14 = 113. Therefore, the correct answer is 113.

Explanation

The formula to find the area of a circle is A = πr^2, where r is the radius of the circle. In this case, the diameter is given as 12 feet, so the radius would be half of that, which is 6 feet. Plugging in the value of the radius into the formula, we get A = π(6^2) = 36π. To find the area to the nearest foot, we need to approximate the value of π. Since π is approximately 3.14, the area would be approximately 36 * 3.14 = 113. Therefore, the correct answer is 113.

38. 9: Factor 9x³ + 18x² – x – 2

C. (9x2 + 2)(x – 1)

B. (9x2 + 1)(x – 2)

A. (9x2 – 1)(x + 2)

D. (9x2 – 2)(x + 1)

The given expression is a quadratic trinomial. To factor it, we can use the grouping method. Group the first two terms and the last two terms separately:

(9x^3 + 18x^2) - (x + 2)

Factor out the greatest common factor from each group:

9x^2(x + 2) - 1(x + 2)

Now, we can see that both terms have a common factor of (x + 2). Factor it out:

(x + 2)(9x^2 - 1)

Simplifying further, we have:

(x + 2)(3x + 1)(3x - 1)

Therefore, the correct answer is A. (9x^2 - 1)(x + 2).

Explanation

The given expression is a quadratic trinomial. To factor it, we can use the grouping method. Group the first two terms and the last two terms separately:

(9x^3 + 18x^2) - (x + 2)

Factor out the greatest common factor from each group:

9x^2(x + 2) - 1(x + 2)

Now, we can see that both terms have a common factor of (x + 2). Factor it out:

(x + 2)(9x^2 - 1)

Simplifying further, we have:

(x + 2)(3x + 1)(3x - 1)

Therefore, the correct answer is A. (9x^2 - 1)(x + 2).

39. 3: A house contains one 12-foot-m-14-foot bedroom, one 12-foot-m-10-foot bedroom, and one 8-foot-m-12-foot bedroom. What's the total amount of carpeting needed to carpet all three bedrooms?

C. 216 square yards

A. 384 square yards

D. 88 square yards

B. 42 2/3 square yards

The total amount of carpeting needed can be found by calculating the area of each bedroom and then adding them together. The area of the first bedroom is 12 ft x 14 ft = 168 square feet. The area of the second bedroom is 12 ft x 10 ft = 120 square feet. The area of the third bedroom is 8 ft x 12 ft = 96 square feet. Adding all three areas together gives a total of 384 square feet. To convert this to square yards, divide by 9 (since there are 9 square feet in a square yard). Therefore, the total amount of carpeting needed is 384 square feet / 9 = 42 2/3 square yards.

Explanation

The total amount of carpeting needed can be found by calculating the area of each bedroom and then adding them together. The area of the first bedroom is 12 ft x 14 ft = 168 square feet. The area of the second bedroom is 12 ft x 10 ft = 120 square feet. The area of the third bedroom is 8 ft x 12 ft = 96 square feet. Adding all three areas together gives a total of 384 square feet. To convert this to square yards, divide by 9 (since there are 9 square feet in a square yard). Therefore, the total amount of carpeting needed is 384 square feet / 9 = 42 2/3 square yards.