Answer:
Not really, actually it depends on the shape given whether it's a rectangle, a square etc. Because you can't conclude that the shape of a rectangle with such dimensions could be guaranteed.
Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10). Match each quadrilateral, described by its vertices, to the sequence of transformations that will show it is congruent to quadrilateral JKLM. W(5,1), X(1,7), Y(9,9), and Z(11,7) O(10,1), P(6,7), Q(14,9), and R(16,7) S(4, 16), T(10, 20), U(12, 12), and V(10, 10) A(-8, -4), B(-4, -10), C(-12, -12), and D(-14, -10) E(5,6), F(1,12), G(9,14), and H(11,12) a translation 2 units right and 3 units down arrowRight a translation 3 units left and 2 units up arrowRight a translation 3 units down and 3 units left arrowRight a sequence of reflections across the x- and y-axes, in any order arrowRight
Answer:
See Explanation
Step-by-step explanation:
Given:
Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10).
(a)If we translate quadrilateral JKLM 3 units down and 3 units left:
(x-3,y-3), we obtain: W(5,1), X(1,7), Y(9,9), and Z(11,7)
Therefore, we match it with: A translation 3 units down and 3 units left
(b)If we translate quadrilateral JKLM 2 units right and 3 units down:
(x+2,y-3), we obtain: O(10,1), P(6,7), Q(14,9), and R(16,7)
Therefore, we match it with:A translation 2 units right and 3 units down
S(4, 16), T(10, 20), U(12, 12), and V(10, 10)
(c) If we transform quadrilateral JKLM by a sequence of reflections across the x- and y-axes, in any order, we obtain:
A(-8, -4), B(-4, -10), C(-12, -12), and D(-14, -10)
(d)If we translate quadrilateral JKLM 3 units left and 2 units up:
(x-3,y+2), we obtain:E(5,6), F(1,12), G(9,14), and H(11,12)
Therefore, we match it with: A translation 3 units left and 2 units up
(e)S(4, 16), T(10, 20), U(12, 12), and V(10, 10)
No suitable transformation is found from JKLM to STUV.
Answer:
a translation 3 units down and 3 units left
W(5,1), X(1,7), Y(9,9), and Z(11,7)
a translation 2 units right and 3 units down
O(10,1), P(6,7), Q(14,9), and R(16,7)
a sequence of reflections across the
x- and y-axes, in any order
S(4, 16), T(10, 20), U(12, 12), and V(10, 10)
a translation 3 units left and 2 units up
E(5,6), F(1,12), G(9,14), and H(11,12)
What is the domain of the function y = 3 l n x graphed below?
On a coordinate plane, a curve starts in quadrant 4 and then increases up into quadrant 1. It crosses the x-axis at (1, 0).
x greater-than 0
x less-than 0
x less-than 3
x greater-than 3
Answer:
x>0
Step-by-step explanation:
The domain are the possible values of x you can use.
For ln functions, x must be positive (the ln of a negative number does not exist).
So, x must be larger than 0. No part of the graph will be left of the y axis.
Answer:
The answer is option A.
x > 0Hope this helps you
g 7. Find Re f and Im f and find their values at the given z. (Both answers should be included) f = z⁄(z + 1), z = 4 − 5
Answer:
The real and imaginary parts of the result are [tex]\frac{1441}{1601}[/tex] and [tex]\frac{4}{1601}[/tex], respectively.
Step-by-step explanation:
Let be [tex]f(z) = \frac{z}{z+1}[/tex], the following expression is expanded by algebraic means:
[tex]f(z) = \frac{z\cdot (z-1)}{(z+1)\cdot (z-1)}[/tex]
[tex]f(z) = \frac{z^{2}-z}{z^{2}-1}[/tex]
[tex]f(z) = \frac{z^{2}}{z^{2}-1}-\frac{z}{z^{2}-1}[/tex]
If [tex]z = 4 - i5[/tex], then:
[tex]z^{2} = (4-i5)\cdot (4-i5)[/tex]
[tex]z^{2} = 16-i20-i20-(-1)\cdot (25)[/tex]
[tex]z^{2} = 41 - i40[/tex]
Then, the variable is substituted in the equation and simplified:
[tex]f(z) = \frac{41-i40}{41-i39} -\frac{4-i5}{41-i39}[/tex]
[tex]f(z) = \frac{37-i35}{41-i39}[/tex]
[tex]f(z) = \frac{(37-i35)\cdot (41+i39)}{(41-i39)\cdot (41+i39)}[/tex]
[tex]f(z) = \frac{1517-i1435+i1443+1365}{3202}[/tex]
[tex]f(z) = \frac{2882+i8}{3202}[/tex]
[tex]f(z) = \frac{1441}{1601} + i\frac{4}{1601}[/tex]
The real and imaginary parts of the result are [tex]\frac{1441}{1601}[/tex] and [tex]\frac{4}{1601}[/tex], respectively.
