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To simplify 48/64, find the greatest common divisor (GCD) of 48 and 64, which is 16. Divide both the numerator and the denominator by 16: 48 ÷ 16 = 3, and 64 ÷ 16 = 4. The simplified fraction is 3/4.
To find 15% of 350, multiply 350 by 0.15: 350 * 0.15 = 52.5. Alternatively, calculate 10% (35.00) and 5% (17.50), and add them together: 35 + 17.5 = 52.50 GHS.
The total ratio parts are 3 + 2 = 5 parts. One part is equal to 600 GHS ÷ 5 = 120 GHS. Since Kofi's share is 3 parts, he receives 3 * 120 GHS = 360 GHS. Ama receives the remaining 240 GHS.
To find the average, sum the numbers and divide by the count: 14 + 17 + 20 + 23 + 26 = 100. Since there are 5 numbers, divide 100 by 5: 100 ÷ 5 = 20. For an arithmetic sequence with an odd number of terms, the mean is also the middle term (20).
The formula for simple interest is I = P * R * T, where P is principal, R is rate, and T is time in years. In this case, I = 1200 * 0.06 * 2 = 144 GHS. The total amount including interest would be 1,344 GHS.
Convert the time to hours: 1 hour and 45 minutes is 1 + 45/60 = 1.75 hours. Using the distance formula (Distance = Speed * Time), calculate: 80 * 1.75 = 140 km. Alternatively, travel 80 km in the first hour and 3/4 of 80 (60 km) in the next 45 minutes: 80 + 60 = 140 km.
To add fractions with different denominators, find the lowest common multiple (LCM) of the denominators 5 and 4, which is 20. Convert the fractions: 2/5 = 8/20, and 1/4 = 5/20. Add the numerators: 8/20 + 5/20 = 13/20.
In equivalent ratios, the relationship between corresponding terms is constant. Since 3 is multiplied by 7 to get 21, multiply the second term 7 by the same factor of 7: 7 * 7 = 49. Therefore, x = 49.
This is an inverse proportion problem because more workers require less time. The total work done is measured in officer-hours: 8 officers * 6 hours = 48 officer-hours. To find the time for 12 officers, divide the total work by 12: 48 ÷ 12 = 4 hours.
Let the age of the son be x. The father's age is 3x. The sum of their ages is x + 3x = 48. Simplify the equation: 4x = 48, which gives x = 12. The son is 12 years old, and the father is 36 years old.
To solve the linear equation, add 9 to both sides to isolate the term with x: 4x = 27 + 9, which simplifies to 4x = 36. Divide both sides by 4: x = 36 ÷ 4 = 9. The value of x is 9.
To find the percentage increase, divide the change in value by the original value, then multiply by 100. The increase is 150 - 120 = 30 GHS. The percentage increase is (30 ÷ 120) * 100 = 0.25 * 100 = 25%.
Multiplying by 0.75 is equivalent to taking three-quarters (3/4) of a number. To find 3/4 of 8, divide 8 by 4 (which is 2) and multiply by 3 (which is 6). Therefore, 0.75 * 8 = 6.0.
The area of a rectangle is calculated by multiplying its length by its width: Area = Length * Width. For this parade ground: Area = 15 meters * 10 meters = 150 square meters.
Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Favorable blue cards = 6; Total cards = 4 + 6 = 10. The probability is 6/10, which simplifies to 3/5 (or 60%).
In a geometric sequence, each term is found by multiplying the previous term by a constant ratio. In this sequence, the common ratio is 2 (3 * 2 = 6; 6 * 2 = 12; 12 * 2 = 24). The next term is 24 * 2 = 48.
Calculate the cost of the notebooks: 5 * 8 GHS = 40 GHS. Calculate the cost of the pens: 3 * 4 GHS = 12 GHS. Add the two costs together to find the total: 40 GHS + 12 GHS = 52 GHS.
Since 1 kilogram (kg) is equal to 1,000 grams (g), to convert kilograms to grams you multiply by 1,000: 2.25 * 1,000 = 2,250 grams.
A number is divisible by 6 if it is divisible by both 2 and 3. All options are even, so they are divisible by 2. To check for 3, add the digits: for 132, 1 + 3 + 2 = 6, which is divisible by 3. Therefore, 132 is divisible by 6 (132 ÷ 6 = 22).
Average speed is calculated as Total Distance divided by Total Time. Total distance = 60 + 60 = 120 km. Time for the first part = 60/30 = 2 hours; time for the second part = 60/60 = 1 hour. Total time = 3 hours. Average speed = 120 km ÷ 3 hours = 40 km/h.
Let the number of male officers be 4x and female officers be 5x. We are given 4x = 20, which yields x = 5. The number of female officers is 5 * 5 = 25. The total number of officers is Male + Female = 20 + 25 = 45 officers.
Let the number be x. The problem states that 0.30 * x = 90. To find x, divide 90 by 0.30: x = 90 ÷ 0.30 = 300. Thus, the number is 300.
