Tüm alıştırma soruları

5556 soru

Soru 5081Soru

A plant physiologist conducted an experiment to investigate stomatal conductance in *Phaseolus vulgaris* (bean plant) leaves under various treatments of a synthetic phytohormone analog, Compound Y. Match each experimental group to its specific baseline or functional role within the experimental design.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Öğeler

Group 1: Intact leaves sprayed with a 0.1%0.1\% ethanol vehicle solution without Compound Y
Group 2: Intact leaves sprayed with 10 μM10\text{ }\mu\text{M} Compound Y dissolved in a 0.1%0.1\% ethanol vehicle solution
Group 3: Leaves on root-excised stems sprayed with 10 μM10\text{ }\mu\text{M} Compound Y dissolved in a 0.1%0.1\% ethanol vehicle solution
Group 4: Intact leaves sprayed with 50 μM50\text{ }\mu\text{M} Compound Y dissolved in a 0.1%0.1\% ethanol vehicle solution

Eşleşmeler

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Cevap

Group 1 matches the negative control for vehicle solvent baseline without Compound Y; Group 2 matches the primary experimental group for moderate chemical concentration; Group 3 matches the control testing the necessity of intact root signaling; Group 4 matches the experimental group assessing high-concentration dose dependency.
Each experimental setup plays a distinct role: Group 1 provides the negative control for solvent effects; Group 2 and Group 4 assess moderate and high active chemical doses; Group 3 controls for systemic root-tissue participation.

Adım Adım Çözüm

1
Identify the group where the independent variable (Compound Y) is completely absent.
Group 1 receives only the vehicle solution (0.1%0.1\% ethanol).
Negative controls isolate background effects of the delivery vehicle/solvent to set a true baseline.
2
Analyze the purpose of modifying plant anatomy in Group 3 while keeping chemical concentration identical to Group 2.
Excising roots isolates leaf-tissue responses from systemic root signaling.
This serves as a targeted control to verify whether systemic root-derived factors mediate stomatal closure.
3
Distinguish between the two intact treatment groups (Group 2 and Group 4).
Group 2 uses a moderate concentration (10 μM10\text{ }\mu\text{M}) whereas Group 4 uses a higher concentration (50 μM50\text{ }\mu\text{M}).
Varying concentration allows researchers to determine dose-dependent physiological relationships.

Anahtar Kavram

Distinguishing between negative baseline controls, structural variable controls, and active treatment groups in multi-variable experimental setups.
Soru 5082Soru

Read the sentence below.

The archival manuscript was entirely devoid from historical details that could verify the author's identity, leaving researchers to rely solely on stylistic analysis.

Which of the following choices produces a grammatically and idiomatically correct sentence?

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Cevap: devoid of

Cevap

The correct option is 'devoid of' because the adjective 'devoid' idiomatically pairs with the preposition 'of'.
In standard English, the adjective 'devoid' must be followed by the preposition 'of' when indicating that something is entirely lacking a specific feature or quality. Therefore, the phrase 'devoid of' creates an idiomatically correct sentence.

Adım Adım Çözüm

1
Identify the underlined expression and determine the target grammatical skill.
The underlined phrase is 'devoid from', which tests an adjective-preposition idiomatic combination.
ACT English frequently tests fixed prepositional idioms paired with specific adjectives, verbs, or nouns.
2
Recall standard English idiomatic usage for the adjective 'devoid'.
The adjective 'devoid' idiomatically requires 'of' (e.g., 'devoid of meaning' or 'devoid of details').
Although phrases like 'free from' use 'from', 'devoid' exclusively takes 'of' to express complete absence or lack.
3
Evaluate the choices to select the idiomatically correct preposition.
Replacing 'devoid from' with 'devoid of' restores standard idiomatic phrasing.
'Devoid of' is the only option that conforms to standard conventions of written English.

Anahtar Kavram

Idiomatic Prepositions
Tahmini Süre:45s
Soru 5083Soru

Arrange the following four mathematical expressions in order from least to greatest value.

Öğeleri doğru sıraya koymak için sürükleyin

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Cevap

The correct order from least to greatest value is 9×1040.5\frac{9 \times 10^{-4}}{0.5}, (5×102)2\left(5 \times 10^{-2}\right)^2, 3.2×1033.2 \times 10^{-3}, and 1.6×105\sqrt{1.6 \times 10^{-5}}.
Converting each expression to standard scientific notation with base power 10310^{-3} allows for direct comparison of coefficients: 9×1040.5=1.8×103\frac{9 \times 10^{-4}}{0.5} = 1.8 \times 10^{-3}, (5×102)2=2.5×103\left(5 \times 10^{-2}\right)^2 = 2.5 \times 10^{-3}, 3.2×1033.2 \times 10^{-3} is already in standard form, and 1.6×105=16×106=4.0×103\sqrt{1.6 \times 10^{-5}} = \sqrt{16 \times 10^{-6}} = 4.0 \times 10^{-3}. Comparing coefficients 1.8<2.5<3.2<4.01.8 < 2.5 < 3.2 < 4.0 confirms the order from least to greatest.

