Tüm alıştırma soruları

Four numerical values are given below. Arrange these values in order from least to greatest.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct order from least to greatest is

55\%

,

0.565

,

\frac{4}{7}

, and

\frac{3}{5}

.

Converting each quantity into a decimal format yields

55\% = 0.55

,

0.565 = 0.565

,

\frac{4}{7} \approx 0.5714

, and

\frac{3}{5} = 0.60

. Ordering these decimal values from least to greatest yields

0.55 < 0.565 < 0.5714 < 0.60

, which corresponds to the sequence

55\%, 0.565, \frac{4}{7}, \frac{3}{5}

.

Adım Adım Çözüm

1

Convert the percentage to a decimal.

55\% = \frac{55}{100} = 0.55

Converting all values to decimals provides a uniform scale for direct comparison.

2

Convert the fractions to decimals.

\frac{4}{7} \approx 0.5714

and

\frac{3}{5} = 0.60

Dividing the numerator by the denominator converts each fraction into decimal form.

3

Compare all four decimal values:

0.55

,

0.565

,

0.5714

, and

0.60

.

0.55 < 0.565 < 0.5714 < 0.60

Aligning decimal places shows that

0.5500 < 0.5650 < 0.5714 < 0.6000

.

4

Map the ordered decimal values back to their original forms.

55\% < 0.565 < \frac{4}{7} < \frac{3}{5}

Replacing each decimal with its original representation produces the required sequence.

Anahtar Kavram

Converting fractions, decimals, and percents to a common representation (decimals) to compare and order them.

Soru 5302Soru →

A group of mechanical engineers conducted an experiment to evaluate how the frequency of ambient mechanical vibration affects the peak electrical voltage output of a piezoelectric cantilever beam. In each trial, a cantilever beam of identical length ( $10\text{ cm}$ ), thickness ( $1\text{ mm}$ ), and material composition (lead zirconate titanate) was mounted on a shaker table maintained at a constant displacement amplitude of $0.5\text{ mm}$ and a room temperature of $22^\circ\text{C}$ . The vibration frequency was varied across $\text{50 Hz}$ , $\text{100 Hz}$ , $\text{150 Hz}$ , and $\text{200 Hz}$ , and the peak output voltage generated across a $100\text{ }\Omega$ load resistor was recorded.

Match each experimental component listed on the left with its corresponding variable classification on the right.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The vibration frequency is the independent variable, the peak voltage output is the dependent variable, and the shaker table displacement amplitude is a controlled variable.

The vibration frequency is manipulated by the experimenter, making it the independent variable. The peak electrical voltage output is the measured response to these changes, making it the dependent variable. The shaker table displacement amplitude is kept constant at 0.5 mm to prevent confounded results, making it a controlled variable.

Adım Adım Çözüm

1

Identify the condition or factor systematically manipulated by the researchers.

The vibration frequency of the shaker table was changed across trials (50 Hz, 100 Hz, 150 Hz, 200 Hz), identifying it as the independent variable.

The independent variable is the factor intentionally varied by the experimenter to test its effect.

2

Identify the factor measured to determine the outcome of the manipulation.

The peak electrical voltage output generated across the resistor was measured, identifying it as the dependent variable.

The dependent variable is the response being measured that changes depending on the independent variable.

3

Identify the parameters held constant throughout all experimental trials.

The shaker table displacement amplitude (0.5 mm), beam dimensions, material, and temperature were kept constant, identifying them as controlled variables.

Controlled variables are kept constant to ensure that any observed changes in the dependent variable are solely attributable to the independent variable.

Anahtar Kavram

Distinguishing between independent, dependent, and controlled variables in an experimental setup.

Soru 5303Soru →

A local bakery recorded the number of custom cakes sold per week over a 6-week period: $12$ , $15$ , $8$ , $15$ , $14$ , and $10$ . If the bakery sells $x$ cakes in the 7th week such that the mean number of cakes sold per week for the entire 7-week period is $13$ , what is the median number of cakes sold over the 7-week period?

12

13

14

15

17

Cevabı ve açıklamayı göster

Cevap: $14$

Cevap

The median number of cakes sold over the 7-week period is

14

.

The total sales required for a 7-week average of

13

cakes is

7 \times 13 = 91

. Subtracting the sum of the first 6 weeks (

74

) gives

17

cakes for the 7th week. Arranging the 7 weekly values in order (

8, 10, 12, 14, 15, 15, 17

) shows that the 4th value, which is the median, is

14

.

Adım Adım Çözüm

1

Calculate the sum of the sales for the first 6 weeks.

12 + 15 + 8 + 15 + 14 + 10 = 74

To find the missing 7th week sales, we first need the total sales of the known weeks.

2

Determine the required total sales for a 7-week mean of 13.

7 \times 13 = 91

Mean is total sum divided by the number of data points, so Total = Mean

\times

Count.

3

Find the sales in the 7th week (

x

).

x = 91 - 74 = 17

Subtracting the 6-week sum from the 7-week total yields the 7th week value.

