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Soru 5421Soru →

A box contains 3030 raffle tickets numbered 11 through 3030. If one ticket is selected at random from the box, what is the probability that the number on the selected ticket is a multiple of 44 or a multiple of 66?

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Cevap: 13\frac{1}{3}

Cevap

The probability that the number on the selected ticket is a multiple of 44 or a multiple of 66 is 13\frac{1}{3}.
The correct answer is determined by applying the addition rule for non-mutually exclusive events: P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B). Out of 3030 tickets, 77 are multiples of 44 and 55 are multiples of 66. The numbers 1212 and 2424 are multiples of both 44 and 66, meaning they belong to the intersection. Calculating the total number of unique favorable tickets gives 7+5−2=107 + 5 - 2 = 10. Dividing 1010 favorable outcomes by the 3030 total tickets yields a probability of 1030=13\frac{10}{30} = \frac{1}{3}.

Adım Adım Çözüm

1
Identify the total number of possible outcomes.
There are 3030 total tickets in the box, so the sample space size is 3030.
Each ticket numbered 1 through 30 is equally likely to be selected.
2
Count the outcomes for each individual event.
Multiples of 44: {4,8,12,16,20,24,28}→7\{4, 8, 12, 16, 20, 24, 28\} \rightarrow 7 outcomes.
Multiples of 66: {6,12,18,24,30}→5\{6, 12, 18, 24, 30\} \rightarrow 5 outcomes.
Listing or dividing 3030 by 44 and 66 determines how many tickets satisfy each separate condition.
3
Identify and count the overlapping outcomes (multiples of both 44 and 66).
Multiples of both 44 and 66 are multiples of LCM(4,6)=12\text{LCM}(4, 6) = 12, which are {12,24}→2\{12, 24\} \rightarrow 2 outcomes.
These numbers are contained in both individual lists and will be double-counted if not accounted for.
4
Apply the Principle of Inclusion-Exclusion to find the total number of favorable outcomes.
\text{Favorable outcomes} = 7 + 5 - 2 = 10.
Subtracting the intersection prevents double-counting the tickets that satisfy both conditions.
5
Calculate the probability.
P(\text{multiple of } 4 \text{ or } 6) = \frac{10}{30} = \frac{1}{3}.
Probability is the ratio of favorable outcomes to total possible outcomes.

Anahtar Kavram

Probability of Non-Mutually Exclusive Events (Inclusion-Exclusion Principle)
Tahmini Süre:1m 0s
Soru 5422Soru →

A student is creating a flag design consisting of 3 vertical stripes in a row. The student can choose from 5 different colors: Red, Blue, Green, Yellow, and White. To ensure visual contrast, any 2 adjacent stripes must be different colors. How many different flag designs can be created under these rules?

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Cevap: 80

Cevap

80
To find the total number of flag designs, apply the Fundamental Counting Principle across the three sequential stripe choices. The first stripe can be any of the 5 colors. The second stripe cannot match the first stripe's color, leaving 4 options. The third stripe cannot match the second stripe's color, which also leaves 4 options (since it can re-use the first stripe's color). Multiplying these choices together gives 5×4×4=805 \times 4 \times 4 = 80 unique flag designs.

Adım Adım Çözüm

1
Determine choices for the first stripe
5 choices
Any of the 5 available colors can be selected for the first stripe.
2
Determine choices for the second stripe
4 choices
The second stripe must differ in color from the first stripe.
3
Determine choices for the third stripe
4 choices
The third stripe must differ in color from the second stripe (it may be the same color as the first stripe).
4
Apply the Fundamental Counting Principle
5×4×4=805 \times 4 \times 4 = 80
Multiply the options available at each stage to calculate the total number of distinct flag designs.

Anahtar Kavram

Fundamental Counting Principle with adjacent restrictions
Tahmini Süre:1m 15s
Soru 5423Soru →

If u=−3u = -3 and v=−12v = -\frac{1}{2}, what is the value of the algebraic expression below? Enter your numerical answer in the blank.

Aşağıdaki boşlukları doldurun

The value of the expression 4uv2−u22v−u\frac{4uv^2 - u^2}{2v - u} is .
Cevabı ve açıklamayı göster

Cevap

The value of the expression when evaluated at u=−3u = -3 and v=−12v = -\frac{1}{2} is −6-6.
Substituting u=−3u = -3 and v=−12v = -\frac{1}{2} into the numerator gives 4(−3)(−12)2−(−3)2=−3−9=−124(-3)(-\frac{1}{2})^2 - (-3)^2 = -3 - 9 = -12. Substituting into the denominator gives 2(−12)−(−3)=−1+3=22(-\frac{1}{2}) - (-3) = -1 + 3 = 2. Dividing −12-12 by 22 results in −6-6.