Adım Adım Çözüm

1
Evaluate the expression 9×1040.5\frac{9 \times 10^{-4}}{0.5}
1.8×1031.8 \times 10^{-3} (or 0.00180.0018)
Dividing the coefficient 99 by 0.50.5 gives 1818. Then convert 18×10418 \times 10^{-4} to standard scientific notation 1.8×1031.8 \times 10^{-3}.
2
Evaluate the expression (5×102)2\left(5 \times 10^{-2}\right)^2
2.5×1032.5 \times 10^{-3} (or 0.00250.0025)
Apply the power of a product rule: 52×(102)2=25×104=2.5×1035^2 \times (10^{-2})^2 = 25 \times 10^{-4} = 2.5 \times 10^{-3}.
3
Evaluate the expression 1.6×105\sqrt{1.6 \times 10^{-5}}
4.0×1034.0 \times 10^{-3} (or 0.00400.0040)
Rewrite 1.6×1051.6 \times 10^{-5} as 16×10616 \times 10^{-6} so the exponent of 1010 is even. Taking the square root gives 16×106=4×103\sqrt{16} \times \sqrt{10^{-6}} = 4 \times 10^{-3}.
4
Compare all expressions in standard scientific notation with power 10310^{-3}
1.8×103<2.5×103<3.2×103<4.0×1031.8 \times 10^{-3} < 2.5 \times 10^{-3} < 3.2 \times 10^{-3} < 4.0 \times 10^{-3}
Since all numbers share the same power of ten (10310^{-3}), compare their coefficients: 1.8<2.5<3.2<4.01.8 < 2.5 < 3.2 < 4.0.

Anahtar Kavram

Comparing quantities in scientific notation by simplifying exponent and radical operations to standard forms.
Soru 5084Soru

A track athlete recorded the following times, in seconds, for five 100-meter sprint trials:

12.4, 11.8, 13.1, 12.0, 12.212.4,\ 11.8,\ 13.1,\ 12.0,\ 12.2

What is the median time, in seconds, for these five trials?

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Cevap: 12.2

Cevap

The median time for the five trials is 12.2 seconds.
To find the median, first arrange the five times in ascending order: 11.8, 12.0, 12.2, 12.4, and 13.1. Since there are 5 values, the median is the middle (3rd) value, which is 12.2.

Adım Adım Çözüm

1
Order the data set in ascending numerical order.
11.8,12.0,12.2,12.4,13.111.8, 12.0, 12.2, 12.4, 13.1
The median is defined as the middle value of an ordered data set.
2
Identify the middle (third) position in the 5-item ordered list.
The third value is 12.212.2.
For an odd number of data points (n=5n = 5), the median is the value at position n+12=3\frac{n+1}{2} = 3.

Anahtar Kavram

Calculating the median of a finite data set
Soru 5085Soru

Read the sentence below from an article on materials science.

"The synthetic polymer developed by the research team proved exceptionally susceptible for chemical erosion when exposed to high ambient temperatures."

Which of the following choices replaces the underlined phrase with the idiomatically correct preposition?

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Cevap: susceptible to

Cevap

The phrase 'susceptible to' provides the idiomatically correct preposition for the sentence.
In standard English, the adjective 'susceptible' idiomatically pairs with the preposition 'to' when expressing vulnerability or liability to an influence. Therefore, 'susceptible to' is the only choice that adheres to conventions of usage.

Adım Adım Çözüm

1
Identify the head word preceding the underlined preposition.
The head word is the adjective 'susceptible'.
Prepositional idioms are fixed expressions determined by the noun, verb, or adjective being modified.
2
Determine the standard English prepositional pairing for 'susceptible'.
In standard written English, 'susceptible' requires the preposition 'to' when indicating vulnerability.
Prepositions such as 'for', 'with', or 'towards' form non-standard prepositional combinations with 'susceptible'.

Anahtar Kavram

Idiomatic Preposition Usage with Adjectives
Soru 5086Soru

An agricultural research facility divides a field with a total area of AA acres into nn individual test plots of equal size after reserving an area of 12 acres for administrative buildings. Which of the following equations correctly expresses the area, pp, in acres, of each individual test plot in terms of AA and nn?

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Cevap: p=A12np = \frac{A - 12}{n}

Cevap

The equation representing the area of each test plot is p=A12np = \frac{A - 12}{n}.
Reserving 12 acres leaves A12A - 12 acres available for testing. Dividing this remaining quantity equally into nn test plots results in an area per plot of p=A12np = \frac{A - 12}{n}.

Adım Adım Çözüm

1
Determine the remaining area allocated for test plots.
Available area = A12A - 12 acres.
The 12 acres used for administrative buildings must be subtracted from the total field area AA.
2
Divide the remaining area by the number of equal test plots nn.
p=A12np = \frac{A - 12}{n}.
Dividing the remaining acreage equally among nn plots gives the area pp of a single plot.