4

Order all 7 data points from least to greatest and identify the middle value.

Ordered list:

8, 10, 12, 14, 15, 15, 17

. The 4th item (median) is

14

.

The median of an odd number of data values is the middle value when arranged in ascending order.

Anahtar Kavram

Descriptive Statistics: Combining mean calculations to solve for missing data and finding the median of an ordered dataset.

Tahmini Süre:1m 0s

Soru 5304Soru →

Experiment 1
Students investigated the rate of carbon dioxide ( $CO_2$ ) evolution during the reaction between calcium carbonate ( $CaCO_3$ ) and hydrochloric acid ( $HCl$ ). The apparatus setup consisted of several components designed to ensure accurate measurement of dry gas at a stable temperature.

Based on the described experimental setup, match each apparatus component on the left with its specific procedural function on the right.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Anhydrous

CaCl_2

drying tube matches with removing moisture from the gas stream; Water bath matches with maintaining constant reaction temperature; Inverted graduated cylinder matches with measuring gas volume by water displacement; Rubber stopper with delivery tube matches with establishing a sealed system to direct gas flow.

Each apparatus component is matched according to its physical function within gas-generating experimental setups: calcium chloride acts as a desiccant to remove moisture, the water bath maintains thermal equilibrium, the inverted cylinder measures gas displacement volume, and the stopper ensures a closed system to channel gas without leakage.

Adım Adım Çözüm

1

Analyze the chemical physical function of anhydrous calcium chloride (

CaCl_2

).

Calcium chloride is a hygroscopic salt that absorbs water vapor, serving as a desiccant to dry the gas.

Accurate gas measurement requires isolating

CO_2

from water vapor.

2

Identify the purpose of the surrounding water bath.

Water has a high specific heat capacity, maintaining a stable temperature around the reaction flask.

Temperature controls reaction rate, so keeping temperature constant isolates the effect of reactant concentration.

3

Determine the function of the inverted graduated cylinder filled with water.

As gas enters the inverted cylinder, it displaces water downward, providing readable volumetric measurements.

Water displacement is a standard method for measuring volume of insoluble or slightly soluble gases.

4

Determine the function of the stopper and delivery tube assembly.

It creates an airtight seal preventing gas escape and creates a direct path for the gas to reach the measuring vessel.

A closed system is required for total gas collection.

Anahtar Kavram

Analyzing apparatus component functions in gas collection and reaction rate experiments

Soru 5305Soru →

In the standard $(x, y)$ coordinate plane, a circle is tangent to the horizontal line $y = 7$ . The equation of the circle is $x^2 + y^2 - 10x + 4y + c = 0$ , where $c$ is a constant. What is the value of $c$ ?

Cevabı ve açıklamayı göster

Cevap: -52

Cevap

The value of

c

is

-52

.

Completing the square gives

(x - 5)^2 + (y + 2)^2 = 29 - c

. The center is

(5, -2)

. The distance from

(5, -2)

to the horizontal line

y = 7

is

|7 - (-2)| = 9

, which is the radius

r

. Squaring the radius gives

r^2 = 81

. Setting

29 - c = 81

gives

c = -52

.

Adım Adım Çözüm

1

Complete the square for

x

and

y

terms.

(x - 5)^2 + (y + 2)^2 = 29 - c

Writing the equation in standard form

(x - h)^2 + (y - k)^2 = r^2

reveals the center

(h, k)

and the expression for

r^2

.

2

Calculate the radius using the distance from the center to the tangent line.

Radius

r = 9

The center is

(5, -2)

and the tangent line is

y = 7

. The distance between

y = -2

and

y = 7

is

|7 - (-2)| = 9

.

3

Set

r^2 = 81

and solve for

c

.

c = -52

Equating the radius squared expression

29 - c

to

81

yields

29 - c = 81 \implies c = -52

.

Anahtar Kavram

Converting circle equations to standard form and using distance to tangent lines to determine radius.

Soru 5306Soru →

A circle in the standard $(x, y)$ coordinate plane is represented by the equation $x^2 + y^2 + 10x - 6y + 9 = 0$ . If this circle is translated $4$ units to the right and $2$ units down, which of the following is the equation of the translated circle?

(x + 1)^2 + (y - 1)^2 = 25

(x - 1)^2 + (y + 1)^2 = 25

(x + 1)^2 + (y - 1)^2 = 5

(x + 9)^2 + (y - 5)^2 = 25

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

Cevabı ve açıklamayı göster

Cevap: $(x + 1)^2 + (y - 1)^2 = 25$

Cevap

(x + 1)^2 + (y - 1)^2 = 25

Completing the square on

x^2 + y^2 + 10x - 6y + 9 = 0

yields

(x + 5)^2 + (y - 3)^2 = 25

, identifying the original center as

(-5, 3)

and

r^2 = 25

. Shifting the center

4

units right and

2

units down moves

(-5, 3)

to

(-5 + 4, 3 - 2) = (-1, 1)

. Substituting the updated center

(-1, 1)

and

r^2 = 25

into the standard equation of a circle

(x - h)^2 + (y - k)^2 = r^2

gives

(x + 1)^2 + (y - 1)^2 = 25

.

