Datasets:

automated-research-group

/

llama2_7b_chat-agieval-results

like 0

-2702417726277228667

Sure! I can help you with that. Based on the information given in the question, we know that the ratio of red sweets to green sweets is 3:4, which means that for every 3 green sweets, there is 1 red sweet. If the bag contains 120 green sweets, then there are 120 x 3 = 360 red sweets in the bag. So, the answer is (

6171869306019167857

Sure! I can help you with that. The question states that the ages of the members of the club are in A.P. with a common difference of 3 months. The youngest member is 7 years old, and the sum of the ages of all the members is 250. Using the formula for nth term of an A.P., we can write: Age of nth member = (n - 1) x 3 Since

1242519054224862097

Sure, I'd be happy to help! Based on the information provided, the correct answer is (A) D/(M-3). Explanation: If 3 men drop out of a group of M men who agreed to purchase a gift for Rs. D, then the remaining M-3 men will have to contribute an amount that is D/(M-3) towards the purchase of the gift. So, the correct answer is (A) D/(

-8573533947549004632

To determine the price at which Karan should mark the sewing machine to make a 20% profit after offering a 20% discount, we need to follow the formula: Profit = Selling Price - Cost Price First, let's calculate the cost price of the sewing machine: Cost Price = Original Price - Discount Discount = 20% of Cost Price Discount = 0.20 x Cost Price Cost

-2435394364374267403

To solve this problem, we need to use the concept of relative speed, which is the speed at which the two trains are moving relative to each other. Let's assume that the distance between Mumbai Central and Lucknow is 400 km. Train 'A' leaves Mumbai Central at 11 am and is moving at 40 kmph, so it covers a distance of 400 km in 40 hours (4

-6836229686698892993

Sure, I'd be happy to help! Based on the information provided in the question, John had Rs.60. Here's how we can calculate it: If John gives Mark one-third of his money, John will have Rs.60 / 3 = Rs.20 left. So, John had Rs.60 to start with. Therefore, the correct answer is (B) 60.

5148663947521329041

To determine the number of days it will take for the lake to be fully covered with water lilies if initially there were 64 water lilies on it, we can use the information provided in the question. According to the question, the number of water lilies on the lake doubles every two days. So, on the third day, there will be 2 x 64 = 128 water lilies on the lake. On the fourth

-4886704263799933406

Sure! I'm happy to help you with that. Based on the information provided in the question, we can set up the following equation: x men working x hours per day can do x units of work in x days We want to find out how much work can be completed by y men working y hours per day in y days, so we can substitute y for x in the equation: y men working y hours per day can do x units of work in x

-69301587464986750

Sure! Based on the information provided, there are 5 different quadrilaterals that can be formed by joining 4 of the points A, B, C, D, and E. Therefore, the answer is (C) 5.

-3064587914707759611

Sure! I can help you with that. Given that minor arc AC is 160° and minor arc BD is 150°, and that B bisects minor arc AC, we can use the angle sum property of a circle to find the measure of minor arc AD. The angle sum of a circle is 360°, so the measure of minor arc AD can be found by subtracting the measure of minor arc AC from 3

3626470368175586784

To find the percentage of employees who take a summer vacation but not a winter vacation, we need to find the percentage of employees who take a summer vacation and subtract the percentage who take a winter vacation. According to the question, 40% of employees take a winter and a summer vacation, so the percentage of employees who take a summer vacation is 40% - 75% = 35%. Therefore, the answer is

-7115073495435876258

To find the depth of the canal, we need to use the formula: Depth = Area of cross-section / Width of cross-section We are given that the area of the cross-section is 640 square meters and the width of the cross-section is 10 meters at the top and 6 meters at the bottom. So, we can plug these values into the formula: Depth = 640 / (10 +

-6315921258161594888

Sure! To solve this problem, we can use the information given in the question: The team won 20 matches and lost 30% of their matches. If the team won 20 matches, that means they played a total of 20 + 30 = 50 matches. So, the number of matches the team lost is 50 - 20 = 30 matches. Therefore, the answer is (B)

-7254288076974547752

To solve this problem, we need to use the formula: Distance = Revolutions x Angular Speed x Time Where: * Revolutions = 300 (since the fan runs at 300 revolutions per minute) * Angular Speed = 10 cm/revolution (since the point is 10 cm from the center of the fan) * Time = 30 seconds So, we can plug these values into the formula: Distance

