All practice questions

An employee at a retail store recorded the number of hours they worked each day for one week in the table below.

Day	Hours Worked
Monday	8
Tuesday	2
Wednesday	10
Thursday	5
Friday	3
Saturday	7
Sunday	7

What is the median number of hours worked per day for this week?

5

6

7

8

36

Show answer & explanation

Answer: 7

Answer

The median number of hours worked per day for this week is 7.

The median of a set of data is the middle value when the numbers are arranged in order. Sorting the given hours worked from least to greatest gives: 2, 3, 5, 7, 7, 8, 10. Since there are 7 data points, the middle value is the 4th value, which is 7.

Step-by-Step Solution

1

Arrange the daily hours worked in ascending order.

The sorted list of hours is: 2, 3, 5, 7, 7, 8, 10.

Finding the median of a data set requires organizing the values from least to greatest.

2

Identify the middle value in the ordered list of 7 values.

The 4th value in the sorted list is 7.

Since the data set has an odd number of values (7), the median is the single middle value, located at the 4th position.

Key Concept

The median of a data set is the middle value when the data are arranged in numerical order.

Question 4682Question →

A chef is preparing a salad dressing. The mixture consists of $\frac{1}{4}$ cup of olive oil, $\frac{1}{5}$ cup of balsamic vinegar, and a certain amount of lemon juice. If the lemon juice accounts for exactly $40\%$ of the total volume of the dressing, what is the total volume, in cups, of the prepared dressing?

\frac{10}{27}

\frac{5}{9}

\frac{3}{4}

\frac{17}{20}

\frac{9}{8}

Show answer & explanation

Answer: $\frac{3}{4}$

Answer

\frac{3}{4}

To find the total volume, first calculate the sum of the volumes of olive oil and balsamic vinegar:

\frac{1}{4} + \frac{1}{5} = \frac{5}{20} + \frac{4}{20} = \frac{9}{20}

cup. Because the lemon juice accounts for

40\%

of the total volume of the dressing, the remaining ingredients (olive oil and balsamic vinegar) must account for the other

60\%

(or

\frac{3}{5}

) of the total volume. Letting

T

represent the total volume, we set up the equation

\frac{3}{5} T = \frac{9}{20}

. Solving for

T

yields

T = \frac{9}{20} \times \frac{5}{3} = \frac{3}{4}

cups. Therefore, the option representing three-fourths of a cup is the correct answer.

Step-by-Step Solution

1

Add the volumes of the two known ingredients, olive oil and balsamic vinegar.

Combined volume is

\frac{1}{4} + \frac{1}{5} = \frac{5}{20} + \frac{4}{20} = \frac{9}{20}

cup (or

0.45

cup).

To find what fraction of the total volume the known ingredients represent, we first need their combined total.

2

Determine the percentage of the total volume that the olive oil and balsamic vinegar represent.

These two ingredients represent

100\% - 40\% = 60\%

(or

\frac{3}{5}

) of the total volume.

Since lemon juice accounts for

40\%

of the total volume, the rest of the ingredients must account for the remaining percentage.

3

Set up a linear equation to solve for the total volume,

T

.

\frac{3}{5} T = \frac{9}{20} \Rightarrow T = \frac{9}{20} \times \frac{5}{3} = \frac{3}{4}

cups (or

0.75

cups).

Solving the equation gives the total volume of the entire dressing.

Key Concept

Solving multi-step word problems involving fractions, decimals, and percentages by relating parts to the whole.

Alternative Method

Convert the fractions to decimals first:

\frac{1}{4} = 0.25

cups of olive oil and

\frac{1}{5} = 0.20

cups of balsamic vinegar. Their combined volume is

0.25 + 0.20 = 0.45

cups. Since lemon juice is

40\%

of the total volume, the other ingredients make up

100\% - 40\% = 60\%

of the total volume. Let the total volume be

T

. We set up the equation

0.60 T = 0.45

, which simplifies to

T = \frac{0.45}{0.60} = 0.75

cups, or

\frac{3}{4}

cups.

Estimated Time:1m 30s

Question 4683Question →

Marie Tharp’s work mapping the ocean floor in the mid-twentieth century revolutionized geology. While her colleague Bruce Heezen collected sonar data at sea, Tharp remained in the lab, meticulously plotting the depth profiles. Through this painstaking process, she discovered a massive rift valley running down the center of the Mid-Atlantic Ridge. This discovery, which Heezen initially dismissed, proved to be a total game-changer for the geological community, ultimately leading to the acceptance of plate tectonics.

Which of the following choices best maintains the formal, academic tone of the passage?

