The most logical and precise word to complete the sentence is: B: Expand
Explanation:
Incorporating hands-on learning is described positively as something that "encourages active participation and deeper comprehension″ so the missing word should align with this positive impact. "Expand" fits logically, as it suggests an increase in student engagement and understanding. The other choices imply negative or irrelevant effects, which don′t fit the context.
Correct Answer: B

However, this option appears to have a grammatical error (it should be commemorated instead of
"commemorations"). If the intended answer was meant to use "commemorates" that would be correct,
as it fits the context of honoring or highlighting resilience and spirit.

Explanation:
The film is described as capturing resilience and spirit, which suggests a positive and respectful tone.
"Negates" "obscures" and "trivializes" are negative terms that contradict the context.
Would you like me to clarify further or confirm if "commemorations" is the intended option?

The most logical and precise word to complete the sentence is:
C: Commemorations

The most logical and precise word to complete the sentence is B: Prescriptive

Explanation:
The sentence contrasts Tanaka’s approach of promoting intellectual autonomy with the editorial approaches of Sophia Bell and Marco Giovanni. This implies their editorial selections were more restrictive or directive, as opposed to allowing for a diversity of theories. "Prescriptive" aligns with this idea, as it refers to enforcing specific rules or guidelines.

The other options do not fit the context:
A: Empirical refers to being based on observation or experience, which is unrelated to the contrast being described.
C: Sporadic suggests irregularity, which doesn′t logically contrast with Tanaka′s humility and autonomy.
D: Informal contradicts the implied structured and authoritative nature of Bell and Giovanni′s editorial approaches.
Correct Answer: B

The most logical and precise word to complete the sentence is D: Augmented

Explanation:
The sentence indicates that recent isotopic analyses have added new dimensions to the interpretation of
the Venus figurines, suggesting their roles extended beyond fertility symbols. “Augmented” fits perfectly
because it means to enhance or expand upon something that already exists, which aligns with the idea
of building on previous interpretations.

The other options do not fit as well:
A: Evidenced implies providing proof but doesn′t convey the sense of expanding or enhancing the interpretation.
B: Elucidated means clarified, which is related but less fitting than “augmented” as the sentence emphasizes adding to previous knowledge rather than merely explaining it.
C: Subverted implies undermining or overturning, which is too strong and doesn′t match the tone of expanding understanding.
Correct Answer: D

The best choice is: D

The speaker presents a metaphorical choice, then describes his careful consideration. This reflects the poem‘s structure, as the speaker metaphorically describes a fork in the road (representing a life choice) and carefully considers each path before making a decision.

The best choice is C

It introduces a new trend that is gradually changing the face of Nevada's tourism industry. The underlined sentence highlights the emerging focus on family-friendly entertainment, signaling a shift in Nevada's tourism landscape without suggesting that the casino industry has been entirely replaced.

The best choice is: C

To highlight Grace’s internal debate over her sense of belonging and source of creative inspiration. The passage emphasizes Grace’s longing for the tranquility of the Yorkshire moors while questioning whether the bustling city is the right place for her art and heart, illustrating her inner conflict.

The best choice is C

As speculative, because it does not fully account for all possible sources of iron and magnesium. Barnett critiques Torres and her team's conclusion for attributing the detected elements solely to asteroid belts or dust clouds, emphasizing that other explanations, such as interstellar gas or supernova remnants, were not considered. This aligns with describing the conclusion as speculative.

The best choice is B

Theodore channels his emotions into his performances, using music to cope with his grief. The text highlights how Theodore’s music becomes even more heartfelt and soul-stirring as he channels his emotions into his performances, suggesting he uses music as a way to process and cope with his grief.

The best choice is A

The speaker is captivated by the sight and sound of a girl reaping and singing alone. The text describes the speaker’s admiration for the solitary girl and the enchanting, melancholy sound of her singing, which fills the valley.

The best choice is C

Oliver's tranquil encounters with the sea are starting to transform his outlook on life. The text emphasizes how the calming coastal environment is having a soothing and transformative effect on Oliver's previously restless and pragmatic nature.