-5980237710315779399

Sure! Based on the given instruction, I will choose the appropriate answer: Answer: (C) 25 < x < 64. Explanation: If n is such that 36 ≤ n ≤ 72, then we can substitute n into the given expression: x = (n2 + 2√n(n + 4) + 16) / (n+ 4√n+ 4)

-2198295925452125399

To solve this problem, we can use the information given in the question to find the length of the space shuttle. We know that the space shuttle can travel 700 meters high in 40 seconds, which means it can cover a distance of 700 meters in that time. We also know that it will take 5 seconds to pass a point, so the space shuttle can cover a distance of 5 meters in 5 seconds

7692850866486353324

To solve this problem, we need to use the information given in the question to find out when C joined the business. We know that A started the business with Rs.40,000, and after 2 months, B joined with Rs.60,000. So, the total amount of money in the business after 2 months is: Rs.40,000 + Rs.60,000 =

-7198484841123448942

To find the area of the remaining paper after cutting the semi circles, we need to use the formula for the area of a circle, which is: Area = πr^2 where r is the radius of the circle. Since the semi circles are drawn as diameters, the radius of each semi circle is half the length of the side of the square. So, the radius of each semi circle is 10 cm (since the side of the square is

6949000197382528226

To find the average speed for these two activities combined, we need to find a way to combine the distances traveled in the same time period. Since the athlete runs M miles in 4 hours and rides a bike N miles in the same number of hours, we can assume that the total time taken to complete both activities is 4 hours. Let's use the formula: Average speed = Total distance / Total time For running, the distance trave

-948809277059465811

Sure! Here's my response: The answer is (C) 95 men. Explanation: If 8 men work for 6 days to complete a task, that means they work for a total of 8 x 6 = 48 man-days. To complete the same task in half a day, we need half the number of men working for half the time, which is 48 / 2 = 24 man-

-3763108281722305744

Sure! Here's my response: The group has 64 boys and 40 girls, and during their membership drive, the same number of boys and girls joined the group. So, the total number of members in the group is: 64 + 40 = 104 If the ratio of boys to girls is 4:3, then the number of boys is 4 times the number of girls, which is: 4 x 4

-2716954804471443377

Sure! To determine how many minutes it will take to travel 48 miles, we can use the formula: Time = Distance / Speed In this case, the distance is 48 miles, and the speed is 12 miles per hour, so we can plug these values into the formula to get: Time = 48 miles / 12 miles/hour = 4 hours Therefore, the answer is (D) 60 minutes.

7511177352634923401

Sure! I can help you with that. Based on the information given in the question, we can set up a simple equation to solve for the distance between A and B: Distance = Speed x Time We know that Kevin drove at a constant speed of 70 mph for the entire trip, so the distance he traveled can be found by multiplying his speed by the time it took him to complete the trip: Distance = 70 mph x

-2178858451428191245

Sure! Here's my response: The correct answer is (A) 22.5. If 30 is subtracted from a number, it is reduced to one-third of its original value. So, if the original number is x, then x - 30 = 1/3x. Now, if we multiply both sides of the equation by 50%, we get: 50% of (1/3x) =

3604151555531487631

Sure! Let's solve this problem. If a man rows at the rate of 4 kmph in still water, that means he is covering a distance of 4 kmph. If his rate against the current is 2 kmph, then the current is flowing in the opposite direction at a speed of 2 kmph. So, the man's rate along the current is the difference between his rate in still water and his rate against the current:

-3352179452731394091

Sure! I can help you with that. Based on the information provided in the question, we can start by analyzing the digits of the number: The sum of the digits of a three-digit number is 17, which means that the digits are 1, 7, and x. The sum of the squares of its digits is 109, which means that the squares of the digits are 1, 7^2, and x^2.

