Using derivatives, the equation for the marginal product of labor is given by:
Q'(L) = 5 - 2L.
What is the marginal product equation?As stated in the problem, the “marginal product of labor” is the change in the total product as we change the amount of hired labor, hence it is given by the derivative of the production as a function of labor.
For this problem, the production function is given by:
Q(L) = 5L - L².
Hence the marginal product of labor is given by:
Q'(L) = 5 - 2L.
Which is the derivative of Q(L), found applying the derivative of a power of x, as follows:
[x^n]' = nx^(n-1).
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Shirley and Pam, working together, can mow the lawn in 6
6
hours. Working alone, Pam takes three times as long as Shirley. How long does it take Shirley to mow the lawn alone?
Answer:
each takes 3 together 3x3=9
A rectangular field is eleven times as long as it is wide. If the perimeter of the field is 1680 feet, what are the dimensions of the field? A) Write an equation you can use to answer the given question. Let w be the width of the field.
Answer:
2(w+11w)=1680
Step-by-step explanation:
If the width is w, then the length is 11w.
Using the formula for the perimeter of the rectangle, the equation is 2(w+11w)=1680
Solve for y.
5. x = 1/3y +2
Answer: y=3x-6
Step-by-step explanation:
ANSWER:y=1/(3x-6)
Step-by-step explanation:
i think you are asking for the change of subject of formula(Transposition of subjects).
x=1/3y+2
multiply both sides by 3y
x × 3y=1/3y × 3y + 2 × 3y
3xy=1+6y
collect like terms
3xy-6y=1
fractionalize
y(3x-6)=1
divide both sides by (3x-6)
y=1/(3x-6)
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Shirley and Pam, working together, can mow the lawn in 6
6
hours. Working alone, Pam takes three times as long as Shirley. How many hours does it take Shirley to mow the lawn alone? Round your answer to two decimal places, if needed.
Shirley will take 8 hours to complete mowing the field alone.
We are given that Shirley and Pam, working together, can mow the lawn in 6 hours.
So, work done if 1 hour together = 1 / 6
Also, we are given that Pam takes three times as long as Shirley when she works alone.
Time taken by Pam = 3 times Time taken by Shirley.
Let the time taken by Shirley be y.
Job done in 1 hour = 1 / y
Time taken by Pam = 3 y
Job done in 1 hour = 1 / 3y
ATQ:
1 / y + 1 / 3 y = 1 / 6
4 / 3 y =1 / 6
24 = 3 y
y = 24 / 3
y = 8 hours.
Therefore, Shirley will take 8 hours to complete mowing the field alone.
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Complete the missing values. (Hint 1 yard-3 feet)
2/ yd =
ft
Answer:
6 ft
Step-by-step explanation:
if 1 yard = 3 feet, you add +3 to the second one because its 2x more
(x³- 3x²+2x+1)/x²-4x+4 dx (dx/dy) + (x²+4y-y²)/(²√4y+y²)
Step-by-step explanation:
y=1
x=1
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You may recall that the area of a rectangle is A=L⋅W, where W is the width and L is the length.
Suppose that the length of a rectangle is 4 times the width. If the area is 900 square feet, then what is the width of the rectangle, in feet?
Answer:
Width = 15 ft
Step-by-step explanation:
Given formula,
→ A = L × W
Let us assume that,
→ Length = 4x
→ Width = x
→ Area = 900 ft²
Then the value of width will be,
→ A = L × W
→ 900 = 4x × x
→ 4x² = 900
→ x² = 900/4
→ x = √225
→ [ x = 15 ft ]
Hence, the value of width is 15 ft.
What are the solutions of this quadratic equation?
x² - 6x+2=0
OA.
O B.
OC.
2-3 ± √7
CD. 2-3 ± √11
-6 ± √7
x=3+√7
Find the x- and y-intercepts of the graph of the equation. (If an
(a)
X^2-xy+4y=49
Answer:
x=±7; y=12.25.
Step-by-step explanation:
1) x-interception:
(y=0): x²=49, ⇒ x=±7;
2) y-interception:
(x=0): 4y=49; ⇒ y=12.25.
You need 6 cups of fruit punch. use 2 cups of pineapple juice add 1 cup of cranberry juice. How many cups of orange juice should you add?
Answer:3
Step-by-step explanation:easy 2 cups of pj plus cranberry juice is 3, get 6 by adding 3 again
Solve the literal equation for x. State any
necessary restrictions on the letters
representing constants in the equation.
a (bx + c) = 0
in the u.s government a memeber if the senate serves for 4 years longer than a member of the House of Representatives. If a member of the House of Representatives serves for h years, write an expression for how many years a member of the senate serves .