The best choice is B

The geographic distribution of P. Dolichoderus fossils encompasses a wide range of ancient marine ecosystems, much broader than those of contemporary terrestrial reptiles. This finding would directly support the hypothesis that the adaptability of P. Dolichoderus allowed it to explore diverse marine habitats, as a wide distribution of fossils in various marine ecosystems aligns with an expanded ecological range.

The best choice is D

The average spending on R&D by both tech and pharmaceutical companies increased over the three periods studied. The graph shows a consistent increase in average spending for both tech and pharmaceutical companies across the three periods, supporting the researchers, conclusion about a growing commitment to innovation and development.

The best choice D.
CM-221c has a solubility of 1.2 g/L and an electrical conductivity of 500 µS/cm, fitting the criteria for a Low-Conductivity Salt. CM-559c, with a solubility of 1.5 g/L and an electrical conductivity of 550 µS/cm, meets  the criteria for a High-Conductivity Salt. This choice aligns with the Max Planck Institute team's assertion that only one compound is categorized as a High-Conductivity Salt and only one other as a Low-Conductivity Salt.

The best is Choice D

because it directly relates to the main point of Zheng's discovery—microorganisms with unique biochemical mechanisms can metabolize sulfur compounds in extremely low temperatures, challenging previous assumptions about life's ability to sustain itself in harsh conditions. This suggests a broader implication for our understanding of life's adaptability and resilience, extending the potential range of environments where  life could exist on Earth.

The best choice is B

The key grammatical convention being tested here is pronoun-antecedent agreement, which means the pronoun must agree in number (singular or plural) with the noun it replaces. The plural pronoun “they” correctly agrees with the plural noun “two iconic bronze sculptures”

The best Choice C

The convention being tested here is punctuation, specifically the use of commas with essential
elements. It correctly associates “James Moore and Haraldur Sigurdsson” with
“geologists” without the use of commas. This makes it clear that they are the geologists indicating the
contribution of the Mount St. Helens eruption to our understanding of volcanoe

Explanation

The best Choice A
The question tests the correct use of finite and nonfinite verb forms in the context of the sentence's structure and intended meaning. It employs the finite past tense verb “helped,” which appropriately pairs with “redefine” to indicate that Armstrong's unique interpretations had a specific impact in the past. The sentence structure also remains grammatically correct, as it contains a main verb (“helped”) for the subject (“His improvisational jazz trumpet and distinctive raspy voice”).

Explanation

 The best Choice C
The convention being tested here is the correct use of punctuation in a sentence. it keeps the flow of the sentence intact and does not result in a sentence fragment. The rest of the sentence provides context about the book, and there is no need for additional punctuation after the book title.

Explanation 

The best choice A
The key grammatical convention being tested here is pronoun-antecedent agreement, which means the pronoun must agree in number (singular or plural) with the noun it replaces. The plural pronoun “them” correctly agrees with the plural noun “minute details”.

Explanation

The best choice is D
The convention being tested here is the punctuation of a supplementary word between two main clauses. Choice D is the correct answer. This choice correctly uses a comma to separate the supplementary adverb “however” from the preceding main clause (“This wasn't the first impressive feat of engineering in the field of architecture”) and a semicolon to join the next main clause (“the construction of the Egyptian pyramids similarly showcased the capabilities of a civilization”) to the rest of the sentence. Further, placing the semicolon after “however” indicates that the information in the preceding main clause is contrary to what might be assumed from the information in the previous sentence (The Great Wall was a monumental achievement in Chinese history).

Explanation

The best choice is B
The context here requires a transition that indicates a contrasting point of view. This contrast is between the critics who argue that technology has reduced our cognitive abilities and those who believe that technology has enhanced them. Choice B) is the best answer. “However,” signals a shift in viewpoint from critics who argue technology has a negative impact to others who believe technology has a positive impact.

Explanation

The best choice is A
The context here requires a transition that indicates a logical consequence or conclusion drawn
from the first statement. This is about how the law of conservation of energy impacts the work of engineers when they design systems. Choice A) is the best answer. “Therefore” is used to introduce a logical conclusion or an effect of the fact just mentioned. In this case, because energy cannot be created or destroyed, engineers must account for this principle in their designs.