Adım Adım Çözüm

1
Evaluate the terms containing exponents in the numerator.
v2=(−12)2=14v^2 = \left(-\frac{1}{2}\right)^2 = \frac{1}{4} and u2=(−3)2=9u^2 = (-3)^2 = 9.
Exponents must be calculated before multiplication according to the order of operations.
2
Evaluate the numerator 4uv2−u24uv^2 - u^2.
4(−3)(14)−9=−3−9=−124(-3)\left(\frac{1}{4}\right) - 9 = -3 - 9 = -12.
Multiply 4×(−3)×144 \times (-3) \times \frac{1}{4} to get −3-3, then subtract 99.
3
Evaluate the denominator 2v−u2v - u.
2(−12)−(−3)=−1+3=22\left(-\frac{1}{2}\right) - (-3) = -1 + 3 = 2.
Multiplying 22 by −12-\frac{1}{2} gives −1-1, and subtracting negative 33 is equivalent to adding 33.
4
Divide the numerator by the denominator.
−122=−6\frac{-12}{2} = -6.
Dividing −12-12 by 22 yields the final result −6-6.

Anahtar Kavram

Evaluating algebraic expressions involving negative numbers, fractions, and order of operations.
Tahmini Süre:1m 30s
Soru 5424Soru →

If a=−3a = -3 and b=−2b = -2, what is the value of the expression 2a2−b3(a−b)2+ab\frac{2a^2 - b^3}{(a - b)^2 + ab}?

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Cevap: 267\frac{26}{7}

Cevap

267\frac{26}{7}
Substituting a=−3a = -3 and b=−2b = -2 directly into the numerator yields 2(−3)2−(−2)3=2(9)−(−8)=262(-3)^2 - (-2)^3 = 2(9) - (-8) = 26. Substituting into the denominator gives ((−3)−(−2))2+(−3)(−2)=(−1)2+6=7((-3) - (-2))^2 + (-3)(-2) = (-1)^2 + 6 = 7. Combining these results gives 267\frac{26}{7}.

Adım Adım Çözüm

1
Substitute a=−3a = -3 and b=−2b = -2 into the numerator 2a2−b32a^2 - b^3.
2(−3)2−(−2)3=2(9)−(−8)=18+8=262(-3)^2 - (-2)^3 = 2(9) - (-8) = 18 + 8 = 26
Squaring −3-3 gives 99, and cubing −2-2 gives −8-8. Subtracting −8-8 is equivalent to adding 88.
2
Substitute a=−3a = -3 and b=−2b = -2 into the denominator (a−b)2+ab(a - b)^2 + ab.
((−3)−(−2))2+(−3)(−2)=(−3+2)2+6=(−1)2+6=1+6=7((-3) - (-2))^2 + (-3)(-2) = (-3 + 2)^2 + 6 = (-1)^2 + 6 = 1 + 6 = 7
Subtracting a negative number becomes addition, and squaring −1-1 yields 11.
3
Form the fraction by dividing the numerator by the denominator.
267\frac{26}{7}
The evaluated numerator is 2626 and the evaluated denominator is 77.

Anahtar Kavram

Order of operations and handling negative signs when evaluating algebraic expressions involving powers and parentheses.
Tahmini Süre:1m 0s
Soru 5425Soru →

If x=−3x = -3, y=−12y = -\frac{1}{2}, and z=8z = 8, what is the value of the algebraic expression x2y−1+z2/32xy−1\frac{x^2 y^{-1} + z^{2/3}}{2xy - 1}?

Cevabı ve açıklamayı göster

Cevap: -7

Cevap

The value of the expression is -7.
Substituting the given values into the expression requires careful application of exponent rules and order of operations. First, (−3)2=9(-3)^2 = 9 and (−12)−1=−2(-\frac{1}{2})^{-1} = -2, so x2y−1=9×(−2)=−18x^2 y^{-1} = 9 \times (-2) = -18. Second, 82/3=(83)2=22=48^{2/3} = (\sqrt[3]{8})^2 = 2^2 = 4. This makes the numerator −18+4=−14-18 + 4 = -14. The denominator evaluates to 2(−3)(−12)−1=3−1=22(-3)(-\frac{1}{2}) - 1 = 3 - 1 = 2. Dividing −14-14 by 22 gives the correct answer of −7-7.

Adım Adım Çözüm

1
Substitute x=−3x = -3 and y=−12y = -\frac{1}{2} into x2y−1x^2 y^{-1}
(−3)2⋅(−2)=−18(-3)^2 \cdot (-2) = -18
Squaring −3-3 yields 99, and taking the reciprocal of −12-\frac{1}{2} yields −2-2.
2
Substitute z=8z = 8 into z2/3z^{2/3}
82/3=48^{2/3} = 4
Taking the cube root of 88 gives 22, and squaring 22 gives 44.
3
Evaluate the numerator
−18+4=−14-18 + 4 = -14
Adding the evaluated terms together.
4
Substitute values into the denominator 2xy−12xy - 1
2(−3)(−12)−1=3−1=22(-3)\left(-\frac{1}{2}\right) - 1 = 3 - 1 = 2
Multiplying 22, −3-3, and −12-\frac{1}{2} produces 33, then subtracting 11 yields 22.
5
Divide the numerator by the denominator
−142=−7\frac{-14}{2} = -7
Simplifying the rational expression yields the final numeric answer.

