(A) Find the marginal cost at a production level of a golf clubs.C'(x) =(B) Find the marginal cost of producing 55 golf clubs.Marginal cost for 55 clubs =
Answers
ANSWER
The marginal cost for producing 55 golf clubs is $31
STEP-BY-STEP EXPLANATION:
Given information
[tex]The\text{ total cost }in\text{ dollars = }550\text{ + 130x - }0.9x^2[/tex]The next step is to find the marginal cost
The formula for finding marginal cost is given below as
[tex]MC\text{ = }\frac{\text{ }\Delta C}{\text{ }\Delta x}[/tex]To find the marginal cost, we need to differentiate the total cost with respect to x
[tex]\begin{gathered} MC\text{ = }\frac{\text{ }\Delta C}{\text{ }\Delta x}\text{ = C'(x)} \\ C^{\prime}(x)\text{ = 0 + 1 }\times130x^{1\text{ - 1}}-2(0.9)x^{2\text{ -1}} \\ C^{\prime}(x)\text{ = 0 + 130 - 1.8x} \end{gathered}[/tex]Therefore, the marginal cost is
[tex]C^{\prime}(x)\text{ = 130 - 1.8x}[/tex]Part b
Find the marginal cost of producing 55 golf clubs
Let x = 55
The next step is to substitute the value of x = 55 into the above marginal cost formula
[tex]\begin{gathered} C^{\prime}(x)\text{ = 130 - 1.8x} \\ C^{\prime}(55)\text{ = 130 - 1.8(55)} \\ C^{\prime}(55)\text{ = 1}30\text{ - 99} \\ C^{\prime}(55)\text{ = \$31} \end{gathered}[/tex]Therefore, the marginal cost for producing 55 golf clubs is $31
Related Questions
Find the value of x.12x-26
Answers
12x-26 = 142
We add 26 on each side:
26 + 12x-26 = 142 + 26
On the left side: 26 - 26 + 12x = 12x
On the right side: 142 + 26 = 168
Now: 12x = 168 => x = 168/12
x = 14 ft
I am going to attach a picture of the question as you can see it's already been answered well my teacher wants me to show how she got that answer.
Answers
C
1) Since the diameter of a circle is at (3,-7) and (5,7) then we can find the radius this way.
(x-h) +(y-k)² = r²
2) The Center is at the midpoint of the Diameter, then let's find out the midpoint of the line whose endpoints are (3,-7) and (5,7)
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2}) \\ M=(\frac{3+5}{2},\frac{7-7}{2}) \\ M=(4,0) \end{gathered}[/tex]2.2) Now, we need to find out the radius. Let's pick one of those points (5,7) and the Midpoint (4,0) and find out the distance:
[tex]\begin{gathered} d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}_{} \\ d=\sqrt[]{(5-4)^2+(7-0)^2} \\ d=\sqrt[]{50} \end{gathered}[/tex]This distance between one of those endpoints and this midpoint is the radius.
3) Finally, let's plug into the equation of the Circle the following:
[tex]\begin{gathered} (x-4)^2+y^2=(\sqrt[]{50})^2 \\ (x-4)^2+y^2=50 \end{gathered}[/tex]Hence, the answer is C
A trucking company transports goods between two cities that are 960 miles apart. The company charges, for each pound, $0.55 per mile for the first 100 miles, $0.40 per mile for the next 300 miles, $0.30 per mile for the next 400 miles, and no charge for the remaining 160 miles.(a) Graph the relationship between the cost of transportation in dollars C(x) and mileage x over the entire 960-mile route.(b) Find the cost as a function of mileage for hauls between 100 and 400 miles from the first city.(c) Find the cost as a function of mileage for hauls between 400 and 800 miles from the first city.
Answers
(a) The relationship between the cost of transportation in dollars C(x) and mileage x over the entire 960-mile route
Option A is the correct answer
(b) The cost as a function of mileage for hauls between 100 and 400 miles from the first city = $0.95
(c) The cost as a function of mileage for hauls between 400 and 800 miles from the first city = $1.25
Which pair of lines are perpendicular? A) y = 4x - 9 and y + 4x = 3 B) y = 3x + 7 and y + 2 = 3(x - 5) C) y = 2x and 2y = x -9 D) y + x = 0 and y = x
Answers
First, take into account that the general form of a linear equation is:
y = mx + b
where m is the slope and b the y-intercept.
When two lines are parallel, their slopes are equal.
