💡First, I need to determine how many weeks and extra days are in 53 days. Since there are 7 days in a week, I'll divide 53 by 7.53 divided by 7 equals 7 weeks with a remainder of 4 days. This means that 53 days from Friday is the same as 4 days after Friday.Next, I'll count 4 days forward from Friday:- Friday + 1 day = Saturday- Saturday + 1 day = Sunday- Sunday + 1 day = Monday- Monday + 1 day = TuesdayTherefore, 53 days from Friday will be a Tuesday.

💡First, I need to express the number 0.02008 in scientific notation while keeping three significant figures.To do this, I'll start by identifying the significant figures in the number. The significant figures are 2, 0, and 0, with the trailing 8 being the fourth significant figure.Next, I'll round the number to three significant figures. Since the fourth figure is 8, which is greater than or equal to 5, I'll round up the third figure from 0 to 1.Now, I'll adjust the decimal point to convert the number into scientific notation. Moving the decimal point two places to the right gives me 2.01, and to balance this, I'll multiply by 10 raised to the power of -2.Finally, the number 0.02008 expressed in scientific notation with three significant figures is 2.01 × 10⁻².

💡First, I need to determine the current ages of both the grandfather and the grandson based on the information provided.I know that the grandfather's age this year is six times the age of his grandson. Let's denote the grandson's current age as ( G ). Therefore, the grandfather's current age can be represented as ( 6G ).Next, the problem states that after four years, the sum of their ages will be 78. This means that in four years, the grandson will be ( G + 4 ) years old, and the grandfather will be ( 6G + 4 ) years old.To find the current age of the grandson, I can set up an equation based on the information given:[(G + 4) + (6G + 4) = 78]Combining like terms, the equation becomes:[7G + 8 = 78]Subtracting 8 from both sides of the equation:[7G = 70]Finally, dividing both sides by 7:[G = 10]Therefore, the grandson is currently 10 years old.

💡First, calculate Jimmy's total earnings from shoveling snow by multiplying the rate per driveway by the number of driveways shoveled.Next, determine the amount Jimmy spent at the candy store by finding one-sixth of his total earnings.Then, calculate the total cost of the candy bars by multiplying the number of candy bars by the cost per candy bar.Subtract the cost of the candy bars from the total amount spent at the candy store to find the amount spent on lollipops.Finally, divide the amount spent on lollipops by the number of lollipops to find the cost per lollipop.

💡Okay, so I need to find the smallest positive whole number that's divisible by five different prime numbers. Hmm, let's see. I remember that prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves. The smallest prime numbers are 2, 3, 5, 7, 11, and so on.If I want a number that's divisible by five different primes, I guess I need to multiply these primes together. That way, the resulting number will have all of them as factors. But wait, is that the smallest possible number? Maybe there's a way to get a smaller number by using exponents or something? No, I think since we're looking for divisibility by five different primes, we just need to multiply the five smallest primes together.Let me list out the first five primes: 2, 3, 5, 7, and 11. If I multiply these together, I should get the smallest number that's divisible by all of them. So, let's do that step by step.First, multiply 2 and 3: 2 * 3 = 6.Next, multiply that result by 5: 6 * 5 = 30.Then, multiply by 7: 30 * 7 = 210.Finally, multiply by 11: 210 * 11 = 2310.So, 2310 is the product of the first five primes. Is there any smaller number that's divisible by five different primes? I don't think so because if I use any smaller primes, I've already included the smallest ones. If I try to use a larger prime instead of one of these, the product would only get bigger.Wait, what if I use exponents on some primes? For example, could I have a number like 2^2 * 3 * 5 * 7? That would be 4 * 3 * 5 * 7 = 420. But that's only four different primes, right? Because 2 is squared, but it's still just one prime. So, that doesn't count as five different primes.Okay, so exponents don't help in this case because they don't add new prime factors. I need five distinct primes, each appearing at least once in the factorization. So, multiplying the first five primes together seems to be the way to go.Let me double-check by listing the factors of 2310. The prime factors are 2, 3, 5, 7, and 11. Any smaller number would have to exclude at least one of these primes or use a larger prime, which would make the overall product larger. So, 2310 is indeed the smallest number divisible by five different primes.I think that's it. 2310 is the smallest positive whole number that's divisible by five different prime numbers.

💡First, I recognize that the expression involves multiple nested radicals: a square root, a cube root, and another square root. To simplify this, I'll start by simplifying the innermost radical.I notice that 4096 is a power of 4, specifically (4^6). This makes it easier to work with exponents.Next, I'll simplify the innermost square root: (sqrt{frac{1}{4096}}). Since (4096 = 4^6), this becomes (sqrt{frac{1}{4^6}}).Simplifying the square root, I get (frac{1}{4^3}).Then, I'll take the cube root of (frac{1}{4^3}), which simplifies to (frac{1}{4}).Finally, I'll take the square root of (frac{1}{4}), resulting in (frac{1}{2}).Thus, the simplified form of the original expression is (boxed{frac{1}{2}}).