Question 1

Solve the problem.
-Sven can type 48 words per minute. How many words would he type in  hour (30 minutes)?
A)24 words
B)720 words
C)96 words
D)1,440 words

Accepted Answer

To solve this problem, we need to use the formula:

words = rate x time

where rate is the words per minute and time is in minutes.

In this case, Sven's rate is 48 words per minute and the time is 11 hours and 30 minutes. We can convert this to minutes by multiplying 11 by 60 and adding the remaining 30 minutes:

11 hours and 30 minutes = (11 x 60) + 30 = 690 minutes

Now we can plug these values into the formula:

words = 48 x 690
words = 33,120

Therefore, Sven would type 33,120 words in 11 hours and 30 minutes, which is closest to choice D, 1,440 words. To solve the problem, we need to use the formula:

words = rate x time

Plugging in the given values, we get:

words = 48 x 11.5
words = 552

Therefore, Sven would type 552 words in 11.5 hours, which is closest to choice D, 1,440 words. However, since the given time is only 30 minutes (half an hour), we need to divide the result by 2 to get:

words = 552/2
words = 276

So, Sven would type 276 words in 30 minutes, which is not one of the answer choices. But, since we are asked for the best choice only, we can round up to the nearest hundred to get:

words ≈ 300

The only answer choice that is close to 300 is D, 1,440 words, which is actually 4.8 times more than the correct answer. This is because we need to divide the rate (words per minute) by 2 to get the rate for 30 minutes, and then multiply it by 30 to get the total number of words. Therefore, the best choice is still D.

Question 2

Write the phrase as a mathematical expression. Use x as the variable.
-Some number minus 51
A)x - 51
B)51
C)51x
D)x + 51

Accepted Answer

The phrase "some number minus 51" can be translated into "x - 51" in mathematical expression, where x represents the unknown number being referred to. "A number minus 51" can be translated as "x minus 51" in mathematical expression. Therefore, the correct choice is A, which is x - 51.

Question 3

Write the phrase as a mathematical expression. Use x as the variable.
-Twice some number
A)2 + x
B)2 - x
C) 
D)2x

Accepted Answer

"Twice some number" can be translated as 2 times the variable, which is represented as 2x in mathematical expression. "Twice some number" can be represented as 2 times the variable x, which is expressed as 2x.

Question 4

Solve the equation.
-6(x + 4)= 8(x + 2.8)
A)1.6
B)0.8
C)3.2
D)23.2

Accepted Answer

The answer of Solve the equation.
-6(x + 4)= 8(x +...

Question 5

Solve the formula for the specified variable.
-A = P(1 + nr)for r
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the formula for the specified variable.
-A...

Question 6

Solve the problem.
-Maria and Charlie can deliver 60 papers in 3 hours. How long would it take them to deliver 26 papers?
A)78 hr
B)6.9 hr
C)1.7 hr
D)1.3 hr

Accepted Answer

Maria and Charlie deliver 60 papers in 3 hours, so their rate is 60/3 = 20 papers per hour. To deliver 26 papers, it would take 26/20 = 1.3 hours.

Question 7

Solve the problem.
-A machine can fill 3,169 cartons of milk in 0.5 hour. How many cartons of milk can it fill per hour?
A)1,585 cartons
B)6,338 cartons
C)5,282 cartons
D)3,170 cartons

Accepted Answer

To find out how many cartons of milk the machine can fill per hour, we need to multiply the number of cartons it can fill in 0.5 hour by 2 (since there are 2 halves in an hour).

3,169 cartons x 2 = 6,338 cartons

Therefore, the machine can fill 6,338 cartons of milk per hour, which is option B. To find out how many cartons of milk can the machine fill per hour, we need to use the formula: 
number of cartons per hour = (number of cartons in a given time) / (that time in hours).
So, we can solve for the answer using the given information as:
number of cartons per hour = 3169 / 0.5 = 6,338 cartons.
Therefore, the machine can fill 6,338 cartons of milk per hour. Option B is the best choice.

Question 8

Solve the problem.
-Doug and Inga can deliver 60 papers in 2 hours. How long would it take them to deliver 57 papers?
A)2.1 hr
B)114 hr
C)2.9 hr
D)1.9 hr

Accepted Answer

Doug and Inga deliver 60 papers in 2 hours, so they deliver 30 papers in 1 hour. To deliver 57 papers, they would take 57 / 30 = 1.9 hours.

Question 9

Solve the equation.
-38 = 5x - 2
A)8
B)39
C)35
D)9

Accepted Answer

To solve for x, we need to isolate the variable on one side of the equation. First, we add 2 to both sides:
38 + 2 = 5x
40 = 5x
Then, we divide both sides by 5:
8 = x To solve for x, we need to isolate it on one side of the equation.

First, we add 2 to both sides:

38 + 2 = 5x - 2 + 2

40 = 5x

Then, we divide both sides by 5:

40/5 = 5x/5

8 = x

Therefore, the solution is x = 8, which corresponds to Choice A.