NO CHANGE

was the foundational basis that served to establish the initial starting point of

engendered the primary conceptual framework and epistemic paradigm of

laid the foundation for

Show answer & explanation

Answer: laid the foundation for

Answer

laid the foundation for

The correct choice is the option that states 'laid the foundation for'. This phrasing is clear, direct, and maintains the established formal and academic tone of the passage without introducing unnecessary complexity or wordiness.

Step-by-Step Solution

1

Analyze the tone of the surrounding text in the passage.

The passage uses formal, informative, and academic language (e.g., 'meticulously plotting', 'painstaking process', 'ultimately leading to').

To establish a baseline register for the sentence.

2

Evaluate the underlined phrase against the established tone.

The phrase 'proved to be a total game-changer for' is highly colloquial and informal, which clashes with the academic register.

To determine if a correction is needed.

3

Assess the remaining choices for conciseness, precision, and tone consistency.

The option containing redundant wording is wordy; the option containing high-level jargon is overly formal; the option 'laid the foundation for' is concise, clear, and matches the passage's academic register.

To find the stylistically appropriate replacement.

Key Concept

Stylistic Appropriateness

Estimated Time:1m 0s

Question 4684Question →

Arrange the following numbers in order from least to greatest: $\left(\frac{1}{4}\right)^3$ , $\sqrt{0.0004}$ , $2.4 \times 10^{-2}$ , and $5^{-2}$ .

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order of the values from least to greatest is

\left(\frac{1}{4}\right)^3

, followed by

\sqrt{0.0004}

, then

2.4 \times 10^{-2}

, and finally

5^{-2}

.

Converting all expressions to decimals allows direct comparison:

\left(\frac{1}{4}\right)^3 = 0.015625

,

\sqrt{0.0004} = 0.02

,

2.4 \times 10^{-2} = 0.024

, and

5^{-2} = 0.04

. Arranging these decimals from smallest to largest results in the sequence

0.015625 < 0.02 < 0.024 < 0.04

.

Step-by-Step Solution

1

Convert each of the exponential, root, and scientific notation expressions into decimal values to make comparison straightforward.

The expressions convert as follows:
-

\left(\frac{1}{4}\right)^3 = \frac{1}{64} = 0.015625

-

\sqrt{0.0004} = \sqrt{4 \times 10^{-4}} = 2 \times 10^{-2} = 0.02

-

2.4 \times 10^{-2} = 0.024

-

5^{-2} = \frac{1}{5^2} = \frac{1}{25} = 0.04

Expressing all values in standard decimal notation eliminates different bases and representations, allowing direct comparison.

2

Compare and arrange the resulting decimals from the smallest value to the largest value.

0.015625 < 0.02 < 0.024 < 0.04

By aligning the place values, we can see that

0.015625

(one hundredth plus fractional parts) is less than

0.02

(two hundredths), which is less than

0.024

(twenty-four thousandths), which is less than

0.04

(four hundredths).

Key Concept

Comparing numerical expressions involving negative exponents, fractional powers, roots, and scientific notation by converting them to a common decimal representation.

Question 4685Question →

The following segments can be arranged to form a single, grammatically correct sentence. Arrange the segments in the correct order to construct a sentence that avoids any misplaced or dangling modifiers.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order of the sentence segments is: 'The museum curator displayed', 'the fragile medieval tapestry,', 'which had been restored over several months,', and 'in a temperature-controlled glass case.'

The correct order ensures that the non-restrictive relative clause starting with 'which' is adjacent to 'tapestry', the noun it logically modifies, preventing any ambiguity or misplaced modification.

Step-by-Step Solution

1

Identify the subject and main verb of the sentence.

The segment 'The museum curator displayed' is identified as the opening clause.

It contains the capitalized subject and the main active verb of the sentence.

2

Locate the direct object that is acted upon by the verb.

The segment 'the fragile medieval tapestry,' is placed immediately after the verb.

The transitive verb 'displayed' requires a direct object to follow it without awkward separation.

3

Position the relative clause modifying the object.

The clause 'which had been restored over several months,' is placed right after 'tapestry,'.

Placing it here ensures that the modifier correctly describes the tapestry, preventing a misplaced modifier.

4

Add the final prepositional phrase describing location.

The segment 'in a temperature-controlled glass case.' is placed at the end.

It provides contextual detail and contains the terminal period for the sentence.

Key Concept

Modifier Placement

Question 4686Question →

In the standard $(x, y)$ coordinate plane, a circle with center $(5, -1)$ is tangent to the $x$ -axis at point $P$ . A line passes through point $P$ and the point $(-3, 6)$ . What is the slope of this line?

