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Gennadij [26K]
3 years ago
6

To solve work problems, find the portion of the job each person completes in 1 unit of time. The sum of these portions is the po

rtion of the job completed in 1 unit of time. You can mop a floor in 8 minutes. Your friend can mop the same floor in 12 minutes. Working together, how much time does it take to mop the floor?
Mathematics
1 answer:
Gwar [14]3 years ago
6 0

Answer:

  4.8 minutes

Step-by-step explanation:

Using the given hint, working together, the amount of floor mopped in 1 minute is ...

  1/8 + 1/12 = 3/24 +2/24 = 5/24 . . . . jobs/minute

The reciprocal of that is the rate in terms of minutes per job. Thus the entire job takes 24/5 = 4.8 minutes.

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3 times a number decreased by 40 equals 14
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Question 2b only! Evaluate using the definition of the definite integral(that means using the limit of a Riemann sum
lara [203]

Answer:

Hello,

Step-by-step explanation:

We divide the interval [a b] in n equal parts.

\Delta x=\dfrac{b-a}{n} \\\\x_i=a+\Delta x *i \ for\ i=1\ to\ n\\\\y_i=x_i^2=(a+\Delta x *i)^2=a^2+(\Delta x *i)^2+2*a*\Delta x *i\\\\\\Area\ of\ i^{th} \ rectangle=R(x_i)=\Delta x * y_i\\

\displaystyle \sum_{i=1}^{n} R(x_i)=\dfrac{b-a}{n}*\sum_{i=1}^{n}\  (a^2 +(\dfrac{b-a}{n})^2*i^2+2*a*\dfrac{b-a}{n}*i)\\

=(b-a)^2*a^2+(\dfrac{b-a}{n})^3*\dfrac{n(n+1)(2n+1)}{6} +2*a*(\dfrac{b-a}{n})^2*\dfrac{n (n+1)} {2} \\\\\displaystyle \int\limits^a_b {x^2} \, dx = \lim_{n \to \infty} \sum_{i=1}^{n} R(x_i)\\\\=(b-a)*a^2+\dfrac{(b-a)^3 }{3} +a(b-a)^2\\\\=a^2b-a^3+\dfrac{1}{3} (b^3-3ab^2+3a^2b-a^3)+a^3+ab^2-2a^2b\\\\=\dfrac{b^3}{3}-ab^2+ab^2+a^2b+a^2b-2a^2b-\dfrac{a^3}{3}  \\\\\\\boxed{\int\limits^a_b {x^2} \, dx =\dfrac{b^3}{3} -\dfrac{a^3}{3}}\\

4 0
2 years ago
70 is 25% of what number
Rina8888 [55]
I hope this helps you



70=?.25%


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3 0
3 years ago
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erastova [34]

Answer:

1. Substitution/Elimination 2. Solve For The Variable 3. Distributive Property 4. Isolate the Variable 5. Combine Like Terms

Step-by-step explanation:

youre welcome

4 0
2 years ago
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Ahat [919]

Answer:

Step-by-step explanation:

I believe the word phrase would look like this:

2 times the sum of 18 and t.

5 0
2 years ago
Read 2 more answers
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