The cost C of building a house is related to the number k of carpenters used and the number x of electricians used by the formula
C
=
15
,
000
+
50
k
2
+
60
x
2
.
(a) Assuming that 10 carpenters are currently being used, find the cost function C, marginal cost function C', and average function ¯
C
, all as a function of x.
C(x) = _____
C'(x) = _____
¯
C
(
x
)
=
_____
(b) Use te functions you obtained in part (a) to compute C'(16) and ¯
C
(16).
C'(16) = $ _____ per spot
¯
C
(16) = $ _____ per spot (Round your answer to two decimal places.)
Use these two answer to say whether the average cost is increasing or decreasing as the number of electricians increases.
a. The average cost is increasing as x increases.
b. The average cost is decreasing as x increases.
Answers
The cost C of building a house is related to the number k of carpenters used and the number x of electricians
For the given condition,
C(x) = 20000 + 60x²
C'(x) = 120x
C(16) = 35360
C'(16) = 1920
Increasing and Decreasing function:
function f(x) is said to be increasing function if,
f'(x) >0 ,for all value of x
function f(x) is said to be decreasing function if,
f'(x) <0 ,for all value of x
where, f'(x) is derivative of f(x)
Given Equation is,
C = 15,000 + 50k² + 60x²
where,
k = number of carpenter.
x = number of electrician.
(a).
10 carpenters are currently being used.
that is,
k = 10
so,
C = 15000 + 50 * 10² + 60x²
= 15000 + 50*100 + 60x²
= 15000 + 5000 + 60x²
= 20000 + 60x²
thus,
C(x) = 20000 + 60x²
Now,
C'(x) = 0 + 60*2x
C'(x) = 120x
(b).
As,
C'(x) = 120x
C'(16) = 120 * 16
= 1920
C'(16) = 1920
As,
C(x) = 20000 + 60x²
C(16) = 20000 + 60 * 16²
= 20000 + 60 * 256
= 20000 + 15360
= 35360
C(16) = 35360
We conclude,
As the number of electrician increases the average cost also increases.
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Related Questions
In the middle school debate club, 30%
of the members are in sixth grade. If
there are 12 sixth graders in the debate
club, how many total members are
there?
a. 30
b. 36
c. 38
d. 40
Answers
Answer:
40
Step-by-step explanation:
I used a calculator tbh but all you have to do is multiply the number by the percentage. 30% * 40 is 12.
There are total 40 members in the middle school, option (d) is correct
What is percentage?Percentage is a measurement to find the value of a given number out of hundred.
Given that,
Percentage of the members present in 6th grade = 30%
Also, the number of the sixth grade members = 12
According to the condition,
30% = 12
1% = 12/30
Total members are 100%,
So, 100% = 40
Total number of members is 40 in the middle school.
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Simplify (-2x^3)^2 x y x y^9
- for anyone that needs this answer
Answers
Answer:
\( 4x}^{6} {y}^{10} \)
Step-by-step explanation:
The reason it is 4x^2 for the first part is because the entirety of -2x^3 is being squared, so we need to do -2×-2 which will give us the 4 and 3×2 which will give us the 6.
It's y^10 because we have y×y^9, so we ADD the powers, giving us the power of 10.
Find the length of the diagonal of a square with perimeter 56
Answers
Answer:
About 19.8
Step-by-step explanation:
First find the side lengths. In this example, 56/4=14
Next use the Pythagorean theorem, to us it, here's the formula a squared plus b squared equals c squared. For this example use 14 squared plus 14 squared which equals 392.
Finally take the square root of 392 because we still need to take the squared out in c. The square root of 392 rounded to the nearest tenth is 19.8.
Translate this phrase into an algebraic expression. Eight less than the product of 7 and a number
Answers
The algebraic expression for this phrase is 7x - 8, where x is the number.