When two lines are perpendicular, you can verify the following relation between slopes:
m1 = -1/m2
Then:
A)
y = 4x - 9
y + 4x = 3 which is the same as
y = -4x + 3
In this case you can notice that the slopes are not the same and m1 ≠ -1/m2.
Hence, the lines are not neither parallel nor perpendicular.
B)
y = 3x + 7
y + 2 = 3(x-5) which is the same as
y = 3x - 15 - 2
y = 3x - 17
In this case the slopes are the same, then, the lines are parallel
C)
y = 2x
2y = x - 9 which is the same as
y = 1/2 x - 9/2
In this case you can notice that the slopes are not the same and m1 ≠ -1/m2.
Hence, the lines are not neither parallel nor perpendicular.
D)
y + x = 0 which is the same as
y = -x
y = x
In this case you can verify that m1 = -1/m2, then, the line are perpendicular.
write an equation to represent the proportional relationshipnote use x for the independent variable and why for the dependent variable for the questiona factory produces three bottles of sparkling water for every eight bottles of plain water. how many bottles of sparkling water does the company produce when it produces 600 bottles of plain water?
Answers
Use the ratio given in the statement to find the equation that represents the proportional relationship:
[tex]\begin{gathered} \frac{8}{3}=\frac{x}{y} \\ 8y=3x \end{gathered}[/tex]Now, replace for the given value and find y. (x represents the number of bottles of plain water and y the number of bottles of sparkling water).
[tex]\begin{gathered} 8y=3\cdot600 \\ y=\frac{1800}{8} \\ y=225 \end{gathered}[/tex]The company produces 225 bottles of sparkling water when it produces 600 bottles of plain water.
Which expression is equivalent to the given expression? Give a step-by-step guide and explain how you got to your answer, so I can actually learn how to do this.
Answers
The Solution:
Given:
Required:
Find an equivalent expression of the given expression.
[tex]\begin{gathered} (2w^{-2})^3(8w^6) \\ \\ 2^3\times8\times w^{-2\times3}\times w^6 \end{gathered}[/tex][tex]\begin{gathered} 8\times8\times w^{-6}\times w^6 \\ \\ 64\times w^{-6+6} \\ 64\times w^0 \\ 64\times1 \\ 64 \end{gathered}[/tex]Answer:
[option B]
Which statement is not true about the pattern shown? 2/3 k 12 24 8 16 12' 24 1) Each fraction is equivalent to 3 1) Each fraction is equal to the previous fraction in the pattern multiplied byz. 1) Each fraction is greater than the previous fraction. The next fraction in the pattern is 32 48
Answers
We need to evaluate the fractions below:
[tex]\frac{2}{3},\frac{4}{6},\frac{8}{12},\frac{16}{24},\ldots[/tex]All these fractions have the same value, they're equivalent to "2/3". On each step there is a product of 2 on the numerator and 2 on the denominator, therefore they're related by the factor of "2/2". If we multiply the last term by the factor we get:
[tex]\frac{16}{24}\cdot\frac{2}{2}=\frac{32}{48}[/tex]The only one statement that is false is: "Each fraction is greater than the previous fraction". They all have the same value, so the correct option is the third.
How does the graph of g(x) -ta's+ 2x-5compare to the graph of the plent function Rx) = ?Ag(x) is shifted 5 units left and 2 units up from f(x).B g(x) is shifted 5 units right and 2 units up from f(x).B g(x) is shifted 5 units left and 2 units down from f(x).B g(x) is shifted 5 units right and 2 units down from f(x).
Answers
Given the parent function below
[tex]f(x)=\frac{1}{x}[/tex]The graph of the function above is shown below
Given that the function f(x) has been transformed and the new function is
[tex]g(x)=\frac{1}{x-5}+2[/tex]The transformation above can be described as
g(x) is shifted 5 units to the right and 2 units up from f(x)
The final answer is Option
How much would you need to deposit in an account now in order to have $6000 in the account in 10years? Assume the account earns 3% interest compounded quarterly. Round your answer to thenearest cent.Submit Question
Answers
$4450.05
Explanations:The formula for calculating the compound ammount is expressed as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Given the following parameters
• Amount after 10 years A = $6000
,• P is the amount deposited
,• r is the rate = 3% = 0.03
,• t is the time t = 10 years
,• n = 4 (compounding time)
Substitute the given parameters
[tex]\begin{gathered} 6000=P(1+\frac{0.03}{4})^{4(10)} \\ 6000=P(1.0075)^{40} \\ 6000=P(1.3483) \end{gathered}[/tex]Divide both sides by 1.3483
[tex]\begin{gathered} P=\frac{6000}{1.3483} \\ P=\$4450.05 \end{gathered}[/tex]Hence the amount you need to deposit now is $4450.05
Find the density of a metal cone with a height of 20 centimeters and a radius of 5 centimeters. The mass is 2500 grams. Round to the nearest hundredth.