Anahtar Kavram

Evaluating algebraic expressions with negative bases, rational exponents, and negative exponents
Soru 5426Soru →

If x=−2x = -2, y=13y = \frac{1}{3}, and z=−3z = -3, what is the value of the algebraic expression 3x2y−z2x+yz\frac{3x^2 y - z^2}{x + yz}?

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Cevap: 53\frac{5}{3}

Cevap

53\frac{5}{3}
Substituting the given values into the expression requires evaluating powers of negative numbers and performing multiplication prior to addition/subtraction. In the numerator, 3(−2)2(13)−(−3)2=3(4)(13)−9=4−9=−53(-2)^2(\frac{1}{3}) - (-3)^2 = 3(4)(\frac{1}{3}) - 9 = 4 - 9 = -5. In the denominator, −2+(13)(−3)=−2−1=−3-2 + (\frac{1}{3})(-3) = -2 - 1 = -3. Simplifying the fraction −5−3\frac{-5}{-3} gives 53\frac{5}{3}.

Adım Adım Çözüm

1
Evaluate the numerator 3x2y−z23x^2 y - z^2 by substituting x=−2x = -2, y=13y = \frac{1}{3}, and z=−3z = -3.
3(−2)2(13)−(−3)2=3(4)(13)−9=4−9=−53(-2)^2\left(\frac{1}{3}\right) - (-3)^2 = 3(4)\left(\frac{1}{3}\right) - 9 = 4 - 9 = -5
Squaring negative numbers yields positive values: (−2)2=4(-2)^2 = 4 and (−3)2=9(-3)^2 = 9.
2
Evaluate the denominator x+yzx + yz using the same variable values.
−2+(13)(−3)=−2+(−1)=−3-2 + \left(\frac{1}{3}\right)(-3) = -2 + (-1) = -3
Perform the multiplication y⋅zy \cdot z before adding to xx according to the order of operations.
3
Divide the evaluated numerator by the evaluated denominator.
−5−3=53\frac{-5}{-3} = \frac{5}{3}
Dividing two negative numbers produces a positive quotient.

Anahtar Kavram

Evaluating Algebraic Expressions with Negative Values and Rational Numbers
Soru 5427Soru →

If m=−4m = -4 and n=−12n = -\frac{1}{2}, what is the value of the algebraic expression m2−4n3(m+2n)2\frac{m^2 - 4n^3}{(m + 2n)^2}?

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Cevap: 3350\frac{33}{50}

Cevap

3350\frac{33}{50}
Substituting m=−4m = -4 and n=−12n = -\frac{1}{2} into the numerator gives (−4)2−4(−12)3=16−(−12)=332(-4)^2 - 4\left(-\frac{1}{2}\right)^3 = 16 - \left(-\frac{1}{2}\right) = \frac{33}{2}. Substituting into the denominator gives (−4+2(−12))2=(−5)2=25\left(-4 + 2\left(-\frac{1}{2}\right)\right)^2 = (-5)^2 = 25. Dividing the numerator by the denominator yields 33/225=3350\frac{33/2}{25} = \frac{33}{50}.

Adım Adım Çözüm

1
Evaluate the terms in the numerator: m2m^2 and 4n34n^3.
m2=(−4)2=16m^2 = (-4)^2 = 16 and 4n3=4(−12)3=4(−18)=−124n^3 = 4\left(-\frac{1}{2}\right)^3 = 4\left(-\frac{1}{8}\right) = -\frac{1}{2}.
Substitute m=−4m = -4 and n=−12n = -\frac{1}{2} while applying powers before multiplication according to PEMDAS.
2
Calculate the complete numerator by subtracting the evaluated terms.
m2−4n3=16−(−12)=16+12=332m^2 - 4n^3 = 16 - \left(-\frac{1}{2}\right) = 16 + \frac{1}{2} = \frac{33}{2}.
Subtracting a negative quantity is equivalent to adding its positive counterpart.
3
Evaluate the expression inside the denominator parentheses, then square it.
m+2n=−4+2(−12)=−4−1=−5m + 2n = -4 + 2\left(-\frac{1}{2}\right) = -4 - 1 = -5, and (−5)2=25(-5)^2 = 25.
Grouped operations inside parentheses must be evaluated prior to applying outer exponents.
4
Divide the numerator by the denominator to get the final simplified fraction.
33225=332×25=3350\frac{\frac{33}{2}}{25} = \frac{33}{2 \times 25} = \frac{33}{50}.
Dividing a fraction by an integer combines the denominators.

Anahtar Kavram

Evaluating algebraic expressions involving negative bases, fractions, and order of operations
Tahmini Süre:1m 30s
Soru 5428Soru →

Evaluate the algebraic expression 3x2−2xy+y23x^2 - 2xy + y^2 for x=−3x = -3 and y=−2y = -2.