To explain this expression, we must consider what it means. The phrase "eight less than the product of 7 and a number" means that we are to take the product of 7 and some other number, and then subtract 8 from that product. The product of 7 and any number is written as 7x. So, 7x is the product of 7 and some number, x. We then subtract 8 from that product, so our expression looks like 7x - 8.To illustrate this expression, let's use an example. Let's say that x is equal to 5. The expression 7x - 8 would be equal to 7(5) - 8, which can be calculated as 35 - 8, or 27. This means that the phrase "eight less than the product of 7 and a number" is equal to 27 when the number is equal to 5.To sum up, the phrase "eight less than the product of 7 and a number" is written as an algebraic expression as 7x - 8, where x is the number. This expression means that we should take the product of 7 and some other number, and then subtract 8 from that product. Using an example with x equal to 5, the expression 7x - 8 would be equal to 27.
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WHAT IS
9x 3/5 IN FRSCTION FORM NEED HELP THASNK you
Answers
Answer:
27/5 or 5 2/5
Step-by-step explanation:
Assuming you mean 9 x 3/5
The answer would be
27/5
in Decimals, it would be
5.4
and in mixed numbers form it would be
5 2/5
write -23 27/50 as a decimal number.
Answers
Answer:
Step-by-step plotttt
Answer:
23.54
Step-by-step explanation:
a critical value, z subscript alphazα, denotes the _______.
Answers
A critical value, z subscript alpha (zα), denotes the boundary or cutoff point for a statistical test where the level of significance, also known as alpha (α), is set.
A critical value, z subscript alpha (zα), denotes the value at which the probability of observing a test statistic in the tail(s) of the sampling distribution equals the pre-determined significance level (alpha).
The critical value can be defined as the value that is compared with the parameter value in the hypothesis test to determine whether the null hypothesis will be rejected. If the value of the parameter is less than the critical value, the null hypothesis is rejected.
However, if the measured value is higher than the critical value, reject the null hypothesis and accept the alternative hypothesis. In other words, cropping divides the image into acceptable and unacceptable areas. If the value of the index falls within the rejection range, the rejection of the fact is rejected, otherwise the negative hypothesis is rejected.
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The measure of an angle is 100.3°. What is the measure of its supplementary angle?
Answers
Answer:
79.7°
Step-by-step explanation:
You hava to do this =
\(180-100.3=79.7\)
Answer:
79.7°
Step-by-step explanation:
Supplementary angles add up to 180°
100.3 + x = 180
Subtract 100.3 from both sides
x = 79.7°
Jonna ran a mile in a physical education class
Answers
the proportion of college football players who have had at least one concussion is estimated to be 34% in the united states. we wanted to know if football players at our university were less likely to have suffered a concussion, so we surveyed a random sample of 100 past and present football players at our university. is this survey valid or not valid for testing the hypothesis that the proportion of college football players at our university with at least one concussion is less than the national average?
Answers
All of the criteria's are fulfilled the survey is valid.
We have the information from the question:
The proportion of college football players who have had at least one concussion is estimated to be 34% in the united states.
Then, 34% = 0.34
The sample size of the data is = 100
p: the ‘proportion’ of ‘college’
The required conditions for testing the hypothesis of population proportion are,
(i) The population is larger than the sample
(ii) np > 10
=> 100 × 0.34
=34
(iii) n(1-p) > 10
100 × (1 - 0.34)
=> 100 × 0.66
=66
iv)The ‘sample’ is drawn randomly from the population.
Since all of the above criteria's are fulfilled the survey is valid.
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use the elimination method to solve the system of equations choose the correct ordered pair 7x+4y=39 2y+4y=14
Answers
\(x = 5 \: and \: y = 1.\)
Step-by-step explanation:
\(7x + 4y = 39 \: - {eq}^{n} (1)\)
\(2x + 4y = 14 \: \: - {eq}^{n} (2)\)
Multiply Equation no (1) with 2 and Equation no (2) with 7.
\(14 x + 8y = 78.\)
\(14x + 28y = 98.\)
\(( - ) \: \: \: ( - ) \: \: \: ( - )\)
\(0x + -20y = - 20\)
\( - 20y = - 20\)
\(y = \frac{ - 20}{ - 20} \)
\(y = 1\)
Substitute the value of "y" in Equation no (1)
\(7x + 4y = 39.\)
\(7x + 4(1) = 39.\)
\(7x + 4 = 39.\)
\(7x = 39 - 4\)
\(7x = 35.\)
\(x = \frac{35}{7} \)
\(x = 5.\)
Answer:
\( \: 7x+4y=39 2x+4y=14 A. 5,4 B. 3,2 C. 5,1 D.\)
Hope it helps
The number of goldfish in a tank is 19, and the volume of the tank is 52 cubic feet. What is the density of the tank?
Answers
Answer:
0.37 goldfish per cubic feet
Step-by-step explanation:
Density has the formula = number/volume
Density = 19/52 = 0.36538 which is rounded to 0.37
Answer:
0.37 goldfish / cu ft. (to the nearest hundredth).
Step-by-step explanation:
Density = number of goldfish / volume of the tank.
That is 19 / 52
= 0.37 goldfish / cu ft.
Verify that each given function is a solution of the differential equation (each 10 pts).1. y"-4y = 0;1) y(t) = e2t,2) y(t) = cosht2. y" + 2y - 3y= 0;1) y(t) = e-31,2) y(t) = et3. 12y" + 5ty' + 4y = 0, t> 0; 1) y(t) = t2,2) y(t) = t2n t4. y" + y = sect; 0
Answers
To verify if each given function is a solution of the differential equation, we need to substitute the function into the differential equation and check if the equation holds true.
For the differential equation y" - 4y = 0:
a) Substitute y(t) = e^(2t):
y" = (e^(2t))'' = 4e^(2t)
4y = 4e^(2t)
The equation y" - 4y = 0 holds true.
b) Substitute y(t) = cosh(t):
y" = (cosh(t))'' = cosh(t)
4y = 4cosh(t)
The equation y" - 4y = 0 holds true.
For the differential equation y" + 2y - 3y = 0:
a) Substitute y(t) = e^(-3t):
y" = (-3e^(-3t))
2y = 2e^(-3t)
The equation y" + 2y - 3y = 0 holds true.
b) Substitute y(t) = e^(t):
y" = e^(t)
2y = 2e^(t)
The equation y" + 2y - 3y = 0 holds true.
For the differential equation 12y" + 5ty' + 4y = 0, t > 0:
a) Substitute y(t) = t^2:
y" = 2
y' = 0
5ty' = 0
12y" + 5ty' + 4y = 12(2) + 0 + 4(t^2) = 24 + 4t^2
The equation 12y" + 5ty' + 4y = 0 holds true.
b) Substitute y(t) = t^2:
y" = 2
y' = 0
5ty' = 0
12y" + 5ty' + 4y = 12(2) + 0 + 4(t^2) = 24 + 4t^2
The equation 12y" + 5ty' + 4y = 0 holds true.
For the differential equation y" + y = sec(t):
a) Substitute y(t) = sec(t):
y" = sec(t)tan(t)
y = sec(t)
The equation y" + y = sec(t) holds true.
b) Substitute y(t) = sec(t):
y" = sec(t)tan(t)
y = sec(t)
The equation y" + y = sec(t) holds true.
Therefore, each given function is a solution to its respective differential equation.
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which of the following give chart elements a realistic, three-dimensional look?A. axisB. chart areaC. legendD. plot area
Answers
The option that gives chart elements a realistic, three-dimensional look is D. Plot Area.
The option that gives chart elements a realistic, three-dimensional look is the plot area. The plot area is the portion of the chart that displays the data points and is typically the main focus of the chart. Adding shading and depth to the plot area, can give the chart a more lifelike appearance and make the data more visually engaging. Additionally, three-dimensional charts can also be created by using specialized charting software that allows for the creation of 3D visualizations. These types of charts can be useful for highlighting patterns and trends in the data, especially when dealing with large datasets.
In a chart, the plot area is the space where the actual data points, bars, lines, or pie slices are displayed. By applying three-dimensional effects to the plot area, you can make the chart elements appear more realistic and visually appealing. This can enhance the viewer's understanding of the data being represented and make the chart more engaging.
In summary, to give chart elements a realistic, three-dimensional look, you should focus on the plot area (Option D). The axis (Option A), chart area (Option B), and legend (Option C) do not directly contribute to creating a three-dimensional appearance for the chart elements.
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How can you determine whether the sum of several numbers, such as 13 + 45 + 24 +17, is odd or even without actually calculating the sum?
Answers
Answer:
Step-by-step explanation:
Hello,
odd + odd gives even
odd + even gives odd
so odd + odd + even + odd = even + even + odd = even + odd = odd
So the sum is a odd number
thanks
The sum of three odd numbers is odd and that added to an even number results in an odd number.
What are some other related concepts?An even number raised to the even or odd power is even and an odd number raised to the power of even or odd is always an odd number.
We know the sum of two even numbers is even, the sum of two odd numbers is also even and the sum of an odd and even number is odd and vice versa.
Given four numbers first two numbers are odd so their sum is even.
The next two numbers are even and odd so their sum is odd, Now the sum of even and odd is odd.
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Solve: (8x − 4) + (−2x + 3)
Answers
Hey there!
(8x - 4) + (-2x + 3)
= 8x - 4 + (-2x) + 3
= 8x - 4 - 2x + 3
COMBINE the LIKE TERMS
= (8x - 2x) - (4 + 3)
= 8x - 2x - 4 + 3
= 6x - 1
Therefore, your answer is: 6x - 1
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Hope I helped.
Natalie is hiking up a mountain while Simone is hiking down. When Natalie begins to ascend, Simone begins to descend at the same time. The graph shows Natalie’s elevation in feet over time in minutes. The table shows Simone’s elevation at different times. Who is hiking at a faster rate? Show your work.
Answers
To know who is hiking at a faster rate, calculate the rate for each hiker using the formula distance/ time and compare the rates.
How to find out who is faster?Calculate how fast each hiker moves or the rate for each hiker.Compare the rates.How to calculate the rate?The rate is equal to distance divided by time. For example,
Natalie travels 100 meters in 5 minutes:100/ 5 = 25 meters per minute.Note: This question is incomplete because the graphs are not provided; due to this, the answer is based on general knowledge.
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simplify:- the following fraction
Answers
Whole part = 2
Fractional part = 59/396
======================================================
Work Shown:
3 & 3/5 = 3 + 3/5
3 & 3/5 = 15/5 + 3/5
3 & 3/5 = 18/5
--------------------
4 & 8/9 = 4 + 8/9
4 & 8/9 = 36/9 + 8/9
4 & 8/9 = 44/9
--------------------
Now apply the rule that 1/(A/B) = B/A. We apply the reciprocal to the fraction A/B to get B/A
That means something like 1/(18/5) becomes 5/18
Also, 1 over (44/9) becomes 9/44
1 over (3/5) becomes 5/3
-------------------
We now have the following:
(5/18) + (9/44) + (5/3)
We'll come back to this later. But first need the LCD, which means we need the LCM of the denominators.
Write out the prime factorization of each denominator
18 = 2*3*344 = 2*2*113 = 1*3The unique prime factors are: 2, 3, 11
We have 2 occur at most twice, so 2^2 is part of the LCM.We have 3 occur at most twice, so 3^2 is part of the LCMWe have 11 occur at most 1 time, so 11^1 is part of the LCMThe LCM is 2^2*3^3*11^1 = 1188, which is also the LCD
-------------------
We need to get each fraction to have the LCD
5/18 = (5/18)*(66/66) = 330/1188
9/44 = (9/44)*(27/27) = 243/1188
5/3 = (5/3)*(396/396) = 1980/1188
We can now add the fractions like so
(5/18) + (9/44) + (5/3)
(330/1188) + (243/1188) + (1980/1188)
(330+243+1980)/1188
2553/1188
-------------------
We're almost done. We just need to convert to a mixed number, aka mixed fraction
Using a calculator or long division, you should find that
2553/1188 = 2.1489898989899
approximately. Focus just on the stuff to the left of the decimal point. That's the whole part of the answer.
We can then say: 2553-1188*2 = 177
This forms the numerator of the fractional part. The denominator stays at the LCD 1188
That forms the fraction 177/1188. Divide both parts of that fraction by 3 to fully reduce it. You should get to 59/396
-------------------
So that's how we end up with the mixed number 2 & 59/396
Calculate the quotient. 3/4 divided by 5 1/5
Answers
The quotient of.tge given fraction and mixed number as required in the task content is; 15 / 104.