Adım Adım Çözüm

1

Group terms and complete the square for both

x

and

y

variables in the original equation.

(x + 5)^2 + (y - 3)^2 = 25

Rearrange

x^2 + y^2 + 10x - 6y + 9 = 0

as

(x^2 + 10x) + (y^2 - 6y) = -9

. Add

(10/2)^2 = 25

and

(-6/2)^2 = 9

to both sides:

(x + 5)^2 + (y - 3)^2 = -9 + 25 + 9 = 25

.

2

Determine the center and radius of the original circle.

Original center is

(-5, 3)

and

r^2 = 25

(radius

r = 5

).

Comparing

(x + 5)^2 + (y - 3)^2 = 25

to

(x - h)^2 + (y - k)^2 = r^2

gives

h = -5

,

k = 3

, and

r^2 = 25

.

3

Calculate the coordinates of the new center after the horizontal and vertical translation.

New center is

(-1, 1)

.

Translating

4

units to the right adds

4

to the

x

-coordinate:

-5 + 4 = -1

. Translating

2

units down subtracts

2

from the

y

-coordinate:

3 - 2 = 1

.

4

Substitute the new center

(-1, 1)

and unchanged radius squared value

r^2 = 25

into standard form.

(x + 1)^2 + (y - 1)^2 = 25

Using

(x - h)^2 + (y - k)^2 = r^2

with

h = -1

and

k = 1

gives

(x - (-1))^2 + (y - 1)^2 = 25

, which simplifies to

(x + 1)^2 + (y - 1)^2 = 25

.

Anahtar Kavram

Converting circle equations to standard form by completing the square and performing translations in the coordinate plane.

Soru 5307Soru →

A beverage company formulates a fruit punch by blending apple juice, cranberry juice, and sparkling water in the ratio $5 : 3 : 2$ by volume. In a specific batch, there are $12$ liters of sparkling water. A technician then adds $10$ liters of cranberry juice and an additional amount of apple juice so that the new ratio of apple juice to cranberry juice becomes $3 : 2$ . How many liters of apple juice were added to the batch?

12

15

27

42

22

Cevabı ve açıklamayı göster

Cevap: $12$

Cevap

The technician added 12 liters of apple juice.

In the initial ratio of

5 : 3 : 2

,

2

parts represent

12

liters of sparkling water, meaning each part is

6

liters. Thus, the original mixture contains

30

liters of apple juice and

18

liters of cranberry juice. Adding

10

liters of cranberry juice brings its total to

28

liters. For the new apple juice to cranberry juice ratio to be

3 : 2

, the required total apple juice is

\frac{3}{2} \times 28 = 42

liters. Subtracting the initial

30

liters yields

12

liters of added apple juice.

Adım Adım Çözüm

1

Determine the unit value per part in the original ratio.

Since

2

parts correspond to

12

liters of sparkling water,

1

part =

\frac{12}{2} = 6

liters.

The original ratio

5 : 3 : 2

defines the relative proportions of apple juice, cranberry juice, and sparkling water.

2

Calculate the original volumes of apple juice and cranberry juice.

Apple juice =

5 \times 6 = 30

liters; Cranberry juice =

3 \times 6 = 18

liters.

Multiply each component's ratio value by the single-part volume of

6

liters.

3

Calculate the new volume of cranberry juice after adding 10 liters.

New cranberry juice volume =

18 + 10 = 28

liters.

10

liters of cranberry juice were added to the initial

18

liters.

4

Set up a proportion for the new ratio of apple juice to cranberry juice and solve for the added amount

x

.

\frac{30 + x}{28} = \frac{3}{2} \implies 2(30 + x) = 3(28) \implies 60 + 2x = 84 \implies 2x = 24 \implies x = 12.

The new ratio of total apple juice (

30 + x

) to total cranberry juice (

28

) must equal

3 : 2

.

Anahtar Kavram

Multi-step proportional reasoning and scaling ratios when quantities change.

Tahmini Süre:1m 15s

Soru 5308Soru →

A high school cafeteria offers a lunch meal combination consisting of 1 main dish, 1 side dish, and 1 drink. There are 4 main dish options, 5 side dish options, and 3 drink options available. However, due to dietary restrictions, 1 specific main dish option cannot be paired with 2 specific side dish options. How many different valid lunch meal combinations of 1 main dish, 1 side dish, and 1 drink can a student choose?

Cevabı ve açıklamayı göster

Cevap: 54

Cevap

The total number of valid lunch meal combinations is 54.

The total number of unrestricted meal options is

4 \times 5 \times 3 = 60

. The restricted main dish cannot be paired with 2 specific side dishes across any of the 3 drink options, creating

1 \times 2 \times 3 = 6

invalid combinations. Subtracting these from the total gives

60 - 6 = 54

valid combinations.