1078080293461805041

To find the ratio of zinc and copper in alloy Z, we need to use the information given in the problem. Alloy X has a ratio of 6:9, so it contains 6 parts of zinc and 9 parts of copper. Alloy Y has a ratio of 7:11, so it contains 7 parts of zinc and 11 parts of copper. When 40 grams of alloy X

1479803504789306092

I cannot

3638693541178081832

Based on the information provided, we can set up the equation: Let x = one of the numbers x^2 - 256000 = 1000 x^2 = 1000 + 256000 x^2 = 257000 x = √257000 x = 640 Therefore, the answer is (C) 6

-4177823279413626875

To find the percentage difference in the astronaut's weight on Venus compared to Earth, we need to divide the weight on Venus by the weight on Earth and multiply by 100. So, the weight of the astronaut on Venus is 182 pounds, and the weight on Earth is 211 pounds. Divide 182 by 211 = 0.83 Multiply 0.83

-6817099798422131661

To find the average speed of the man, we need to find the total distance traveled and divide it by the total time taken. From the question, we know that the man walked at 5 kmph for 6 hours, which means he traveled a distance of 6 x 5 = 30 km. He also walked at 4 kmph for 12 hours, which means he traveled a distance of 12 x 4

8910759121932222392

To complete the calculation, we need to follow the order of operations (PEMDAS): 1. Parentheses: 17 x 15 = 255 2. Exponents (none in this case) 3. Multiplication: 272 - 32 = 240 4. Multiplication: 124 + 176 = 300 5. Division: 240 /

-2979237747361019837

Sure! Based on the information provided, we can calculate the total number of members in the family as follows: The total income of the family per month is $9000. The median income is $3000. To find the number of members in the family, we can divide the total income by the median income: $9000 ÷ $3000 = 3 So, there are 3 members in the family.

-1544750213348363826

Sure, I can help you with that! Based on the information provided in the question, the total bus fare of 4 adults and 3 children between Ranchi and Patna would be: 4 adults x Rs. 140 = Rs. 560 3 children x half the fare of one adult = Rs. 135 Therefore, the total bus fare would be: Rs. 560 + Rs

-1664608765157539983

To solve this problem, we need to use the information given in the question to find the number of employees in the organization. Let's break down the information: * The organization decided to raise Rs. 6 lakh by collecting equal contributions from each of its employees. * If each of them had contributed Rs. 60 extra, the contribution would have been Rs. 6.24 lakh. So, the total contribution from all

1160254543576702995

To solve this problem, we need to use the information given in the question to find the total number of eligible voters and then calculate the number of votes received by the winning candidate. Let's break down the information given in the question: * There are 5,000 voters. * 20% of the voters are not eligible to vote, which means 1000 voters are not eligible.

-1890717322244195621

To solve this problem, we need to use the information given in the question. The coin-diver gets 20 cents for each copper coin she brings from the bottom of the river. Since she got $3.40 after one dive, that means she brought a total of $3.40 / 0.20 = 17 copper coins. Therefore, the minimum number of copper coins the coin-diver

4583142849405744440

To solve this problem, we need to use the concept of relative speed, which is the speed at which the two objects are moving relative to each other. In this case, Ram is moving at a speed of 20m/s, and Krishna is moving at a speed of 40m/s, so their relative speed is 40m/s (40 - 20 = 20). Since they are traveling towards each other,

-2922348508278615099

To find the difference in the speed of the two cars, we need to divide the distance covered by each car by the time taken to cover that distance. For car 'X', the distance covered is 320 kms and the time taken is 8 hours, so the speed is: Speed of car 'X' = Distance / Time = 320 kms / 8 hours = 40 kms/hr For car 'Y', the

-986242293197168129

Sure! I can help you with that. Based on the information given in the question, we know that Winson runs from his home to his school at an average speed of 10 miles per hour, which means he covers a distance of 10 miles in one hour. Then, he walks home along the same route at an average speed of 5 miles per hour, which means he covers a distance of 5 miles in one hour. So, the

-323936630104036860

Sure! Here's my response: The store had 240 yellow golf balls to begin the day. Reasoning: If the store sold 80% of its inventory of golf balls, that means it sold 80% of 600 golf balls, which is 480 golf balls. Since the store sold an equal number of yellow and white golf balls, and it sold all of its white golf balls, the number of yellow

7533973032829411083

To solve this problem, we need to use the concept of similar triangles. The given information can be represented as: Flagstaff height = 17.5 m Shadow length = 40.25 m We can draw a triangle with the flagstaff as the hypotenuse and the shadow as the other two sides. The height of the building can be found by using the similar triangles concept. So, the height of the building =

