Answer:
The manufacturer should decrease the level of unskilled labor by 2 for the total output to stay the same.
Step-by-step explanation:
Q(x,y) = 60 x^⅓ y^⅔
Take the partial derivatives with respect to x and y.
∂Q/∂x = 20 x^-⅔ y^⅔
∂Q/∂y = 40 x^⅓ y^-⅓
So the total differential is:
dQ = ∂Q/∂x dx + ∂Q/∂y dy
dQ = 20 x^-⅔ y^⅔ dx + 40 x^⅓ y^-⅓ dy
If dQ = 0:
0 = 20 x^-⅔ y^⅔ dx + 40 x^⅓ y^-⅓ dy
If x = 10, y = 40, and dx = 1:
0 = 20 (10)^-⅔ (40)^⅔ (1) + 40 (10)^⅓ (40)^-⅓ dy
0 = 20 (4)^⅔ + 40 (1/4)^⅓ dy
-20 (4)^⅔ = 40 (1/4)^⅓ dy
-20 (4)^⅔ (1/4)^⅔ = 40 (1/4)^⅓ (1/4)^⅔ dy
-20 = 40 (1/4) dy
-20 = 10 dy
dy = -2
The manufacturer should decrease the level of unskilled labor by 2 for the total output to stay the same.
To maintain the same level of production when adding one skilled worker, we use calculus to find the necessary change in the number of unskilled workers based on the manufacturer's production function.
Explanation:The question deals with partial derivatives and their application in the context of production functions. Using calculus, specifically the concept of partial derivatives, we can estimate the change in the number of unskilled workers required to maintain the same level of production when there is an increase in the number of skilled workers. Given the manufacturer's production function Q(x, y) = 60x1/3y2/3, where x is the number of skilled workers and y is the number of unskilled workers, we first calculate the partial derivative of Q with respect to x, Qx, and then find the partial derivative with respect to y, Qy. We then use these derivatives to form an equation that represents the change in y needed to offset the change in x. With x initially at 10 and increasing by 1, and y initially at 40, we can solve for the change in y that keeps the total output constant.
Latisha has two pieces of ribbon she plans
to cut. One piece of ribbon is 48 inches and
the other is 80 inches. She plans to cut
all the ribbon into pieces of equal lengths.
What is the greatest possible length of each
piece?
The greatest possible length of each piece is 16 inches
Solution:Latisha has two pieces of ribbon. One piece of ribbon is 48 inches and the other is 80 inches
Ribbon is to be cut into pieces of equal length
To find the greatest possible length of each piece, we have to find greatest common divisor of 48 and 80
The greatest common factor, or GCF, is the greatest factor that divides two numbers
Steps to find G.C.F of 48 and 80
1) Find the prime factorization of 48
[tex]48 = 2 \times 2 \times 2 \times 2 \times 3[/tex]
2) Find the prime factorization of 80
[tex]80 = 2 \times 2 \times 2 \times 2 \times 5[/tex]
3) To find the GCF, multiply all the prime factors common to both numbers:
Therefore, [tex]GCF = 2 \times 2 \times 2 \times 2 = 16[/tex]
So, 16 inches is the greatest possible length to cut so that every piece is of equal length.
Explain how you could convert 152 cups into gallons.
Answer: There are 16 cups in every gallon so we could divide 152 by 16 and get our number of gallons which would give us 9.63 or a little over 9 and a half gallons.
Step-by-step explanation:
Which choice is a factor of 62?
A.13
B.20
C.62
D.3
Answer:
C, the answer is 62.
Step-by-step explanation:
Well, 1 x 62 is 62 so that's the only factor of 62 out of all of them.
Prove that using: X ∩ (Y ∪ Z ) =(X∩Y) ∪ (Y ∩ Z )
Listing Method; or
Membership Table.
Given
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
X = {2, 5, 8, 9}
Y = {1, 4, 6, 7, 8}
Z = {5, 7, 9}
There should be a typo in the question: the correct formula would be
[tex]X\cap(Y\cup Z)=(X\cap Y)\cup (X\cap Z)[/tex]
Let's compute [tex]X\cap (Y\cup Z)[/tex] first. We have
[tex](Y\cup Z)=\{1, 4, 5, 6, 7, 8, 9\}[/tex]
If we intersect this set with X, we have
[tex]X\cap (Y\cup Z) = \{5, 8, 9\}[/tex]
So, that would be the left hand side. For the right hand side, we have
[tex]X\cap Y = \{8\},\quad X\cap Z = \{5,9\}[/tex]
And their union is again [tex]\{5,8,9\}[/tex]
Final answer:
The intersection of two sets can be proven using a membership table for the given sets X, Y, and Z.