Adım Adım Çözüm

1

Calculate the total number of unrestricted meal choices

4 \times 5 \times 3 = 60

total combinations

By the Fundamental Counting Principle, multiplying the available choices for each dish component yields the total possible combinations without restrictions.

2

Determine the number of invalid combinations caused by dietary restrictions

1 \times 2 \times 3 = 6

invalid combinations

The 1 restricted main dish cannot be paired with 2 specific side dishes, and each of those 2 pairs can still be matched with any of the 3 drinks.

3

Subtract invalid combinations from the unrestricted total

60 - 6 = 54

valid combinations

Subtracting the disallowed combinations leaves only the combinations that satisfy all dietary restrictions.

Anahtar Kavram

Fundamental Counting Principle with Restrictions

Soru 5309Soru →

Experiment 1
Students measured the heat of combustion of three liquid fuel samples using a bomb calorimeter apparatus. A small sample of fuel was placed in a sealed steel reaction vessel (the bomb) filled with pure oxygen. The bomb was submerged in an insulated container filled with $2,000\text{ mL}$ of distilled water. An electric ignition wire ignited the fuel. A motorized stirrer continuously agitated the surrounding water bath, while a digital thermal sensor recorded the temperature of the water every 5 seconds until a maximum temperature was observed.

What was the primary purpose of continuously operating the motorized stirrer during this experimental procedure?

To ensure uniform thermal distribution throughout the water bath so that the sensor reading accurately reflects total heat transferred from the reaction

To accelerate the rate of the combustion reaction occurring inside the sealed steel bomb

To act as a negative control to prevent thermal energy from escaping through the insulated outer container

To directly measure the independent variable by altering the chemical composition of the water

Cevabı ve açıklamayı göster

Cevap: To ensure uniform thermal distribution throughout the water bath so that the sensor reading accurately reflects total heat transferred from the reaction

Cevap

To ensure uniform thermal distribution throughout the water bath so that the sensor reading accurately reflects total heat transferred from the reaction.

The correct option correctly identifies that stirring the water bath mixes heated water near the steel bomb with cooler surrounding water. This ensures thermal equilibrium across the entire

2,000\text{ mL}

volume of water, allowing the thermal sensor to accurately capture the true overall temperature change required for calorimetry calculations.

Adım Adım Çözüm

1

Analyze the spatial layout of the bomb calorimeter apparatus described in the procedure.

The combustion reaction occurs inside a sealed steel vessel (bomb), which is surrounded by a separate bath of distilled water.

Understanding where each component is located establishes what physical interactions can occur.

2

Evaluate the function of the motorized stirrer within the surrounding water bath.

As heat transfers from the outer wall of the steel bomb into the adjacent water, water near the bomb heats up faster than water near the outer edges of the container.

Static fluids conduct heat relatively slowly, creating thermal gradients (hot spots).

3

Determine why temperature uniformity is critical for calculating heat of combustion.

Continuous stirring circulates the water, eliminating temperature gradients so the single thermal sensor measures a representative temperature of the entire water mass.

Calculations of released heat energy (

q = mc\Delta T

) assume the entire mass (

m

) undergoes the measured temperature change (

\Delta T

).

Anahtar Kavram

Function of Equipment and Procedural Mechanics in Calorimetry

Tahmini Süre:1m 0s

Soru 5310Soru →

A contractor prepares a concrete mixture by combining cement, sand, and gravel in a ratio of $2 : 3 : 5$ by weight. The contractor currently has a batch of this mixture weighing $150\text{ pounds}$ . If the contractor adds $10\text{ pounds}$ of pure cement to this batch, what fraction of the total weight of the modified mixture is cement?

\frac{1}{5}

\frac{3}{40}

\frac{1}{4}

\frac{4}{15}

\frac{1}{3}

Cevabı ve açıklamayı göster

Cevap: $\frac{1}{4}$

Cevap

The fraction of the total weight of the modified mixture that is cement is

\frac{1}{4}

.

In the original ratio of

2 : 3 : 5

, there are

10

total parts. Cement accounts for

\frac{2}{10} = \frac{1}{5}

of the initial

150\text{-pound}

mixture, which is

30\text{ pounds}

. When

10\text{ pounds}

of cement is added, the new cement weight becomes

40\text{ pounds}

and the total mixture weight increases to

160\text{ pounds}

. The fraction of cement in the modified mixture is

\frac{40}{160} = \frac{1}{4}

.

Adım Adım Çözüm

1

Calculate the total ratio parts and the initial amount of cement in the mixture.

Total ratio parts =

2 + 3 + 5 = 10

. Initial cement weight =

\frac{2}{10} \times 150 = 30\text{ pounds}

.

Determining the weight of cement in the original

150\text{-pound}

batch is necessary before adding extra cement.

2

Determine the new weight of cement and the new total weight after adding

10\text{ pounds}

of cement.