-530007934653270527

To solve this problem, we need to use the concept of relative speed, which is the speed at which the two cars are moving relative to each other. The relative speed between the two cars is the difference between their speeds. So, the relative speed between the two cars is: Relative speed = 55 mph - 52 mph = 3 mph Now, we need to find the time it takes for the cars to travel a certain distance, which

5088989525140903612

Sure! Based on the information provided, we can use the concept of conditional probability to find the probability of event B occurring. The probability of at least one of events A or B occurring is 0.96, which means the probability of event A or event B occurring is 1 - 0.04 = 0.96. Since event A has a probability of 0.6, the probability of event A occurring is 0.

622729040743404333

Sure! The answer to the question is (C) 8:2. The volume of a cube is given by the formula V = s³, where s is the length of a side of the cube. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. Since the cube and sphere have different dimensions, we cannot

-155378305646641303

Sure! Based on the information provided, the answer is (B) 3. To ensure that you have at least two ties of the same color, you should take out 3 ties from the rack.

2609121894862919597

Sure! To complete the task, we need to multiply 25 by 12, which gives us 300. Then, we multiply 300 by 5, which gives us 1500. Therefore, the answer is (C) 3.3987.

-3895261036083998977

Sure! The value of log2 4 is (B) 4.

438372870517979925

To calculate the percentage gain, we need to use the following formula: Percentage gain = (Selling price - Purchasing price) / Purchasing price x 100 In this case, the purchasing price of oranges is Rs. 450, and the selling price is Rs. 7.50 per kg. So, the calculation is: Percentage gain = (7.50 - 450

1253121003599583369

To solve this problem, we need to find the time at which the two trains cross each other. Let's analyze the information given in the question: Train M leaves City A at 5 am and reaches City B at 9 am, so it takes 4 hours to cover the distance between the two cities. Train N leaves City B at 7 am and reaches City A at 10:30 am, so it takes 3 hours and

3160832498483779962

Sure! Here's my response: The answer is (B) 2 minutes. Janice bikes at 10 miles per hour, which means she can cover 1 mile in 60 minutes (10 miles / 10 miles per hour = 60 minutes). Jennie bikes at 20 miles per hour, which means she can cover 1 mile in 30 minutes (20 miles / 20 miles

7670216619059195089

To solve this problem, we can use the information given in the question to find the value of M. We know that the candidate secured 504 marks out of a maximum of M. If M is converted into 800 marks, the candidate would have secured 420 marks. So, we can set up the following equation: 504 = x/800 Where x is the value of M. Now, we can solve for

-3852915404393270608

Sure! Based on the information provided in the question, Jill will need to buy 12 bottles of soda for a party with 12 attendees. Therefore, the correct answer is (D) 12.

7815916283683080407

Sure! Here's my response: The length of the shadow that the taller ant casts is (B) 28 inches. Explanation: The shorter ant casts a shadow that is 10 inches long, and the taller ant is 6 inches taller than the shorter ant. Therefore, the length of the shadow cast by the taller ant is 10 + (6 - 4) = 28 inches.

-5832066706146541142

To find the height of the room, we need to use the given information: The height of the room to its semi-perimeter is 2:5. The semi-perimeter of a rectangle is 2(2L + 2w), where L is the length and w is the width. Given that the height of the room is 2:5 of the semi-perimeter, we can set up the equation: 2(2L +

6086738760399474395

Sure! I can help you with that. The sum of k consecutive integers is 51, and the least integer is -50. Therefore, we can set up the equation: 51 = -50 + k Simplifying the equation, we get: k = 51 - (-50) k = 101 So, the answer is (E) 102.