Aşağıdaki boşlukları doldurun

The value of the expression 3x2−2xy+y23x^2 - 2xy + y^2 when x=−3x = -3 and y=−2y = -2 is .
Cevabı ve açıklamayı göster

Cevap

19
Substituting x=−3x = -3 and y=−2y = -2 into 3x2−2xy+y23x^2 - 2xy + y^2 yields 3(−3)2−2(−3)(−2)+(−2)2=3(9)−12+4=27−12+4=193(-3)^2 - 2(-3)(-2) + (-2)^2 = 3(9) - 12 + 4 = 27 - 12 + 4 = 19.

Adım Adım Çözüm

1
Substitute x=−3x = -3 and y=−2y = -2 into the expression
3(−3)2−2(−3)(−2)+(−2)23(-3)^2 - 2(-3)(-2) + (-2)^2
Replace each variable with its assigned value, using parentheses to properly preserve negative signs.
2
Evaluate the exponent terms
3(9)−2(−3)(−2)+43(9) - 2(-3)(-2) + 4
Follow the order of operations (PEMDAS) by evaluating powers first: (−3)2=9(-3)^2 = 9 and (−2)2=4(-2)^2 = 4.
3
Perform the multiplications
27−12+427 - 12 + 4
Multiply the numerical factors: 3×9=273 \times 9 = 27 and −2×(−3)×(−2)=−12-2 \times (-3) \times (-2) = -12.
4
Perform addition and subtraction from left to right
1919
Subtract 1212 from 2727 to get 1515, then add 44 to arrive at 1919.

Anahtar Kavram

Evaluating Algebraic Expressions with Negative Values
Soru 5429Soru →

If x=−3x = -3, y=−12y = -\frac{1}{2}, and z=4z = 4, what is the numerical value of the algebraic expression x2−4y2x+yz\frac{x^2 - 4y^2}{x + yz}?

Cevabı ve açıklamayı göster

Cevap: -1.6

Cevap

The numerical value of the expression is −1.6-1.6.
Substituting x=−3x = -3, y=−12y = -\frac{1}{2}, and z=4z = 4 into x2−4y2x+yz\frac{x^2 - 4y^2}{x + yz} gives a numerator of (−3)2−4(−12)2=9−4(14)=8(-3)^2 - 4\left(-\frac{1}{2}\right)^2 = 9 - 4\left(\frac{1}{4}\right) = 8 and a denominator of −3+(−12)(4)=−3−2=−5-3 + \left(-\frac{1}{2}\right)(4) = -3 - 2 = -5. Evaluating 8−5\frac{8}{-5} yields −1.6-1.6.

Adım Adım Çözüm

1
Evaluate the numerator x2−4y2x^2 - 4y^2
8
Squaring −3-3 gives 99, and squaring −12-\frac{1}{2} gives 14\frac{1}{4}. Thus, 9−4(14)=9−1=89 - 4\left(\frac{1}{4}\right) = 9 - 1 = 8.
2
Evaluate the denominator x+yzx + yz
-5
Multiplying −12-\frac{1}{2} by 44 gives −2-2. Adding −3+(−2)-3 + (-2) yields −5-5.
3
Compute the final fraction quotient
-1.6
Dividing the numerator 88 by the denominator −5-5 yields −1.6-1.6.

Anahtar Kavram

Evaluating algebraic expressions using order of operations with negative bases and fractional values.
Tahmini Süre:1m 30s
Soru 5430Soru →

If a=−2a = -2, b=−12b = -\frac{1}{2}, and c=3c = 3, what is the value of the algebraic expression a3b−2c2a−b−2\frac{a^3 b - 2c^2}{a - b^{-2}}?

Cevabı ve açıklamayı göster

Cevap: 73\frac{7}{3}

Cevap

The correct answer is 73\frac{7}{3}.
Substituting a=−2a = -2, b=−12b = -\frac{1}{2}, and c=3c = 3 gives a numerator of (−2)3(−12)−2(3)2=(−8)(−12)−18=4−18=−14(-2)^3 \left(-\frac{1}{2}\right) - 2(3)^2 = (-8)\left(-\frac{1}{2}\right) - 18 = 4 - 18 = -14, and a denominator of −2−(−12)−2=−2−4=−6-2 - \left(-\frac{1}{2}\right)^{-2} = -2 - 4 = -6. Dividing −14-14 by −6-6 simplifies to 73\frac{7}{3}.