-\frac{4}{3}

-\frac{7}{8}

-\frac{3}{4}

\frac{3}{4}

-\frac{7}{3}

Show answer & explanation

Answer: $-\frac{3}{4}$

Answer

-\frac{3}{4}

The circle with center

(5, -1)

is tangent to the

x

-axis, meaning the radius is

1

and the point of tangency

P

lies on the

x

-axis directly above the center at

(5, 0)

. The line passes through

P(5, 0)

and

(-3, 6)

. Applying the slope formula

m = \frac{y_2 - y_1}{x_2 - x_1}

gives

m = \frac{6 - 0}{-3 - 5} = \frac{6}{-8} = -\frac{3}{4}

.

Step-by-Step Solution

1

Determine the coordinates of the point of tangency

P

.

P = (5, 0)

Since the circle has center

(5, -1)

and is tangent to the

x

-axis, the point of tangency must lie on the

x

-axis (where

y = 0

). The point on the

x

-axis directly above the center

(5, -1)

is

(5, 0)

.

2

Set up the slope formula for the line passing through point

P(5, 0)

and point

(-3, 6)

.

m = \frac{6 - 0}{-3 - 5}

The slope of a line passing through

(x_1, y_1)

and

(x_2, y_2)

is given by the formula

m = \frac{y_2 - y_1}{x_2 - x_1}

.

3

Simplify the expression to find the slope.

m = -\frac{3}{4}

Calculate the difference in the numerator and denominator:

\frac{6}{-8}

, then reduce the fraction to simplest form:

-\frac{3}{4}

.

Key Concept

Calculating the slope of a line using the coordinates of two points, where one point is determined by a geometric tangency property.

Estimated Time:1m 0s

Question 4687Question →

A local shipping warehouse records the number of packages shipped during each hour of a 6-hour morning shift in the table below:

Hour	Packages Shipped
Hour 1	$15$
Hour 2	$27$
Hour 3	$18$
Hour 4	$32$
Hour 5	$12$
Hour 6	$22$

What is the median number of packages shipped per hour during this shift?

20

21

22

25

29

Show answer & explanation

Answer: $20$

Answer

The median number of packages shipped per hour is

20

.

The correct answer is

20

. To find the median, we first arrange the numbers in ascending order:

12, 15, 18, 22, 27, 32

. Since there is an even number of values (

6

), the median is the average of the two middle values,

18

and

22

. The average is

\frac{18 + 22}{2} = 20

.

Step-by-Step Solution

1

Sort the package counts in ascending order.

The sorted dataset is

12, 15, 18, 22, 27, 32

.

Finding the median of a dataset requires the data to be ordered from least to greatest.

2

Identify the two middle numbers in the ordered dataset.

Since there is an even number of data points (

6

values), the two middle numbers are the 3rd and 4th values:

18

and

22

.

For an even number of data points, the median is the average of the two central values.

3

Calculate the average of the two middle numbers.

\frac{18 + 22}{2} = \frac{40}{2} = 20

.

The average of

18

and

22

yields the median value of

20

.

Key Concept

Calculating the median of a dataset with an even number of values.

Question 4688Question →

The following passage is about the discovery of hydrothermal vents in 1977.

In 1977, oceanographers aboard the research vessel *Alvin* made a startling discovery at the bottom of the Pacific Ocean. Near the Galápagos Rift, they found hydrothermal vents spewing superheated, mineral-rich water into the freezing depths. To their surprise, these pitch-black environments, completely cut off from sunlight, teem with complex life, including giant tubeworms and unique crabs. This discovery fundamentally changed our understanding of life's adaptability.

Which choice best maintains the consistency of verb tense in the passage?

NO CHANGE

teemed

will teem

have teemed

Show answer & explanation

Answer: teemed

Answer

teemed

The correct answer is the past tense verb 'teemed' because it maintains consistency with the other past tense verbs ('made', 'found', and 'changed') that establish the passage's historical narrative.

Step-by-Step Solution

1

Analyze the context of the surrounding sentences to determine the passage's primary tense.

The verbs 'made', 'found', and 'changed' are all in the simple past tense, indicating that the passage is a historical narrative set in the past.

Verb tense consistency is required across a passage unless there is a logical reason to shift tenses.

2

Evaluate the underlined verb 'teem' in relation to the established past tense.

The present tense verb 'teem' creates an inconsistent tense shift in the middle of a past-tense narrative.

To maintain grammatical consistency, the underlined verb must also be in the simple past tense.

3

Select the option that provides the simple past tense form of the verb.

The verb form 'teemed' is the simple past tense and matches the surrounding context.

Choosing this form eliminates the inconsistent tense shift.

Key Concept

Verb tense consistency requires verbs within a passage to match in tense unless a clear shift in time is indicated.