A member of the senate will serve for (h+4) years.
An expression, in mathematics, is a finite set of combinations and/ or numbers and variables that accurately represents the the context in question. When two or more expressions are connected using the equality sign then an equation is formed.
Here, we are given that in the US government a member of the senate serves for 4 years longer than a member of the House of Representatives.
Also the House of Representatives serves for- h years
Thus, the number of years a member of the Senate will serve will be 4 more than the number h
= h + 4
Thus, a member of the senate serves for (h+4) years.
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Help
Find a if A = 8a
Answer:
a(A) = 0
Step-by-step explanation:
Point B is on line segment
AC
. Given AB=3x, BC=4x+8, and AC=5x+10, determine the numerical length of
AC
.
Answer:
The length of AC is 15 units
Step-by-step explanation:
Drag the decimal values to match the corresponding fraction values.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
1/3 =
1/2 =
1/4 =
3/4 =
2/3 =
to choose from: 0.50 0.75 0.25 0.66 0.33
please help
[tex]1/3 \longrightarrow 0.33 \\ \\ 1/2 \longrightarrow 0.50 \\ \\ 1/4 \longrightarrow 0.25 \\ \\ 3/4 \longrightarrow 0.75 \\ \\ 2/3 \longrightarrow 0.66[/tex]
Simplify : p^2-p-12/p^2-10p+24
Step-by-step explanation:
[tex] = \frac{ {p}^{2} - p - 12 }{ {p}^{2} - 10 + 24} \\ [/tex]
[tex] = \frac{ {p}^{2} - (4 - 3)p - 12 }{ {p }^{2} - (6 + 4)p + 6 \times 4} \\ [/tex]
[tex] = \frac{ {p}^{2} - 4p + 3p - 4 \times 3 }{ {p}^{2} - 6p - 4p + 6 \times 4 } \\ [/tex]
[tex] = \frac{p(p - 4) + 3(p - 4)}{p(p - 6) - 4(p - 6)} \\ [/tex]
[tex] = \frac{(p + 3)(p - 4)}{(p - 4)(p - 6)} \\ [/tex]
[tex] = \frac{p + 3}{p - 6} \\ [/tex]
☘️☘️☘️...
Find the area of the triangle. Show your reasoning. If you get stuck, carefully consider which side of the triangle to use as the base.
The area of the triangle is found as 12 unit².
What is defined as the triangle?A triangle is a three-sided polygon with three sides that closes a space.
The three sides are formed by lines, line segments, or rays (in just about any combination). Three vertices, or corners, are formed if three sides form or meet.A triangle's height or altitude is calculated by drawing a perpendicular line through one side to the opposite angle.The base is the side with which the altitude intersects wherever it is built.The formula for the area of the triangle is;
Area of triangle= ½ × base × height
The base is given as 6 units and the height is 4 units. (count 1 column of graph as 1 unit).
Put the values in formula.
Area of triangle = ½(6)(4)
Area of triangle = 12 unit.²
Therefore, the area of the triangle is found as 12 unit.²
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What is the equation of the tangent of f(x) 3 X at (1, 3)?
The Equation of the tangent line is y = 4x - 1.
According to the statement
We have to find that the equation of the tangent of the line.
So, For this purpose, we know that the
Equation of the tangent line can be found using the formula y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate points of the line.
From the given information:
f(x) = 3 X at (1, 3)
Then
The tangent line of a curve y = f(x) is a line that touches the curve at a point (x0, y0). Its slope (m) is found by substituting the point where it is drawn in the derivative f'(x) and its equation is found by using y - y0 = m (x - x0).
From the given it is clear that the slope of the equation is a 3.
Then m = 3
then
y – y1 = m (x – x1)
Substitute the points here
y - 3 = 4(x - 1)
Then
y = 4x - 4 +3
y = 4x - 1.
So, The Equation of the tangent line is y = 4x - 1.
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if x=2 then solve |-3x - 5| + |-1 - x^2| + 2x^3
Answer:
32
_____
Work[tex]\left|-3\left(2\right)-5\right|+\left|-1-2^2\right|+2\cdot \:2^3\\\left|-3\cdot \:2-5\right|+\left|-1-2^2\right|+2\cdot \:2^3\\-3 \cdot 2 - 5 = -11\\\left|-11\right|+\left|-1-2^2\right|+2\cdot \:2^3\\-1 - 2^2 = -1 - 4 = -5\\\left|-11\right|+\left|-5\right|+2\cdot \:2^3\\|-11| = 11\\|-5| = 5\\2 \cdot 2^3 = 2 \cdot 8 = 16\\11+5+16\\=32[/tex]
_____
(b) If you put $7750 in the ATM each day, what percent of the days in a month should you expect to run out of cash?
