💡First, I'll assign a variable to Rona's age. Let's say Rona's age is ( R ) years.According to the problem, Rachel is twice as old as Rona. So, Rachel's age is ( 2R ).Collete's age is half of Rona's age, which means Collete is ( frac{R}{2} ) years old.The problem states that the difference between Rachel's age and Collete's age is 12 years. This gives me the equation:[2R - frac{R}{2} = 12]To solve for ( R ), I'll first eliminate the fraction by multiplying the entire equation by 2:[4R - R = 24][3R = 24][R = 8]So, Rona is 8 years old.

💡To convert (85_{10}) to base four, I need to determine how many times each power of 4 fits into 85 and find the corresponding coefficients.First, I identify the largest power of 4 less than 85, which is (4^3 = 64). I calculate the coefficient for (4^3) by dividing 85 by 64, resulting in 1. Subtracting (1 times 64) from 85 leaves a remainder of 21.Next, I consider (4^2 = 16). Dividing the remainder 21 by 16 gives a coefficient of 1. Subtracting (1 times 16) from 21 leaves a remainder of 5.Then, I look at (4^1 = 4). Dividing the remainder 5 by 4 gives a coefficient of 1. Subtracting (1 times 4) from 5 leaves a remainder of 1.Finally, I consider (4^0 = 1). Dividing the remainder 1 by 1 gives a coefficient of 1. Subtracting (1 times 1) from 1 leaves no remainder.Combining all the coefficients, I find that the base four equivalent of (85_{10}) is (1111_4).

💡Okay, so I need to figure out how many days Jaylen can feed her dog with a 32-cup bag of dog food. Let me start by understanding the problem step by step.First, the dog eats 1 cup in the morning and 1 cup in the evening. So, that's 1 + 1 cups per day. That means the dog consumes 2 cups of dog food each day.Now, Jaylen has a bag that has 32 cups of dog food. To find out how many days this will last, I need to divide the total amount of dog food by the daily consumption. So, 32 cups divided by 2 cups per day.Let me write that down: 32 ÷ 2 = ?Hmm, 32 divided by 2 is 16. So, that means the bag will last for 16 days.Wait, let me double-check to make sure I didn't make a mistake. If the dog eats 2 cups each day, then over 16 days, it would consume 16 × 2 = 32 cups. Yep, that matches the total amount in the bag. So, it looks like my calculation is correct.I think that's all there is to it. The bag will last for 16 days.