New cement weight =

30 + 10 = 40\text{ pounds}

. New total weight =

150 + 10 = 160\text{ pounds}

.

Adding pure cement increases both the weight of the cement component and the total weight of the batch.

3

Form the part-to-whole ratio for the new mixture and simplify the fraction.

\frac{40}{160} = \frac{1}{4}

.

The fraction of cement relative to the whole mixture is found by dividing the new cement weight by the new total weight.

Anahtar Kavram

Part-to-whole ratios and adjusting totals when components are added

Soru 5311Soru →

A music ensemble director must randomly select 3 students from a group consisting of 5 vocalists and 4 instrumentalists to perform at a ceremony. What is the probability that the chosen group contains at least 1 vocalist and at least 1 instrumentalist?

\frac{1}{6}

\frac{10}{21}

\frac{5}{21}

\frac{20}{81}

\frac{5}{6}

Cevabı ve açıklamayı göster

Cevap: $\frac{5}{6}$

Cevap

\frac{5}{6}

To find the probability that the selected trio includes at least 1 vocalist and at least 1 instrumentalist, calculate the total possible combinations of picking 3 students from 9:

\binom{9}{3} = 84

. Next, identify the unfavorable combinations where all 3 students are of the same type:

\binom{5}{3} = 10

ways for all vocalists and

\binom{4}{3} = 4

ways for all instrumentalists, totaling

10 + 4 = 14

unfavorable outcomes. Subtracting these from 84 leaves 70 favorable combinations. Thus, the probability is

\frac{70}{84} = \frac{5}{6}

.

Adım Adım Çözüm

1

Calculate the total number of ways to choose any 3 students from the total group of 9 students.

\binom{9}{3} = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} = 84

total outcomes.

Establishes the size of the sample space for selecting 3 students without replacement out of 9 (5 vocalists + 4 instrumentalists).

2

Determine the number of unfavorable outcomes (groups consisting entirely of one type of student).

Ways to choose 3 vocalists:

\binom{5}{3} = 10

.
Ways to choose 3 instrumentalists:

\binom{4}{3} = 4

.
Total unfavorable outcomes =

10 + 4 = 14

.

The complement of having 'at least 1 vocalist and at least 1 instrumentalist' is selecting a group of 3 composed entirely of vocalists or entirely of instrumentalists.

3

Subtract the unfavorable outcomes from the total outcomes to get the favorable outcomes.

84 - 14 = 70

favorable combinations.

Finding the complementary set count is direct and prevents missing valid composition cases.

4

Calculate the probability by dividing favorable outcomes by total outcomes.

Probability =

\frac{70}{84} = \frac{5}{6}

.

Dividing favorable combinations by the total size of the sample space gives the required probability.

Anahtar Kavram

Complementary Probability and Combinations

Tahmini Süre:1m 30s

Soru 5312Soru →

A music festival stage technician mounts a series of $n$ identical LED light panels side-by-side along the main stage frame. The main stage frame has a total length of $168$ feet, and each LED light panel spans a length of $3.5$ feet. Which of the following equations can be solved to find $n$ , the total number of LED light panels mounted along the frame?

n + 3.5 = 168

\frac{n}{3.5} = 168

3.5n = 168

n - 3.5 = 168

168n = 3.5

Cevabı ve açıklamayı göster

Cevap: $3.5n = 168$

Cevap

The equation

3.5n = 168

can be solved to find the total number of LED light panels.

The total length of the stage frame is equal to the length of a single panel multiplied by the total number of panels. Since each panel is

3.5

feet long and there are

n

panels, the expression for total length is

3.5n

. Setting this product equal to the total length of

168

feet gives

3.5n = 168

.

Adım Adım Çözüm

1

Identify the relationship between total length, individual length, and quantity.

Total Length = (Length of 1 Panel)

\times

(Number of Panels)

Since all panels are identical and placed end-to-end, their combined length is equal to the total frame length.

2

Substitute given values and variables into the rate relationship.

168 = 3.5 \times n

or

3.5n = 168

Given that length per panel is

3.5

feet, number of panels is

n

, and total frame length is

168

feet.

Anahtar Kavram

Translating real-world multiplicative rate scenarios into one-step linear equations.

Tahmini Süre:1m 0s

Soru 5313Soru →

Read the passage below:

When conservator Henri Laurent completed the gear cleaning of the Rouen celestial globe in 1993, he immediately set to work recalibrating its intricate lunar phase mechanism—a crucial task he had been forced to postpone ever since revealing the inner gear trains two years prior. Long before he ever touched a screwdriver to the device, however, Laurent had spent five years systematically photographing each of the globe's constellation engravings, a documentation process he concluded just before embarking on the main gear disassembly in 1991. The entire project had been delayed until 1988, when the museum board finally granted official approval for a full restoration. Yet even before that approval was secured, Laurent had already published his landmark monograph identifying the clockmaker's mark, having initially pulled the corroded artifact from the museum's damp basement back in 1984.