2323522015302520730

Sure! Based on the information provided in the question, we can determine that each student selected 2 songs from a list of 10 songs. If each song was selected 5 times, then the total number of songs selected by each student is 2 x 5 = 10. Since there are 10 songs in the list, and each student selected 10 songs, the total number of songs selected by all the students is 10 x 10

-85827389713209714

Sure! To find the value of m, we can use the fact that one of the roots of the quadratic equation x^2 + mx + 22 = 0 is 1.5. So, we can set x = 1.5 in the equation and solve for m: x^2 + mx + 22 = 0 x^2 + 1.5x + 22 = 0 Subtracting

1960331779410478398

To determine the number of ways the meeting can be held, we need to consider the order in which the speakers address the meeting. Since the PM should speak before the MP and the MP should speak before the MLA, we can create a pattern of speaker order as follows: PM, MP, MLA, PM, MP, MLA, PM, MP, MLA, PM There are 3 speakers in total, so the number of ways the meeting can be

7453171395219546985

Sure! Here's my response: The new selling price of each article after the price decrease is: (C)$13.6 Explanation: If the price of each article decreased by 15%, that means the new price is 85% of the original price. So, if the original price of each article was $100, the new price would be: $100 x 0.85 =

-8057256313981192884

Sure, I can help you with that! Based on the information provided in the question, if Radha is shifted to the left by 2 places and Neha is shifted to the right by 2 places, then the positions of the children in the row would be: Radha - 6 places to the left of Neha Neha - 6 places to the right of Radha So, there are 6 children between Radha and Neha. Therefore

2672862836755691061

To make the mixture contain equal quantities of clay and sand, we need to remove a portion of the mixture and replace it with an equal amount of pure sand. Let's use the given information to solve the problem: The mixture contains 10 kg of the mixture, which contains 30% sand and 70% clay. So, the amount of sand in the mixture is: 30% of 10 kg = 3 kg of

3664201895401806074

Sure! Here's the answer: The correct answer is (B) 62.5%. If the man's income increases by 20%, then his new income will be: New income = Old income x 1.20 = $100 x 1.20 = $120 If he spends 70% of his income, then his new expenditure will be: New expenditure = $

-8536656803321339323

Sure! I can help you with that. The greatest number of identical bouquets that can be made out of 28 white and 98 red tulips is (C) 10. To see why, let's use the given information: * No flowers are to be left out, so we need to use all 28 white tulips and all 98 red tulips. * Since there are 28 white

-4810617221419906261

Sure! Here's my response: The answer is (B) 2 hours. Sharon works for 5 hours to earn enough tips to buy an ice cream cake, while Karen works for 4 hours. Together, they will be able to buy the cake in 2 hours.

-3913970163436076213

Sure! Based on the given information, we can conclude that: (B) y^2 > x^2 Explanation: If x < 0, then x^3 will be negative, and |x^3| > |y^2| implies that y^2 is positive. Therefore, y^2 > x^2. So, the correct answer is (B) y^2 > x^2.

1615659428744226812

Sure! Here's my response: The answer is (C) 100 seconds. If Printer A and Printer B can each print 1/2 page per second, then together they can print 100 pages in 100 seconds.

2276968114848907981

To solve this problem, we need to use the concept of relative speed, which is the speed at which the ants are moving relative to each other. The relative speed between ant A and ant B is the difference between their speeds: Relative speed = Ant B's speed - Ant A's speed = 6 cm/h - 9 cm/h = -3 cm/h Now, we need to find the time it takes for ant A to travel

7648093177495370648

Sure! Based on the information provided in the question, the answer is (C) $35.62. The instruction states that the recorded property worth is written as the greatest positive even integer less than or equal to the actual property worth, which is $1023.65, and is divisible by 100. So, the recorded property worth can be calculated as follows: Recorded property worth = Greatest positive even integer less than or

1744646654789320420

Sure! Based on the information provided in the question, the maximum number of trousers that the man can purchase is 8. Therefore, the correct answer is (B) 8 Trousers.

3211213535018849055

To find the cover price per issue, we need to use the information given in the question: The subscription for 15 issues costs $42.00, which means the total cost of 15 issues is: $42.00 / 15 = $2.80 per issue So, the cover price per issue is: $2.80 / 25% = $11.20 Therefore, the

2335782893339359509

Sure! Based on the information provided in the question, we can see that Christopher and Jonathan made a bet where they flipped a coin 20 times, and each time the coin landed on heads, Christopher gave $2 to Jonathan, and each time it landed on tails, Jonathan gave $3 to Christopher. Since none of them won or lost any amount after flipping the coin 20 times, we can conclude that the number of times the coin landed