Anahtar Kavram

Translating contextual verbal scenarios into basic algebraic expressions using grouping and division.
Soru 5087Soru

A circular swimming pool cover has a total area of 64π64\pi square feet. A specific section of the cover, formed by a circular sector with a central angle of 135135^\circ, is made of a reinforced heavy-duty material. What is the perimeter, in feet, of this reinforced sector?

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Cevap: 6π+166\pi + 16

Cevap

The perimeter of the reinforced sector is 6π+166\pi + 16 feet.
First, find the radius from the circle area formula: πr2=64π    r=8\pi r^2 = 64\pi \implies r = 8 feet. Next, calculate the arc length of the sector using the angle fraction 135360=38\frac{135^\circ}{360^\circ} = \frac{3}{8}. Multiplying by the total circumference 2π(8)=16π2\pi(8) = 16\pi gives an arc length of 6π6\pi feet. Finally, add the two straight radius edges to get the total perimeter: 6π+8+8=6π+166\pi + 8 + 8 = 6\pi + 16 feet.

Adım Adım Çözüm

1
Find the radius of the circular pool cover using the given area.
Since Total Area =πr2=64π= \pi r^2 = 64\pi, dividing by π\pi yields r2=64r^2 = 64, so r=8r = 8 feet.
The radius is required to determine both the arc length and the lengths of the straight boundary edges.
2
Calculate the arc length of the sector.
Arc length =θ360×2πr=135360×2π(8)=38×16π=6π= \frac{\theta}{360^\circ} \times 2\pi r = \frac{135^\circ}{360^\circ} \times 2\pi(8) = \frac{3}{8} \times 16\pi = 6\pi feet.
The curved boundary of the sector is a fraction of the circle's full circumference.
3
Calculate the total perimeter of the sector by adding the arc length and the two radii.
Perimeter =Arc length+2r=6π+2(8)=6π+16= \text{Arc length} + 2r = 6\pi + 2(8) = 6\pi + 16 feet.
The perimeter of any sector consists of its curved outer arc plus its two straight side radii.

Anahtar Kavram

Perimeter of a Circular Sector
Tahmini Süre:1m 0s
Soru 5088Soru

Art conservators working on delicate medieval manuscripts must remove centuries of accumulated grime without damaging the fragile parchment beneath. To accomplish this, specialists apply a specialized synthetic gel that gently binds to surface contaminants. Unlike liquid solutions that might saturate the fibers, this gel is formulated to [evaporate] the dirt particles so they can be safely wiped away.

Which choice best maintains the precise, academic tone of the passage and accurately describes the function of the gel?

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Cevap: lift

Cevap

The word 'lift' accurately describes the gentle separation of dirt particles from the surface while maintaining an appropriate academic register.
The word 'lift' is the most precise and contextually appropriate verb because it accurately describes the physical separation of bound dirt particles from fragile manuscript surfaces while preserving the passage's formal, technical register.

Adım Adım Çözüm

1
Analyze the context and physical process described in the sentence.
The passage discusses using a cleaning gel to separate surface dirt from delicate manuscript fibers.
Understanding the physical context helps evaluate whether the verb choice is accurate.
2
Evaluate the precision and tone of each option.
'Evaporate' is scientifically inaccurate for solid particles; 'banish' is overly dramatic; 'eradicate' carries an unfitting connotation of total destruction.
Standard assessment requires selecting a word that is both factually precise and tone-appropriate.
3
Select the choice that best fits both precision and tone.
'Lift' correctly identifies the technical process of removing dirt particles without damaging the underlying surface.
It fulfills the requirement for word precision and clarity in an academic context.

Anahtar Kavram

Selecting words that precisely convey the intended physical action and fit the academic tone of the context.
Soru 5089Soru

Researchers conducted an experiment to measure the rate of crude engine oil degradation by the soil bacterium *Pseudomonas putida* in the presence of varying concentrations of a chemical surfactant (Surfactant X). Five culture flasks were prepared with identical volumes (100 mL100\text{ mL}) of sterile mineral salts growth medium and equal amounts (2.0 g2.0\text{ g}) of crude oil:

- Flask 1: Growth medium + engine oil (no bacteria, no Surfactant X)
- Flask 2: Growth medium + engine oil + 1.0 mL1.0\text{ mL} bacterial culture (no Surfactant X)
- Flask 3: Growth medium + engine oil + 1.0 mL1.0\text{ mL} bacterial culture + 0.5 g0.5\text{ g} Surfactant X
- Flask 4: Growth medium + engine oil + 1.0 mL1.0\text{ mL} bacterial culture + 1.0 g1.0\text{ g} Surfactant X
- Flask 5: Growth medium + engine oil + 1.0 mL1.0\text{ mL} bacterial culture + 2.0 g2.0\text{ g} Surfactant X

All flasks were incubated at 30C30^\circ\text{C} for 14 days, after which the total percentage of degraded oil was measured.