Adım Adım Çözüm

1
Substitute a=−2a = -2, b=−12b = -\frac{1}{2}, and c=3c = 3 into the numerator a3b−2c2a^3 b - 2c^2.
Numerator =(−2)3⋅(−12)−2(3)2=(−8)⋅(−12)−2(9)=4−18=−14= (-2)^3 \cdot \left(-\frac{1}{2}\right) - 2(3)^2 = (-8) \cdot \left(-\frac{1}{2}\right) - 2(9) = 4 - 18 = -14.
Apply exponents first, then multiplication, and finally subtraction.
2
Substitute a=−2a = -2 and b=−12b = -\frac{1}{2} into the denominator a−b−2a - b^{-2}.
Denominator =−2−(−12)−2=−2−(−2)2=−2−4=−6= -2 - \left(-\frac{1}{2}\right)^{-2} = -2 - (-2)^2 = -2 - 4 = -6.
A negative exponent indicates the reciprocal of the base, so (−12)−2=(−2)2=4\left(-\frac{1}{2}\right)^{-2} = (-2)^2 = 4.
3
Divide the numerator by the denominator and simplify the fraction.
−14−6=146=73.\frac{-14}{-6} = \frac{14}{6} = \frac{7}{3}.
Dividing two negative numbers yields a positive quotient, which simplifies by dividing the numerator and denominator by 2.

Anahtar Kavram

Evaluating algebraic expressions with negative bases and negative integer exponents
Tahmini Süre:1m 30s
Soru 5431Soru →

The following sentence is missing a pronoun. To ensure grammatically correct pronoun-antecedent agreement, what word should be placed in the blank?

Aşağıdaki boşlukları doldurun

Although the research team expected the cluster of stars to drift together, each of the stellar bodies in the outer ring has maintained independent trajectory.
Cevabı ve açıklamayı göster

Cevap

its
The correct answer is the singular possessive pronoun 'its.' In the sentence, the pronoun must refer back to its antecedent. The subject of the clause is the singular indefinite pronoun 'each.' Although the intervening prepositional phrase 'of the stellar bodies in the outer ring' contains the plural noun 'bodies,' the pronoun must agree in number with the actual subject 'each.' Since 'each' is singular and refers to an inanimate object, the singular neuter possessive pronoun 'its' is grammatically correct.

Adım Adım Çözüm

1
Identify the antecedent of the missing pronoun.
The subject and antecedent of the clause containing the blank is the singular indefinite pronoun 'each.'
The prepositional phrase 'of the stellar bodies in the outer ring' contains plural nouns but functions only as a modifier, not as the grammatical subject of the clause.
2
Determine the grammatical number of the antecedent.
The pronoun 'each' is singular, which is also confirmed by the singular verb 'has maintained.'
Indefinite pronouns such as 'each' are always singular in standard formal English.
3
Select the correct pronoun that matches the antecedent in number and gender.
The singular possessive pronoun 'its' is selected.
Because 'each' is singular and refers to inanimate stellar bodies, the singular neuter possessive pronoun 'its' must be used to agree with it.

Anahtar Kavram

Pronoun-Antecedent Agreement with Indefinite Pronouns
Tahmini Süre:1m 0s
Soru 5432Soru →

In the late nineteenth century, many pioneering female journalists found that they could establish their careers by writing under pseudonyms, reporting from overseas conflict zones, and they investigated municipal corruption in major cities.

Which choice best replaces the underlined portion to maintain a parallel structure in the sentence?

Cevabı ve açıklamayı göster

Cevap: investigating

Cevap

investigating
The correct answer is 'investigating' because it is a gerund phrase ('investigating municipal corruption in major cities') that matches the grammatical format of the other two elements in the series ('writing under pseudonyms' and 'reporting from overseas conflict zones'), which are also gerund phrases.

Adım Adım Çözüm

1
Identify the items in the list and their grammatical structures.
The preposition 'by' introduces a list of three actions: 'writing under pseudonyms' (gerund phrase) and 'reporting from overseas conflict zones' (gerund phrase).
To maintain parallel structure, all items in a list governed by the same preposition must share the same grammatical form.
2
Analyze the underlined portion to see if it matches the established pattern.
The underlined portion 'they investigated' is a clause (subject + verb), which does not match the gerund structure of the first two list items.
Identifying the grammatical mismatch highlights the structural error that needs correction.
3
Select the choice that uses the gerund form to make the third item parallel.
The choice 'investigating' is a gerund, which matches 'writing' and 'reporting' perfectly.
Using the gerund form completes the list with a consistent, parallel grammatical structure.

Anahtar Kavram

Parallel structure in lists requires all items in a series to share the same grammatical form (e.g., all gerunds, all infinitives, or all clauses).
Soru 5433Soru →

In 1967, astrophysicist Jocelyn Bell Burnell detected a series of highly regular radio pulses in her telescopic data. Her advisor initially dismissed the signals as man-made interference, but Bell Burnell persisted in analyzing the anomaly, eventually proving the existence of pulsars.

Which choice is the most grammatically correct and logical version of the underlined portion of the sentence?

Cevabı ve açıklamayı göster

Cevap: advisor initially dismissed the signals as man-made interference, but Bell Burnell

Cevap

The correct choice is the original phrasing, which uses the coordinating conjunction 'but' along with a comma to join two independent clauses.
The correct option preserves the grammatical integrity of the sentence by correctly linking two independent clauses using the coordinating conjunction 'but' preceded by a comma.