According to the passage, which of the following events occurred FIRST chronologically?

Laurent pulling the corroded celestial globe from the museum basement

Laurent publishing his monograph identifying the clockmaker's mark

Laurent receiving official approval from the museum board for full restoration

Laurent concluding the five-year photographic documentation of the engravings

Cevabı ve açıklamayı göster

Cevap: Laurent pulling the corroded celestial globe from the museum basement

Cevap

Laurent pulling the corroded celestial globe from the museum basement

The text explicitly states that Laurent pulled the corroded artifact from the museum basement in 1984. Because all other events occurred after this date—publishing the monograph occurred between 1984 and 1988, board approval occurred in 1988, and documentation concluded in 1991—retrieving the globe from the basement is the earliest event chronologically.

Adım Adım Çözüm

1

Identify temporal markers for each mentioned event in the passage.

Discovered/pulled from basement: 1984; Monograph published: between 1984 and 1988; Board approval: 1988; Concluded photographic documentation: 1991; Inner gear trains revealed: 1991; Gear cleaning completed: 1993.

Tracking explicitly stated dates and relative time indicators establishes the true chronological sequence despite the non-linear structure of the narrative.

2

Compare the dates to determine which event happened first.

1984 (pulled from basement) is the earliest date in the passage.

The initial retrieval of the artifact in 1984 pre-dates all subsequent research, board approvals, and physical restoration steps.

Anahtar Kavram

Determining Stated Sequence of Events

Tahmini Süre:1m 0s

Soru 5314Soru →

A team of marine biologists studied the acoustic activity of the snapping shrimp (*Alpheus heterochaelis*) under controlled laboratory conditions. They measured the average snap rate (in snaps per minute) across three water temperatures and two salinity levels ( $30\text{ PSU}$ and $36\text{ PSU}$ ).

Table 1

Water Temperature ( $^\circ\text{C}$ )	Snap Rate at $30\text{ PSU}$ (snaps/min)	Snap Rate at $36\text{ PSU}$ (snaps/min)
$18$	$45$	$50$
$22$	$65$	$85$
$26$	$109$	$130$

Based on Table 1, what was the average rate of increase in snap rate (in snaps/min per $1^\circ\text{C}$ ) for shrimp kept at a salinity of $36\text{ PSU}$ as the water temperature increased from $18^\circ\text{C}$ to $26^\circ\text{C}$ ?

8.0\text{ snaps/min per }^\circ\text{C}

10.0\text{ snaps/min per }^\circ\text{C}

40.0\text{ snaps/min per }^\circ\text{C}

80.0\text{ snaps/min per }^\circ\text{C}

Cevabı ve açıklamayı göster

Cevap: $10.0\text{ snaps/min per }^\circ\text{C}$

Cevap

The average rate of increase in snap rate for shrimp at

36\text{ PSU}

from

18^\circ\text{C}

to

26^\circ\text{C}

is

10.0\text{ snaps/min per }^\circ\text{C}

.

To find the average rate of increase per

1^\circ\text{C}

, determine the difference in snap rate at

36\text{ PSU}

between

18^\circ\text{C}

and

26^\circ\text{C}

, which is

130 - 50 = 80\text{ snaps/min}

. Then divide by the temperature span of

26 - 18 = 8^\circ\text{C}

, yielding

80 / 8 = 10.0\text{ snaps/min per }^\circ\text{C}

.

Adım Adım Çözüm

1

Locate the snap rates for

36\text{ PSU}

at

18^\circ\text{C}

and

26^\circ\text{C}

in Table 1.

At

18^\circ\text{C}

, snap rate =

50\text{ snaps/min}

; at

26^\circ\text{C}

, snap rate =

130\text{ snaps/min}

.

The question asks specifically about the

36\text{ PSU}

salinity condition.

2

Calculate the total change in snap rate and total change in temperature.

Change in snap rate =

130 - 50 = 80\text{ snaps/min}

; Change in temperature =

26 - 18 = 8^\circ\text{C}

.

Rate of change requires dividing the change in the dependent variable by the change in the independent variable.

3

Divide the change in snap rate by the change in temperature.

80\text{ snaps/min} / 8^\circ\text{C} = 10.0\text{ snaps/min per }^\circ\text{C}

.

This yields the average change per

1^\circ\text{C}

increase.

Anahtar Kavram

Calculating rate of change from tabular data

Tahmini Süre:1m 15s

Soru 5315Soru →

At a local bookstore, $40\%$ of the total inventory consists of fiction books. Of the remaining inventory, $\frac{5}{8}$ consists of non-fiction books, and the rest are children's books. If there are $270$ children's books in the bookstore, what is the total number of books in the inventory?

450

675

720

1,200

1,800

Cevabı ve açıklamayı göster

Cevap: $1,200$

Cevap

1,200

Fiction books account for

40\%

of the total inventory, leaving

60\%

as the remaining portion. Since

\frac{5}{8}

of this remainder is non-fiction, the children's books represent the other

\frac{3}{8}

of that

60\%

remainder. Multiplying

\frac{3}{8} \times 0.60 = 0.225

, or

22.5\%

of the total inventory. Given that there are

270

children's books, dividing

270

by

0.225

yields the total inventory of

1,200

books.