6447495332102760417

To solve this problem, we need to use the concept of relative speed, which is the speed at which two objects move relative to each other. In this case, Allen and Bob are moving towards each other, so their relative speed is the difference between their speeds. Allen travels at 54 kmph, so Bob's speed is 78 kmph - 54 kmph = 24 kmph. Now, Bob covers 48 km

-1187453496441387700

To find the percentage difference between the cost of new tires and the cost of repairing the current tires, we need to calculate the total cost of new tires over the four-year period and compare it to the total cost of repairing the current tires over the same period. The total cost of new tires over four years is: $180 x 4 = $720 The total cost of repairing the current tires over one year

7191609467562032992

Sure! Here's my response: The longer piece of rope is 8.9 meters long. Reasoning: If the rope was 20 meters long and it was cut into two pieces, then the length of the longer piece of rope must be 20 - 3 = 17 meters. Since the length of the other piece of rope is 3 meters shorter than the longer piece, the length of the other piece is

8435617028773781722

To determine the amount of interest that has accrued on a bond, we need to use the formula: Interest = Principal x Rate x Time / 2. In this case, the principal is $5,000, the interest rate is 12% compounded every 6 months, and the time is 1 year. So, the interest accrued can be calculated as follows: Interest = $5,000 x

3470883574783153905

Sure! Based on the multiplication table provided, the answer is: (B) 9 2 0 9

6480115993834510730

Sure, I'd be happy to help! Based on the information provided in the question, we can set up the following equation: Sachin's age = Ajay's age + 10 Since Sachin will be 40 years old in 10 years, we can substitute this value for Sachin's age in the equation: 40 = Ajay's age + 10 Now, we can solve for A

-6618769396273538803

Sure! Based on the information provided in the question, the cost of gardening a 1-meter broad boundary around a rectangular plot having a perimeter of 340 meters at the rate of 10 per square meter can be calculated as follows: Perimeter of the plot = 340 meters Area of the plot = Perimeter x Width (in meters) = 340 x 1 = 340 meters square Since the boundary

7952804800579956467

To complete the task, we need to use the information provided in the question to find the ratio of Ace Book Company's revenue from novels to revenue from biographies. Last year, 34 percent of Ace Book Company's sales revenue came from the sale of novels, which means that the company's revenue from novels was 34/100 = 0.34 times its total revenue. The

-8460796476583063403

Sure! To determine how many flowers the bee will fly by to bypass 8 flowers, we need to use the information provided in the question. The bee bypasses 0.05% of flowers it flies by, so we can use this percentage to calculate the number of flowers the bee will fly by. 0.05% of 8 flowers is equal to 0.004 (or 4/100) flowers.

-5970486219927710867

The answer is (C) 5C2*4C4. Explanation: Fernando has a total of 3 lunches and 3 dinners per week, and the cafeteria is closed on weekends. This means that he has 3 lunches and 3 dinners available to him during the week, and he always goes home for dinner on Friday nights. To determine the number of options Fernando has to allocate his me

6194580696626501291

Sure! Here's the answer to the question: The correct answer is (B) (a - b)2. Explanation: The given expression is (?) = (a - b)2. To find the value of the question mark, we need to determine what value can replace the question mark and make the expression true. In this case, we can replace the question mark with the value of (a - b), which gives us (a - b

7871187199457201950

Sure! Based on the information provided in the question, the number is: (B) 56 Explanation: The question states that the number is as much greater than 36 as it is less than 86. This means that if the number is greater than 36, it must be less than 86. Therefore, the number can be any number between 36 and 86, inclusive. The options provided are

-8647513384128283468

Sure! Based on the information provided in the question, we can calculate the total number of phones shipped as follows: A crate consists of p pallets, and each pallet holds 1250 phones. Therefore, the total number of phones in a crate is: 1250 phones/pallet x p pallets = 1250p phones/crate Since there are 4 crates, the total

8223393106179944422

Sure! Here's my response: The answer is (C) 23 minutes. If A can construct a wall in 40 minutes and B can construct the wall in 45 minutes, then together they can construct the wall in 40 + 45 = 85 minutes.