The charitable foundation for a large metropolitan hospital is conducting a study to characterize its donor base. In the past, most donations have come from relatively wealthy individuals; the average annual donor income in the most recent survey was right at $100,000. The foundation believes the average has now increased. A random sample of 200 current donors showed a mean annual income of $103,157 and a standard deviation of $27,498.a. To perform this study, we should form a null hypothesis stating that the average is ______________ 100,000. (Please fill in only one of the following: "less than", "less than or equal to", "equal to", "greater than", "greater than or equal to". Please do not use symbols.)b. At the 10% significant level, the p-value/statistics is _____________________ (Please keep three decimal points) so we should __________________ the null hypothesis (Please only fill in "reject" or "not reject".).c. Hence, we may conclude that the average _________________ increased (Please only fill in "has" or "has not") and the probability that our conclusion is correct is at least _________________ percent.
Answer:
Step-by-step explanation:
a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ equal to 100000
For the alternative hypothesis,
H1: µ greater than 100000
This is a right tailed test
Since the population standard deviation is nit given, the distribution is a student's t.
Since n = 200
Degrees of freedom, df = n - 1 = 200 - 1 = 199
t = (x - µ)/(s/√n)
Where
x = sample mean = 103157
µ = population mean = 100000
s = samples standard deviation = 27498
t = (103157 - 100000)/(27498/√200) = 1.62
We would determine the p value using the t test calculator.
p = 0.053
Alpha = 10% = 0.1
Since alpha, 0.1 > than the p value, 0.053, then
b) At the 10% significant level, the p-value/statistics is 0.053, so we should not reject the null hypothesis.
c) Hence, we may conclude that the average has not increased and the probability that our conclusion is correct is at least 90 percent.
What is the simplified value of this expression pls help
Answer:
7
Step-by-step explanation:
Remove parentheses.
[tex]\frac{-8+4(4.5)}{6.25-8.25} \\[/tex]
Add −8 and 4.5.
[tex]\frac{4(-3.5)}{6.25 - 8.25} \\\\[/tex]
Subtract 8.25 from 6.25.
[tex]\frac{4*-3.5}{-2}[/tex]
Multiply 4 by −3.5.
[tex]\frac{-14}{-2}[/tex]
Divide −14 by −2.
= 7
Select the correct answer from each drop-down menu. Gino is buying wood screws at the corner hardware store. The table shows different numbers of bags of screws and their corresponding prices. Bags of Screws Price ($) 2 10 4 20 7 35 According to the table, the relationship between the number of bags and the price is proportional or not proportional
Hunter is 9 years older than 3 times the age of his nephew. Hunter is 33 years old. How old is his nephew?
Answer:
8 years old.
(3x+9)
(3(8)+9)=33
Mario and tabitha are calculating the probability of getting a 4 and a 2 if they roll a die twice. Who is correct?
Answer:
[tex]\frac{2}{12}[/tex] simplified to [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
4 = [tex]\frac{1}{12}[/tex]
2 = [tex]\frac{1}{12}[/tex]
[tex]\frac{1}{12}[/tex] + [tex]\frac{1}{12}[/tex] = [tex]\frac{2}{12}[/tex] ÷ 2 = [tex]\frac{1}{6}[/tex]
Which number is irrational??
Answer:
√6
Step-by-step explanation:
√6 = 2.44948974278...
The number never ends and the values don't repeat therefore, the correct answer is √6.
Hope this helps! :)
Answer:
B. The square root of 5
Step-by-step explanation:
You can only square root a number that can be the answer to an equation like x*x=5, which it is not.
The equation x2 − 6x − 27 = 0 when solved is:
Answer:
-3 , 9
Step-by-step explanation:
Sum = - 6
Product = -27
Factors = 3, -9
x² - 6x-27 = 0
x² + 3x - 9x - 9*3 = 0
x(x + 3) - 9(x + 3) = 0
(x + 3) (x - 9) = 0
x +3 = 0 ; x - 9 = 0
x = - 3 ; x = 9
Solution: x = -3 , 9
Which of the following relations is a function?
a{(1, 3), (2, 3), (4,3), (9,3)}
b{(1, 2), (1, 3), (1, 4), (1,5)}
c{(5, 4), (-6, 5), (4, 5), (4, 0)}
d{(6,-1), (1,4), (2, 3), (6, 1)}
Answer:
a{(1, 3), (2, 3), (4,3), (9,3)}
Step-by-step explanation:
For the relation to be a function, each x can only go to 1 y
a{(1, 3), (2, 3), (4,3), (9,3)}
function
b{(1, 2), (1, 3), (1, 4), (1,5)}
x=1 goes to 4 different y's so not a function
c{(5, 4), (-6, 5), (4, 5), (4, 0)}
x=4 goes to 2 different y's so not a function
d{(6,-1), (1,4), (2, 3), (6, 1)}
x = 6 goes to 2 different y's so not a function
Please help fast!!!! What are the center and radius of the circle defined by the equation x2 + y2 - 6x+By+21=0 ?