Which flask was included to establish the baseline rate of non-biological (abiotic) oil breakdown in the absence of bacterial activity?

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Cevap: Flask 1

Cevap

Flask 1
Flask 1 establishes the baseline for abiotic oil breakdown because it omits the biological agent (bacterial culture) as well as the chemical treatment (surfactant). Comparing degradation in active bacterial flasks to Flask 1 ensures that any observed oil loss is attributed to bacterial action rather than spontaneous non-biological weathering.

Adım Adım Çözüm

1
Identify the variable whose baseline effect needs to be isolated.
The target baseline is non-biological (abiotic) oil breakdown, which requires removing all biological activity (bacterial culture).
Control groups isolate specific variables by withholding the key independent variable or treatment.
2
Examine the composition of each flask to find the one omitting bacterial culture.
Flask 1 contains only growth medium and engine oil, with no bacterial culture or surfactant added.
Omitting bacteria ensures any measured degradation in this flask is solely due to non-biological processes.
3
Confirm that Flask 1 serves as the abiotic negative control.
Flask 1 establishes the reference rate of non-biological degradation against which biological rates in Flasks 2–5 can be compared.
Subtracting abiotic losses observed in Flask 1 from total losses in bacterial flasks isolates true biodegradation.

Anahtar Kavram

Identifying Negative Control Groups for Abiotic Baseline Conditions
Soru 5090Soru

A civil engineer is designing a triangular bridge support structure with vertices PP, QQ, and RR. The support beam PQPQ is 8080 feet long, the beam QRQR is 5050 feet long, and the interior angle PQR\angle PQR measures 6060^\circ. What is the length, in feet, of the support beam PRPR?

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Cevap: 70

Cevap

The length of the support beam PRPR is 7070 feet.
Using the Law of Cosines formula c2=a2+b22abcos(C)c^2 = a^2 + b^2 - 2ab\cos(C) with side lengths 8080 and 5050 and included angle 6060^\circ, we calculate PR2=802+5022(80)(50)cos(60)=6400+25004000=4900PR^2 = 80^2 + 50^2 - 2(80)(50)\cos(60^\circ) = 6400 + 2500 - 4000 = 4900. Taking the square root gives PR=70PR = 70 feet.

Adım Adım Çözüm

1
Identify the given dimensions and included angle
Side PQ=80PQ = 80 ft, side QR=50QR = 50 ft, and included angle PQR=60\angle PQR = 60^\circ.
The Law of Cosines applies directly when two side lengths and the included angle (SAS) are known.
2
Set up the Law of Cosines equation for the unknown side PRPR
PR2=PQ2+QR22(PQ)(QR)cos(PQR)PR^2 = PQ^2 + QR^2 - 2(PQ)(QR)\cos(\angle PQR)
This formula generalizes the Pythagorean theorem to non-right triangles.
3
Substitute the known values into the equation and evaluate
PR2=802+5022(80)(50)cos(60)=6400+25004000=4900PR^2 = 80^2 + 50^2 - 2(80)(50)\cos(60^\circ) = 6400 + 2500 - 4000 = 4900
Evaluating squares and using cos(60)=0.5\cos(60^\circ) = 0.5 simplifies the calculation.
4
Take the positive square root to find PRPR
PR=4900=70PR = \sqrt{4900} = 70
Side length must be a positive real number.

Anahtar Kavram

Applying the Law of Cosines to solve for an unknown side in a Side-Angle-Side (SAS) triangle.
Soru 5091Soru

Hydrogeologists evaluated the hydraulic conductivity (KK, in m/day\text{m/day}) of four sediment types under three compaction levels (1.4 g/cm31.4\text{ g/cm}^3, 1.6 g/cm31.6\text{ g/cm}^3, and 1.8 g/cm31.8\text{ g/cm}^3). The results are presented in the following table:

Sediment TypeKK at 1.4 g/cm31.4\text{ g/cm}^3 (m/day)KK at 1.6 g/cm31.6\text{ g/cm}^3 (m/day)KK at 1.8 g/cm31.8\text{ g/cm}^3 (m/day)
Clay0.0020.0020.0010.0010.00050.0005
Silt0.050.050.020.020.0080.008
Fine Sand4.54.52.12.10.90.9
Coarse Gravel120.0120.085.085.050.050.0

Statement: If this data were translated into a line graph with compaction density on the horizontal axis and hydraulic conductivity (KK) on the vertical axis, the lines for all four sediment types would show a positive slope from left to right.

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Cevap: False

Cevap

The statement is False because higher compaction density leads to lower hydraulic conductivity for all four sediment types, which translates to a negative slope on a line graph.
The statement is incorrect because the tabular data shows an inverse relationship between compaction density and hydraulic conductivity (KK). As compaction density increases from left to right along the table headers (1.41.61.8 g/cm31.4 \rightarrow 1.6 \rightarrow 1.8\text{ g/cm}^3), the corresponding KK values decrease for all four sediment types. When translated into a line graph with density on the x-axis and KK on the y-axis, lines that fall from left to right exhibit a negative slope, not a positive slope.