The percent of the days in month that the cash will run out is given as: 23.33%. See the computation below.
What is the explanation that justified the above answer?Money put in ATM per day=$7750
We have to find the percent of days in a month you should expect to run out of cash.
From the given information
There are 7 days in which you run out cash more than $7750
Assuming that the total number of days in a month = 30
Hence, we can arrive at the above value by saying:
(Corresponding days/Total number of Days) * 100
From we above we state:
(7/30) * 100
= 23.33%
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6.1 Define the term inflation.
Answer:
the action of inflating something or the condition of being inflated.
"the inflation of a balloon"
ASTRONOMY
(in some theories of cosmology) a very brief exponential expansion of the universe postulated to have interrupted the standard linear expansion shortly after the Big Bang.
2.
ECONOMICS
a general increase in prices and fall in the purchasing value of money.
"policies aimed at controlling inflation"
Find the future value (in dollars) of an 18-month investment of $4,300 into a simple interest rate account that has an annual simple interest rate of 5.1%.
keeping in mind that a year has 12 months, thus 18 months is really 18/12 of a year, so
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4300\\ r=rate\to 5.1\%\to \frac{5.1}{100}\dotfill &0.051\\ t=years\to \frac{18}{12}\dotfill &\frac{3}{2} \end{cases} \\\\\\ A=4300[1+(0.051)(\frac{3}{2})] \implies A=4628.95[/tex]
Create and solve a proportion: to find the cost of 4 hamburgers if 5 hamburgers cost $21.98.
Answer:
4/x = 5/21.98 ; x=17.584
Step-by-step explanation:
subes la x al otro lado , multiplicas el 21.98 con el 4 y luego lo divides entre 5, así resulta q x es igual a 17.584
Answer:
ehuyqkqbdksjs
usual
Menem
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meme
Help please Im confused becuz i got 19.4 but its wronggg
Answer:
20.75
Step-by-step explanation:
1cm=10mm
so:1mm=0.1cm
0.1/2=0.05
if it asks lower bound:
5.2-0.05=5.15 +
6.3-0.05=6.25 +
9.4-0.05=9.35
The steel is more dense than lake water
Answer:
true
Step-by-step explanation:
That is a true statement.
The density of steel is approx. 7.85 g/cm³.
The density of water is approximately 1 g/cm³.
please help me with this math homework
Answer:
Step-by-step explanation:
(2*9/5d*9)-(1*5/9d*5)
18/45d-5/45d
13/45d
Which measurement is closest to the circumference of the circle in square centimeters
Answer:
the measurement of the circumference of a circle is 21
Which polynomial represents the sum below?
+
2x² + 5x+4
5x2+
Answer:
????
Step-by-step explanation:
I don't get this
at all
Question 3
1 pts
A survey was conducted by visiting a student parking lot to estimate the proportion of
cars that were red. Which of the following is NOT correct?
A. If another sample of cars was chosen, it is likely that a different proportion of cars that are red
would be obtained.
B. The sample would be representative of the population if 100 cars were chosen regardless if
randomization was used or not.
C. Even though a random sample was taken from cars in the parking lot, the sample may not be
representative of the cars driven by students because the decision to park in that particular lot is
self-selected.
D. If the sampled stall was empty, we can simply choose another stall, at random, to take its place
because it is not likely that the stall being vacant is related to a car being red.
The sample would be representative of the population if 100 cars were chosen regardless if randomization was used or not; this statement is not correct;
A survey was carried out by visiting a student parking lot to estimate the number of red cars.
If a different sample of cars was picked, the proportion of red cars would most likely be different. This statement is correct.
The sample would be representative of the population if 100 cars were chosen regardless if randomization was used or not. This statement is not correct because you select only 100 cars to represent whole population that too without randomization;
Despite the fact that a random sample was obtained from cars in the parking lot, the sample may not be representative.
because the decision to park in that particular lot is typical of the cars driven by students self-selected.
If the sampled stall was empty, we can simply choose another stall at random to take its place because the stall being unoccupied is unlikely to be associated to a red car.
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Calculator is showing a result of 78.987625. What is this to 2 decimal places
Answer:
78.99
Step-by-step explanation:
Rounding to the 2nd decimal place the number 78.987625
Write down everything upto and including the 2nd decimal: 78.98
Check out the next digit. If >= 5, then increase the 2nd decimal digit above by 1, if not leave it as is.
For 78.987625 the digit next to the 2 decimal digit is 7 so we increase 78.98 to 78.99