Adım Adım Çözüm

1
Identify the clauses in the passage.
The text contains two primary assertions: 'Her advisor initially dismissed the signals as man-made interference' and 'Bell Burnell persisted in analyzing the anomaly.'
Understanding the boundary between clauses is essential to determine whether we are connecting independent or dependent ideas.
2
Analyze the grammatical status of each clause.
Both assertions can stand alone as complete sentences, meaning they are both independent clauses.
Identifying the clauses as independent dictates that we must use a proper coordinating conjunction with a comma, a semicolon, or separate them into two sentences.
3
Evaluate the choices based on coordination and subordination rules.
The original phrasing correctly links these two independent clauses with a comma and the coordinating conjunction 'but', establishing a logical contrast between the advisor's dismissal and Bell Burnell's persistence.
This ensures the sentence is grammatically correct and expresses the intended relationship between the ideas.

Anahtar Kavram

Using coordinating conjunctions to join independent clauses and avoiding run-ons, comma splices, or sentence fragments.
Tahmini Süre:1m 0s
Soru 5434Soru →

During the mid-nineteenth century, naturalists frequently traveled alongside surveyors to document the flora of the American West. While the surveyors mapped the rugged terrain, the naturalists collected specimens of rare wildflowers. Because they were often preoccupied with the physical demands of the journey, many specimens remained undocumented for decades.

Which of the following choices most effectively clarifies the underlined pronoun in the passage?

Cevabı ve açıklamayı göster

Cevap: the naturalists

Cevap

The correct answer is the option that replaces the pronoun with 'the naturalists' to resolve the ambiguity.
The correct choice replaces the ambiguous pronoun 'they' with the specific noun 'the naturalists.' In the original sentence, 'they' could refer to either 'the surveyors' or 'the naturalists,' both of which are plural nouns in the preceding sentence. Specifying 'the naturalists' clarifies who was preoccupied with the demands of the journey.

Adım Adım Çözüm

1
Identify the underlined pronoun and its potential antecedents in the preceding context.
The pronoun 'they' is plural and has multiple potential plural antecedents: 'naturalists,' 'surveyors,' and 'wildflowers.'
To evaluate pronoun clarity, you must trace the pronoun back to its logical antecedent in the sentence.
2
Determine if the pronoun reference is clear or ambiguous.
The reference is ambiguous because both 'naturalists' and 'surveyors' could logically be preoccupied with the physical demands of the journey.
Pronouns must refer clearly and unambiguously to a single noun antecedent.
3
Evaluate the choices to find the one that replaces the pronoun with a clear, specific noun.
Replacing 'they' with 'the naturalists' directly resolves the ambiguity without introducing redundancy or grammatical errors.
ACT English questions require choosing the most clear, precise, and grammatically correct phrasing.

Anahtar Kavram

Pronoun Clarity and Reference
Soru 5435Soru →

The restoration of the medieval cathedral's stained glass windows required a painstaking process of chemical stabilization, because the glass was susceptible to "glass disease," a progressive decay caused by moisture. Artists had to apply a protective silica coating to the exterior surfaces, however, this intervention, which successfully halted the decay, slightly altered the refraction of light through the glass. Consequently, the team had to calibrate the coating's thickness to preserve the windows' original luminosity.

Which of the following options is the most grammatically correct replacement for the underlined portion?

Cevabı ve açıklamayı göster

Cevap: surfaces; however, this intervention, which

Cevap

The correct answer is the option that replaces the underlined text with a semicolon followed by 'however,' a comma, and the relative pronoun 'which'.
The correct answer correctly uses a semicolon to separate the two independent clauses before the conjunctive adverb 'however.' It also properly punctuates the non-restrictive relative clause ('which successfully halted the decay') with commas.

Adım Adım Çözüm

1
Analyze the clause structure of the passage surrounding the transition word 'however'.
The clauses before and after 'however' are both independent clauses capable of standing alone as complete sentences.
This determines that a strong punctuation mark (like a semicolon or period) or a coordinating conjunction is required to connect them.
2
Evaluate the grammar of the original sentence (Option A).
The original sentence joins the independent clauses with only a comma before 'however,' which is a conjunctive adverb, resulting in a comma splice.
This rules out the option containing the original punctuation.
3
Examine the remaining options for sentence structure and punctuation errors.
Adding 'because' after 'however' (Option C) creates a dependent clause and a fragment. Using 'that' within commas (Option D) creates a restrictive comma error since 'that' clauses cannot be set off by commas. Only Option B correctly uses a semicolon to join the clauses and maintains the proper non-restrictive pronoun 'which'.
This confirms the correct choice by process of elimination of standard grammatical errors.