Adım Adım Çözüm

1

Determine the fraction of inventory remaining after accounting for fiction books.

Remaining fraction =

100\% - 40\% = 60\% = 0.6 = \frac{3}{5}

Fiction accounts for

40\%

, leaving

60\%

of the total inventory for other genres.

2

Find the fraction of the remaining inventory that consists of children's books.

Children's fraction of remaining =

1 - \frac{5}{8} = \frac{3}{8}

Since

\frac{5}{8}

of the remaining inventory is non-fiction, the rest (

\frac{3}{8}

) must be children's books.

3

Calculate the proportion of the total inventory that children's books represent.

Children's proportion of total =

\frac{3}{8} \times \frac{3}{5} = \frac{9}{40} = 0.225 = 22.5\%

Multiply the fraction of the remainder by the fraction of the total remaining.

4

Set up an equation with total inventory

T

and solve for

T

.

0.225 \times T = 270 \implies T = \frac{270}{0.225} = 1,200

Divide the known count of children's books (

270

) by its fractional share of the total inventory.

Anahtar Kavram

Solving multi-step word problems involving fractions, decimals, and percentages of a whole

Tahmini Süre:1m 15s

Soru 5316Soru →

A team of atmospheric scientists investigated how varying the relative humidity inside a sealed reaction chamber affects the rate of ozone ( $\text{O}_3$ ) depletion by aerosolized sea salt particles. In five separate trials, the relative humidity was set to 20%, 35%, 50%, 65%, and 80%, while the initial ozone concentration, temperature, and mass of sea salt particles were held constant. Based on the description of the experiment, which parameter was the dependent variable?

The rate of ozone depletion

The relative humidity inside the chamber

The mass of aerosolized sea salt particles

The initial concentration of ozone

Cevabı ve açıklamayı göster

Cevap: The rate of ozone depletion

Cevap

The rate of ozone depletion was the dependent variable in the experiment.

The rate of ozone depletion is the measured response in the experiment that changes based on the relative humidity, satisfying the definition of a dependent variable.

Adım Adım Çözüm

1

Identify the factor intentionally altered by the experimenters across trials.

Relative humidity was set to different values (20%, 35%, 50%, 65%, and 80%), identifying it as the independent variable.

The independent variable is the condition that is systematically varied by the researcher.

2

Identify the outcome or quantity measured to evaluate the effect of the manipulated factor.

The rate of ozone depletion is observed and measured as a response to changes in humidity.

The dependent variable is the measurable response that changes as a function of the independent variable.

3

Match the measured outcome to the options provided.

The rate of ozone depletion represents the dependent variable.

It directly measures the result of changing the independent variable under controlled conditions.

Anahtar Kavram

Identifying Independent, Dependent, and Controlled Variables

Soru 5317Soru →

A digital audio engineer uses a software tool where the total duration $t$ , in seconds, of an electronic music composition is modeled by the equation $t = \frac{b}{2.4}$ , where $b$ represents the total number of beats in the track. If a composition has a total duration of $180$ seconds, what is the total number of beats, $b$ , in the track?

75

177.6

252

432

450

Cevabı ve açıklamayı göster

Cevap: $432$

Cevap

The total number of beats in the track is

432

.

To solve for

b

in the one-step equation

180 = \frac{b}{2.4}

, multiply both sides of the equation by

2.4

. Performing

180 \times 2.4

yields

432

, which is the total number of beats in the track.

Adım Adım Çözüm

1

Substitute the given duration into the formula

180 = \frac{b}{2.4}

The track duration

t

is given as

180

seconds.

2

Isolate the variable

b

by multiplying both sides by

2.4

b = 180 \times 2.4 = 432

Multiplication is the inverse operation of division.

Anahtar Kavram

Solving one-step linear equations involving division by isolating the variable using multiplication.

Tahmini Süre:1m 0s

Soru 5318Soru →

A coffee shop blend initially consists of a $20$ -pound mixture of Arabica and Robusta beans, of which $45\%$ by weight is Arabica. The shop manager adds pure Arabica beans to the mixture to increase the proportion of Arabica beans to $56\%$ by weight. How many pounds of pure Arabica beans must be added to the mixture?

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

5 pounds of pure Arabica beans must be added to the mixture.

To solve for the required added weight, first compute the original mass of Arabica beans:

45\%

of

20

pounds is

0.45 \times 20 = 9

pounds. Letting

x

represent the pounds of pure Arabica added, the updated mass of Arabica is

9 + x

pounds and the updated total mass of the coffee batch is

20 + x

pounds. Setting the ratio

\frac{9 + x}{20 + x} = 0.56

gives

9 + x = 0.56(20 + x)

. Expanding the right side results in

9 + x = 11.2 + 0.56x

. Subtracting

0.56x

and

9

from both sides gives

0.44x = 2.2

, which simplifies to

x = 5

pounds.