Answers
We are asked to find the density of the metal cone.
The density of a body is given by:
[tex]density(\rho_{})=\frac{Mass}{\text{Volume}}(gcm^{-3})_{}[/tex]We have been given the Mass of the body as 2500 grams
All we need to find is the volume in order to find the density of the metal
The metal is a cone. The volume of a cone is given by:
[tex]\begin{gathered} \text{Volume}=\frac{1}{3}\times\pi\times r^2\times h \\ \\ r=\text{radius}=5\operatorname{cm} \\ h=height=20\operatorname{cm} \end{gathered}[/tex]Now we can find the volume of the metallic cone:
[tex]\text{Volume}=\frac{1}{3}\times\pi\times5^2\times20=523.599\operatorname{cm}^3[/tex]We have been given the mass of the cone and we just finished calculating the volume of the metal, therefore, we can find the density of the metal as:
[tex]\begin{gathered} density(\rho)=\frac{Mass}{Volume} \\ \\ \therefore\rho=\frac{2500}{523.599}\text{gcm}^{-3} \\ \\ \rho=4.7746\text{gcm}^{-3}\approx4.78\text{gcm}^{-3} \end{gathered}[/tex]Therefore, the final answer is: 4.78g/cubic
The price of Quiktrip stock dropped a total of $372.33 over a 7 day period. The stock dropped the same amount each day. What amount did they lose each day?
Answers
Stella, this is the solution:
• Average amount the stock dropped each day = 372.33/7
,• Average amount the stock dropped each day = $ 53.19
The diameter of a circle is 18 feet. What is the length of a 150° arc?
Answers
The general working equation to find the length of the arc given the angle is
[tex]\text{arc}=2\pi r(\frac{\theta}{360})[/tex]The angle given in the problem is 150 degrees. Also, the diameter of the circle is given in the problem. What we need is the radius of the circle before we proceed with the calculation of the arc length of the 150 degrees arc. The radius of the circle is just half of the diameter, hence, we have
[tex]r=\frac{d}{2}=\frac{18ft}{2}=9ft[/tex]We can now proceed with the calculation of the length of the arc. Just substitute the angle and the radius on the working equation and compute
[tex]\text{arc}=2\pi(9ft)(\frac{150}{360})=23.56\approx24ft[/tex]Therefore, the length of the 150-degree arc is equal to 24 ft.
The speed of light is about 300,000,000 m/s. The distance of Earth to Sol is about 148,490,000,000 meters. How long does it take the light from Sol to reach Earth ? Express your answer in seconds in scientific notation. Express your answer in hours in scientific notation. And express your answer in days in scientific notation.
Answers
To make things easier, we first write both quantities with scientific notation:
[tex]\begin{gathered} \text{Speed of light:} \\ 300,000,000\text{ m/s }\rightarrow3\cdot10^8\text{ m/s} \\ 148490000000\text{ m }\rightarrow14849\cdot10^7\text{ m} \end{gathered}[/tex]Now we can find how many seconds will it take the light to reach the sun with a simple division:
[tex]\frac{14849\cdot10^7}{3\cdot10^8}=4.9496\cdot10^2\text{ }[/tex]Therefore, it will take the light 4.9496x10^2 seconds to reach the sun.
Finally, to convert it to hours and days, we just have to divide by the corresponding equivalence:
[tex]\begin{gathered} 1\text{ hour}\rightarrow3600\text{ seconds} \\ \Rightarrow\frac{494.96}{3600}=0.13748=13\cdot10^{-2} \\ 1\text{ day }\rightarrow86400\text{ seconds} \\ \Rightarrow\frac{494.96}{86400}=0.005728=57.28\cdot10^{-4} \end{gathered}[/tex]Therefore, it will take the light 13.748x10^(-2) hours or 57.28x10^(-4) days to reach the sun.
The width of a rectangle is 2x + 4, and the length of therectangle is 8x + 16. Determine the ratio of the width to thelength.Enter your answer as a fraction in the form a/b.
