Answer:
Step-by-step explanation:
Given that:
If C(x) = the cost of producing x units of a commodity
Then;
then the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
We are to consider a given function:
[tex]C(x) = 54,000 + 130x + 4x^{3/2}[/tex]
And the objectives are to determine the following:
a) the total cost at a production level of 1000 units.
So;
If C(1000) = the cost of producing 1000 units of a commodity
[tex]C(1000) = 54,000 + 130(1000) + 4(1000)^{3/2}[/tex]
[tex]C(1000) = 54,000 + 130000 + 4( \sqrt[2]{1000^3} )[/tex]
[tex]C(1000) = 54,000 + 130000 + 4(31622.7766)[/tex]
[tex]C(1000) = 54,000 + 130000 + 126491.1064[/tex]
[tex]C(1000) = $310491.1064[/tex]
[tex]\mathbf{C(1000) \approx $310491.11 }[/tex]
(b) Find the average cost at a production level of 1000 units.
Recall that :
the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
SO;
[tex]c(x) =\dfrac{(54,000 + 130x + 4x^{3/2})}{x}[/tex]
Using the law of indices
[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]
[tex]c(1000) = \dfrac{54000}{1000}+ 130 + {4(1000)^{1/2}}[/tex]
c(1000) =$ 310.49 per unit
(c) Find the marginal cost at a production level of 1000 units.
The marginal cost is C'(x)
Differentiating C(x) = 54,000 + 130x + 4x^{3/2} to get C'(x) ; we Have:
[tex]C'(x) = 0 + 130 + 4 \times \dfrac{3}{2} \ x^{\dfrac{3}{2}-1}[/tex]
[tex]C'(x) = 0 + 130 + 2 \times \ {3} \ x^{\frac{1}{2}}[/tex]
[tex]C'(x) = 0 + 130 + \ {6}\ x^{\frac{1}{2}}[/tex]
[tex]C'(1000) = 0 + 130 + \ {6} \ (1000)^{\frac{1}{2}}[/tex]
[tex]C'(1000) = 319.7366596[/tex]
[tex]\mathbf{C'(1000) = \$319.74 \ per \ unit}[/tex]
(d) Find the production level that will minimize the average cost.
the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]
the production level that will minimize the average cost is c'(x)
differentiating [tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex] to get c'(x); we have
[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{4}{2 \sqrt{x} }[/tex]
[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{2}{ \sqrt{x} }[/tex]
Also
[tex]c''(x)= \dfrac{108000}{x^3} -x^{-3/2}[/tex]
[tex]c'(x)= \dfrac{54000}{x^2} + \dfrac{4}{2 \sqrt{x} } = 0[/tex]
[tex]x^2 = 27000\sqrt{x}[/tex]
[tex]\sqrt{x} (x^{3/2} - 27000) =0[/tex]
x= 0; or [tex]x= (27000)^{2/3}[/tex] = [tex]\sqrt[3]{27000^2}[/tex] = 30² = 900
Since production cost can never be zero; then the production cost = 900 units
(e) What is the minimum average cost?
the minimum average cost of c(900) is
[tex]c(900) =\dfrac{54000}{900} + 130 + 4(900)^{1/2}[/tex]
c(900) = 60 + 130 + 4(30)
c(900) = 60 +130 + 120
c(900) = $310 per unit
surface area of a equilateral by hand
surface area of a equilateral by hand a 140.4 cm and 9cm
The equation to the graph is y = -1/2 x - 3
Answer:
Hope it helps <3
━━━━━━━☆☆━━━━━━━
▹ Answer
Use a graphing calculator. Attached is an image.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Please show step by step of working out the value of r for which is A minimum and calculate the minimum surface area of the container.
The total surface area, Acm^2, of each container is modelled by function A= πr^2+100/r.
(remember to use the derivative to show you have found the minimum)
Answer:
A = 59.63cm^2
Step-by-step explanation:
You have the following function for the surface area of the container:
[tex]A=\pi r^2+\frac{100}{r}[/tex] (1)
where r is the radius of the cross sectional area of the container.
In order to find the minimum surface are you first calculate the derivative of A respect to r, to find the value of r that makes the surface area a minimum.