Question 4689Question →

At a certain high school, the ratio of the number of students in the band to the number of students in the orchestra is $3:2$ . The ratio of the number of students in the orchestra to the number of students in the choir is $4:5$ . If there are $120$ students in the band, how many students are in the choir?

64

80

100

200

225

Show answer & explanation

Answer: $100$

Answer

100 students are in the choir

To find the number of students in the choir, we first use the ratio of band students to orchestra students (

3:2

) to determine the number of orchestra students. Since there are

120

band students, we set up the proportion

\frac{120}{\text{orchestra}} = \frac{3}{2}

, which yields

80

orchestra students. Next, we use the ratio of orchestra students to choir students (

4:5

) to find the number of choir students. Setting up the proportion

\frac{80}{\text{choir}} = \frac{4}{5}

gives

\text{choir} = 80 \times \frac{5}{4} = 100

students.

Step-by-Step Solution

1

Use the ratio of band students to orchestra students to find the number of orchestra students.

The number of orchestra students is

80

.

Since the ratio of band to orchestra is

3:2

, and there are

120

band students, we solve the proportion

\frac{120}{\text{Orchestra}} = \frac{3}{2}

, giving

\text{Orchestra} = 120 \times \frac{2}{3} = 80

.

2

Use the ratio of orchestra students to choir students to find the number of choir students.

The number of choir students is

100

.

Since the ratio of orchestra to choir is

4:5

, and there are

80

orchestra students, we solve the proportion

\frac{80}{\text{Choir}} = \frac{4}{5}

, giving

\text{Choir} = 80 \times \frac{5}{4} = 100

.

Key Concept

Solving multi-step ratio problems by finding a common linking quantity.

Question 4690Question →

A manufacturing assembly line produces a batch of $B$ electronic components in $h$ hours. To increase efficiency, a new assembly line is installed that can produce the same batch of components in $\frac{1}{3}$ of the time. Which of the following expressions represents the rate, in components per hour, at which the new assembly line produces these components?

\frac{3B}{h}

\frac{B}{3h}

\frac{3h}{B}

3Bh

\frac{h}{3B}

Show answer & explanation

Answer: $\frac{3B}{h}$

Answer

The expression

\frac{3B}{h}

represents the rate of production of the new assembly line.

The correct answer shows that the rate of production is the number of components divided by the new time, which is one-third of the original time. Since the original time is

h

hours, the new time is

\frac{h}{3}

hours. Dividing the number of components

B

by

\frac{h}{3}

yields

B \div \frac{h}{3} = B \times \frac{3}{h} = \frac{3B}{h}

components per hour.

Step-by-Step Solution

1

Determine the time it takes for the new assembly line to produce the batch of components.

The new assembly line takes

\frac{h}{3}

hours.

The problem states the new line produces the batch in

\frac{1}{3}

of the original time,

h

.

2

Set up the algebraic expression for the rate of production in components per hour.

\text{Rate} = \frac{\text{Total Components}}{\text{Total Time}} = \frac{B}{\frac{h}{3}}

Rate is defined as quantity produced divided by time elapsed.

3

Simplify the fraction to find the final expression.

\text{Rate} = B \times \frac{3}{h} = \frac{3B}{h}

Dividing by a fraction is equivalent to multiplying by its reciprocal.

Key Concept

Formulating algebraic rate expressions from word problems

Question 4691Question →

The table below shows the distribution of the number of books read by a group of students during a summer reading program.

Number of Books Read	Number of Students
1	1
2	4
3	8
4	$x$
5	4

If the median number of books read by the students is 3, what is the maximum possible value for the mean number of books read by these students?

3.0

3.2

3.4

3.6

3.8

Show answer & explanation

Answer: 3.4

Answer

The maximum possible value for the mean number of books read is 3.4.

To maximize the mean, we want to maximize the number of students who read 4 books, which is

x

. However,

x

is constrained by the requirement that the median must remain 3. The total number of students is

17 + x

. The 3s occupy sorted positions 6 through 13. For the median to be 3, the middle position(s) of the sorted list must not exceed position 13. When

N = 17+x

is odd (so

x

is even), the median position is

\frac{18+x}{2}

. Setting

\frac{18+x}{2} \le 13

yields

x \le 8

. For

x = 8

, the total number of students is 25, and the 13th student is the last one who read 3 books, making the median 3. If

x = 9

, the total is 26, and the median is the average of the 13th (3) and 14th (4) values, which is 3.5. Therefore, the maximum integer value of

x

is 8. The mean with

x=8

is the sum of all books read divided by the total number of students:

(1 \times 1 + 2 \times 4 + 3 \times 8 + 4 \times 8 + 5 \times 4) / 25 = 85 / 25 = 3.4

.