Explanation:
The intersection of two sets, written as AnB, is a set consisting of all elements that are both in A and B. We can use a membership table to prove the following equation: X ∩ (Y ∪ Z) = (X ∩ Y) ∪ (Y ∩ Z).
A digital clock displays military time in hh:mm format. Find the probability that the number made up of the first two digits is more than 25
Answer:
0
Step-by-step explanation:
In military time format, first two digits are in hours. We know that, on a digital clock, the first two digits always shows between 01 to 24.
So, there is no probability that the first two digits will show more than 25.
As there is no probability, the probability will be zero or 0. Because probability of any incident is whether 0 or 1; where 1 is for certain event.
11. The distance from Mac's house to school
is 575 yards. Mac's goal is to walk to
school in 5 minutes. How many yards
does Mac need to walk each minute to
meet his goal?
Answer:
115 yards per minute
Step-by-step explanation:
575/5= 115
Answer:
115 yds per minute
The drawing will help
Which of the following is the perimeter of a triangle with side lengths of 7 inches, 8 inches, and 13 inches?
15 inches
13 inches
28 inches
27 inches
Answer: 28 inches
Step-by-step explanation:
Side1 + side 2 + side 3 =
7 inches + 8 inches + 13 inches =
28 inches
f the chance of rain for tomorrow is 30%, what is the chance that it will NOT rain?
A. 70%
B. 0%
C. 50%
D. 30%
Select EACH correct answer!
If there is a 30% chance of it raining, then that means there is a 70% chance of it not raining.
100%-30%=70%
Answer: 70%
Step-by-step explanation: In terms of probability, 100% is the maximum which means something is certain. There are some occasions where it can be higher than 100% like dealing with percent increase or decrease, but in this case, we're talking about 100%.
In this problem, we're given that the probability of rain for tomorrow is 30% and we're asked to find the probability that it will not rain.
Since 100% will be the maximum when dealing with probability, we will subtract the chance it will rain tomorrow which is 30% from 100%.
100% - 30% = 70%.
Therefore, the probability/chance it will not rain is 70% which means it's likely it will not rain.
Factor 3x2 - 18x + 27 completely.
Answer:
3(x - 3)²
Step-by-step explanation:
Given
3x² - 18x + 27 ← factor out 3 from each term
= 3(x² - 6x + 9)
= 3(x - 3)² ← in factored form
25 + 11/12b =47 please answer
Answer:
The answer is b = 1/24.
Step-by-step explanation:
Given:
25+11/12b=47.
Now, to solve the equation to get the value of b:
[tex]25+\frac{11}{12b}=47[/tex]
Subtracting both sides with 25 we get:
[tex]\frac{11}{12b}=22[/tex]
Multiplying both sides by 12b we get:
[tex]11=264b[/tex]
Dividing both sides by 264 we get:
[tex]\frac{1}{24}=b[/tex]
Therefore, the answer is b = 1/24.
The price of peaches at Al’s supermarket can be determined by the equation p=0.28n, where P is the price and n is the number of pounds of peaches what is the constant of proportionality
Answer:
k = 0.28
Step-by-step explanation:
The price of peaches at Al's supermarket can be determined by the equation P = 0.28n ........... (1)
where P is the price and n is the number of pounds of peaches.
Now, it is clear that the price of peaches is proportional to the number of pounds of peaches.
So, we can write,
P ∝ n
⇒ P = kn ............. (2) where k is the constant which we have to multiply to covert from proportionality to equation form.
Now, comparing equations (1) and (2) we get k = 0.28 which is the value of the constant of proportionality. (Answer)
Final answer:
The constant of proportionality in the equation p = 0.28n is 0.28, representing the price per pound of peaches at Al's supermarket.