[tex]\frac{dA}{dr}=\frac{d}{dr}[\pi r^2+\frac{100}{r}]\\\\\frac{dA}{dr}=2\pi r-\frac{100}{r^2}[/tex] (2)
Next, you equal the expression (2) to zero and solve for r:
[tex]2\pi r-\frac{100}{r^2}=0\\\\2\pi r=\frac{100}{r^2}\\\\r^3=\frac{50}{\pi}\\\\r=(\frac{50}{\pi})^{1/3}[/tex]
Finally, you replace the previous result in the equation (1):
[tex]A=\pi (\frac{50}{\pi})^{2/3}+\frac{100}{(\frac{50}{\pi})^{1/3}}}[/tex]
[tex]A=59.63[/tex]
The minimum total surface area is 59.63cm^2
David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15:1. He currently has 40 grams of the spice blend, and he can go buy more if necessary. He wants to make 10 servings, where each serving has 75 grams of rice. Overall, David spends 4.50 dollars on rice.
Answer:
8 servings
Step-by-step explanation:
Given:Rice-to-spice ratio = 15:1Amount of spice = 40 gramsRice required for one serving = 75 gramsTo find:Number of servingsSolution:Spice required for one serving, using the rice-to-spice ratio to calculate:
75 grams/15 = 5 gramsDavid can make servings according to amount of spice he has:
40 grams / 5 grams = 8Answer: David will be able to make 8 servings
Answer: 8
Step-by-step explanation:
Colossus Added to six flags st. Louis in 1986, the Colossus is a giant Ferris wheel. Its diameter is 165 feet, it rotates at a rate of about 1.6 revolutions per minute, and the bottom of the wheel is 15 feet above the ground. Determine an equation that relates a rider's height the ride at the bottom of the wheel.
Given:
D=165 feet and the frequency of the motion is 1.6 revolutions per minute.
Solution:
The radius is half of the diameter.
The radius of the wheel is 82.5 feet.
[tex]T=\frac{1}{1.6} \text{ minutes}[/tex]
As we know: [tex]\omega=\frac{2\pi}{T}[/tex]
Substitute the value of T in the above formula.
[tex]\omega=\frac{2\pi}{\frac{1}{1.6}}\\\omega=3.2\pi[/tex]
If the center of the wheel is at the origin then for [tex]t=0[/tex] the rest position is [tex]-a[/tex].
This can be written as:
[tex]h(t)=-a\cos(\omega t)\\h(t)=-82.5cos(32.\pi t)[/tex]
The actual height of the rider from the ground is:
[tex]h(t)=\text{ Initial height from bottom}+\text{ radius}-82.5\cos(3.2\pi t)\\h(t)=15+82.5-82.5\cos(3.2\pi t)\\h(t)=97.5-82.5\cos(3.2\pi t)[/tex]
The required equation is [tex]h(t)=97.5-82.5\cos(3.2\pi t)[/tex].
The length of a rectangle is six times its width. The area of the
rectangle is 294 square centimeters. Find the dimensions of the
rectangle.
Answer:
length= 42
width = 7
Step-by-step explanation:
A concert starts at 7:45pm and ends at 1:35 am. How long was the concert?
Answer:
The concert starts at 7:45 pm and ended at 1:35 am which mean the concert going on 5 hours and 50 minutes.
The equation that represents the canned goods order is 24x + 64y = 384, where x = number of minutes for producing fruit cans and y = number of minutes for producing vegetable cans.
What is the meaning of the y-intercept?
Answer:
The y-intercept is the number of minutes for producing vegetable cans when no minutes are used for fruit cans
Step-by-step explanation:
The problem statement tells you y is the number of minutes for producing vegetable cans. The y-intercept is the y-value when x = 0.
The y-intercept is the number of minutes for producing vegetable cans when no minutes are used for fruit cans.
Answer:
The y-intercept, at the point (0, 6), designates the choice to compose vegetables for 6 minutes. In 6 minutes, making 64 cans of vegetables per minute, 384 cans for the order decree performed. The 0 for the x-value designs that no time spent producing cans of fruit.