Explanation 

The best choice is B

It outlines the monumental impact of Salk′s vaccine by mentioning that it “drastically reduced the
global incidence of polio” and led to “great improvements in global public health”. This aligns
perfectly with the student's goal to emphasize the vaccine's significance.

Explanation 

The best choice is B

Choice B is the best answer because it uses the relevant information from the notes to emphasize the commonality that both the Chinook salmon and the Sockeye salmon can be found in the Pacific Ocean.

Explanation 

The best choice is D

It encapsulates the main findings by stating that coral bleaching increased with water temperature. This directly aligns with the students’ aim to summarize the key points of the study effectively

Explanation 

The best choice is A

Choice A is the best answer because it captures the significance of Watson and Crick's discovery by stating that it “revolutionized the understanding of genetics, leading to breakthroughs in medical treatments”. This option accurately reflects the key points in the students’ notes.

Explanation

The best Choice is A

The word needed to complete the text must describe the condition of metabolic functions as supported by a balanced diet. The context provided by Soto's argument, which states that varied nutrients can improve health and vitality, suggests that the metabolic functions should be at their most favorable level. Choice A “Optimal” correctly suggests the most favorable condition for metabolic functions, aligning with the context of a balanced diet improving health.

Explanation

The best choice is C 

The word that completes the sentence should logically relate to Michael Johnson's view on the impact of technology on education quality. The second part of the sentence provides a clue with “facilitating access to a wealth of information and diverse learning tools,” suggesting that technology has a positive effect on education when used responsibly. Choice C “Advantageous” means providing a benefit or advantage, which aligns with the idea that technology can improve the quality of education.

Explanation

The best choice is C

The correct word to complete the sentence should logically align with Wangari Maathai's impact on environmental activism and the success of the Green Belt Movement. The latter part of the sentence provides a key hint with “led to the planting of over 50 million trees, empowering communities”‚ suggesting a role in initiating or accelerating a positive process. Choice C “Promote” means to support or actively encourage, which directly corresponds with Maathai's role in fostering significant environmental action and change through her movement. This choice best reflects the positive and proactive impact of the Green Belt Movement on environmental sustainability.

Explanation

The best choice is B

The word that completes the sentence should logically relate to Virginia Woolf's narrative style and her approach to character development in her novels. The second part of the sentence provides a clue with “delving deeply into the inner thoughts and emotions of her characters,” suggesting that Woolf's writing captured the deep psychological complexity of individuals. Choice B) “Introspective” means examining one's own thoughts and feelings, which aligns with the idea that Woolf's narrative style involved a deep reflection of her characters' inner worlds.

Explanation

The best choice is B

Words in Context questions always provide clues to the correct answer, usually by reinforcing the meaning of the blank elsewhere in the passage. Keeping this in mind, let's reduce the passage to its fundamental elements: B) “Innovative”, which typically means introducing or using new ideas or methods, aligns perfectly with this anticipation. The artwork is not reserved, unintelligible, or perplexing—it's “innovative”, highlighting the original techniques employed in the exhibit.

Explanation

The best choice is C

Words in Context questions always provide clues to the correct answer, usually by reinforcing the meaning of the blank elsewhere in the passage. Keeping this in mind, let's reduce the passage to its fundamental elements: C “Enables”, which typically means giving someone the authority or means doing something, aligns perfectly with this anticipation. Good public speaking skills do not convoke, enjoy, or demur the audience; they “enable” the audience to fully grasp and appreciate the speakers” ideas.

Explanation

The best choice is B

It accurately reflects the function of the underlined sentence. It captures the essence of Kaya's internal conflict and her yearning to establish an individual identity that is distinct from the inherited narratives of her multicultural background.

Explanation 

The best choice is B

Text 2 indicates Everett's caution against hastily equating Neanderthal cognitive abilities with those of Homo sapiens, even in light of the cave art findings.

Explanation

The best Choice is B

The text clearly demonstrates Eli's preference for the peace and quiet of the cosmos over engaging with his fellow crewmates on Endeavour. His interest in the star chart and relative disinterest in social activities illustrate this point.