What is the quotient of the given numbers?It follows from. the task content that the quotient of the fraction and mixed number given is to be determined.
Since the given numbers whose quotient is to be determined are; 3/4 divided by 5 1/5.
The mixed number 5 ⅕ can be converted to a fraction so that we have; 26 / 5.
On this note, the required quotient is;
3/4 ÷ 26/5
= 3/4 × 5/26
= 15 / 104
On this note, the quotient of the two numbers as required is; 15 / 104.
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Which calculation and answer show how to convert 3/12 to a decimal
Plz help ASAP
Answers
Answer:
Its C
Step-by-step explanation:
It is C becuase when converting a fraction to a decimal, you just divide the numerator by the denominator
Basically solve the fraction
3/12=1/4
1/4 is a bencmark so right away you should know that should equal to 0.25 since its a quarter.
Or you can always look it like this
3 is the numerator
the “/“ between is basically ”divided by”
And the 12 is the denominator
Now read the equation in that order
3/12= 3 DIVIDED BY 12
There you go!
A store sells 12 cans of soup for $7. 50 how much would it cost to purchase 6 cans of soup?.
Answers
Answer: $3.75
Step-by-step explanation:
Answer:
The cost of 6 cans of soup is 3.75
Step-by-step explanation:
12 = 7.50
1 can = x
12x = 7.50
We need to find the cost of 1 can. So we divide 7.50 by 12.
x = 0.625
Then multiply by 6.
0.625 x 6 = 3.75
As a result the cost of 6 cans of sup is $3.75
What is the value of x?
A. 60°
B. 155
C. 25°
D. 35°
Answers
Answer:
D. 35°
Step-by-step explanation:
1. The bottom right angle and 95° add up to 180°. Solve for that angle.
95 + y = 180
y = 85
2. Triangles have a total of 180°. Set up the equation.
60 + 85 + x = 180°
3. Simplify
145 + x = 180
4. Solve for x by subtracting 145 from both sides
x = 35°
Answer:
x = 35
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
60+x = 95
Subtract 60 from each side
60 +x-60 = 95-60
x = 35
Which of the following statements is true about the Law of Large Numbers (LLN)?The LLN states that the empirical probability that is observed will simulate the theoretical probability that is expected for any finite number of trials, so a simulation or experiment need not have an excessive number of trials.The LLN states that if you simulate or conduct an experiment or simulation enough times the empirical probability observed will always match the theoretical probability that is expected.The LLN states that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability.***The LLN does not apply to probability theory.The LLN is almost always true, but there are special occasions, even when outcomes are random, when the LLN can be broken.
Answers
The LLN states that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability.
The Law of Large Numbers (LLN) is a statistical theorem which states that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability. This means that the empirical probability will approximate the theoretical probability as the number of trials increases. Therefore, the statement that is true about the LLN is that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability.
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A certain freely falling object requires 1.20 s to travel the last 24.0 m before it hits the ground. From what height above the qround did it fall? Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m
Answers
The object fell from a height of approximately 7.057 meters above the ground.
We can solve this problem using the equations of motion for a freely falling object. The equation we’ll use is:
H = (1/2) * g * t^2
Where h is the initial height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time taken to travel the last distance. Rearranging the equation, we get:
H = (24.0 m) + (1/2) * (9.8 m/s^2) * (1.20 s)^2
Calculating this expression, we find that h is approximately 7.057 meters. Therefore, the object fell from a height of approximately 7.057 meters above the ground.
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henry's hamburger heaven offers its hamburgers with the following condiments: ketchup, mustard, mayonnaise, tomato, lettuce, pickles, cheese, and onions. a customer can choose one, two, or three meat patties, and any collection of condiments. how many different kinds of hamburgers can be ordered?
Answers
In linear equation, the total number of possible hamburgers is 768.
What are a definition and an example of a linear equation?