💡Okay, so Tommy ordered a bunch of fruits, and I need to figure out two things: the percentage of each fruit in his total order and the total cost for all the fruits. Let me break this down step by step.First, the total weight of all the fruits Tommy ordered is 20 kilograms. That's good to know because percentages will be calculated based on this total. Now, let's list out the quantities and prices for each fruit:- Apples: 4 kg at 2 per kg- Oranges: 2 kg at 3 per kg- Grapes: 4 kg at 2.5 per kg- Strawberries: 3 kg at 4 per kg- Bananas: 1 kg at 1.5 per kg- Pineapples: 3 kg at 3.5 per kgAlright, so for the percentages, I need to find out what portion each fruit's weight is of the total 20 kg. To do that, I'll divide the weight of each fruit by the total weight and then multiply by 100 to get the percentage.Starting with apples: 4 kg divided by 20 kg is 0.2, and multiplying by 100 gives 20%. So, apples make up 20% of the total order.Next, oranges: 2 kg divided by 20 kg is 0.1, which is 10%. So, oranges are 10% of the order.Grapes are also 4 kg, so just like apples, that's 20%.Strawberries are 3 kg, so 3 divided by 20 is 0.15, which is 15%.Bananas are only 1 kg, so 1 divided by 20 is 0.05, or 5%.Lastly, pineapples are 3 kg, same as strawberries, so that's also 15%.Let me double-check that all these percentages add up to 100%. 20% (apples) + 10% (oranges) + 20% (grapes) + 15% (strawberries) + 5% (bananas) + 15% (pineapples) equals 85%. Wait, that's not 100%. Did I make a mistake somewhere?Oh no, I think I missed something. Let me recount the weights:Apples: 4 kgOranges: 2 kgGrapes: 4 kgStrawberries: 3 kgBananas: 1 kgPineapples: 3 kgAdding those up: 4 + 2 + 4 + 3 + 1 + 3 equals 17 kg. But the total was supposed to be 20 kg. Hmm, there's a discrepancy here. Maybe I misread the quantities.Wait, let me check again:Apples: 4 kgOranges: 2 kgGrapes: 4 kgStrawberries: 3 kgBananas: 1 kgPineapples: 3 kg4 + 2 is 6, plus 4 is 10, plus 3 is 13, plus 1 is 14, plus 3 is 17 kg. So, it's only 17 kg, but the total was supposed to be 20 kg. Did Tommy order more fruits that weren't listed? Or maybe there's a typo in the quantities?Assuming that the total is indeed 20 kg, and the given quantities add up to 17 kg, there might be an error in the problem statement. Alternatively, perhaps I misread the quantities. Let me check once more.Apples: 4 kgOranges: 2 kgGrapes: 4 kgStrawberries: 3 kgBananas: 1 kgPineapples: 3 kgYes, that's 17 kg. So, unless there's an additional fruit or a correction in the quantities, the percentages will be based on 17 kg instead of 20 kg. But the problem states that the total is 20 kg, so I need to reconcile this.Perhaps the quantities are correct, and the total is 20 kg, meaning there might be an error in the given quantities. Alternatively, maybe I need to adjust the percentages accordingly.Assuming the given quantities are correct and the total is 20 kg, then the percentages would be based on 20 kg, even though the sum of the given quantities is 17 kg. This might mean that there's an error in the problem, or perhaps some fruits are missing from the list.For the sake of solving the problem, I'll proceed with the given quantities and calculate the percentages based on the total of 20 kg, even though the sum of the given weights is less than that. Alternatively, I can calculate the percentages based on the actual total of 17 kg.But since the problem states that the total is 20 kg, I'll proceed with that, keeping in mind that there might be an inconsistency.Now, moving on to the total cost. For each fruit, I'll multiply the quantity by the price per kilogram and then sum up all the costs.Starting with apples: 4 kg at 2/kg is 4 * 2 = 8.Oranges: 2 kg at 3/kg is 2 * 3 = 6.Grapes: 4 kg at 2.5/kg is 4 * 2.5 = 10.Strawberries: 3 kg at 4/kg is 3 * 4 = 12.Bananas: 1 kg at 1.5/kg is 1 * 1.5 = 1.5.Pineapples: 3 kg at 3.5/kg is 3 * 3.5 = 10.5.Now, adding up all these costs: 8 + 6 + 10 + 12 + 1.5 + 10.5.Let's do this step by step:8 + 6 = 1414 + 10 = 2424 + 12 = 3636 + 1.5 = 37.537.5 + 10.5 = 48So, the total cost is 48.But wait, earlier I noticed that the total weight doesn't add up to 20 kg. If the total weight is supposed to be 20 kg, but the sum of the given quantities is 17 kg, then either there's an error in the quantities or in the total weight. For the purpose of this problem, I'll proceed with the given quantities and the calculated total cost of 48.In summary, the percentages of each fruit based on the given quantities (assuming the total is 20 kg) are:- Apples: 20%- Oranges: 10%- Grapes: 20%- Strawberries: 15%- Bananas: 5%- Pineapples: 15%And the total cost for all the fruits is 48.

💡Alright, so I need to find the molecular weight of 6 moles of calcium hydride. Hmm, calcium hydride is CaH2, right? Okay, so first, I think I need to figure out the molecular weight of one mole of calcium hydride, and then multiply that by 6 to get the total weight for 6 moles.Let me start by recalling the atomic weights of calcium and hydrogen. I remember that calcium has an atomic weight of about 40.08 g/mol, and hydrogen is approximately 1.008 g/mol. So, for calcium hydride, which is CaH2, I need to add the atomic weight of calcium to twice the atomic weight of hydrogen because there are two hydrogen atoms in each molecule.So, the molecular weight of CaH2 would be 40.08 g/mol (for calcium) plus 2 times 1.008 g/mol (for hydrogen). Let me do that calculation: 40.08 plus 2 times 1.008. That would be 40.08 plus 2.016, which equals 42.096 g/mol. Okay, so the molecular weight of calcium hydride is 42.096 grams per mole.Now, I need to find the weight of 6 moles of calcium hydride. To do that, I'll multiply the molecular weight by the number of moles. So, 6 moles times 42.096 g/mol. Let me calculate that: 6 times 42.096. Hmm, 6 times 40 is 240, and 6 times 2.096 is 12.576. Adding those together, 240 plus 12.576 equals 252.576 grams.Wait, does that make sense? Let me double-check my calculations. The molecular weight of CaH2 is indeed 42.096 g/mol, and multiplying that by 6 gives 252.576 grams. Yeah, that seems right. I think I've got it.

💡First, I need to determine how much I spent on lunch. Let's denote this amount as ( x ) dollars.According to the problem, my friend spent 5 more than me, so my friend's spending can be represented as ( x + 5 ) dollars.The total amount spent by both of us is 22. Therefore, I can set up the equation:[x + (x + 5) = 22]Combining like terms, the equation simplifies to:[2x + 5 = 22]Next, I'll isolate the variable ( x ) by subtracting 5 from both sides:[2x = 17]Then, I'll solve for ( x ) by dividing both sides by 2:[x = 8.5]So, I spent 8.50 on my lunch. To find out how much my friend spent, I'll add 5 to my amount:[text{Friend's lunch} = 8.5 + 5 = 13.5]Therefore, my friend spent 13.50 on their lunch.