Step-by-Step Solution

1

Express the total number of students,

N

, in terms of

x

.

N = 1 + 4 + 8 + x + 4 = 17 + x

To calculate the mean and locate the median, we need the total count of data points.

2

Determine the range of positions that the value 3 occupies in the sorted dataset.

Positions 6 through 13.

Since the ratings are sorted, the single 1 is at position 1, the four 2s are at positions 2–5, and the eight 3s are at positions 6–13.

3

Find the maximum integer value of

x

that keeps the median at 3.

x = 8

If

x = 8

, the total number of students is

25

. The median is the 13th value, which is 3. If

x = 9

, the total is

26

, and the median is the average of the 13th (3) and 14th (4) values, which is 3.5.

4

Calculate the mean of the dataset when

x = 8

.

Mean =

85 / 25 = 3.4

The sum of the books read is

1(1) + 2(4) + 3(8) + 4(8) + 5(4) = 85

. Dividing this by the total of 25 students gives the maximum mean.

Key Concept

Finding the maximum mean of a frequency distribution given a median constraint by setting up inequalities for the median position.

Question 4692Question →

The members of the drama club worked tirelessly to prepare for opening night. Although the actors were nervous about performing in front of a live audience, they delivered their lines perfectly, and the show received a standing ovation.

Which choice best punctuates the underlined portion of the sentence?

audience, they delivered their lines perfectly, and the show

audience; they delivered their lines perfectly, and the show

audience, they delivered their lines perfectly, the show

audience they delivered their lines perfectly, and the show

Show answer & explanation

Answer: audience, they delivered their lines perfectly, and the show

Answer

The correct option is the one that uses a comma after the word 'audience' and keeps the comma and coordinating conjunction before 'the show'.

The correct choice properly uses a comma to set off the introductory dependent clause starting with 'Although' and another comma before the coordinating conjunction 'and' to connect the two independent clauses.

Step-by-Step Solution

1

Identify the types of clauses in the sentence.

The clause beginning with 'Although' is a dependent clause, whereas 'they delivered their lines perfectly' and 'the show received a standing ovation' are independent clauses.

Understanding clause boundaries helps determine the correct punctuation needed to connect them.

2

Apply the rule for introductory dependent clauses.

A comma must be placed after the introductory clause ending with the word 'audience'.

An introductory dependent clause that precedes an independent clause must be set off with a comma.

3

Apply the rule for connecting two independent clauses.

A comma must be placed before the coordinating conjunction 'and' before the clause starting with 'the show'.

When joining two independent clauses with a coordinating conjunction like 'and', a comma must precede the conjunction.

Key Concept

Punctuation of introductory dependent clauses and joining of independent clauses with coordinating conjunctions.

Estimated Time:45s

Question 4693Question →

A scientist is preparing a mixture by combining liquid A, liquid B, and liquid C. Initially, the ratio of the volume of liquid A to the volume of liquid B is $2:3$ , and the ratio of the volume of liquid B to the volume of liquid C is $4:5$ . The scientist then adds $120$ milliliters of liquid A to the mixture, while the volumes of liquid B and liquid C remain unchanged. This addition changes the ratio of the volume of liquid A to the volume of liquid B to $5:6$ . What was the original total volume of the mixture, in milliliters?

900

990

1,200

2,100

2,220

Show answer & explanation

Answer: 2,100

Answer

The correct total original volume of the mixture is 2,100 milliliters.

The correct answer shows the sum of the initial volumes of all three liquids. By aligning the two ratios, the original ratio is established as

A:B:C = 8:12:15

, representing a total of

35

parts. Setting up the equation for adding

120

milliliters of liquid A relative to liquid B reveals that each part corresponds to

60

milliliters. Multiplying the total of

35

parts by

60

milliliters yields

2,100

milliliters.

Step-by-Step Solution

1

Align the two given ratios by finding a common multiple for the shared component, liquid B.

The ratio of liquid A to liquid B is

2:3 = 8:12

, and the ratio of liquid B to liquid C is

4:5 = 12:15

. This yields the combined ratio

A:B:C = 8:12:15

.

To analyze changes in mixtures with multiple components, all ratio terms must be defined relative to a common unit value.

2

Define the initial volumes using a variable

x

and set up a proportion representing the addition of liquid A.

Let the initial volumes be

A = 8x

,

B = 12x

, and

C = 15x

. Adding

120

milliliters of liquid A gives the new volume

8x + 120

. The new ratio equation is

\frac{8x + 120}{12x} = \frac{5}{6}

.