Explanation 

The best choice is A

The metaphor "Like grains of sand slipping through fingers, so were the days of that unforgettable summer" clearly deals with the concept of time passing quickly. The image of sand slipping through fingers is commonly associated with fleeting time, making it a fitting choice to illustrate the claim about the novel's use of metaphors to describe the passage of time.

Explanation 

The best choice is A

The PixelPro model meets all the photographer's requirements: it has a zoom capability of 30x, a battery life of 12 hours, and is priced at $450. This aligns with the specified criteria of having at least 30x zoom, at least 12 hours of battery life, and a price no greater than $500.

Explanation 

The best choice is D

If alumni of art programs report increased confidence in engaging with culturally diverse communities, this finding directly supports the researchers’ prediction about the long-term benefits of art education on

Explanation 

The best choice is A

Choice A is correct because it directly challenges the theory of fixed intelligence. If participants who underwent cognitive training showed significant improvements in problem-solving abilities and an increase in IQ scores, it would suggest that intelligence can be developed and is not entirely static.

Explanation 

The best choice is D

The fact that the number of plant species also decreased in the plot without grasshoppers suggests that there could be other factors, beyond the presence of grasshoppers, contributing to the decrease in plant diversity. This weakens Smith's assertion that the decrease was entirely due to the grasshoppers.

Explanation

The best choice is C

The shift towards electric mobility is described as a pathway to decarbonize transportation and contribute to cleaner air quality. Such a significant shift would likely introduce new technological challenges and opportunities for innovation, consistent with the themes of the passage.

Explanation 

The best choice is C

Since calm and turbulent sea conditions could likely affect a penguin's navigation ability, comparing penguins tracked under both conditions as if they were the same could lead to misinterpretations.

Explanation

The best choice is A

The simple present tense verb "reveals" correctly matches the present tense narrative of the sentence, indicating a current or general statement of fact that the study shows the reason behind bowerbird behavior.

Explanation

The best choice is A

It uses a comma before the coordinating conjunction "but" to connect two independent clauses within a single sentence. The first clause is complete on its own ("In most... book's appeal"), and the second clause provides a contrast to the first ("when the ... historical value"). The use of the comma before "but" is necessary because it is joining two independent clauses.

Explanation

The best choice is A
The key grammatical convention being tested here is the use of possessive nouns. The possessive form must correctly reflect ownership or association. In this sentence, the ownership of the "lifestyles" is attributed to "followers," which is plural. Choice "followers’ lifestyles" is correct because it uses the possessive form for the plural noun "followers," indicating that the lifestyles belong to the followers.

Explanation

The best choice is B

Choice B "they" is the correct answer. It is a third-person plural pronoun that correctly refers back to the plural noun "residents," maintaining proper agreement in number and person.

Explanation

The best choice is A
The finite past tense verb "supported" aligns with the sentence's past tense context, indicating that Hubble's past actions supported the idea of an expanding universe.

Explanation 

The best choice is C

It appropriately associates "Li Jing and Wang Wei" with
"archaeologists" without the use of commas, making it clear that they are the ones reporting the threats to the Great Wall.

Explanation

The best choice is C

This possessive determiner correctly indicates that the work belongs to or is associated with both John Lennon and Paul McCartney.

Explanation 

The best choice is A

Choice  "for example" is the correct answer because it introduces an instance that illustrates the exception to the rule mentioned in the previous sentence.

Explanation

The best choice is D

Choice D "In response" is the correct answer as it indicates that the research into alternative methods is being conducted as a direct reaction to the challenges faced by honeybee populations.

Explanation

The best choice is A

It properly indicates that despite the emphasis on creativity and innovation through active participation, there's also a need for structured guidelines and protocols to keep discussions on track.

Explanation

The best choice is D

It directly addresses the student's goal by stating that the Arctic Tern's annual migration distance is "further than that of most bird species." It also adds context by mentioning the Great Snipe, making the information about the Arctic Tern more impactful.

Explanation

We are given the equation:

6x=24

To find the value of x, we can simply divide both sides of the equation by 6:

x=4

Since the question asks for the value of 9x, we multiply the value of x by 9:

9x=9

Therefore, the value of 9x is C) 36.

Explanation
When multiplying expressions with the same base, we add the exponents. The bases in our case are a, b, and c.