Step-by-step explanation:
I got it right on edgenuity
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.? y = 2 + sec(x), −π/3 ≤ x ≤ π/3, y = 4; about y = 2
Answer:
The volume of the solid is: [tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]
Step-by-step explanation:
GIven that :
[tex]y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2[/tex]
This implies that the distance between the x-axis and the axis of the rotation = 2 units
The distance between the x-axis and the inner ring is r = (2+sec x) -2
Let R be the outer radius and r be the inner radius
By integration; the volume of the of the solid can be calculated as follows:
[tex]V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx[/tex]
[tex]V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ][/tex]
[tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]
[PLEASE HELP] in the function above, the slope of it will be multiplied by 1/2 and it’s y value of its y intercept will be increased by 3 units, which of the graphs below best shows the new function???
Answer:
The graph at the bottom left in your group of possible answers.
Step-by-step explanation:
Notice that the original given graph corresponds to the equation:
[tex]y=2x+1[/tex]
since the line's slope is 2/1 = 2 and the y-intercept is at the point (0, 1).
So if one modifies the equation multiplying the current slope by 1/2, and the y intercept increased by 3 units, Then the new function would be:
[tex]y=x+4[/tex]
A line of slope 1 and y-intercept at (0, 4)
Notice that the graph at the bottom left in your possible answers is representing such function.
Answer:
Answer Y: or Bottom Left of Given Answers
Step-by-step explanation:
Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$, and $D$ are integers, $D$ is positive, and $B$ is not divisible by the square of any prime. If the greatest common divisor of $A$, $C$, and $D$ is 1, find $A+B+C+D$.
Answer:
[tex]A +B+C+D = 3[/tex] is the correct answer.
Step-by-step explanation:
Given:
[tex]$\frac{5}{2+\sqrt{6}}$[/tex]
To find:
[tex]A+B+C+D = ?[/tex] if given term is written as following:
[tex]$\frac{A\sqrt{B}+C}{D}$[/tex]
Solution:
We can see that the resulting expression does not contain anything under [tex]\sqrt[/tex] (square root) so we need to rationalize the denominator to remove the square root from denominator.
The rule to rationalize is:
Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.
Applying this rule to rationalize the given expression:
[tex]\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \ (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}[/tex]
Comparing the above expression with:
[tex]$\frac{A\sqrt{B}+C}{D}$[/tex]
A = 5, B = 6 (Not divisible by square of any prime)
C = -10
D = 2 (positive)
GCD of A, C and D is 1.
So, [tex]A +B+C+D = 5+6-10+2 = \bold3[/tex]
2x - y = 6
4
x-y
13
anch
Answer:
x=-7, y= -20
Step-by-step explanation:
2x - y =6
x - y = 13
when I subract (x-y =13 ) from (2x-y =6)
2x -y =6
-x +y=-13
______________
x = -7
substitute x=-7 in the second equation
-7 - y =13
-y = 13 +7
-Y = 20
Y=-20
x=-7, y= -20
Answer:
x= -7/6
y= -25/3
Step-by-step explanation:
2x-y =6
4 x-y =13
Firstly, 4x-y=13(-) =>> - 4x+y=-13
Then we make the sum and result 6x= -7. Result x= -7/6.
We need to find y. So:
-y= 6-2x =>> y= -6 +2x =>> y= -6 +2*(-7/6) =>> y= -6-7/3 =>> y=(-18-7)/3 =>>y= -25/3
Please explain what this means! (no math needs to be done as I got the answers but I don't understand the explanation...)
you can imagine this as a venn diagram. the "or" event would consist of everything in both sides and the middle of the venn diagram because you can choose form either event x or event y.
the "and" event would consist of everything in the middle of the venn diagram because you choice must be a part of both event x and event y.
the complement of an event is just everything that is not included in the event. for example, in a coin flip, the complement of heads is tails. in a dice roll, the complement of {1,2} is {3,4,5,6}
so if you come across these just think "either or" or "both and." and remember that the complement is everything excluding what is listed.
i apologize if this does not help, im not that great at explaining things
Monica’s school band held a car wash to raise money for a trip to a parade in New York City. After washing 125 cars, they made $775 from a combination of $5.00 quick washes and $8.00 premium washes. This system of equations models the situation. x + y =125 5x + 8y = 775
Step-by-step explanation:
5q+8p=775
q + p = 125
5q + 8q = 775
-5q -5q = -625
3q = 150
q = 50 premium
q + 50 = 125
q = 75 quick
Correct answer is
A: 5x+8y=775 and x+y =125
Next Answer is
50 premium car washes
75 Quick Car Washes
find the area of the triangle shown
Answer
B. 27
firist divide 9÷2=4.5
the formula
=1/2×4.5×6
=13.5
cause there are 2 triangles. let's multiply 13.5 with 2
13.5×2= 27²
Please answer this correctly without making mistakes
Answer:
16 km
Step-by-step explanation:
From Washington, as the question asks, will now be considered 0 aka the starting point.