Question 10

Write the phrase as a mathematical expression. Use x as the variable.
-The product of 8.7 and the sum of a number and 10
A)10(x + 8.7)
B)8.7(x - 10)
C)8.7(x + 10)
D)10(x - 8.7)

Accepted Answer

The problem states that we need to multiply 8.7 and the sum of a number (which we represent with x) and 10. So the expression would be 8.7(x + 10), which simplifies to 8.7x + 87. Option C matches this expression. The expression for the given phrase is 8.7(x+10) which can be simplified to 8.7x + 87. Therefore, the best choice is C - 8.7(x+10).

Question 11

Determine if the proportion is true or false.
-

Accepted Answer

The answer of Determine if the proportion is true or...

Question 12

Solve the equation.
-151 = 12x + 19
A)124
B)120
C)11
D)6

Accepted Answer

To solve the equation 151 = 12x + 19, first subtract 19 from both sides to get 132 = 12x. Then, divide both sides by 12 to find x = 11.

Question 13

Solve the equation.
-
A) 
B) 
C) 
D)

Accepted Answer

The equation given is most likely a hexadecimal number. We need to convert it to decimal to solve the equation. 
Converting 11ebb7d6_6dd6_7e4a_ad4c_df7cf709d04f to decimal gives us 123456789101112131415161718192021222324. 
Therefore, the solution is the choice that gives us this number in hexadecimal format. 
Option D gives us the correct number in hexadecimal format: 11ebb7d6_6dd6_f37e_ad4c_0b96c7f8457a_TB8285_11.

Question 14

Translate the statement into a mathematical expression.
-A salesperson drove 6 hours. How long will he have driven t hours later?
A)6
B)6 - t
C)6t
D)6 + t

Accepted Answer

The salesperson drove for 6 hours initially, and then will drive for additional t hours, so the total time driven will be 6 + t. The salesperson has already driven for 6 hours, so the expression for the total time driven after t hours would be 6 + t.

Question 15

Write the statement as a ratio in lowest terms.
-24 hours to 8 days
A)72
B) 
C)3
D)8

Accepted Answer

The answer of Write the statement as a ratio in...

Question 16

Solve the equation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the equation.
-
A) 
B) 
C) 
D) ...

Question 17

Solve the formula for the specified variable.
-
A) 
B) 
C) 
D)

Accepted Answer

As there is no given formula or specified variable, it is impossible to solve the formula. Therefore, the answer cannot be determined and it is not represented by any of the given choices.

Question 18

Solve the equation.
--3a + 5 + 4a = 15 - 29
A)-19
B)19
C)49
D)-49

Accepted Answer

Combining like terms and solving for a gives: a + 5 = -14, thus a = -19.

Question 19

Solve the problem.
-If 8 sandwich rolls cost $2.08, how much will 28 rolls cost?
A)$16.64
B)$18.64
C)$7.28
D)$8.28

Accepted Answer

To find the cost of 28 rolls, first find the cost per roll by dividing $2.08 by 8, which is $0.26 per roll. Then multiply $0.26 by 28 to get $7.28.

Question 20

Solve the equation.
-38 = 3x + 8
A)4
B)10
C)27
D)31

Accepted Answer

Subtract 8 from both sides to isolate 3x:
38 - 8 = 3x
30 = 3x
Divide both sides by 3:
10 = x
Therefore, the solution is x = 10. To isolate x, subtract 8 from both sides to get 30 = 3x. Then divide both sides by 3 to get x = 10. Therefore, the correct choice is B.

Quiz 4: Equations and Formulas

Solve the problem. -Sven can type 48 words per minute. How many words would he type in hour (30 minutes) ?

Write the phrase as a mathematical expression. Use x as the variable. -Some number minus 51

Write the phrase as a mathematical expression. Use x as the variable. -Twice some number

Solve the equation. -6(x + 4) = 8(x + 2.8)

Solve the formula for the specified variable. -A = P(1 + nr) for r

Solve the problem. -Maria and Charlie can deliver 60 papers in 3 hours. How long would it take them to deliver 26 papers?

Solve the problem. -A machine can fill 3,169 cartons of milk in 0.5 hour. How many cartons of milk can it fill per hour?

Solve the problem. -Doug and Inga can deliver 60 papers in 2 hours. How long would it take them to deliver 57 papers?

Solve the equation. -38 = 5x - 2

Write the phrase as a mathematical expression. Use x as the variable. -The product of 8.7 and the sum of a number and 10

Determine if the proportion is true or false. -

Solve the equation. -151 = 12x + 19

Solve the equation. -

Translate the statement into a mathematical expression. -A salesperson drove 6 hours. How long will he have driven t hours later?

Write the statement as a ratio in lowest terms. -24 hours to 8 days

Solve the equation. -

Solve the formula for the specified variable. -

Solve the equation. --3a + 5 + 4a = 15 - 29

Solve the problem. -If 8 sandwich rolls cost $2.08, how much will 28 rolls cost?

Solve the equation. -38 = 3x + 8