Three and a half divided by seven-eighth equals seven over two times eight over seven equals fifty over fourteen equals four
Answer: 5 benches and 23 students
Step-by-step explanation:
I will answer in English.
We have E students and B benches.
If we sit 4 students per bench, we have 3 students left.
then:
E = 4*B + 3
And if we sit 5 students per bench, there are two places with no students sited.
E = 5*B - 2
now we can replace the E in the second equation with the right part in the first equation:
4*B + 3 = 5*B - 2
3 + 2 = 5*B - 4*B
5 = B
So we have 5 benches, and:
E = 4*5 + 3 = 23 students.
Answer:
- y = 81-x
- the domain of P(x) is [0, 81]
- P is maximized at (x, y) = (54, 27)
Step-by-step explanation:
<u>Given</u>
- x plus y equals 81
- x and y are non-negative
<u>Find</u>
- P equals x squared y is maximized
<u>Solution</u>
a. Solve x plus y equals 81 for y.
y equals 81 minus x
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b. Substitute the result from part a into the equation P equals x squared y for the variable that is to be maximized.
P equals x squared left parenthesis 81 minus x right parenthesis
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c. Find the domain of the function P found in part b.
left bracket 0 comma 81 right bracket
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d. Find dP/dx. Solve the equation dP/dx = 0.
P = 81x² -x³
dP/dx = 162x -3x² = 3x(54 -x) = 0
The zero product rule tells us the solutions to this equation are x=0 and x=54, the values of x that make the factors be zero. x=0 is an extraneous solution for this problem so ...
P is maximized at (x, y) = (54, 27).
Answer:
The fourth choice
24.2° and 114.2°
Step-by-step explanation:
Complementary angles add up to 90°
Supplementary angles add up to 180°
*a trick to remember this is to know that C is before S in the alphabet, and 90 is before 180, so Complementary is 90 and Supplementary is 180
Step 1: Find the complementary angle
Take 90° and subtract the give angle to find the angle you would need...
90° - 65.8° = 24.2°
Step 1: Find the supplementary angle
Take 180° and subtract the give angle to find the angle you would need...
180° - 65.8° = 114.2°
Answer:
Let us consider that ,
The worker can complete the work in x hours .
So, he can complete 1/x part of work in 1 hour.
Now, The workers does 2/3 of what he does. So they do 2/3(1/x) part of work in 1 hour . 2/3x work in 1 hour .
Consider them all working together,
So work done in one hour, = 1/x + 2/3x + 2/3x = 3 + 4 / 3x = 7/3x .
So, They taken 1 hour to complete 7/3th part of work. So, In 3x/7 hours , They all can complete the work.
Ratio of the time taken by all instead of only one = 3x/7 : x = 3/7 .
So ,The required option is 3/7
Hope my answer helped you!
Step-by-step explanation:
