Working together, two secretaries can stuff the envelopes for a political fund-raising letter in 4 hours. Working alone, it takes the slower worker 6 hours longer to do the job than the faster worker. How long does it take each to do the job alone
Answers
Answer: The faster one needs 6 hours, the slower one needs 12 hours.
Step-by-step explanation:
Let's define Sa and Sb as the times that each worker needs to stuff the envelopes for a political fundraising letter.
Sa is the faster one
Sb is the slower one.
Let's define 1 as a complete task.
Then:
when they both work together, they need 4 hours:
(1/Sa + 1/Sb)*4h = 1.
The slower one needs 6 more hours than the faster one:
Sb = (Sa + 6h).
We can replace this in the first equation and get:
(1/Sa + 1/(Sa + 6h))*4h = 1.
let's solve this for Sa.
1/Sa + 1/(Sa + 6h) = 1/4h.
(Sa + 6h) + Sa = Sa*(Sa + 6h)/4h.
2*Sa + 6h = Sa^2/4h + Sa*(6/4)
Then we have a quadratic equation:
(1/4h)*Sa^2 - (2/4)*Sa - 6h = 0h
(0.25*1/h)*Sa^2 - 0.5*Sa - 6h = 0h
The solutions come from the Bhaskara equation:
Then we have two solutions:
Sa = ((0.5 + 2.5)/0.5 )h = 6h.
Sb = ( (0.5 - 2.5)/0.5) = -4h
The one that makes sense is the positive option (the negative one has no physical meaning in this situation)
Then the faster worker needs 6 hours to stuff all the envelopes.
And the slower one needs 6h + 6h = 12hours to stuff all the envelopes.
So when they work together, the combined rate is:
(1/6h + 1/12h) = (2/12h + 1/12h) = (3/12h) = (1/4h)
So working together they need 4 hours to stuff all the envelopes.
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Emily sold 2 small boxes of grapefruits and 3 large boxes of grape fruit for a total $61 chelsea sold 3 small boxes of grapefruit and 3 large boxes of grapefruit for a total of $72 what is the cost of one small box of grape fruit and one large box of grapefruit
Answers
Answer:
$54
Step-by-step explanation:
[3,000 / 100] x 6 = 180 - Liters of gas will be used on a 3,000 Km trip.
180 x 1.20 = 216 - total cost of gas over 3,000 Km trip.
216/4 = $54 - share of each one of the 4 people
Answers
Explanation:
The common difference in the X factors is 2, and t he common difference in the y factors is 1.
Answer:
its b but i am not sure because my text was different
Answers
Answer:
I = 1.47001
Step-by-step explanation:
we have the function
In polar coordinates we have
and dA is given by
Hence, the integral that we have to solve is
This integral can be solved in a convenient program of your choice (it is very difficult to solve in an analytical way, I use Wolfram Alpha on line)
I = 1.47001
Hope this helps!!!
It is assumed that the number of trees still alive is given by N = art
where / is the number of trees still alive t years after 1st September 2014.
a) Write down the value
c) Show that on 1st September 2040
the number of trees still alive is predicted
o have decreased by over 65% compared
with September 2014.
b) Show that r = 0.96
Answers
Answer:
1. a = 5400
2. r = 0.96
3. Percentage decrement = 65.4%
Step-by-step explanation:
Given
N = ar^t
Solving (a): Write down the value of a
a implies the first term
And from the question, we understand that the initial number of trees is 5400.
Hence,
a = 5400
Solving (b): Show that r = 0.96
Using
N = ar^t
When a = 5400, t = 1 i.e. the first year and N = 5184
Substitute these values in the above expression
5184 = 5400 * r¹
5184 = 5400 * r
5184 = 5400r
Solve for r
r = 5184/5400
r = 0.96
Solving (c): Show that the trees has decreased by over 65% in 2040
First, we need to calculate number of years (t) in 2040
t = 2040 - 2014
t = 26
Substitute 26 for t, 5400 for a and 0.96 for r in N = ar^t to get the number of trees left
N = 5400 * 0.96^26
N = 1868.29658019
N = 1868 (approximated)
Next, we calculate the percentage change as thus:
%Change = (Final - Initial)/Initial * 100%
Where the initial number of trees =5400 and final = 1868
%Change = (1868 - 5400)/5400 * 100%
%Change = -3532/5400 * 100%
%Change = -3532%/54
%Change = -65.4%
The negative sign indicates a decrements or reduction.
Hence, percentage decrement = 65.4% and this is over 65%
1/2m+3/4n=13 5/6m-2/9n=4
Answers
Answer:
.
21
Step-by-step explanation:
Answers
The expression can be simplified as .
What is an expression?
An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)
A phrase in language may contain an action on its own, but it does not constitute a whole sentence.
Given:
The expression =
Factorize 686 we get 7³ × 2
=
=
Therefore, the expression can be simplified as .
To know more about the expression:
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Final answer:
The simplified form of the expression \sqrt[3]{686x {}^{4}} * y {}^{7} is 2y^7x * \sqrt[3]{x}. This is achieved by breaking down 686 into its prime factors and simplifying under the cube root.
Explanation:
To simplify the given expression \sqrt[3]{686x {}^{4} } y {}^{7}, we first break down 686 into its prime factors. 686 = 2 * 7 * 7 * 7 or 2 * 7^3. Now we can simplify the given expression by solving it inside the cube root first: \sqrt[3]{2 * 7^3 * x^4}, which simplifies to 2y^7x * \sqrt[3]{x}
\sqrt[3]{686x {}^{4}} * y {}^{7} = 2y^7x * \sqrt[3]{x}
Learn more about Solving Expressions here:
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