Anahtar Kavram

Run-on Sentences and Comma Splices
Tahmini Süre:1m 0s
Soru 5436Soru →

Restoring vintage arcade cabinets is a rewarding hobby that requires both woodworking and electronic skills. Enthusiasts often spend months sourcing original parts, they must also carefully repair the cathode-ray tube monitors. Once the cabinet is fully restored, it serves as a functional piece of gaming history.

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

Cevabı ve açıklamayı göster

Cevap: parts; they

Cevap

parts; they
The option 'parts; they' is correct because a semicolon is a standard and grammatically sound punctuation mark used to separate two closely related independent clauses.

Adım Adım Çözüm

1
Identify the two clauses in the sentence.
The clauses are 'Enthusiasts often spend months sourcing original parts' and 'they must also carefully repair the cathode-ray tube monitors'. Both can stand alone as independent sentences.
Determining clause type is necessary to apply correct punctuation rules.
2
Check the punctuation connecting the independent clauses.
The original text uses only a comma, which creates a comma splice.
Two independent clauses cannot be joined by a comma alone without a coordinating conjunction.
3
Evaluate the choices to find a grammatically correct way to separate the clauses.
Using a semicolon without a subordinating conjunction correctly separates the two clauses.
A semicolon is designed to connect independent clauses without creating a fragment or comma splice.

Anahtar Kavram

Run-on Sentences and Comma Splices
Soru 5437Soru →

The following passage describes a challenge in modern astronomy. What is the correct present-tense form of the verb 'to explain' that completes the passage to maintain proper subject-verb agreement?

Aşağıdaki boşlukları doldurun

In the field of astronomy, researchers constantly analyze anomalies in the night sky. Neither of the proposed mathematical models the strange orbital decay observed in the outer rings of Saturn. Consequently, astrophysicists must continue to refine their hypotheses to account for this data.
Cevabı ve açıklamayı göster

Cevap

The correct answer is 'explains'.
The verb must agree in number with its subject, which is the singular indefinite pronoun 'Neither'. The correct present-tense form for a singular subject is 'explains'. The intervening prepositional phrase 'of the proposed mathematical models' contains the plural noun 'models', but nouns within modifying prepositional phrases do not affect subject-verb agreement.

Adım Adım Çözüm

1
Identify the subject of the verb in the sentence containing the blank.
The subject is the indefinite pronoun 'Neither'.
The prepositional phrase 'of the proposed mathematical models' modifies the subject but does not change it; the head of the subject phrase is the pronoun 'Neither'.
2
Determine the number of the subject to establish agreement.
The subject 'Neither' is singular.
Indefinite pronouns such as 'each', 'either', and 'neither' are singular and require singular verbs.
3
Form the correct present-tense verb that agrees with the singular subject.
The correct present-tense form is 'explains'.
For a singular subject in the third person, the verb must end in '-s' (explains) to agree with the subject 'Neither'.

Anahtar Kavram

Subject-Verb Agreement with Indefinite Pronouns
Tahmini Süre:1m 0s
Soru 5438Soru →

The new library features large glass windows; it receives a significant amount of natural light during the day.

Which of the following options is the best replacement for the underlined portion of the sentence?

Cevabı ve açıklamayı göster

Cevap: windows; it

Cevap

The correct option is the one that uses a semicolon to connect the two independent clauses: 'windows; it'.
The correct option uses a semicolon to properly join two related independent clauses. Both parts of the sentence express complete thoughts and can stand alone as sentences, making the semicolon the correct punctuation mark.

Adım Adım Çözüm

1
Analyze the grammatical structure of the clauses surrounding the underlined portion.
The clause before the punctuation ('The new library features large glass windows') and the clause after ('it receives a significant amount of natural light during the day') are both independent clauses because they can each stand alone as a complete sentence.
Identifying whether clauses are independent or dependent determines which punctuation mark is appropriate to connect them.
2
Select the correct punctuation mark to join the two independent clauses without a coordinating conjunction.
A semicolon is the correct grammatical choice to link two closely related independent clauses. Therefore, the original sentence structure is correct.
This punctuation prevents errors such as comma splices and sentence fragments.

Anahtar Kavram

Using a semicolon to link two closely related independent clauses.
Soru 5439Soru →

The economic advisors recommended a series of abrupt, radical, policy changes to curb inflation, the treasury department delayed implementation until the next fiscal quarter.

Which of the following options best punctuates the underlined portion of the sentence?

Cevabı ve açıklamayı göster

Cevap: abrupt, radical policy changes to curb inflation; the treasury department delayed

Cevap

The option that reads 'abrupt, radical policy changes to curb inflation; the treasury department delayed' is correct because it properly punctuates the coordinate adjectives, avoids inserting a comma before a restrictive modifier, and correctly separates the two independent clauses with a semicolon.
The correct option correctly punctuates the coordinate adjectives 'abrupt' and 'radical' with a comma while omitting any punctuation before the noun phrase 'policy changes'. It also correctly avoids commas around the restrictive modifier 'to curb inflation' and properly connects the two independent clauses using a semicolon.