1062925796420029368

To find the time it takes for the train to pass through the tunnel, we need to use the information given in the question. The train takes exactly 3 seconds to enter the tunnel, which is 1 mile long. Therefore, to pass through the entire tunnel, the train will take: Time = Distance / Speed Time = 1 mile / 120 mph Time = 0.0083 seconds So, the answer is (

4967479118560321360

To determine the highest simple interest rate at which the merchant can afford to borrow money to take advantage of the discount, we need to use the following formula: Simple Interest = (Discount Amount / Number of Payments) x Interest Rate In this case, the discount amount is $20,000, and the number of payments is 30. So, the formula becomes: Simple Interest = ($20,000 /

2519911218019973544

Sure! Here's my response: The answer is (B) 105. There are 10 lime soda bottles in total, and there are two groups of customers to divide them among. Each group can have 5 members, so there are 5! = 105 different ways to create these 2 groups.

4658929321955789535

Sure! Based on the information provided in the question, we can set up a ratio of rice:wheat:corn as 2:3:5. If the bag of mixture contains 3 pounds of rice, we can find the weight of corn by using the ratio: Corn = Total weight of mixture - Weight of rice = 3 pounds - 2 pounds = 1 pound So, the answer is (B) 7.

3233084225959124299

Sure! Here's my response: The cost in cents of six sodas and seven bars is: (A) 500 cents Explanation: If the cost of one soda is 150 cents and the cost of one energy bar is 100 cents, then the cost of six sodas is 6 x 150 = 900 cents. The cost of seven bars is

7449188851327094984

To find the manufactured cost of each pen, we need to subtract the estimated percentage of defective pens from the total number of pens produced. According to the question, the company produces 7200 pens and estimates that 10% of them are defective, which means 720 defective pens. So, the total number of good pens = 7200 - 720 = 6480 pens. Now,

6788842907785346376

Sure! I can help you with that. The instruction given is: "A two digit number exceeds the sum of the digits of that number by 18. If the digit at the unit's place is double the digit in the ten's place, what is the number?" Let's analyze the information given in the question: * The number is two digits long. * The sum of the digits of the number is greater than 18.

-1649393683041026280

Sure! Let's analyze the given instruction and choose the appropriate answer. Question: Suppose for any real number x, [x] denotes the greatest integer less than or equal to x. Let L(x,y) = [x] + [y] + [x + y] and R(x,y) = [2x] + [2y]. Then it is impossible to find any two positive real numbers x and y for which The given instruction describes a

5486735822553236898

Sure! Here's my response: The bells will ring together again after 18 minutes. Explanation: The bells ring at intervals of 36 seconds, 40 seconds, and 48 seconds, respectively. To find when they will ring together again, we need to find the least common multiple (LCM) of 36, 40, and 48. The LCM of 36,

5888123034162446817

Sure! Here's my response: The height of the tree that casts a shadow of 15 meters under similar conditions is (B) 22 meters. Explanation: The instruction states that an electric pole, which is 14 meters high, casts a shadow of 10 meters. To find the height of the tree that casts a shadow of 15 meters, we can use the same ratio as the one used to find the

3199508519116125353

Sure! Based on the information provided, we can see that the cost of each fruit is directly proportional to its weight. Therefore, if we know the cost of an orange, a pineapple, and a grape, we can use the same logic to determine the cost of a mango. Using the information given in the question, we can calculate the cost of a mango as follows: Mango weight = Orange weight + Pineapple weight + Grape weight M

-466848129897936670

Sure! I can help you with that. The question is asking for the area of a triangle in the coordinate plane, given its vertices at (a,0), (b,0), and (x,y). To find the area of the triangle, we can use the formula: Area = (base × height) / 2 In this case, the base of the triangle is x, and the height is y. So, the area of the triangle is: Area

-1095675660231944446

To solve this problem, we need to use the formula: Speed = Distance / Time We are given that the car finishes a journey of 20 hours at a speed of 60 km/hr, so we can use this as the initial value: Speed = 60 km/hr Now, we want to find the speed at which the car will cover the same distance in 10 hours, so we can use the formula: New Speed

4301167494703028144

To find the probability that the question is answered correctly, but not via cheating, we need to find the probability of Alan's guess, Roger's cheating, and Peter's calculation, and then subtract the probability of cheating. The probability of Alan's guess is 1/5, as he randomly guesses the answer. The probability of Roger's cheating is 2/3, as he looks at the paper of the student in front of