Adım Adım Çözüm

1
Identify the independent variable for the horizontal axis and the dependent variable for the vertical axis.
Compaction density (1.41.4, 1.61.6, 1.8 g/cm31.8\text{ g/cm}^3) is on the horizontal (xx) axis, and hydraulic conductivity (KK) is on the vertical (yy) axis.
Establishing axis assignment is the first step in translating tabular data into graphical form.
2
Examine the trend of hydraulic conductivity (KK) values as compaction density increases across each row.
For Clay (0.0020.0010.00050.002 \rightarrow 0.001 \rightarrow 0.0005), Silt (0.050.020.0080.05 \rightarrow 0.02 \rightarrow 0.008), Fine Sand (4.52.10.94.5 \rightarrow 2.1 \rightarrow 0.9), and Coarse Gravel (120.085.050.0120.0 \rightarrow 85.0 \rightarrow 50.0), KK consistently decreases as density increases.
Determining the direction of change in yy relative to xx reveals the graphical slope.
3
Translate the observed mathematical trend into a graphical feature (slope direction).
A relationship where yy decreases as xx increases forms a downward line from left to right, which defines a negative slope, making the claim of a positive slope false.
Translating inverse data trends to graphs requires correctly associating decreasing values with negative slopes.

Anahtar Kavram

Translating Tabular Relationships to Graphical Slopes
Tahmini Süre:1m 0s
Soru 5092Soru

Read the sentence below:

During an investigation into spatial memory consolidation, cognitive neuroscientists observed that chronic sleep restriction was particularly detrimental for a subject's ability to navigate novel virtual environments.

Which of the following choices produces a grammatically correct and idiomatically appropriate sentence?

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Cevap: detrimental to

Cevap

Replacing the underlined phrase with 'detrimental to' establishes correct idiomatic preposition usage in standard written English.
In standard written English, the adjective 'detrimental' idiomatically pairs with the preposition 'to' (e.g., 'detrimental to health' or 'detrimental to performance'). Therefore, substituting 'detrimental to' produces a grammatically and idiomatically correct sentence.

Adım Adım Çözüm

1
Identify the head adjective and its accompanying preposition in the underlined segment.
The target word is the adjective 'detrimental' paired with the preposition 'for'.
Prepositional idiom rules depend on fixed conventions governing which preposition pairs with a specific adjective.
2
Evaluate standard English idiomatic conventions for the adjective 'detrimental'.
Standard English requires 'detrimental to' rather than 'detrimental for', 'detrimental with', or 'detrimental on'.
Certain adjectives mandate specific prepositional complements to convey directional or relational impact correctly.
3
Select the option that correctly substitutes 'detrimental to'.
The option offering 'detrimental to' resolves the idiomatic usage error.
This substitution satisfies standard conventions of written English required on the ACT.

Anahtar Kavram

Idiomatic Preposition Usage with Adjectives
Soru 5093Soru

Read the following passage adapted from an essay on the history of sound recording technology:

In 1857, French printer and bookseller Édouard-Léon Scott de Martinville patented the phonautograph, the earliest known device for recording sound. Unlike Thomas Edison, who twenty years later would invent a machine capable of both recording and playing back sound, Scott de Martinville intended his device solely to visually transcribe sound waves onto paper or glass for visual analysis. The phonautograph utilized a barrel-shaped horn to funnel sound waves toward a flexible membrane made of parchment. Attached to the membrane was a delicate stylus crafted from a pig's bristle. When sound vibrations caused the parchment membrane to oscillate, the bristle traced undulating lines onto a rotating cylinder coated with a thin layer of lampblack—a fine black soot produced by burning oil lamps.

Scott de Martinville envisioned that his recordings, termed "phonautograms," would allow scientists and musicians to read vocal performances and instrumental tones directly from paper, much like reading written text. On April 9, 1860, Scott recorded a ten-second fragment of the French folk song "Au clair de la lune," which remains the oldest known intelligible sound recording of the human voice. Because Scott never intended for the sound to be converted back into audible sound waves, his phonautograms remained silent visual artifacts for nearly a century and a half. It was not until 2008 that audio historians at First Sounds, a collaborative research project, used high-resolution digital scanning and optical imaging techniques to reconstruct the spatial tracings of the 1860 lampblack paper cylinder into an audible sound file, revealing Scott's own voice singing the ballad.

According to the passage, what specific material did Scott de Martinville use to craft the stylus attached to the parchment membrane?

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Cevap: A bristle taken from a pig

Cevap

Scott de Martinville crafted the stylus using a pig's bristle.
The correct answer directly accurately reflects the explicitly stated detail in the first paragraph: 'Attached to the membrane was a delicate stylus crafted from a pig's bristle.'

