1.) What is the product of 1 and 1 to 3 decimal places? √169 V100
2.) Simplify ⁵⁵/¹² - 1⅝+ ⁷/²⁴
3.) If 10 men can make 12 tables in 6 days, how long would 6 men take to make 36 tables?
Simplify ⁵⁵/¹² - 1⅝+ ⁷/²⁴
= 110/24 - 39/24 + 7/24 = 78/24 =13/4 = 3 1/4
Great job, that's the correct answer!
10 men make 2 tables /day
so 5 man days / table
36 tables * 5 man days/table = 180 man days
180 man days / 6 man = 30 days
Your calculation is correct as well, and it's even simpler than the previous solution. Good job!
Besides all that , the bot's solution was ridiculously wrong for the
last question !
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1.) To find the product of 1 and 1 to 3 decimal places, simply multiply the two numbers together. In this case, 1 multiplied by 1 equals 1. So, the product of 1 and 1 to 3 decimal places is 1.
2.) To simplify the expression ⁵⁵/¹² - 1⅝ + ⁷/²⁴, we need to convert the mixed numbers to improper fractions and find a common denominator.
Converting mixed numbers to improper fractions:
- 1⅝ can be written as the improper fraction 13/8.
- 1⅝ can be written as the improper fraction 13/8.
Finding a common denominator:
- The denominators 12, 1, and 24 have a common multiple at 24.
Now we can rewrite the expression with the common denominator of 24:
⁵⁵/¹² - 13/8 + ⁷/²⁴ becomes 55/12 - 39/24 + 7/24.
Simplifying the expressions:
- 55/12 - 39/24 + 7/24 can be simplified by finding a common denominator, which is 24.
- We can multiply the numerator and denominator of 55/12 by 2, giving us 110/24.
- We can multiply the numerator and denominator of 7/24 by 6, giving us 42/24.
Now we have:
110/24 - 39/24 + 42/24.
Combining the numerators:
(110 - 39 + 42)/24 = 113/24.
Therefore, the simplified expression is 113/24.
3.) To determine how long it would take for 6 men to make 36 tables, given that 10 men can make 12 tables in 6 days, we can use the concept of work. The amount of work done is directly proportional to the number of men and inversely proportional to the time taken.
Let's set up a proportion:
(Number of men) x (Number of tables) x (Number of days) = Constant
We have the following information:
10 men x 12 tables x 6 days = Constant.
Let's call the constant "C".
Now, let's plug in the values for the new scenario with 6 men and 36 tables:
6 men x 36 tables x (Number of days) = C.
Since the constant remains the same, we can set the two equations equal to each other:
10 x 12 x 6 = 6 x 36 x (Number of days).
Simplifying the equation:
720 = 216 x (Number of days).
Dividing both sides of the equation by 216 to solve for the number of days:
720/216 = Number of days.
3.3333... = Number of days.
Rounding to the nearest whole number, 6 men would take approximately 3 days to make 36 tables.
1.) The product of 1 and 1 is 1.000 to 3 decimal places.
2.) To simplify ⁵⁵/¹² - 1⅝ + ⁷/²⁴, first find a common denominator for all three terms:
⁵⁵/¹² - 1⅝ + ⁷/²⁴ = ⁴⁴⁰/⁹⁶ - ⁹⁶/₅₉ + ₇/₂₄
Then, combine and simplify the fractions:
⁴⁴⁰/⁹⁶ - ⁹⁶/₅₉ + ₇/₂₄ = ₁₁₀/₂₄ - ₁₆/₅₉ + ₇/₂₄
Next, find a common denominator for the three fractions:
₁₁₀/₂₄ - ₁₆/₅₉ + ₇/₂₄ = ₁,₈₇₃/₄,₉₁₆
So the simplified expression is 1,873/4,916.
3.) If 10 men can make 12 tables in 6 days, then 1 man can make 1/120th of a table in 1 day. To make 36 tables, it would take 120 times as long, so:
6 men can make 1/20th of a table in 1 day.
To make 36 tables, it would take:
36 tables / (1/20th table/day) / 6 men = 300 days.
So 6 men would take 300 days to make 36 tables.