Answers
Given the parameters of the rectangle:
length = (8x + 16)
width = (2x + 4)
The ratio of the width to the length of the rectangle is evaluated as
[tex]\begin{gathered} \frac{\text{width}}{length}\text{ = }\frac{(2x\text{ + 4)}}{(8x\text{ + 16)}} \\ \text{factorize the denominator} \\ \Rightarrow\frac{(2x\text{ + 4)}}{4(2x\text{ + 4)}} \\ =\frac{1}{4} \end{gathered}[/tex]Hence, the ratio of the width to the length is
[tex]\frac{1}{4}[/tex]
Choose the best answer: 8 +9 * 3a. 35b. 51c. 14d. 11
Answers
From the order of operations, solve multiplications first and then solve additions:
[tex]8+9\cdot3=8+27=35[/tex]Therefore:
[tex]8+9\cdot3=35[/tex]what is the one value in the range of this function?
Answers
Given the function:
[tex]\mleft\lbrace(^-6,14),(0,4),(3,^-1),(9,^-9)\mright\rbrace[/tex]Since one valid point in the function is (0, 4)
Therefore, the one value in the range of the function is 4
how do i graph this equation ?Is this relation a function ?Is the graph discrete or continuous?
Answers
Graph of a function
A typical function can be expressed as
y = f(x)
which means we can give x any value and we obtain a value for y
It's said that y depends on x
The equation given in the question has the form
x = -3
Note there is no y in the equation, which means the value of y is unknown, only the value of x is certain.
In other words, when x = -3, y can have any value, and no other value of x can be used
The graph of the function is shown below
The graph is shown as a red line
for a relation to be a function, each value of x must have one and only one value of y
the relation is not a function because the only value of x has many values of y
express this number in scientific notation:19 hundred-thousands
Answers
we have that
19 hundred-thousands is the same that
19*100*1,000=19*100,000=1
1 log in a 1 8.5. MR-6 Question H. Do the data suggest a linear, quadratic, or an exponential function? Use regression to find a model for the data set
Answers
Using a graphing calculator, we determined its behavior
As you can observe in the graph above, the points form a parabola, which belongs to a quadratic expression.
The data suggest a(n) is a quadratic function because the
the ratio of trucks to Cars in the grocery store parking lot is 2 to 3. which statement is ALWAYS true? A: Two out every five vehicles in the parking lot are trucks. B: for every three cars in the parking lot, there are two trucks C: three out of every five vehicles in a parking lot are cars D: for every three trucks in the parking lot there are five cars.
Answers
The given ratio of trucks to Cars in the grocery store parking lot is 2 to 3.
We have to check which statements are always true. For that, let's evaluate each statement.
A: Two out every five vehicles in the parking lot are trucks.
The given ratio of trucks to cars is 2:3. That means, the total number of trucks would be 2/5 and cars would be 3/5. Therefore, there would be 2 trucks in five vehicles. Therefore, this statement is true.
B: for every three cars in the parking lot, there are two trucks
As explained in the above scenario, the number of cars would be 3/5 * x and trucks would be 2/5 * x. if x = 5, cars = 3/5 * 5 = 3 and trucks = 2/5 * 5 = 2. Therefore, this statement is true.
C: three out of every five vehicles in a parking lot are cars
Well, the ratio of trucks to cars is 2:3. But, the parking can have other vehicles as well. Therefore, it is not always true that three out of every five vehicles in a parking lot are cars. Therefore, this statement is false.
D: for every three trucks in the parking lot there are five cars.
The given ratio of trucks to cars is 2:3. But this statement makes the ratio 3:5 that is not equal to 2:3. Therefore, this statement is false.
hence, the first two options are correct.
Without using technology, describe the end behavior of f(x) = 3x32 + 8x2 − 22x + 43.
Answers
In order to find the end behavior of a polynomial we simply must observe the higher exponential behavior. Since it is so much higher than the others terms it will indicate the end behavior of the total function.
In the case:
[tex]f(x)=3x^{32}+8x^2-22x+43.[/tex]It is enough to analyze the end behavior of 3x³² in order to find the end behavior of the whole polynomial.
When x tends to infinityWhen x tends to infinity
x ⇒ ∞
then
3x³² grows and grows (infinitely!)
3x³² ⇒ ∞
When x tends to minus infinityWhen x tends to minus infinity
x ⇒ -∞
x takes negative numbers however x³² is always positive, because it has an even exponent, then
when x ⇒ -∞
then
3x³² grows and grows (infinitely too)
3x³² ⇒ ∞
Answer- as x ⇒ -∞, 3x³² ⇒ ∞ and as x ⇒ ∞, 3x³² ⇒ ∞
What is 0.2 written as a fraction?