The new ratio of liquid A to liquid B is given as

5:6

while the volume of liquid B remains unchanged.

3

Solve the proportion for

x

by cross-multiplying.

6(8x + 120) = 5(12x) \implies 48x + 720 = 60x \implies 12x = 720 \implies x = 60

.

Finding the value of

x

allows us to calculate the actual volumes of all three components.

4

Calculate the original total volume of the mixture.

Original total volume

= 8x + 12x + 15x = 35x = 35(60) = 2,100

milliliters.

The question asks for the sum of the initial volumes of all three liquids.

Key Concept

Combining multiple ratios to solve multi-step mixture and rate problems.

Alternative Method

Observe that the volume of liquid B does not change. Initially, the ratio of B to A is

3:2

, which can be scaled to

12:8

. After adding liquid A, the ratio of B to A becomes

6:5

, which is equivalent to

12:10

. The change in liquid A's ratio units is

10 - 8 = 2

units. Since the actual change is

120

milliliters, each unit represents

120 \div 2 = 60

milliliters. The original mixture has

8 + 12 + 15 = 35

units of volume, giving a total of

35 \times 60 = 2,100

milliliters.

Estimated Time:1m 30s

Question 4694Question →

Which precise verb best completes the blank in the passage below to maintain a formal, scientific tone?

Fill in the blanks below

Although two species of forest warblers may appear nearly identical in plumage, field researchers can readily between them by analyzing their unique vocalizations. Each species produces a distinct pattern of notes that serves to attract mates and establish territory. This vocal divergence prevents interbreeding and helps maintain species boundaries in shared habitats.

Show answer & explanation

Answer

distinguish (or differentiate)

The verb 'distinguish' (or 'differentiate') is the most precise and idiomatically appropriate choice in this context. It specifically means to recognize or point out a difference between things, which aligns with the scientific task of identifying different bird species. Furthermore, it collocates correctly with the preposition 'between'.

Step-by-Step Solution

1

Analyze the context of the sentence to determine the meaning needed for the blank.

The sentence describes how researchers can identify differences between two very similar species of warblers by listening to their songs.

Understanding the context helps identify the required semantic meaning of the verb.

2

Evaluate the grammar and idiom constraints surrounding the blank.

The blank is followed by the preposition 'between', meaning the correct verb must idiomatically pair with 'between' to indicate discerning differences.

Grammatical collocation is key to word precision.

3

Select the verb that matches both the semantic meaning and the formal, scientific register of the passage.

The verb 'distinguish' (or 'differentiate') fits perfectly, as it is formal and means to perceive a difference.

Formal writing requires precise vocabulary over informal or vague synonyms.

Key Concept

Word Precision and Clarity

Question 4695Question →

The frequency table below shows the number of siblings reported by a group of $10$ students in a class.

Number of Siblings	Number of Students
$0$	$2$
$1$	$4$
$2$	$3$
$3$	$1$

What is the mean number of siblings per student for this group?

1.0

1.5

1.3

2.5

3.25

Show answer & explanation

Answer: $1.3$

Answer

The mean number of siblings per student is

1.3

.

To find the mean number of siblings per student, first determine the total number of siblings by multiplying each sibling category by its frequency:

(0 \times 2) + (1 \times 4) + (2 \times 3) + (3 \times 1) = 13

. Next, determine the total number of students by summing the frequencies:

2 + 4 + 3 + 1 = 10

. Finally, divide the total siblings by the total students:

\frac{13}{10} = 1.3

.

Step-by-Step Solution

1

Find the total number of students by adding the frequencies in the second column.

2 + 4 + 3 + 1 = 10

students

This sum represents the total number of observations in the dataset.

2

Calculate the total number of siblings by multiplying each sibling count by the number of students reporting that count, then summing the products.

(0 \times 2) + (1 \times 4) + (2 \times 3) + (3 \times 1) = 0 + 4 + 6 + 3 = 13

siblings

This gives the sum of all data values across the entire group.

3

Divide the total number of siblings by the total number of students to find the mean.

\frac{13}{10} = 1.3

The mean is calculated as the sum of all values divided by the number of observations.

Key Concept

Calculating the mean from a frequency table.

Estimated Time:1m 0s

Question 4696Question →

In the late nineteenth century, the invention of steel-frame construction revolutionized urban architecture. By distributing the weight of the building to a metal grid, heavy masonry walls were no longer needed by architects to support upper floors. This innovation allowed structures to rise to unprecedented heights, paving the way for the modern skyline.

Which of the following is the best replacement for the underlined portion of the passage?

NO CHANGE

the steel frame, along with new elevator designs, eliminate the need for heavy masonry walls to support upper floors.

the steel frame eliminated the need for heavy masonry walls, this allowed for much taller structures.

the steel frame eliminated the need for heavy masonry walls to support upper floors.