For a, we add the exponents from the two terms:

a3a=a3+1=a4

For b we add the exponents from the two terms:

b2b3=b2+3=b5

For c, we add the exponents from the two terms:

c−1c2=c−1+2=c.

Therefore, the equivalent expression is C) a4b5c.

Explanation

To find out what percentage 375 is of 500, we divide 375 by 500 and then multiply the result by 100% to convert it to a percentage:

375/500 x 100% =75%

Therefore, 375 is 75%of 500, which corresponds to Choice B

Explanation

We're given that x/5 = 7

First, we solve x by multiplying both sides of the equation by 5:

x = 5 * 7

x = 35

Knowing this, we can determine that x/5 is equivalent to 5/35, which simplifies to 1/7.

Another way to look at this is that the reciprocal of x/5 (which is 5/x) will be the reciprocal of 7. The reciprocal of 7 is 1/7.

Explanation

In similar triangles, corresponding angles are equal. Therefore, since angle A corresponds to angle D and is given as 10°, angle D is also 10°.

The sum of angles in a triangle is always 180°.

Since angle E (which corresponds to angle B) is a right angle, it measures 90°.

So, to find the measure of angle F, we subtract the measures of angles D and E from 180°:

180°−10°−90°=80°

Thus, the measure of angle F is 80°, which corresponds to Choice B.

Explanation.

B) For x = 22,

4 . 2 + 1 = 9 which is greater than y = 7

For x = 3

4 . 3 + 1 = 13 which is greater than y = 12

For x = 4

4 . 4 + 1 = 17 which is greater than y = 16

So, all the y-values in B are less than 4x + 1

Explanation

The given equations are x/y = 3 and 18x/ny = 3

Setting these two equal to each other, we have

x/y = 18x/ ny

x/y cancels out on both sides of the equation:

1 = 18/n

n = 18

Therefore, the value of n is C 18.

Explanation

We are given:

g(x) = 1/5 x

Set g(x) = 50:

50 = 1/5 x

To solve for x, multiply both sides by 5:

x = 50 . 5

x = 250

So, the value of x for which g(x) = 50 is 250.

Explanation

We can set up the following equation to represent the area of the rectangle:

x(x + 4) = 117

To solve for x, we expand the left side of the equation and then solve for x:

x² + 4x = 117

x² + 4x - 117 = 0

(x - 9)(x + 13) = 0

Setting each factor equal to zero gives the solutions x = 9 and x = -13. However, since a length can't be negative, we discard x = -13.

Therefore, the value of x is D = 9.

Explanation
Box plots provide a way to visualize the distribution of a dataset: the box represents the middle 50% of values, the line inside the box is the median, and the whiskers (lines extending from the box) indicate the minimum and the maximum.

From the given box plots, we can see that the median height for Group A is at 120 centimeters and the median height for Group B is at 140 centimeters.

Therefore, we can conclude that the median height of the sunflowers in Group A is less than the median height of the sunflowers in Group B, which corresponds to Choice D.

Explanation
To express aa in terms of b and c, we need to isolate a on one side of the equation. We can achieve this by multiplying both sides of the equation by (4b+6):

c(4b+6)=a

Therefore, the correct expression for aa in terms of b and cc is a=c(4b+6), which
corresponds to Choice C.

Explanation
Each year (each increment in t), we multiply the initial population by 2 to find the new population size.

Thus, after t years, we've multiplied the initial population by 2 a total of t times. This is equivalent to raising 2 to the power of t and then multiplying by the initial population.

Therefore, we can represent the size of the rabbit population after t years as: r=1,000(2)t

Here, 1,000 is the initial size of the population (also known as the base population or starting quantity), 22 is the growth factor (how much the population size increases every year), and t is the time, in years, that has passed since the start of the observation.

Thus, the correct answer is Choice D.

Explanation

Let's break down the expression (xy)^{9/5} using the rules of exponents.

The exponent of 9/5 can be thought of as a combination of the exponent 9 (which means raising to the ninth power) and the exponent 1/5 (which is the same as taking the fifth root). The order of operations doesn't matter here, so we can first take the ninth power and then the fifth root, or vice versa.