The square root of 225 is 15 (since 15 * 15 = 225). The square root of 64 is 8 (since 8 * 8 = 64). Subtracting the two values: 15 - 8 = 7.
The area of a triangle is calculated using the formula: Area = 0.5 * Base * Height. For this triangle: Area = 0.5 * 12 cm * 8 cm = 6 * 8 = 48 square cm.
Profit is calculated as Selling Price - Cost Price = 52 - 40 = 12 GHS. The profit percentage is the profit divided by the cost price, multiplied by 100: (12 ÷ 40) * 100 = 0.30 * 100 = 30%.
The pronoun 'Each' is singular and acts as the subject of the sentence, requiring a singular verb. The prepositional phrase 'of the candidates' modifies the subject but does not change its number. Therefore, 'is' is the correct singular verb.
'Benevolent' is an adjective that means well-meaning, kindly, or charitable. 'Generous' shares a similar meaning of giving or showing kindness. Synonyms are words that have nearly the same meaning in a language.
'Obsolete' means no longer produced or used, or out of date. The antonym is 'Modern', which refers to the present or recent times and current technology. Antonyms are words opposite in meaning.
'Mitigate' means to make less severe, serious, or painful. In this context, the judge is reducing the penalty because the offender showed remorse. This fits the logical structure of the sentence.
The correct spelling is 'Accommodate', which contains two 'c's and two 'm's. It is a common spelling test word because people frequently omit one of the double letters.
The pronoun is part of the compound object of the verb 'invited' (invited the Sergeant and me). Therefore, the objective case pronoun 'me' must be used. You can verify this by removing the other object: 'invited me' is grammatically correct, whereas 'invited I' is not.
The idiom 'spill the beans' means to reveal secret information, often unintentionally or prematurely. An example is: 'We were planning a surprise promotion, but someone spilled the beans.'
'Vigilant' means keeping careful watch for possible danger or difficulties. 'Watchful' is a direct synonym. Security personnel and police officers are expected to remain vigilant on duty.
'Hostile' means unfriendly, antagonistic, or opposed to someone or something. The antonym is 'Friendly', which describes a kind and welcoming attitude. Antonyms are opposite meanings.
'Complement' means to add to or improve something, while 'compliment' is an expression of praise. 'Effect' is a noun meaning the result of an action, whereas 'affect' is typically a verb meaning to influence. This sentence correctly uses 'complement' (verb) and 'effect' (noun).
The correct spelling is 'Correspondence', which has a double 'r' and ends in '-ence'. It refers to communication by exchanging letters or emails.
A sentence is in the passive voice when the subject is acted upon by the verb. In 'A comprehensive report was submitted by the patrol team', the subject 'report' is receiving the action 'submitted'. The actor (patrol team) is introduced by the preposition 'by'.
The idiom 'piece of cake' refers to a task or activity that is very easy to accomplish. For example: 'The written exam was a piece of cake because I studied hard.'
The adjective 'interested' is conventionally followed by the preposition 'in' when introducing the object of interest. Therefore, 'interested in joining' is the correct idiomatic phrasing.
'Resilient' means able to withstand or recover quickly from difficult conditions. 'Adaptable' shares a similar meaning of being flexible and able to adjust to change. Resilient individuals recover easily from setbacks.
'Trivial' means of little value or importance. The antonym is 'Significant', which means sufficiently great or important to be worthy of attention. Antonyms are opposite in meaning.
'Their' is a possessive pronoun indicating ownership by a group (the officers). In this sentence, it modifies 'equipment' to show who owns it. 'There' refers to location, and 'they're' is a contraction of 'they are'.
If 'leave is canceled', it means officers cannot take time off and must report for duty. The cancellation is linked to 'national celebrations', implying that more personnel are required for security. Therefore, we can infer that all officers must work.
The correct spelling is 'Occurred', which contains a double 'c' and a double 'r'. When a verb ends in a consonant preceded by a single vowel, the final consonant is doubled before adding '-ed'.
This is a third conditional sentence, which describes a hypothetical condition in the past and its past result. The condition clause uses 'had + past participle' (had arrived) and the result clause uses 'would have + past participle' (would have prevented).
The verb 'accuse' is conventionally paired with the preposition 'of' (accused of something). This is a fixed prepositional collocation in English grammar.
'Meticulous' means showing great attention to detail, very careful and precise. 'Precise' is a direct synonym. Crime scene investigators must be meticulous in collecting evidence.
'Plausible' means seeming reasonable or probable, or believable. The antonym is 'Improbable', which means not likely to be true or to happen. Antonyms are opposite meanings.
A 'Lexicographer' is a person who writes, compiles, or edits dictionaries. The root 'lexico-' relates to words or vocabulary, and '-grapher' relates to one who writes.
The sentence is grammatically correct. It contains a subordinate clause ('Although the recruit was tired'), a main clause ('he kept running'), and a participial phrase modifying the subject ('refusing to give up'). The punctuation and structure are correct.