Show answer & explanation

Answer: the steel frame eliminated the need for heavy masonry walls to support upper floors.

Answer

the steel frame eliminated the need for heavy masonry walls to support upper floors.

The correct option resolves the dangling modifier by placing the logical subject 'the steel frame' immediately after the comma. This ensures that the introductory phrase 'By distributing the weight of the building to a metal grid' correctly modifies 'the steel frame' rather than 'heavy masonry walls.'

Step-by-Step Solution

1

Identify the action in the introductory modifying phrase: 'By distributing the weight of the building to a metal grid'.

The action requires a subject that is capable of distributing weight.

An introductory modifier must logically modify the subject that immediately follows the comma.

2

Analyze the subject of the main clause in the original sentence: 'heavy masonry walls'.

Heavy masonry walls cannot distribute the weight of the building; instead, the grid or steel frame does this.

This is a dangling modifier error, meaning the original sentence must be changed.

3

Evaluate the choices to locate a logical subject that should follow the introductory phrase.

The correct subject is 'the steel frame'. This rules out the option keeping the original phrasing.

Placing 'the steel frame' immediately after the comma ensures the modifier correctly describes the subject.

4

Check the remaining options for grammatical errors like subject-verb agreement and comma splices.

The option using the plural verb 'eliminate' with 'the steel frame' is incorrect due to subject-verb agreement, and the option containing two independent clauses joined by only a comma is a comma splice.

The final selection must be entirely free of grammar and punctuation errors.

Key Concept

Modifier Placement

Question 4697Question →

In 1856, Eunice Foote, an American scientist and women's rights activist, conducted groundbreaking experiments on the interaction of sunlight with different gases. Utilizing simple equipment—specifically, glass cylinders, thermometers, and an air pump—she demonstrated that carbon dioxide and moist air trapped more heat than dry atmospheric air. In her paper, she hypothesized that an atmosphere containing higher concentrations of carbon dioxide would result in a warmer Earth. Although her work was presented at an academic conference, it was totally sidelined and ignored by dudes in the scientific establishment for decades. Despite this lack of recognition, Foote’s experiments laid the essential foundation for modern climate science.

Which of the following choices best restores stylistic consistency and appropriate tone to the passage?

NO CHANGE

it was largely overlooked by the scientific community

it didn't really get any traction with the science crowd

it was characterized by a complete absence of recognition and notice from the established scientific community

Show answer & explanation

Answer: it was largely overlooked by the scientific community

Answer

The correct answer is the option that states 'it was largely overlooked by the scientific community'.

The correct option is the one that states 'it was largely overlooked by the scientific community'. This choice aligns with the established formal, objective, and academic register of the passage. It also expresses the idea clearly and concisely without wordiness or colloquialisms.

Step-by-Step Solution

1

Analyze the tone and style of the surrounding passage.

The passage maintains a formal, objective, and academic tone suitable for a historical profile of a scientific discovery.

Establishing the target tone helps identify word choices that are out of place.

2

Evaluate the underlined text for tone errors, wordiness, and redundancy.

The original phrasing is informal due to the word 'dudes' and redundant due to the pair 'sidelined and ignored'.

This confirms that the original option must be changed to restore appropriate style.

3

Review the remaining options to select the one that matches the target tone while remaining concise and grammatically correct.

The option referring to being 'largely overlooked by the scientific community' matches the formal tone and is concise. The other choices are either too conversational or overly wordy.

This determines the correct option based on stylistic consistency and conciseness.

Key Concept

Stylistic Appropriateness

Question 4698Question →

Psychologist Leon Festinger first proposed the theory of cognitive dissonance in 1957. When individuals hold two conflicting beliefs, they experience psychological discomfort, consequently, they are motivated to resolve this tension by altering their attitudes. This drive to reduce discomfort explains many otherwise puzzling human behaviors.

Which option best corrects the underlined portion of the passage?

NO CHANGE

discomfort; consequently, they are motivated to resolve this tension

discomfort; consequently because they are motivated to resolve this tension

discomfort, that they are motivated to resolve

Show answer & explanation

Answer: discomfort; consequently, they are motivated to resolve this tension

Answer

The correct choice is the one that uses a semicolon to separate the two independent clauses and follows the conjunctive adverb with a comma: 'discomfort; consequently, they are motivated to resolve this tension'.

The correct option correctly uses a semicolon to separate two independent clauses. The conjunctive adverb 'consequently' is then followed by a comma, which is the proper punctuation pattern for linking two complete thoughts with a transition.