Explanation:
The constant of proportionality in the equation p = 0.28n, where P is the price and n is the number of pounds of peaches, is 0.28. This constant represents the price per pound of peaches at Al's supermarket. When you want to compute the amount spent on peaches, you multiply the quantity (in pounds) by this constant of proportionality, which is the price per pound. As an example, if you have 10 pounds of peaches, the total cost would be calculated as 10 pounds × $0.28 per pound, resulting in a total of $2.80 for the peaches.
Mr. Davies opened a new retail store. During the first week, 360 customers visited the store. During the second week, 300 customers visited the store.
What is the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week?
Answer: C
Step-by-step explanation:
The answer is C because it says 360 and 300. If you do a problem solve for that one on a peace of paper I think it would be 16.7%
Answer:
Step-by-step explanation:
Change in number = number visited in 1st week - number visited in 2nd week
= 360-300 = 60
So percentage change in number= 60/360×100=16.67
Andre wants to make an open box by cutting out corners of a 22 inch by 28 inch poster board and then folding up the sides. The volume V(x) in cubic inches of the open top box is a function of the side length x in inches of the square cutouts. Write and expression for v(x)
Answer:
v(x) = x(22 - 2x)(28 - 2x)
Step-by-step explanation:
The length of the box = 28 - 2x inches,
The width = 22 - 2x inches and the height = x inches.
v(x) = x * width * length.
The volume of the open top box is [tex]V(x) = (28 - 2x)(22 - 2x)(x)[/tex] cubic inches
The volume of the box is V = (length)(width)(height).
Let the cutout side length be [tex]x[/tex] inch,
We are to cut out [tex]x[/tex] by
So, the length of the box is [tex]28 - 2x[/tex] inch
the width of the box is [tex]22 - 2x[/tex] inch and
the height of the box is [tex]x[/tex] inch
Now, substituting the values in the volume formula, we get
[tex]V(x) = (28 - 2x)(22 - 2x)(x)[/tex] cubic inches
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abraham lincoln declared thanksgiving a holiday in 1863 what is the prime factorization of 1863
3 x 3 x 3 x 3 x 23 = 1,863. It can also be written in exponential form as 3 to the power of four times 23.
Answer:
1863 = 3 · 3 · 3 · 3 · 23Step-by-step explanation:
[tex]\begin{array}{c|cc}1863&3\\621&3\\207&3\\69&3\\23&23\\1\end{array}[/tex]
What is the constant of proportionality in the equation y=0.41x
Answer:
0.41
Step-by-step explanation:
formula; y = kx (where k is the constant variation)
the standard equation representing direct variation
y = 0.41 x is the equation to find the constant of proportionality
so, K = 0.41
On a certain hot summer's day, 643 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled
$1161.50. How many children and how many adults swam at the public pool that day?
249 children and 394 adults swam at the public pool.
Step-by-step explanation:
Number of people swam at pool = 643
Receipts = $1161.50
Cost for one child = $1.50
Cost for one adult = $2.00
Let,
x be the number of children
y be the number of adults
According to given statement;
x+y=643 Eqn 1
1.50x+2.00y = 1161.50 Eqn 2
Multiplying Eqn 1 by 2
[tex]2(x+y=643)\\2x+2y=1286\ \ \ Eqn\ 3\\[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](2x+2y)-(1.50x+2.00y)=1286-1161.50\\2x+2y-1.50x-2.00y=124.50\\0.5x=124.50[/tex]
Dividing both sides by 0.5
[tex]\frac{0.5x}{0.5}=\frac{124.50}{0.5}\\x=249[/tex]
Putting x=249 in Eqn 1
[tex]249+y=643\\y=643-249\\y=394[/tex]
249 children and 394 adults swam at the public pool.
Keywords: linear equation, subtraction
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State under which condition the original and the simplified expressions are equivalent.
The expressions are equivalent if...
a) a≠0
b) a≠x
c) a≠-x
[tex]\frac{a^2}{ax-x^2} +\frac{x}{x-a}[/tex]
Answer:
a doesn't equal 0
Step-by-step explanation:
State under which condition the original and the simplified expressions are equivalent
How do I solve this? ( explanation with answer)
Answer:
a.) x= 11
d.) -7
g.) -5
Step-by-step explanation:
a.) x+1 = 4*3
x=12-1
d.)3x+1=-4*5
3x+1=-20
x=-7
g.)11x-1=-8*7
11x-1=-56
11x=-56+1
x=-5
Answer:
a) x = 11, d) x = -7, g) x = -5Step-by-step explanation:
[tex]a)\\\dfrac{x+1}{3}=4\\\\\dfrac{x+1}{3}=\dfrac{4}{1}\qquad\text{cross multiply}\\\\(x+1)(1)=(3)(4)\\\\x+1=12\qquad\text{subtract 1 from both sides}\\\\x+1-1=12-1\\\\\boxed{x=11}[/tex]
[tex]d)\\\\\dfrac{3x+1}{4}=-5\\\\\dfrac{3x+1}{4}=\dfrac{-5}{1}\qquad\text{cross multiply}\\\\(3x+1)(1)=(4)(-5)\\\\3x+1=-20\qquad\text{subtract 1 from both sides}\\\\3x+1-1=-20-1\\\\3x=-21\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}=\dfrac{-21}{3}\\\\\boxed{x=-7}[/tex]
[tex]g)\\\dfrac{11x-1}{8}=-7\\\\\dfrac{11x-1}{8}=\dfrac{-7}{1}\qquad\text{cross multiply}\\\\(11x-1)(1)=(8)(-7)\\\\11x-1=-56\qquad\text{add 1 to both sides}\\\\11x-1+1=-56+1\\\\11x=-55\qquad\text{divide both sides by 11}\\\\\dfrac{11x}{11}=\dfrac{-55}{11}\\\\\boxed{x=-5}[/tex]
[tex]5x - 15 + 130 = x - 2 [/tex]
Answer:
x=-117/4
Step-by-step explanation:
5x-15+130=x-2
5x-x+115=-2
4x+115=-2
4x=-2-115
4x=-117
x=-117/4
33. Sarah has $200 in her bank account now. If she
deposits $10 weekly, which of the following formulas
will show her deposits (D) at the end of h weeks?
(1) D=200+ 10
in
(2) D = (200)(10n)
(3) D = 200 + 10
(4) D = 200 + 10
(5) D = 200n + 10
Answer:2
Step-by-step explanation:if she deposits 10 dollars every week she would be adding 10 dollars which means we have to multiply 10 by however many weeks she saves
Sarah's weekly deposits after h weeks can be calculated using the linear equation D = 200 + 10h. This equation includes her starting balance of $200 and adds $10 for each week.
Explanation:The subject of this question is Mathematics, specifically focusing on the concept of linear equations.
The correct formula to show Sarah's deposits at the end of h weeks would be (3) D = 200 + 10h. This formula works by establishing 200 as her starting amount (her current bank balance), and adding $10 for each week (h).
For instance, if h was 5 weeks, Sarah would have D = 200 + 10 * 5 = 200 + 50 = $250 in her bank account. This demonstrates how the formula allows you to calculate her weekly deposits effectively.
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Please help!!
The answers and question is in the picture!
conservation imporoper fraction to mixed number answer
Rachel has 8/12 of a fun of frosting. If she used 1/4 of it, how much was left?
Answer:
6/12
Step-by-step explanation:
A fourth of 8 is 2, so there would be 6/12 of the tub of frosting left.
Answer:
5/12
Step-by-step explanation:
8/12=2/3
2/3-1/4=8/12-3/12=5/12
For every part produced by a factory, there are 5 ounces of scrap aluminum that can be recycled. There are16 ounces in 1 pound and 2,000 pounds in 1 ton. How many parts must the factory produce so that there is 1 ton of scrap aluminum for recycling
Answer:
The factory must produce 6,400 parts so that there is 1 ton of scrap aluminum for recycling.
Step-by-step explanation:
1 part produced ⇒ 5 ounces scrap aluminium recycled.
So, the ratio of parts produced : Scrap of aluminium = 1 : 5 .... (a)
Let us assume for m parts produced , 1 ton of scrap is recycled.
Also, 1 ton = 2, 000 pounds
and 1 pound = 16 ounces
⇒ 1 ton = 2000 x (16 ounces) = 32,000 ounces
So, for m parts made in the factory, 32,000 ounces scrap is recycled.
So, the ratio of parts produced : Scrap of aluminium = m : 32,000 .... (b)
From both the given ratio, we get
1 : 5 = m : 32,000
or, [tex]\frac{1}{5} = \frac{m}{32,000} \implies m = \frac{32,000}{5} = 6,400[/tex]
⇒ m = 6,400
Hence, the factory must produce 6,400 parts so that there is 1 ton of scrap aluminum for recycling.