We'll first raise to the ninth power and then take the fifth root. That gives us 5√(xy)9, which is equal to 5√(x9y9).

So, the equivalent expression is A) 5√(x9y9).

Explanation

Square both sides to eliminate the square root:

(x + 5)²

x² + 10x + 25 = x + 35

x² + 9x - 10 = 0

Factor the equation:

(x + 10)(x - 1) = 0

From this, we have got two possible solutions:

x + 10 = 0 which gives x = -10

x - 1 = 0, which gives x = 1

Checking both solutions in the original equation:

For x = -10,

-10 + 5 = √(-10 + 35)

-5 = √25

-5 ≠ 5 (there is an implied positive sign in front of √25)

For x = 1:

1 + 5 = √(1 + 35)

6 = √36

6 = 6

Therefore, only x = 1 is the correct solution, which corresponds:

Choice B.

Explanation

To determine the value of x, which is the number of months it took Julia to pay for the appliances, we first need to subtract the down payment from the total cost of the appliances:

1,800 (total cost) - 300 (down payment) = 1,500

Next, we divide this amount by the monthly payment amount to find out how many months it took to pay the remaining balance:

1,500 / 100 (monthly payment) = 15 months

So, the correct answer is 15.

Explanation

Every 3 hours, the number of bacteria in the colony doubles.

The number of bacteria:

• After 3 hours: 2 × 10 = 20
• After 6 hours: 2 × 20 = 40
• After 9 hours: 2 × 40 = 80
• After 12 hours: 2 × 80 = 160

Therefore, after 12 hours, there will be 160 bacteria in the colony. Thus, the correct answer is Choice D.

Explanation

The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to it. If we assign the value x to the side opposite to angle S, then the side adjacent to angle S would have a length of √3 x (because tan(S) = 1/√3).

Now, using the Pythagorean theorem, we can find the length of the hypotenuse.

RS = √(x2 + (√3 x)2) = √4x2 = 2x

The sine of an angle in a right triangle is the ratio of the length of the side opposite to the angle to the length of the hypotenuse.

Notice, we are looking for the value of sin(R), not sin(S).

sin(R) = √3x⁄2x = √3⁄2, making the correct answer Choice B.

Explanation

To find the x-intercept, we set y = 0 in the equation and solve for x. So:

3x + 6(0) = -23

3x = -23

x = -23/3

Therefore, the x-intercept is a = -23/3.

To find the y-intercept, we set x = 0 in the equation and solve for y. So:

3(0) + 6y = -23

6y = -23

y = -23/6

Therefore, the y-intercept is b = -23/6.

Finally, to find the value of b/a, we divide -23/6 by -23/3:

b / a = -23/6 / -23/3

= 23/6 · 3/23

= 3/6

b / a = 1/2

Therefore, the answer is 1/2.

Explanation

If the population increases by 10% each year, this means that the new population is 110% (or 1.10 times) the size of the previous year's population.

To find out how much the population has increased after two years (from 2015 to 2017), we can multiply 1.10 (the yearly increase) by itself:

1.10 × 1.10 = 1.21

Therefore, the 2017 population is 1.21 times the size of the 2015 population.

So, the correct answer is Choice D.

Explanation

The function f(x) = 6x² - 10x - 16 is a quadratic function, and it has the general form f(x) = ax² + bx + c where a, b, and c are constants, and a ≠ 0.

The x-coordinate of the vertex (the point at which the function reaches its minimum or maximum value) of a parabola given by

f(x) = ax² + bx + c is -b/2a.

In this case, a = 6 and b = -10, so the x-coordinate of the vertex is:

-[-10/2.6] = 10/12 = 5/6

So, the function f(x) reaches its minimum when x = 5/6.

Explanation

We are given a square park with a circular fountain at its center. The shortest distance from the edge of the fountain to each side of the park is 10 meters, and the diagonal of the square park is 40 meters. Graphically, it looks like this:

Calculating the Fountain's Dimensions

We can find the side length of the square park using the given diagonal and Pythagorean theorem:

side² + side² = diagonal²

2 · side² = (40)²

side² = 1600 / 2

side = √800

The entire side length of the square minus the shortest distance from the edge of the fountain to each side of the park (which is 10 meters from each side) gives us the diameter of the fountain. So, the diameter of the fountain is:

diameter = side - 10 - 10

diameter = √800 - 20

The radius of the fountain is half of its diameter, so:

radius = (√800 - 20) / 2 ≈ 4.142

Finally, we can calculate the area of the circular fountain using the formula A = πr²:

area = πr²

= π(4.142)²

area = 53.9

Therefore, the correct answer is Choice A.