Step-by-Step Solution

1

Analyze the structure of the clauses surrounding the underlined portion.

The clause before the underline ('When individuals hold two conflicting beliefs, they experience psychological discomfort') is independent, and the clause after ('they are motivated to resolve this tension by altering their attitudes') is also independent.

Identifying the clause types helps determine whether they can be joined by a comma, semicolon, or conjunction.

2

Evaluate the transition word and punctuation connecting these clauses.

The transition word 'consequently' is a conjunctive adverb. Two independent clauses joined by a conjunctive adverb must be separated by a semicolon (or a period) before the adverb and a comma after it.

Using only a comma with a conjunctive adverb creates a comma splice, which is a grammatical error.

3

Evaluate the other options to ensure they do not introduce new errors.

Adding 'because' after the semicolon makes the second clause dependent, creating a fragment. Using 'that' with a comma incorrectly punctuates a restrictive clause. The only grammatically sound option is using a semicolon followed by a comma after the transition.

Eliminating options with structural or punctuation errors confirms the correct choice.

Key Concept

Two independent clauses joined by a conjunctive adverb must be separated by a semicolon and followed by a comma to avoid run-on sentences and comma splices.

Question 4699Question →

A school club is raising money by selling rolls of wrapping paper. The club keeps $40\%$ of the total sales revenue as profit. If the club made a profit of $\$220$ from selling $r$ rolls of wrapping paper that cost $\$10$ each, which of the following equations can be used to find $r$ ?

0.40r = 220

10r = 220

4r = 220

10r + 0.40 = 220

25r = 220

Show answer & explanation

Answer: $4r = 220$

Answer

The equation expressing the profit is the profit per roll multiplied by the number of rolls, which yields

4r = 220

.

To find the correct equation, we calculate the profit per roll of wrapping paper. Since each roll is sold for

\$10

and the club keeps

40\%

of the revenue as profit, the profit per roll is

0.40 \times 10 = 4

dollars. For

r

rolls sold, the total profit is

4r

dollars. Setting this equal to the given profit of

\$220

yields the equation

4r = 220

.

Step-by-Step Solution

1

Determine the expression for the total sales revenue.

The total revenue is

10r

dollars.

Each of the

r

rolls of wrapping paper is sold for

\$10

.

2

Express the profit as a fraction of the total sales revenue.

The profit is

0.40 \times 10r = 4r

dollars.

The club keeps

40\%

(

0.40

) of the total revenue as profit.

3

Set the profit expression equal to the actual profit made to form the equation.

4r = 220

The total profit made by the club is given as

\$220

.

Key Concept

Translating a multi-step real-world scenario into a one-step linear equation

Alternative Method

Find the profit per roll first:

40\%

of

\$10

is

\$4

. Thus, the profit for

r

rolls is

4r

. Since the total profit is

\$220

, the equation is

4r = 220

.

Estimated Time:1m 30s

Question 4700Question →

While exploring the deep canopy of the rainforest, the biologist identified a rare, vibrant species of bromeliad, and she carefully documented its growth habits.

Which choice best maintains conventions of punctuation in the sentence?

NO CHANGE

rare, vibrant species of bromeliad; and she

rare, vibrant, species of bromeliad, and she

rare vibrant species of bromeliad, she

Show answer & explanation

Answer: NO CHANGE

Answer

The original phrasing, which includes a comma between the coordinate adjectives 'rare' and 'vibrant' and a comma before the coordinating conjunction 'and' to separate two independent clauses, is correct.

The original sentence correctly separates the coordinate adjectives 'rare' and 'vibrant' with a comma and uses a comma before the coordinating conjunction 'and' to connect two independent clauses.

Step-by-Step Solution

1

Determine if 'rare' and 'vibrant' are coordinate adjectives.

They are coordinate adjectives because they can be reordered ('vibrant, rare species') and joined by 'and' ('rare and vibrant species') while maintaining the same meaning. Therefore, a comma must separate them.

Coordinate adjectives require a comma or the word 'and' between them.

2

Analyze the clause structure following the noun 'bromeliad'.

The sentence consists of two independent clauses: 'the biologist identified...' and 'she carefully documented...'. These clauses are connected by the coordinating conjunction 'and'.

When joining two independent clauses with a coordinating conjunction, a comma must precede the conjunction.

3

Evaluate the choices to check for errors.

The original sentence correctly applies all punctuation conventions, while the other choices introduce errors such as misplaced commas, incorrect semicolons, or comma splices.

Selecting the option that correctly adheres to all grammar and punctuation rules is necessary.

Key Concept

Using commas to separate coordinate adjectives and using a comma with a coordinating conjunction to join independent clauses.

Estimated Time:1m 0s

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