An equation in which there is only one variable is known as a linear equation in one variable.It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value.One such linear equation in one variable is 9x + 78 = 18.Total number of possible hamburgers is 768
Given,
The number of condiments = 8
Total number of combinations with 8 condiments = 2⁸ = 256
A customer can choose one, two or three meat patties
Total number of possible hamburgers = 256×3= 768
Hence, the total number of possible hamburgers is 768
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if one face of a cube has an area of 6in²,what is the total surface area of the cube
Answers
The face of a cube is in the shape of square :
The area of one face of cube is 6 in²
i.e. Area of square = 6 in²
Since the general expression for the area of square is Side x Side
\(\begin{gathered} \text{ Area of side face =6} \\ \text{side}\times side=6 \\ \text{side}^{2}=6 \\ \text{side}=\sqrt[]{6} \end{gathered}\)
The general expression for the total surface area of cube is : 6 side²
Substitute the value of side :
\(\begin{gathered} \text{ Total surface of area = 6 a}^{2} \\ \text{Total surface of area =6}\times(\sqrt[]{6})^2 \\ \text{Total surface of area =6}\times6 \\ \text{Total surface of area =}36in^2 \end{gathered}\)Total surface area of cube is 36 in²
Find the most general real-valued solution to the linear system of differential equations.
Answers
To provide a general real-valued solution to a linear system of differential equations, specific equations need to be provided. Without the specific equations, it is not possible to determine the exact solution.
In general, a linear system of differential equations can be written in matrix form as follows:
dY/dt = AY,
where Y is a vector of functions, t is the independent variable, and A is a constant matrix.
To solve this system, one can use methods such as matrix diagonalization, eigenvalues, and eigenvectors, or the method of variation of parameters. These methods allow you to find the general solution of the system, which represents a family of solutions that satisfy the given equations.
It is important to note that the specific form of matrix A and the initial or boundary conditions if provided, will determine the exact solution to the system of differential equations.
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If the sun were the size of an exercise ball (75. 0 cm) and if jupiter were the size of a golf ball (4. 3 cm), how big would earth be on this scale?.
Answers
The scale where the Sun is represented by an exercise ball and Jupiter is represented by a golf ball, Earth would be approximately 126,750 km in size.
To determine the size of Earth on the scale where the Sun is represented by an exercise ball (75.0 cm) and Jupiter is represented by a golf ball (4.3 cm), we need to calculate the proportional size of Earth.
The diameter of the Sun (represented by the exercise ball) is 75.0 cm, and the diameter of Jupiter (represented by the golf ball) is 4.3 cm. We can use the ratio of these diameters to find the proportional size of Earth.
Let's calculate it:
Proportional size of Earth = (Diameter of Earth / Diameter of Jupiter) × Diameter of the Sun
Proportional size of Earth = (Diameter of Earth / 4.3 cm) × 75.0 cm
To find the diameter of Earth on this scale, we need to determine the ratio of Earth's diameter to Jupiter's diameter and then multiply it by the diameter of the Sun:
Proportional size of Earth = (12,742 km / 139,820 km) × 1,391,000 km
Calculating this expression:
Proportional size of Earth = (0.09108) × 1,391,000 km
Proportional size of Earth ≈ 126,750 km
Therefore, on the scale where the Sun is represented by an exercise ball and Jupiter is represented by a golf ball, Earth would be approximately 126,750 km in size.
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find the 5th term of this sequence: 3/2,4/3,5/4,6/5
Answers
The 5th term of the sequence is 7/6.
Step-by-step Explanation:
To find the 5th term of the sequence 3/2, 4/3, 5/4, 6/5, we need to determine the pattern in the sequence.
Looking at the sequence, we can see that each term is obtained by adding 1 to both the numerator and the denominator of the previous term.
Using this pattern, we can find the 5th term as follows:
Starting with the 4th term, 6/5, we add 1 to the numerator and 1 to the denominator to get the 5th term:
(6 + 1) / (5 + 1) = 7/6
Therefore, the 5th term of the sequence is 7/6.
Solve for a
6a-15=72
Answers
Answer:
a=
Step-by-step explanation:
72+15=87
87/6= 14.5
a= 14.5
Answer: 14.5
Step-by-step explanation:
6a - 15 = 72
add 15 on both sides
6a = 87
divide by 6 on both sides
a = 14.5