Adım Adım Çözüm

1
Locate the section of the passage discussing the components of the phonautograph.
The first paragraph describes the barrel-shaped horn, the parchment membrane, the stylus, and the cylinder.
Explicit detail questions require finding the exact sentence in the text addressing the component in question.
2
Identify the sentence describing the stylus.
The text states: 'Attached to the membrane was a delicate stylus crafted from a pig's bristle.'
This directly answers what material was used for the stylus.
3
Match the explicit statement from the text to the option expressing the exact same detail.
The option specifying 'A bristle taken from a pig' directly matches the passage.
Literal comprehension questions rely strictly on explicit facts directly stated in the text.

Anahtar Kavram

Identifying Explicit Details
Soru 5094Soru

A surveyor standing at point AA on level ground measures the angle of elevation to the top, point CC, of a vertical observation tower. The base of the tower is at point BB, forming right triangle ABCABC with the right angle at vertex BB. The horizontal distance along the ground from point AA to base BB is 4040 meters. If sin(A)=941\sin(\angle A) = \frac{9}{41}, what is the height, in meters, of the tower?

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Cevap: 99

Cevap

The height of the tower is 99 meters.
By definition of SOHCAHTOA, sin(A)=oppositehypotenuse=BCAC=941\sin(\angle A) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{BC}{AC} = \frac{9}{41}. Since cos(A)=adjacenthypotenuse=ABAC\cos(\angle A) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{AB}{AC}, and using the Pythagorean triple 99-4040-4141, we find cos(A)=4041\cos(\angle A) = \frac{40}{41}. Given that the adjacent side AB=40AB = 40 meters, the hypotenuse ACAC must be 4141 meters, which means the opposite side (tower height BCBC) is 99 meters.

Adım Adım Çözüm

1
Identify the given trigonometric ratio and sides of the right triangle.
In right triangle ABCABC with right angle at BB, the adjacent side to A\angle A is AB=40AB = 40, the opposite side is BCBC (height of the tower), and the hypotenuse is ACAC. We are given sin(A)=BCAC=941\sin(\angle A) = \frac{BC}{AC} = \frac{9}{41}.
SOHCAHTOA defines sine as the ratio of the opposite side to the hypotenuse.
2
Determine the relationship between the sides using the Pythagorean theorem or cosine ratio.
Since sin(A)=941\sin(\angle A) = \frac{9}{41}, we know cos(A)=ABAC=1(941)2=1681811681=16001681=4041\cos(\angle A) = \frac{AB}{AC} = \sqrt{1 - \left(\frac{9}{41}\right)^2} = \sqrt{\frac{1681 - 81}{1681}} = \sqrt{\frac{1600}{1681}} = \frac{40}{41}.
The Pythagorean identity sin2(θ)+cos2(θ)=1\sin^2(\theta) + \cos^2(\theta) = 1 relates sine and cosine for any acute angle in a right triangle.
3
Calculate the length of the hypotenuse and the height of the tower.
Setting cos(A)=40AC=4041\cos(\angle A) = \frac{40}{AC} = \frac{40}{41} gives AC=41AC = 41 meters. Then, BC=41×sin(A)=41×941=9BC = 41 \times \sin(\angle A) = 41 \times \frac{9}{41} = 9 meters.
Substituting the known adjacent length of 4040 meters into the ratio yields the exact vertical height.

Anahtar Kavram

Right Triangle Trigonometry (SOHCAHTOA) and Pythagorean Triples
Tahmini Süre:1m 0s
Soru 5095Soru

A microchip manufacturer produces 2.4×1082.4 \times 10^8 components per day across 4 identical production lines. Each line operates for 20 hours per day. On average, how many components are produced per hour on a single production line?

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Cevap: 3.0×1063.0 \times 10^6

Cevap

3.0×1063.0 \times 10^6 components per hour
To find the hourly output of a single line, first divide the total components (2.4×1082.4 \times 10^8) by the 4 lines to get 6.0×1076.0 \times 10^7 components per line per day. Then, divide by the 20 operating hours (2.0×1012.0 \times 10^1) to obtain 3.0×1063.0 \times 10^6 components per hour per line.

Adım Adım Çözüm

1
Calculate daily production per single line
2.4×1084=0.6×108=6.0×107\frac{2.4 \times 10^8}{4} = 0.6 \times 10^8 = 6.0 \times 10^7 components per line per day
The total daily output is split equally among 4 identical lines.
2
Calculate hourly production per single line
6.0×10720=6.0×1072.0×101=3.0×106\frac{6.0 \times 10^7}{20} = \frac{6.0 \times 10^7}{2.0 \times 10^1} = 3.0 \times 10^6 components per hour
Dividing daily output per line by the 20 operating hours per day gives the hourly rate per line.

Anahtar Kavram

Division of numbers expressed in scientific notation
Soru 5096Soru

On a vertical number line representing elevation relative to sea level (00 meters), Submersible XX is located at a coordinate of 45-45 meters. Submersible YY is located at a depth such that the distance between Submersible XX and Submersible YY is 3030 meters. If Submersible YY is closer to sea level than Submersible XX, what is the value of 2YX|2Y - X|?