Answers
ANSWER
1/5
EXPLANATION
We want to find the value of 0.2 written as a fraction.
To do this, we have that since 2 is directly after the decimal, its place value is tenths, and so we can write that:
[tex]\begin{gathered} \frac{2}{10} \\ \text{write this in lowest terms:} \\ \frac{1}{5} \end{gathered}[/tex]That is the answer.
there are 15 male teachers in the school and 35 female teachers in a school what is the ratio
Answers
Ratio of male to female teachers = 3 : 7
Explanations:Number of male teachers = 15
Number of female teachers = 35
[tex]\begin{gathered} \text{Ratio of male to female teachers = }\frac{Number\text{ of male teachers}}{\text{Number of female teachers}} \\ \text{Ratio of male to female teachers = }\frac{15}{35} \\ \operatorname{Re}duce\text{ to the lowest term by dividing the numerator and denominator by 5} \\ \text{Ratio of male to female teachers = }\frac{15\div5}{35\div5} \\ \text{Ratio of male to female teachers = }\frac{3}{7} \end{gathered}[/tex]Ratio of male to female teachers = 3 : 7
What are all the zeros of the function f(x) = 4x^2 +8x +3?
Answers
To solve this question let's first understand what is a zero of a function f(x):
"The zeros of a function are all the values of f(x) for which x =0."
Once we understand that we can calculate the zeros of our function f(x) using the following equations:
So let's calculate first our theta:
[tex]\Delta=b^2-4ac=8^2-4\cdot4\cdot3=16[/tex]Now let's calculate the zeros of the function:
[tex]undefined[/tex]36. If WX = 7, WY = a, WV = 6, and VZ = a -9, find WY. W V Х Y N
Answers
36)
Triangle WVX is similar to triangle WZY. If two traingles are similar, it means that the ratio of their corresponding sides is equal. This means that
WV/WZ = VX/ZY = WX/WY
From the information given,
WX = 7, WY = a, WV = 6, VZ = a - 9
WZ = WV + VZ = 6 + a - 9 = a - 3
Thus, we have
6/(a - 3) = 7/a
By crossmultiplying, it becomes
6 x a = 7(a - 3)
6a = 7a - 21
7a - 6a = 21
a = 21
Since WY = a, then
WY = 21
75% of what number is 187.5?
Answers
Answer: 140.63
Explanation
The proportion of 75% is:
[tex]\frac{75\%}{100\%}=0.75[/tex]Finally, multiplying the proportion times the quantity:
[tex]187.5\cdot0.75=140.63[/tex]Question..Which statements is not true of dot plotAnswer choices :The data must be sorted before the graph can can be made.You need to know know the extreme values to write the number line The total number of mraks tells you the size of the data set. An outliner will show as a gap inthe data.
Answers
Answer:
The data must be sorted before the graph can be made.
Explanation:
A dot plot is can be made as a number line with dots above each number. The number of dots above each number represents the number of times that the number appears in the data.
Therefore, we will need to know the extreme values to write the number line, the total number of marks or dots will tell the size of the data and if there are outliers, there will be a gap in the graph.
So, the statement that is not true is:
The data must be sorted before the graph can be made.
E su primer día de viaje en bicicleta a campo traviesa,Marco recorrió 120 millas .Planea recorrer 100 millas más cada día. Escribe una expresión algebraica para representar el número total de millas que habrá recorrido después de d dias.
Answers
M = distance or total number of miles
d = number of days
M = 120+ 100d
S = 1000 + 30s
S = total amaunt of money
s = number of weeks
Hi can I please have some help. The sentence at the the top says “Ellie’s family go shopping on Saturday. The pie chart shows how they spend their money”
Answers
The amount spent on petrol is a quarter of the total, then as the total is 120 they spent
[tex]\frac{120}{4}=30[/tex]on petrol.
Assume that the situation can be expressed as a linear cost function. Find the cost function.Fixed cost is $100; 30 items cost $1000 to produce.The linear cost function is C(x)=___
Answers
Given that C(x) is a linear function, it can be expressed as:
[tex]C(x)=a+bx,[/tex]where a, and b are constants.
Now, we are given that there is a fixed cost of 100, therefore, a=100. Now, we know that
[tex]C(30)=1000.[/tex]Therefore:
[tex]1000=100+b(30).[/tex]Solving the above equation for b, we get:
[tex]\begin{gathered} 1000-100=30b, \\ 900=30b, \\ b=\frac{900}{30}, \\ b=30. \end{gathered}[/tex]Answer: [tex]C(x)=100+30x.[/tex]