Explanation

To solve this problem, we first need to manipulate the expression 27^x / 9^y using exponent rules.

Since 27 = 3³ and 9 = 3²,

27^x / 9^y = (3³)^x / (3²)^y

= 3^3x / 3^2y

27^x / 9^y = 3^{3x - 2y}   •   (1)

We are also given that 6x - 4y = 8. If we divide both sides by 2, we get:

6x - 4y = 8

3x - 2y = 4 •  (2)

Substituting equation (2) into equation (1):

&frac27;y = 3^{3x - 2y}

= 3⁴

= 81

Therefore, the correct answer is Choice C.

Explanation

We are given:

x+43=75

First, we isolate xx by subtracting 43 from both sides:

x=75−43

Simplifying:

x=32

Therefore, the solution to the given equation is B, x=32

Explanation
To find the value of f(6) for the function ff defined by f(x)=3x2, we substitute

x=6 into the equation and calculate the result.

f(x)=3x2
f(6)=3(62)
=3(36)

f(6)=108

Therefore, the correct answer is Choice D 108.

Explanation
Area formula for a rectangle is: area = length ⋅width

We are given:

area = 48 square inches
length = 8 inches

To find the width:

width = area / length
=(48 square inches) / (8 inches)
=6 inches

Therefore, the width of the rectangle is 6 inches, which corresponds to Choice B.

Explanation

First Approach: Find the value of x and substitute.
Solve for x :

x=9−5
x=4

Substitute x=4 into 3x+15:

3(4)+15=12+15=27

Alternative Approach: Recognize a pattern in the expression.

Notice that 3x+15 is three times (5+x).

Since 5+x=9, multiply this by 3:

3x+15=3(5+x)=3(9)=27

Either way, the value of 3x+15 is B= 27

Explanation:

Distribute the 3 inside the parentheses:

3(4z−2)=3(4z)−3(2)=12z−6

Now, the expression is 9z+(12z−6)

Combine like terms and simplify:

(9z+12z)−6=21z−6

Therefore, the correct answer is Choice A.

Explanation: 

To find the probability of drawing an odd-numbered ticket from a container holding 9 tickets numbered consecutively from 1to 9, calculate the ratio of the number of favorable outcomes (drawing an odd-numbered ticket) to the total number of possible outcomes

(drawing any of the 9 tickets).

In the range from 1 to 9, there are 5 odd numbers (1,3,5,7,9), so there are 5 favorable

outcomes. The total number of possible outcomes is 9, as there are 9 tickets.

Therefore, the probability is calculated as:

5 favorable outcomes
(odd numbered tickets)=599 possible outcomes

Hence, the probability is D 5/9

Explanation

We are given:

10x=5y/2z

To express x in terms of y and z, divide both sides of the equation by 10 :

x=5y/2z⋅1/10x

Simplify the right side of the equation:

x=5y/20z
x=y/4z

Therefore, the correct answer is Choice A.

Explanation

To find the total expense for a 24-month subscription to an online service, we can plug in the monthly fee and calculate.

Given the total expense g(y)=24y+500g and the monthly fee y=200

g(y)=24y+500g(y)
g(200)=24(200)+500g(200)
=4800+500
g(200)=5300

Therefore, the total expense for the subscription is $5,300, which corresponds to Choice A.

Explanation

We are given:

perimeter=(2w+6) meters

width=w meters

Perimeter of a rectangle is:

perimeter=2⋅(length + width)

So,

2w+6=2⋅(length + w)
2w+6=2⋅length+2w
6=2⋅length

length=3

Therefore, the correct answer is Choice B.

Explanation

The statement “z is 50 more than ww”; means that when you add 50 to w, you get z. In mathematical terms, this can be expressed as z=w+50z

Therefore, the correct answer is Choice A.