Adım Adım Çözüm

1

Determine the initial weight of Arabica beans.

Arabica weight =

0.45 \times 20 = 9

pounds.

The starting

20

-pound batch contains

45\%

Arabica beans.

2

Formulate the mixture fraction with the unknown added weight

x

.

\frac{9 + x}{20 + x} = 0.56

Adding

x

pounds of pure Arabica increases both the total Arabica weight (numerator) and the total mixture weight (denominator).

3

Solve the algebraic equation for

x

.

9 + x = 11.2 + 0.56x \implies 0.44x = 2.2 \implies x = 5

Isolating

x

yields the exact amount of pure Arabica required.

Anahtar Kavram

Solving percentage mixture problems using algebraic proportions

Tahmini Süre:1m 30s

Soru 5319Soru →

A team of materials engineers conducted an experiment to evaluate how different zirconium dioxide ( $\text{ZrO}_2$ ) additive concentrations in ceramic heat-shield tiles affect peak thermal conductivity under simulated re-entry conditions. In each trial, ceramic tiles of identical dimensions were exposed to a $1200^\circ\text{C}$ plasma jet at a constant chamber atmospheric pressure of $1.0\text{ atm}$ for exactly 300 seconds. Match each experimental component to its correct variable classification.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

\text{ZrO}_2

additive concentration corresponds to the Independent Variable; Peak thermal conductivity corresponds to the Dependent Variable; Chamber atmospheric pressure corresponds to the Controlled Variable.

In scientific investigations, the independent variable is the parameter systematically changed by the experimenter to test its effect (the

\text{ZrO}_2

concentration). The dependent variable is the measurable result or response observed (peak thermal conductivity). Controlled variables are all conditions held constant across trials (such as the chamber pressure of

1.0\text{ atm}

, plasma temperature, exposure time, and tile size) to prevent confounding factors from influencing the outcome.

Adım Adım Çözüm

1

Identify the variable that is systematically varied or manipulated by the experimenter.

The researchers explicitly change the

\text{ZrO}_2

additive concentration (

0\%, 5\%, 10\%, 15\%

) across test trials, establishing it as the independent variable.

The independent variable is the cause or factor directly controlled and varied by the researchers.

2

Identify the variable that is observed and measured to quantify the effect of the manipulation.

Peak thermal conductivity is recorded during exposure to determine how it responds to changes in

\text{ZrO}_2

concentration, establishing it as the dependent variable.

The dependent variable represents the effect or measured response resulting from changes in the independent variable.

3

Identify experimental conditions that are held constant throughout all trials.

Chamber atmospheric pressure (

1.0\text{ atm}

), plasma jet temperature (

1200^\circ\text{C}

), exposure time (300 seconds), and tile dimensions are held identical across all tests, establishing them as controlled variables.

Controlled variables must remain constant so that any observed changes in thermal conductivity can be attributed solely to the independent variable.

Anahtar Kavram

Identifying Independent, Dependent, and Controlled Variables

Soru 5320Soru →

At a regional debate tournament, Team Alpha has $6$ members with a mean score of $84$ points, and Team Beta has $4$ members with a mean score of $94$ points. If $2$ new members join Team Alpha such that the overall mean score for all $12$ members on both teams increases to $89$ points, what is the mean score of the $2$ new members?

89

90

94

104

188

Cevabı ve açıklamayı göster

Cevap: 94

Cevap

The mean score of the 2 new members is 94.

To find the mean score of the 2 new members, first determine the total points scored by the initial 10 members. Team Alpha scored

6 \times 84 = 504

points, and Team Beta scored

4 \times 94 = 376

points, giving an initial combined total of

880

points. Next, determine the total points required for all 12 members to have a mean score of 89, which is

12 \times 89 = 1068

points. The difference,

1068 - 880 = 188

points, represents the total points scored by the 2 new members. Dividing this sum by 2 yields a mean score of 94 points.

Adım Adım Çözüm

1

Calculate the total initial points for both teams combined.

Team Alpha total =

6 \times 84 = 504

. Team Beta total =

4 \times 94 = 376

. Combined initial total =

504 + 376 = 880

points.

The sum of data values equals the mean multiplied by the number of values.

2

Calculate the required total points for all 12 members to achieve the target overall mean.

Target total points =

12 \times 89 = 1068

points.

The total points required for

12

members with a mean of

89

is

12 \times 89

.

3

Determine the total points contributed by the 2 new members.

Points contributed =

1068 - 880 = 188

points.

Subtracting the initial combined points from the required total points isolates the points added by the

2

new members.

4

Calculate the mean score of the 2 new members.

Mean score =

188 \div 2 = 94

points.

Dividing the total points of the new members by the count of new members (

2

) yields their mean score.

Anahtar Kavram

Weighted Mean and Target Mean Problem Solving

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram