The daily operating budget should be increasing at a rate of approximately $0.02 per day in order to meet the increased demand for 80 automobiles per year.
We are given a Cobb-Douglas production function: P = 20[tex]x^0.5[/tex] * [tex]y^0.5[/tex], where P represents the number of automobiles produced per year, x represents the number of employees, and y represents the daily operating budget in dollars.
To meet the increased demand for 80 automobiles per year, we need to determine the rate at which the daily operating budget should be increasing. Since we are maintaining a constant workforce of 130 workers, the number of employees (x) remains constant.
Using the production function, we can calculate the current production level as P = 1200 automobiles per year. To increase the production level by 80 automobiles per year, we set up the following equation: 1200 + 80 = 20[tex]x^0.5[/tex] * [tex]y^0.5[/tex].
Since the number of employees (x) remains constant at 130, we can solve the equation for the rate at which the daily operating budget (y) should be increasing.
By rearranging the equation and solving for y, we find that y should be increasing at a rate of approximately $0.02 per day.
Therefore, the daily operating budget should be increased at a rate of approximately $0.02 per day in order to meet the increased demand for 80 automobiles per year, while maintaining a constant workforce of 130 workers.
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Given the following formula, solve for a. 8=a+b+c/2
Making "a" the subject of the formula would give us: a = 8 - b - c/2
How to Solve for the Subject of Formula?Given the formula, 8 = a+b+c/2, to make a the subject of the formula, we would isolate a in the equation.
8 = a+b+c/2
8 = (2a + 2b + c)/2
2(8) = 2a + 2b + c
16 = 2a + 2b + c
16 - 2b - c = 2a
Divide both sides by 2
16/2 - 2b/2 - c/2 = 2a/2
8 - b - c/2 = a
a = 8 - b - c/2
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The function g(x) is graphed.
to
4
34
24
1
-3+
Mark this and retum
2
Which statements about the function are true? Choose
three options.
g(1) = -1
□g(0) = 0
O
0
g(4) = -2
g(1) = 1
g(-1) = 1
Answer: Options (2), (4), (5)
Step-by-step explanation:
When x = 1, y = 1. So, g(1)=1.
Using similar logic to test the other options, we see that the correct answers are options (2), (4), and (5).
Fill in the coefficients for the polynomial with degree 3, roots: x = 2, X =
-1, and x = 3, and with a leading coefficient of 1
The coefficients for the polynomial with degree 3, roots: x = 2, x =
-1, and x = 3, and with a leading coefficient of 1 is given as -4 and 6. Hence, the polynomial turns out as x³ + (-4)x² + x + 6.
It is given that the polynomial is of degree 3 and its roots are,
x = 2
x = -1
x = 3
Thus, the factors of the polynomial would be,
(x - 2), (x + 1), and (x - 3)
The polynomial an be written in terms of its factors, with a leading coefficient of 1, as follows,
(x - 2)(x + 1)(x - 3)
= (x² -2x + x -2)(x - 3)
= (x² -x -2)(x - 3)
= x³ - 3x² - x² + 3x - 2x + 6
= x³ - 4x² + x + 6
= x³ + (-4)x² + x + 6
Hence, the required coefficients of the polynomial are, (-4) and 6.
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Im one paragraph, summarize the purpose of the graphic and its key findings
The purpose of the graphic is to show the relationship between different educational qualifications and unemployment rate.
What is Unemployment?This is a situation in which employable individuals look for jobs and are unable to find one.
The key findings in this graphic is that the higher the level of education, the lesser the unemployment rate.
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An elf, a dwarf, a hobbit, a wizard, and a man are sitting in a line.How many different ways can they sit if the elf and the dwarf insist on sitting next to each other
Answer: 24
Step-by-step explanation:
1. Number Them
Elf and Dwarf = 1
Hobbit = 2
Wizard = 3
Man = 4
* Elf and Dwarf are put together so that they are always sitting together
2. Multiply
1 x 2 x 3 x 4 = 24
Machine A produces 300 bolts less than three times the number machine B produces. If
machine A produces 4,800 bolts, then how many does machine B produce?
Step-by-step explanation:
what is the best definition of luminous
i need a detailed explanation
The equation of the line in explicit form is y = - 2 · x + 5, whose implicit form is 2 · x + y = 5. (Correct choice: D)
How to find the equation of the line for the height of a triangle
In this question we must find the equation of the line perpendicular to the segment BC and that goes through the point A(x, y) = (1, 3). First, the slope of the line segment BC is:
m = [1 - (- 3)]/[5 - (- 3)]
m = 4/8
m = 1/2
And the slope of the line is:
m' = - 1/(1/2) = - 2
The intercept of the line is found by using the explicit form of equation of the line, m' = - 2 and (x, y) = (1, 3):
3 = - 2 · 1 + b
b = 5
The equation of the line in explicit form is y = - 2 · x + 5, whose implicit form is 2 · x + y = 5. (Correct choice: D)
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Circle S is shown. Line segment R T is a diameter. The length of S T is 4. Sector R S T is shaded.
The measure of central angle RST is radians.
What is the area of the shaded sector?
4Pi units squared
8Pi units squared
16Pi units squared
20Pi units squared
The area of the sector in radians is calculated as: B. 8π units squared.
What is the Area of a Shaded Sector?The area of a sector where the central angle of the sector that is shaded in a circle is given in radians is calculated using the formula that is expressed as:
Area of sector = (1/2) × r²θ; where we have:
θ = the angle subtended at the center/central angle measure in radians
r = the radius of the circle
Given the following:
The shaded area is half of the circle. Its measure would be 180 degrees which when expressed in radians would be π.
Central angle measure in radians (θ) = π
Radius (r) = 4 units
Plug in the values into the area of sector formula
Area of sector = (1/2) × r²θ = (1/2) × (4²)(π)
Area of sector = (1/2) × (16)(π)
Area of sector = (1 × 16 × π)(2)
Area of sector = (16π)(2)
Area of sector = 8π units squared
In conclusion, the area of the shaded sector in the image given below is calculated as: B. 8π units squared.
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Clarie has $300 in an account. She decides she is going to take out half of what's left in there at the end of the month. (This is for geometric sequence, Math 1 btw and I gotta graph it)
The expected money deposited in Clarie's account in next 12 months is listed below:
300 (Initial value)1507537.5018.759.384.692.341.170.590.290.140.07How to derive and graph a geometric sequence
First, we must derive a formula that will generate the geometric sequence for the money remaining in Clarie's account:
[tex]c = c_{o}\cdot \left(1 + \frac{r}{100} \right)^{t}[/tex] (1)
Where:
[tex]c_{o}[/tex] - Initial money deposited in Clarie's account.r - Decrease rate, in percentage.t - Number of periods, in months.If we know that [tex]c_{o} = 300[/tex] and r = - 50, then the money left for each month is shown in the image attached below.
RemarkThe image quality is poor to the point of being very hard to read. However, it coincides with the complete statement, which is presented in the question.
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Consider the three functions:
f(x) = Three-halves(4)x g(x) = Three-halves(4)–x h(x) = –Three-halves(4)x
Which statements are true about the domain and range of f(x), g(x), and h(x)? Check all that apply.
f(x) has a domain of all real numbers.
g(x) has a range of y < 0.
h(x) has a range of y > 0.
g(x) has a domain of all real numbers.
h(x) has a domain of x > 0.
The statements that are true about the domain and range of the functions f(x), g(x), and h(x) include:
f(x) has a domain of all real numbers.g(x) has a domain of all real numbers.What is a function?It should be noted that a function simply means a relation between a set of inputs to a set of possible outputs.
In this case, f(x) has a domain of all real numbers as well as g(x) which also has a domain of all real numbers.
In conclusion, the correct options are A and D.
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Answer:
A and D
Step-by-step explanation:
Edge 2022
If the hypotenuse of a right triangle is 2 [tex]\sqrt{3}[/tex] units long and one of the legs is [tex]\sqrt{3}[/tex] units long, then how long is the other leg?
[tex]\sqrt{3}[/tex]
2[tex]\sqrt{3}[/tex]
3
Answer:
3
Step-by-step explanation:
a = the other leg:
[tex]a^{2} =(2\sqrt{3} )^{2} -(\sqrt{3}) ^{2} =(4)(3)-3=12-3[/tex]
[tex]a^{2} =9[/tex]
[tex]a=\sqrt{9}[/tex]
[tex]a=3[/tex]
Hope this helps
IS ANYONE ABLE TO HELP ME PLEASE ASAP
Answer:
36
Step-by-step explanation:
To answer this question, we need to first understand the notation (f · x)(-2). This is a composite function, and another way to write this is f(g(-2)). This means that we have to find g(-2) and apply the function f to whatever this value is. Let's start by finding g(-2):
[tex]g(x)=x-2\\g(-2)=-2-2\\g(-2)=-4[/tex]
Now that we know g(-2) is -4, we can apply this to f:
[tex]f(x)=x^2-4x+4\\f(-4)=(-4)^2-4(-4)+4\\f(-4)=16-(-16)+4\\f(-4)=16+16+4\\f(-4)=36[/tex]
Therefore, our answer is 36
Questions, are all in picture, please solve
The function represents a cosine graph with axis at y = - 1, period of 6, and amplitude of 2.5.
How to analyze sinusoidal functions
In this question we have a sinusoidal function, of which we are supposed to find the following variables based on given picture:
Equation of the axis - Horizontal that represents the mean of the bounds of the function.Period - Horizontal distance needed between two maxima or two minima.Amplitude - Mean of the difference of the bounds of the function.Type of sinusoidal function - The function represents either a sine or a cosine if and only if trigonometric function is continuous and bounded between - 1 and 1.Then, we have the following results:
Equation of the axis: y = - 1Period: 6Amplitude: 2.5The graph may be represented by a cosine with no angular phase and a sine with angular phase, based on the following trigonometric expression:To learn more on sinusoidal functions: https://brainly.com/question/12060967
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9. shyam travelled 8 km 52 m by bus, 2 km 265 m by car. how much distance did he travel in all
Shyam travel total [tex]10km 317m[/tex] distance ,when he travelled [tex]8 km 52 m[/tex] by bus and [tex]2 km 265 m[/tex] by car .
How to find the total distance travel by Shyam ?
Shyam travelled distance by bus [tex]=8 km 52 m[/tex]
Shyam travelled distance by car [tex]=2 km 265 m[/tex]
Total distance travelled by shyam is
Total distance= distance travelled by car + distance travelled by bus
Total distance
[tex]=2 km 265 m+8 km 52 m\\=(2+8)km(265+52)m\\=10km317m[/tex]
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The ratio of broken ribs to broken collarbones
during last year's rugby season was 2 to 3. If
there were 18 broken ribs, how many broken
collarbones were there?
If a wall is built in a room at a 36 degree angle. The angle formed in the other room by the wall is 144 degrees. What kind of angles are formed when they are added together
They form supplementary angles when they are added together.
Reason for Being Called Supplementary Angles
It is given that the angle made by the wall in one room is 36° and the angle formed by the same wall in the other room is 144°.
This implies that,
∠1 = 36°
∠2 = 144°
∠1 and ∠2 are adjacent angles and,
∠1 + ∠2 = 36° + 144°
⇒ ∠1 + ∠2 = 180°
Hence, these two adjacent angles make a straight-line angle. Hence, they are supplementary angles.
What are supplementary angles?
Two angles that form a straight line angle, that is, angle equal to 180°, when they are added together are said to be a pair of supplementary angles.
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The vertices of polygon ABCD are at A(1,1), B(2,3), C(3,2), and D(2,1). ABCD is reflected across the x-axis and translated 2 units up to form polygon A' B'C'D' to it's coordinates.
The coordinates of the polygon A'B'C'D' following a reflection across the x-axis and a translation 2 units up are;
A'(1, 1), B'(2, -1), C'(3, 0), and D'(2, 1)How can the coordinates of the image be found?The vertices of the polygon are;
A(1, 1), B(2, 3), C(3, 2), and D(2, 1)
Reflection over the x-axis gives;
(x, y) reflection across the x-axis → (x, -y)
Which gives;
A(1, 1) R x-axis → A''(1, -1)
B(2, 3) R x-axis → B''(2, -3)
C(3, 2) R x-axis → C''(3, -2)
D(2, 1) R x-axis → D''(2, -1)
Translation of the points ABCD 2 units up gives;
A''(1, -1) T(0, 2) → A'(1, -1 + 2) = A'(1, 1)
B''(2, -3) T(0, 2) → B'(2, -3 + 2) = B'(2, -1)
C''(3, -2) T(0, 2) → C'(3, -2 + 2) = C'(3, 0)
D''(2, -1) T(0, 2) → D'(2, -1 + 2) = D'(2, 1)
The coordinates of A'B'C'D' are therefore;
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Robert, Richard and David were working on a project to redesign coke cans. First, Robert measured the original coke can and found the circumference to be 8.6 inches. Richard measured the height to be 15.2 cm.
David calculated the volume to be 131.3 cm3.
Choose the true statement(s) below.
Select one or more:
a.David's calculations are incorrect, he needed to convert centimeters to inches before finding the radius then use the area of the base times the height .
b.David is correct.
c.David's calculations are incorrect, he used the circumference and the height to find the volume.
The true statement is David's calculations are incorrect, he used the circumference and the height to find the volume.
VolumeCorrect calculation:
Height = 15.2 cmCircumference = 8.6 inchesC = 2πr
8.6 = 2 × 3.14 × r
8.6 = 6.28r
r = 8.6/6.28
r = 1.36942675159235 inches
convert 1.36942675159235 inches to cm
= 3.478343949044569 cm
Approximately,
r = 3.5 cm
Volume = πr²h
= 3.14 × 3.5² × 15.2
= 3.14 × 12.25 × 15.2
= 584.668 cm³
Approximately,
volume = 584.7 cm³
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Given: Line l and line m intersect Prove: Image of perpendicular lines l and m with 1, 2, 3, and 4 as angles at the point of intersection Statements Reasons 1. Line l and line m intersect 1. given 2. is supplementary to 2. linear pair theorem 3. ? 3. ? 4. 4. congruent supplements theorem Which statement and reason best completes the proof? A. 3. is supplementary to 3. linear pair theorem B. 3. 3. definition of supplementary angles C. 3. 3. definition of supplementary angles D. 3. is supplementary to 3. linear pair theorem
An angle will always be formed when two or more lines intersect. These can form a series of complementary or supplementary angles. Complementary angles add upt o a right angle, while supplementary angles are two or more angles formed that add up to [tex]180^{o}[/tex]. Thus two supplementary angles can be referred to as a linear pair.
Therefore the required statements and reasons for the question are stated below:
STATEMENT REASONS
1. Line l and line m intersect Given
2. <1 is supplementary to <2,
<3 is supplementary to <4 Linear pair theorem
3. m<2 + m<3 = [tex]180^{o}[/tex],
m<3 + m<4 = [tex]180^{o}[/tex] Definition of Supplementary angles
4. m<1 + m<2 = m<3 + m<4 = [tex]180^{o}[/tex] Congruent Supplement Theorem
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Answer:
Step-by-step explanation:
<3 is supplementary to <4 Linear pair theorem
I took the plato test and got it right
can someone help me!!
If im trying to get 20 million dollars and i get 300$ per second how long will it take to reach my goal
Answer:
66666.66 seconds, or 1111.12 minutes
Step-by-step explanation:
Since you are earning 300 dollars per second, and you want to earn 20 million, or 20000000 dollars, you can divide 20 million by 300 to get the time it takes to reach your goal in terms of seconds:
[tex]\frac{20000000}{300}=66666.66[/tex] seconds
It will take you approximately 66667 seconds to reach your goal. If we divide by 60 to get this in terms of minutes, we get that it takes about 1111.12 minutes
Answer:
66.666.6 seconds
1,111.11 minutes
18.518518518499999 hours
Step-by-step explanation:
20,000,000÷300
=66,666.6666666
Change in minutes= 66,666.6666666÷60 =1,111.1111111
Change in hours= 1,111.11111111÷60=18.518518518499999
What is the slope of the line that passes through the points ( 8 , − 6 ) (8,−6) and ( 8 , − 9 ) (8,−9)? Write your answer in simplest form
As slope is undefined, then the slope of the line is parallel to the x axis.
How to determine the slope of a line
In this problem we have a line that passes through two points, the slope is determined by definition of secant line:
m = [- 9 - (- 6)]/(8 - 8)
m = - 3/0
As slope is undefined, then the slope of the line is parallel to the x axis.
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The side lengths of a triangle are 9, 12, and 15. Is this a right triang
O A. Yes, because 9² + 12² > 15².
O B. No, because 9 + 12 ‡ 15.
OC. Yes, because 9² + 12² = 15².
OD. No, because 9² + 12² # 15².
A car is valued at $35400 at the start of the year, and at $25700 at the end of that year. During that year, the car travelled 25000kms.
a) Find the total depreciation of the car in that year in dollars
b) Find the depreciation per kilometre for this car
c) Using (initial value) -> V₀ = 35400, write down a rule for the value of the car Vₙ after ₙ kilometres
d) How many kilometres are travelled when the value of the car is $6688?
e) Including the first year of travel, how many kilometres in total is this car expected to drive before it has a value of 0?
a. Total depreciation = $9700
b. Depreciation per kilometer = $0. 388 per kilometer
c. Vₙ = $35400 + ₙt
d. Distance = 4723. 16 kilometers
e. Total distance = 29723. 16 kilometers.
How to determine the depreciation
i. The formula for total depreciation is given as;
Total depreciation = Cost of asset - Residual value
Cost of car = $ 35400
Residual value = $25700
Total depreciation = $35400 - $25700
Total depreciation = $9700
b. Depreciation per kilometer = Total depreciation/ distance travelled in kilometers
Depreciation per kilometer = $ [tex]\frac{9700}{25000}[/tex]
Depreciation per kilometer = $0. 388 per kilometer
c. Vₙ = V₀ + ₙt
t = time of depreciation
V₀ = $35400
Vₙ = $35400 + ₙt
d. When the car costs $35400, it travelled 25000 kilometers
It costs $6688, it would travel 'x' kilometers
Cross multiply
$35400 × x = $ 6688 × 25000 kilometers
Make 'x' subject
x = [tex]\frac{6688 * 25000}{35400}[/tex]
x = [tex]\frac{167200000}{35400}[/tex]
x = [tex]4723. 16[/tex] kilometers
The car would travel 4723. 16 kilometers
e. To find the total distance
Total distance = 25000 + 4723. 16
Total distance = 29723. 16 kilometers.
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the accompanying diagram shows a kit that has been secured to skate in the ground with a 20-foot string. the kit is located 12 feet from the ground, directly over point X. what is the distance, in feet, between the skate and point X.
The distance between the skate and point X is 16 feet
Given that the distance between point X and kite is 12 feet
and the distance between stake and kite is 20 feet
We need to find the distance between the stake and point X
Here,
Perpendicular = 12 feet
Hypotenuse = 20 feet
Base = ?
According to Pythagoras Theorem
(Hypotenuse)² = (Perpendicular)²+(Base)²
(20)² = (12)² + (Base)²
∴ (Base)² = 400 - 144
∴ (Base)² = 256
∴ Base = 16 feet
Hence the distance between the Point X and the stake is 16 feet
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The minimum point on the graph of the equation y=f(x) is (−1,−3). What is the minimum point on the graph of the equation y=f(x−5)? A. (4,−3) B. (−1,−8) C. (−1,−3) D. (−7,−3)
Answer:
(4, -3)
Step-by-step explanation:
y = f(x -5) means y = f(x) shifted 5 units to the right. So the minimum point would shift 5 units to the right as well.
Evaluate the expression 21 ÷ 3 + 8 − 4.
A) 19
B) 17
C) 15
D) 11
Answer:
D
Step-by-step explanation:
We will use the order of operations to evaluate the expression.
From left to right , Multiplication/Division followed by Addition/Subtraction.
21 / 3 + 8 - 4
= 7 + 8 - 4
= 15 - 4
= 11
Therefore, the answer is D
Answer:
D) 11
Step-by-step explanation:
Division and multiplication always comes first in an equation. Since there is no multiplication in the expression, we can divde first.
21 / 3 = 7
Our new expression will be: 7 + 8 - 4
Now we can just add (7) , (8), and (-4) not caring about the order, since they are all addition or subtraction.
I'll do the addition first, but order does not matter.
7 + 8 = 15
15 - 4 = 11
So 11 is our final answer.
Looking at the answer choices, D has 11, so D is our answer for this question.
HELP! 10 POINTS+Braniest
A shipment of 60 highly sensitive accelerometers is to be accepted or rejected based on the testing of 5 chosen randomly from the lot. The shipment will be rejected if more than 1 of the 5 fail. It is known that 10% of the shipment does not meet the specifications. Let X denote the number of units that fail.
The value of X that number of unit fails are 1/12.
According to the statement
we have a given that the there is a shipment of 60 highly sensitive accelerometer. And there is a testing of randomly 5 accelerometers.
And we have to find that the how much units that fails in the specifications.
So,
We find the value of X by use of Probability.
The probability that unit fails = number of units that chosen randomly / total units.
So, substitute the values in it then
The probability that unit fails = 5 / 60
The probability that unit fails = 1 / 12.
The probability that unit fails from 60 accelemoters is 1 / 12.
So, The value of X that number of unit fails are 1/12.
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Solve the congruence 3x=2(mod4)
Answer:
Step-by-step explanation:
jello :
3x=2(mod4)
multiply by ; 5
5×3x=5×2(mod4)
15x=10(mod4)
but : 15= -1 (mod4) and 10= 2 (mod4)
-x=2 (mod4)
now multiply by ; -1 you have : x= -2 (mod4)
-2=2(mod4)
conclusion : x=2 (mod4) means : x=4k+2 k in Z