So as of now, we know Washington from Oakdale is 6.2 km.
And from Stanford to Salem is 11.9 km, also Salem to Washington is 10.3 km. Hence the addition of 11.9 km and 10.3 km to figure out the whole distance between Stanford and Washington.
11.9 km + 10.3 km = 22.2 km
Now we subtract 22.2 km to 6.2 km for the product of 16 km.
Find The measure of the unknown angle.
1. Add the two known angles:___+___=___
2. Subtract the sum from 180°: 180-___=___
3. The measure of the unknown angle is:____
Answer:
L = 45°
Step-by-step explanation:
1. 82° + 53° = 135°
2. 180° - 135° = 45°
3. Angle L is 45°
I hope this helps.
hellllllllppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
see below.
Step-by-step explanation:
1st row has four small boxes
2nd row has three big boxes
big box 1 has no items ragged in it.
big box 2 has small box 1 and also small box 1 dragged into it.
big box 3 has small box 3 and small box 4 dragged into it.
Calculate the length of the unknown side of this right angled triangle
Answer:
12.04
Step-by-step explanation:
Well to solve for the unknown side "c" we need to use the Pythagorean Theorem formula,
[tex]a^2 + b^2 = c^2[/tex]
We already have a and b which are 8 and 9 so we plug them in.
[tex](8)^2 + (9)^2 = c^2[/tex]
64 + 81 = c^2
145 = c^2
c = 12.04 rounded to the nearest hundredth.
Thus,
the unknown side is about 12.04.
Hope this helps :)
The doubling time of a cityʹs population is 8 years. How long does it take for the population to quadruple.
Answer:
16 Years
Step-by-step explanation:
Find the area of the shaded triangle, if the side of each square is 1 unit long.
Answer:
10 units²
Step-by-step explanation:
The shape is a triangle.
The area can be found by multiplying the base (in units) with height (in units) divided by 2.
base = 4 units
height = 5 units
[tex]\frac{4 \times 5}{2}[/tex]
[tex]\frac{20}{2} =10[/tex]
4+9(3x-7)=-42x-13+23(3x-2)
Answer:
x = 0
Step-by-step explanation:
[tex]4+9(3x-7)=-42x-13+23(3x-2)\\4+27x-63=-42x-13+69x-46\\27x+4-63=-42x+69x-13-46\\27x-59=25x-59\\2x-59=-59\\2x=0\\x=0[/tex]
Which of the following is false? Correlation measures the strength of linear association between two numerical variables. If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them. Correlation coefficient and the slope always have the same sign (positive or negative). If the correlation coefficient is 1, then the slope must be 1 as well.
Answer:
If the correlation coefficient is 1, then the slope must be 1 as well.
Step-by-step explanation:
Coefficient of correlation is used in statistics to determine the relationship between two variables. Correlation coefficient and slope always have same sign. It measures the strength of linear relation between two variables. The values of correlation coefficient ranges between 0 to 1. where 0 determines that there is no relationship between two variables.
Which graph shows all the values that satisfy Two-ninths x + 3 greater-than 4 and five-ninths
Answer:
It is the first graph
Step-by-step explanation:
Just got it right on the test review :)
Inequalities help us to compare two unequal expressions. The graph shows that all the values of x that satisfies the given inequality are x>7. Thus, the correct option is A.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given inequality can be solved as,
[tex]\dfrac29(x+3) > 4(\dfrac59)\\\\\dfrac{2x+6}{9} > \dfrac{20}{9}\\\\2x + 6 > 20\\\\2x > 20 - 6\\\\x > \dfrac{14}{2}\\\\x > 7[/tex]
Hence, the graph shows that all the values of x that satisfies the given inequality are x>7. Thus, the correct option is A.