Adım Adım Çözüm

1
Analyze the relationship between the adjectives 'abrupt' and 'radical' modifying 'policy changes'.
The adjectives are coordinate because they can be reversed ('radical, abrupt') and joined by 'and' ('abrupt and radical') while retaining the same meaning. Thus, they must be separated by a comma, but no comma should be placed between the final adjective 'radical' and the modified noun phrase 'policy changes'.
Coordinate adjectives require separating punctuation, but the final adjective must not be separated from the noun it modifies.
2
Determine if the phrase 'to curb inflation' is essential (restrictive) or nonessential (nonrestrictive) to the meaning of the noun 'policy changes'.
The infinitive phrase 'to curb inflation' is restrictive because it specifies the exact purpose of the recommended policy changes. Therefore, no comma should separate it from the noun it modifies.
Restrictive modifiers must not be set off by commas.
3
Analyze the clause structures surrounding the boundary between 'inflation' and the second part of the sentence.
The clause before the boundary ('The economic advisors recommended a series of abrupt, radical policy changes to curb inflation') and the clause after ('the treasury department delayed implementation until the next fiscal quarter') are both independent. To join them without a coordinating conjunction, a semicolon must be used.
Joining two independent clauses with only a comma creates a comma splice, while placing a subordinating conjunction after a semicolon creates a dependent clause fragment.

Anahtar Kavram

Coordinate adjectives, restrictive modifiers, and independent clause punctuation rules
Tahmini Süre:1m 30s
Soru 5440Soru →

Safeguarding the Future: The Svalbard Global Seed Vault

[1]
Deep inside a sandstone mountain on the Norwegian island of Spitsbergen, halfway between mainland Norway and the North Pole, lies the Svalbard Global Seed Vault. Often referred to as the "Doomsday Vault," this facility is designed to withstand both natural and man-made disasters. It serves as a safety net for the world's agricultural heritage, protecting millions of seed samples from around the globe against accidental loss in traditional genebanks.

[2]
The vault's location was chosen with meticulous care. Svalbard is geologically stable, reducing the risk of earthquakes. Furthermore, its extreme northern latitude offers natural permafrost, which helps keep the seeds frozen even if the facility's mechanical cooling systems fail. The seeds are stored at a constant temperature of minus eighteen degrees Celsius. Wrapped in moisture-resistant foil packages and placed in sealed boxes, the seeds are shielded from moisture and oxygen, ensuring their viability for decades or even centuries.

[3]
While local genebanks exist in almost every country, they are vulnerable to war, political instability, and natural disasters. For example, during the Syrian Civil War, researchers at the International Center for Agricultural Research in the Dry Areas (ICARDA) in Aleppo were forced to abandon their facility. Fortunately, because they had previously deposited duplicates of their seed collection in the Svalbard vault, they were able to retrieve the seeds and re-establish their operations in Lebanon and Morocco. This real-world test demonstrated the indispensable role of the vault in global food security.

Suppose the writer's goal had been to write an essay that describes the construction challenges and architectural engineering details of building the Svalbard Global Seed Vault. Would this essay successfully accomplish this goal?

Cevabı ve açıklamayı göster

Cevap: No, because the essay focuses on the purpose, environmental suitability of the location, and real-world utility of the vault rather than the specific construction methods and engineering plans used to build it.

Cevap

No, because the essay focuses on the purpose, environmental suitability of the location, and real-world utility of the vault rather than the specific construction methods and engineering plans used to build it.
The correct answer is the option stating that the essay would not accomplish the goal because it focuses on the purpose, environmental suitability of the location, and real-world utility of the vault rather than specific construction methods and engineering plans. The passage provides a general overview of why the vault exists and where it is located, but it does not detail the technical blueprints, machinery used, or architectural engineering challenges involved in its physical creation.

Adım Adım Çözüm

1
Analyze the proposed writing goal.
The goal is to describe the construction challenges and architectural engineering details of building the Svalbard Global Seed Vault.
Understanding the target goal allows for comparison with the actual content of the passage.
2
Evaluate the passage content against the proposed goal.
The passage discusses the vault's geographic location, its preservation mechanism (permafrost, foil packaging), and its real-world utility (ICARDA case study). It does not discuss blueprints, excavation techniques, construction materials, structural engineering, or specific construction challenges.
Determining what the passage actually covers helps identify whether it meets the proposed goal.
3
Select the correct option that matches the evaluation.
The correct option must state that the goal was not met ('No') and provide the reason that the essay focuses on the purpose and utility rather than the construction and engineering details.
This aligns the logical analysis of the passage with the correct answer choice.

Anahtar Kavram

Evaluating whole-essay goals requires analyzing the primary focus and scope of the entire passage to determine if it aligns with a newly proposed writing purpose.
Tahmini Süre:1m 30s
ÖncekiSayfa 272 / 278Sonraki
Tüm alıştırma soruları — ACT | Examkin