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Cevap: 1515

Cevap

The value of 2YX|2Y - X| is 1515.
Submersible XX is at 45-45. Being 3030 meters away means Submersible YY is at either 15-15 or 75-75. Since Submersible YY is closer to sea level (00), its coordinate is 15-15. Substituting X=45X = -45 and Y=15Y = -15 into 2YX|2Y - X| gives 2(15)(45)=30+45=15=15|2(-15) - (-45)| = |-30 + 45| = |15| = 15.

Adım Adım Çözüm

1
Determine the possible coordinates for Submersible YY.
Since X=45X = -45 and the distance between XX and YY is 3030, Y=45+30=15Y = -45 + 30 = -15 or Y=4530=75Y = -45 - 30 = -75.
Distance on a number line from coordinate xx is given by x±dx \pm d.
2
Select the correct coordinate for YY based on the given constraint.
Y=15Y = -15, because 15=15<45=45|-15| = 15 < 45 = |-45|, meaning YY is closer to sea level (00).
The problem states that Submersible YY is closer to sea level than Submersible XX.
3
Substitute X=45X = -45 and Y=15Y = -15 into the expression 2YX|2Y - X| and evaluate.
2(15)(45)=30+45=15=15|2(-15) - (-45)| = |-30 + 45| = |15| = 15.
Multiplying 22 by 15-15 yields 30-30, and subtracting 45-45 is equivalent to adding 4545.

Anahtar Kavram

Distance on a Number Line and Absolute Value Evaluation
Tahmini Süre:1m 15s
Soru 5097Soru

Consider the following passage:

Urban heat islands significantly elevate surface temperatures in metropolitan regions during summer months. To counteract this thermal buildup, municipal architects in Chicago retrofitted city hall with an expansive rooftop garden, [these green layers effectively absorbed solar energy, they also retained] rainwater. Recent environmental monitoring confirms that energy consumption in the building decreased by fifteen percent over five years.

Which choice produces a grammatically correct sentence that properly joins the clauses?

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Cevap: which effectively absorbed solar energy while retaining

Cevap

The correct option is 'which effectively absorbed solar energy while retaining', as it transforms the run-on structure into a grammatically correct nonrestrictive relative clause that properly modifies the preceding noun phrase.
The correct choice seamlessly converts the second clause into a dependent relative clause starting with 'which', eliminating the comma splice and correctly describing the rooftop garden.

Adım Adım Çözüm

1
Identify the clause boundary and error in the original passage.
The original text joins two complete independent clauses ('municipal architects... retrofitted city hall...' and 'these green layers effectively absorbed...') with only a comma, creating a comma splice.
Two independent clauses cannot be joined by a comma alone without a coordinating conjunction (FANBOYS) or proper subordination.
2
Evaluate the choices for proper punctuation and clause structure.
The phrase starting with 'which effectively absorbed...' subordinately connects the descriptive details to 'expansive rooftop garden' without forming an ungrammatical run-on or fragment.
A relative pronoun ('which') appropriately introduces a nonrestrictive clause after a comma, eliminating the independent clause collision.

Anahtar Kavram

Run-on Sentences and Comma Splices
Tahmini Süre:1m 0s
Soru 5098Soru

A cafe offers a lunch special where a customer selects 11 sandwich from 44 available options, 11 side dish from 33 available options, and 11 drink from 55 available options. How many different total lunch combinations consisting of one sandwich, one side dish, and one drink can a customer choose?

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Cevap: 60

Cevap

60 combinations
According to the Fundamental Counting Principle, if one event can occur in mm ways, a second in nn ways, and a third in pp ways, the total number of combinations for all three events occurring together is m×n×pm \times n \times p. Multiplying 44 sandwiches by 33 sides by 55 drinks yields 4×3×5=604 \times 3 \times 5 = 60 distinct lunch combinations.

Adım Adım Çözüm

1
Identify the number of options available for each independent selection.
4 sandwiches, 3 side dishes, 5 drinks
The total outcomes depend on making one selection from each distinct category.
2
Apply the Fundamental Counting Principle.
4 × 3 × 5 = 60
The total number of outcomes for independent sequential choices is the product of the number of options for each choice.

Anahtar Kavram

Fundamental Counting Principle
Tahmini Süre:45s
Soru 5099Soru

Read the following passage adapted from an essay on maritime history and scientific innovation:

In 1714, the British Parliament passed the Longitude Act, establishing the Board of Longitude and offering a public prize of up to £20,000 to anyone who could solve the longstanding challenge of determining a ship's precise longitude at sea. Navigators could easily calculate latitude by observing the angle of the sun or the North Star, but calculating longitude required knowing the exact time at a reference point, such as Greenwich, simultaneously with local solar time. Standard pendulum clocks of the era were useless on the rolling ocean, as the ship's motion disrupted their mechanisms, and temperature fluctuations continually altered their timekeeping rate.

