All categories

3 years ago

The total cost to produce x handcrafted wagons is C(x) = 110 + 7x - x^2 + 2x^3. Find the marginal cost when x = 8.

Mathematics

1 answer:

nataly862011 [7]3 years ago

8 0

<h2>Answer:</h2>

The marginal cost when x=8 is:

375

<h2>Step-by-step explanation:</h2>

We know that the marginal function for a cost function C(x) at x=a

is given by:

C'(x) at x=a

Here we have the cost function C(x) as:

$C(x)=110+7x-x^2+2x^3$

Now we find the derivative of C(x) with respect to x.

i.e.

$C'(x)=0+7-2x+6x^2$

( Since,

$\dfrac{d}{dx} x^n=nx^{n-1}$ )

$C'(x)=7-2x+6x^2$

Hence, we get:

$C'(8)=7-2\times 8+6\times (8)^2\\\\i.e.\\\\C'(8)=7-16+384\\\\C'(8)=375$

You might be interested in

Solve the equation.<br> 5x = 2x^2 +1

Bogdan [553]

Answer:

x= 5/4 + −1/4√17 or x = 5/4 + 1/4√17

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

What transformation of f(x) will result in g(x) ?

Amanda [17]

Answer:

Vertical stretch across the y-axis, reflection across the x-axis, horizontal shift 2 units to the left, and vertical shift 1 unit down

3 0

3 years ago

In the figure, m<1=7x+8, m<2=4x+11, and m<4=12x+7. What is the m<1?

Licemer1 [7]

Answer:

Basic Definitions of Geometry

A collinear set of points is a set of points all of which lie on the same straight line.
A noncollinear set of points s a set of three or more points that do not all line on the same straight
line.
A Line has no end points.
A Ray has one end point.
. Line Segment has two end points
Congruent segments are segments that have the same measure.
The Midpoint of a line segment is a point of that line segment that divides the segment into two
congruent segments.

The Bisector of a line segment is any line, or subset of a line that intersects the segment at the midpoint.
An Angle is a set of points that is the union of two rays having the same endpoint.

4 0

3 years ago

I need helpppppppp I don’t like remainders :/

den301095 [7]

Answer:

The correct answer is 67 9/11

4 0

3 years ago

Read 2 more answers

Suppose that the sample standard deviation was s = 5.1. Compute a 98% confidence interval for μ, the mean time spent volunteerin

NISA [10]

Answer:

The 95% confidence interval would be given by (5.139;5.861)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

2) Confidence interval

Assuming that $\bar X =5.5$ and the ranfom sample n=1086.

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=1086-1=1085$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,1085)".And we see that $t_{\alpha/2}=2.33$

Now we have everything in order to replace into formula (1):

$5.5-2.33\frac{5.1}{\sqrt{1086}}=5.139$

$5.5+2.333\frac{5.1}{\sqrt{1086}}=5.861$

So on this case the 95% confidence interval would be given by (5.139;5.861) We are 98% confident that the mean time spent volunteering for the population of parents of school-aged children is between these two values.

5 0

3 years ago