Answer:
6,400
Step-by-step explanation
if im late then my bad, how ya'll day going? and Byeee, i'm at school ;)
which graph represents a function?
Answer:
This graph does not represent a function.
Step-by-step explanation:
This graph does not pass the vertical line test. The vertical line test states that if a vertical line drawn intersects the graph of the relation more than once, then the relation is a NOT a function.
what is slope of a line that passes through (1,4) (-2,6) awarding more points
Answer:
-2/3
Step-by-step explanation:
m=(6-4)/(-2-1)=2/-3=-2/3
Answer:
[tex]\large\boxed{m=-\dfrac{2}{3}}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (1, 4) and (-2, 6).
Substitute:
[tex]m=\dfrac{6-4}{-2-1}=\dfrac{2}{-3}=-\dfrac{2}{3}}[/tex]
A basketball arena can hold approximately 7,000 people. Fans bought 5,134 tickets before the game. About how many more seats are left to fill before the game.
To determine the number of seats left in the basketball arena, the number of tickets sold (5,134) is subtracted from the total arena capacity (7,000), resulting in 1,866 seats remaining available.
A basketball arena can hold approximately 7,000 people.
Fans bought 5,134 tickets before the game.
The number of seats left to fill before the game can be calculated by subtracting the tickets bought from the total arena capacity: 7,000 - 5,134 = 1,866 seats left to fill.
what is 3.1n - 1.1n =
A cookie recipe calls for 6 cups of flour
and 2 cups of sugar. What is the ratio of
the amount of sugar to the amount of
flour?
Answer:
1:3
Step-by-step explanation:
Sugar : Flour
2 : 6 (substitute the numbers of cups)
1 : 3 (simplify by reducing. divide both sides by 2)
The ratio is 1:3.
Answer:
1:3
Step-by-step explanation:
2:6[sugar is to flour]
1:3[to simplify divide both sides by two]
Line 1 passes through the points -2,7 and 3,3. Line 2 passes through the points 5,1 and 9,1. Find the slope of each line. Which line has the greater slope?
Answer:
The slope of the given line 1 is -4/5.
The slope of the given line 2 is 0.
The line 2 has a greater slope then line 1.
Step-by-step explanation:
The slope of a line with points (x1,y1) and (x2,y2) is given as:
[tex]m = \frac{y_2- y_1}{x_2-x_1}[/tex]
Now, Here the, points of the line 1 are A (-2,7) and B (3,3)
So, here, the slope of line AB is [tex]m = \frac{3 -7}{3-(-2)} = \frac{-4}{3 +2} = \frac{-4}{5}[/tex]
Hence, the slope of the given line 1 is -4/5.
Now, Here the, points of the line 2 are P (5,1) and Q (9,1)
So, here, the slope of line PQ is [tex]m = \frac{1-1}{9-5} = \frac{0}{4} = 0[/tex]
Hence, the slope of the given line 2 is 0.
Now, as we can see 0 > ( -4 / 5)
So, the line 2 has a greater slope then line 1.
I need serious help can anyone help me atleast with 3?
Answer:
z = 14
Step-by-step explanation:
Solve for z:
(4 z)/7 - 15 = -7
Put each term in (4 z)/7 - 15 over the common denominator 7: (4 z)/7 - 15 = (4 z)/7 - 105/7:
(4 z)/7 - 105/7 = -7
(4 z)/7 - 105/7 = (4 z - 105)/7:
1/7 (4 z - 105) = -7
Multiply both sides of (4 z - 105)/7 = -7 by 7:
(7 (4 z - 105))/7 = -7×7
(7 (4 z - 105))/7 = 7/7×(4 z - 105) = 4 z - 105:
4 z - 105 = -7×7
7 (-7) = -49:
4 z - 105 = -49
Add 105 to both sides:
4 z + (105 - 105) = 105 - 49
105 - 105 = 0:
4 z = 105 - 49
105 - 49 = 56:
4 z = 56
Divide both sides of 4 z = 56 by 4:
(4 z)/4 = 56/4
4/4 = 1:
z = 56/4
The gcd of 56 and 4 is 4, so 56/4 = (4×14)/(4×1) = 4/4×14 = 14:
Answer: z = 14