John Harrison, a self-taught Yorkshire carpenter and clockmaker, dedicated his life to solving this problem by designing mechanical clocks capable of functioning accurately on ocean vessels. After spending years building three large, spring-driven marine clocks—designated H1, H2, and H3—Harrison realized that a radical shift in approach was required. Rather than constructing another large clock, he designed a revolutionary, pocket-watch-sized marine timekeeper finished in 1759, which became known as H4. Encased in silver and measuring roughly five inches in diameter, H4 incorporated diamond and ruby bearings to reduce friction, along with a newly designed balance spring that compensated for thermal changes without requiring liquid lubricants.

To prove its efficacy to the Board of Longitude, H4 had to undergo an extensive ocean trial across the Atlantic Ocean. On November 18, 1761, William Harrison, John Harrison's son, embarked from Portsmouth, England, aboard the HMS Deptford bound for Kingston, Jamaica, carrying H4 in a cushioned wooden chest to safeguard it against humidity and vibration. John Harrison remained in London to continue refined adjustments on a backup mechanism. During the voyage, William carefully wound H4 daily and recorded its readings alongside astronomical calculations made by the ship's captain, Dudley Digges.

Upon arriving in Kingston on January 19, 1762, after eighty-one days at sea, H4 was evaluated by local astronomical observers. The watch had lost just 5.1 seconds during the transatlantic crossing when corrected for its known rate of error. This performance corresponded to an error in longitude of barely 1.25 nautical miles, easily surpassing the accuracy threshold of 30 nautical miles demanded by Parliament for the maximum prize. Despite this success, the Board of Longitude delayed awarding the full monetary prize, demanding additional verification trials that were later carried out in Barbados in 1764.

Based on the passage, evaluate the truth of the following statement:
John Harrison personally sailed aboard the HMS Deptford to Kingston, Jamaica, in 1761 to monitor the performance of the H4 timekeeper.

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Cevap: False

Cevap

The statement is False. The passage explicitly states that John Harrison's son, William Harrison, sailed aboard the HMS Deptford in 1761 while John Harrison remained in London.
The statement is false because the passage explicitly indicates that William Harrison, the son of inventor John Harrison, sailed aboard the HMS Deptford to transport and monitor H4, while John Harrison remained behind in London.

Adım Adım Çözüm

1
Identify the key subject and event in the statement to verify.
The statement claims that John Harrison personally sailed on the HMS Deptford to Jamaica in 1761.
Literal comprehension questions require matching stated details in the text against the claim.
2
Locate the explicit mention of the 1761 voyage aboard the HMS Deptford in the third paragraph of the passage.
The text states: 'On November 18, 1761, William Harrison, John Harrison's son, embarked from Portsmouth, England, aboard the HMS Deptford bound for Kingston, Jamaica... John Harrison remained in London...'
Direct textual evidence reveals who actually undertook the trip.
3
Compare the claim in the statement with the explicit detail in the text.
The statement attributes the voyage to John Harrison, whereas the text explicitly states William Harrison made the trip.
Because the text directly contradicts the statement regarding who sailed, the statement is false.

Anahtar Kavram

Identifying Explicit Details
Soru 5100Soru

Consider the underlined portion in the sentence below:

While examining ice core samples from the Antarctic sheet, paleoclimatologists measured dense, ancient ice layers, analyzed trapped dust particles, and recorded atmospheric temperature fluctuations over the last century.

Which choice best maintains standard written English conventions for the underlined portion?

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Cevap: NO CHANGE

Cevap

dense, ancient ice layers, analyzed trapped dust particles, and recorded
The original text correctly places a comma between the coordinate adjectives 'dense' and 'ancient' because both independently modify 'ice layers'. Additionally, it correctly separates the three parallel past-tense verbs ('measured', 'analyzed', 'recorded') with commas, maintaining proper list punctuation and parallel structure.

Adım Adım Çözüm

1
Analyze coordinate adjectives modifying 'ice layers'.
The adjectives 'dense' and 'ancient' can be joined by 'and' ('dense and ancient ice layers') and their order can be reversed ('ancient, dense ice layers'), confirming they are coordinate adjectives that require a separating comma.
Coordinate adjectives modifying the same noun must be separated by a comma, but no comma should separate the final adjective from the noun.
2
Evaluate the structure of the series of actions.
The subject 'paleoclimatologists' performs three parallel actions: 'measured...', 'analyzed...', and 'recorded...'.
Items in a series of three or more actions must be separated by commas and maintain parallel grammatical form.
3
Select the choice that correctly implements comma rules for coordinate adjectives and serial lists.
The option stating 'NO CHANGE' correctly uses 'dense, ancient ice layers, analyzed trapped dust particles, and recorded'.
This option correctly places a comma between coordinate adjectives, avoids placing a comma between the adjective and noun, and maintains a parallel series of past-tense verbs separated by commas.

Anahtar Kavram

Commas with Coordinate Adjectives and Lists
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