Learn more about Inequality:
https://brainly.com/question/19491153
#SPJ2
The dot plots show the number of hours a group of fifth graders and seventh graders spent playing outdoors over a one-
week period.
Time Spent Playing Outdoors
for Fifth Graders and Seventh Graders
.
5th Grade
0
ta
1 2 3 4 5
Hours
7
8
9 10
7th Grade
.
Answer: B
Step-by-step explanation:
Answer:B
Step-by-step explanation: I took the edge quiz and it was right.
The probability of a potential employee passing a drug test is 91%. If you selected 15 potential employees and gave them a drug test, how many would you expect to pass the test
Answer:
The number expected to pass that test is [tex]k = 14 \ employees[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.91
The sample size is n = 15
The number of employee that will pass the test is mathematically represented as
[tex]k = n * p[/tex]
substituting values
[tex]k = 15 * 0.91[/tex]
[tex]k = 14 \ employees[/tex]
Simplify the expression:
1 – 5b + – b + – 8b – 2b
Answer:
The answer is 1 - 16b.
Step-by-step explanation:
You have to collect like-terms :
[tex]1 - 5b - b - 8b - 2b[/tex]
[tex] = 1 + b( - 5 - 1 - 8 - 2)[/tex]
[tex] = 1 + b( - 16)[/tex]
[tex] = 1 - 16b[/tex]
Answer:
The answer is
1 - 16bStep-by-step explanation:
1 – 5b + – b + – 8b – 2b can be written as
1 - 5b - b- 8b - 2b
Subtract the like terms
That's
We have the final answer as
1 - 16b
Hope this helps you
Which of the following points are on the line given by the equation y= 1/2x ?
Check all that apply.
D A. (-2,-1)
DB. (-2,1)
| C. (3,6)
D. (3, 15)
D E. (2.1)
D F. (4,2)
Answer:
(-2,-1), (2,1), (4,2)
Step-by-step explanation:
This is how I did it: (took me like a minute)
Draw a graph or get graph paper. You could also probably find a graph online that you can write on. (remember to label)
Now mark two points of the line. So for this question you could use (0,0) and (2,1).
Now draw a line connecting both points.
Finally you can check whether the points are on the line or are not.
Hope this helps!
Find the circumference of a circular field with a diameter of 16 yards.
(Let it = 3.14)
Answer:
Hey there!
The circumference of a circle is [tex]\pi(d)[/tex], where d is the diameter, and [tex]\\\pi[/tex] is a constant roughly equal to 3.14.
The diameter is 16, so plugging this into the equation, we get 3.14(16)=50.24.
The circumference of the circle is 50.24 yards.
Hope this helps :)
Which of the following
examples have a constant rate of change?
A : You drive from Colorado to Texas. In the first 4 hours, you cover 240 miles, and in the second 5 hours, you cover another 240 miles.
B : The money you put in the bank earns 5% Interest. This means that the bank pays you 5% of the amount of the money kept in the bank each year.
C : A salesperson earns $50 plus $10 for every $100 of merchandise he sells.
D : The amount bacteria double every hour.
Answer:
C : A salesperson earns $50 plus $10 for every $100 of merchandise he sells.
Step-by-step explanation:
If a salesperson earns $50 plus $10 for every $100 of merchandise he sells, the rate of change is 100. The linear equation is T = 50 + 100h, where T is the total amount he earns and h is the number of $100 in merchandise he sells.
The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.
What is the average rate change?It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.
Let's check all the options, then we have
A: You drive from Colorado to Texas. In the first 4 hours, you cover 240 miles, and in the second 5 hours, you cover another 240 miles. It is an example of a linear function but the slope gets changed after 2 hours.
B: The money you put in the bank earns 5% Interest. This means that the bank pays you 5% of the amount of the money kept in the bank each year. It is an example of the exponential function.
C: A salesperson earns $50 plus $10 for every $100 of merchandise he sells. It is an example of a linear function.
D: The number of bacteria doubles every hour. It is an example of the exponential function.
The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.
More about the average rate change link is given below.
https://brainly.com/question/28744270
#SPJ5