Answer:
Option A
Step-by-step explanation:
The first thing we want to do here is to rewrite the equation given to us, in standard circle equation -
[tex]x^2+y^2-6x+8y+21=0,\\\left(x-3\right)^2+\left(y-\left(-4\right)\right)^2=2^2[/tex]
The " standard form " of a circle is given to be in the following form,[tex](x-a)^{2} + (y-b)^{2} = r^2[/tex] where r = radius, centered at ( a, b )
Now as you can see, the center ( given by ( a, b ) ) should be ( 3, - 4 ). Respectively the radius is 2, and therefore the circle properties are -
Center [tex]( 3, - 4 )[/tex]; radius [tex]2[/tex]
Hope that helps!
PLEASE HELP ASAP DUE IN 10 MINUTES PLEASE!!!!!!!!!!!!!The president of the United States produces a new national plan to reduce water pollution which of these would most likely provide the revenue to pay for this new public service
Answer
i think its federal income tax increase. 2nd one i believe
Step-by-step explanation:
The President of the United States proposes a new national plan to reduce water pollution.
Which of these would most likely provide the revenue to pay for this new public service?
Step-by-step explanation:
answer is :
the united states senate passes a bill that increases the federal income tax rate , which then pays for the service read it b4 yhu answer your question.have a good day!!and DM meh if yhu need a question answer here for 24/7pls if yhu want to mark meh as brainlist.....Suppose f(x)=x^2 and g(x) =7x^2 which statement best compares the graph of g(x) with the graph f(x)
Answer:
The graph g(x) is the graph f(x) vertically stretched by a factor of 7.
Step-by-step explanation:
Quadratic Equation: f(x) = a(bx - h)² + k
Since we are modifying the variable a, we are dealing with vertical stretch (a > 1) or vertical shrink (a < 1). Since a > 1 (7 > 1), we are dealing with a vertical stretch by a factor of 7.
Answer:
The graph g(x) is the graph f(x) vertically stretched by a factor of 7.
Step-by-step explanation:
Quadratic Equation: f(x) = a(bx - h)² + k
Since we are modifying the variable a, we are dealing with vertical stretch (a > 1) or vertical shrink (a < 1). Since a > 1 (7 > 1), we are dealing with a vertical stretch by a factor of 7.
If the density of an object is 8 g/cm³, and the mass is 200M m g. What is the volume of the object?
Answer:
Step-by-step explanation:
the mass is 2000 mg, or 2 g.
the density is 8 g/cm^3
divide 2 by 8
0.25 cm^3
if this helped, mark as brainliest :)
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) g(y) = y − 5 y2 − 3y + 15
Answer:
0, 10
Step-by-step explanation:
The given function is:
[tex]g(y) = \frac{y-5}{y^2-3y+15}[/tex]
According to the quotient rule:
[tex]d(\frac{f(y)}{h(y)}) = \frac{f(y)*h'(y)-h(y)*f'(y)}{h^2(y)}[/tex]
Applying the quotient rule:
[tex]g(y) = \frac{y-5}{y^2-3y+15}\\g'(y)=\frac{(y-5)*(2y-3)-(y^2-3y+15)*(1)}{(y^2-3y+15)^2}[/tex]
The values for which g'(y) are zero are the critical points:
[tex]g'(y)=0=\frac{(y-5)*(2y-3)-(y^2-3y+15)*(1)}{(y^2-3y+15)^2}\\(y-5)*(2y-3)-(y^2-3y+15)=0\\2y^2-3y-10y+15-y^2+3y-15\\y^2-10y=0\\y=\frac{10\pm \sqrt 100}{2}\\y_1=\frac{10-10}{2}= 0\\y_2=\frac{10+10}{2}=10[/tex]
The critical values are y = 0 and y = 10.
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. (If an answer does not exist, enter DNE.) 2 + 0.6 + 0.18 + 0.054 + ...
Answer:
sum: 2 6/7
Step-by-step explanation:
The first term is 2, and the common ratio is 0.6/2 = 0.3. This value is less than 1, so the series converges.
The sum is ...
S = a0/(1 -r) = 2/(1 -0.3) = 2/0.7
S = 2 6/7
Which point is a solution to the inequality shown in this graph?
5
(3,-1)
(-3,-3)
O A. (5,-5)
O B. (1,5)
C. (-3,-3)
D. (3, -1)
Hey there!
To find the answer, we just need to see which point falls in this blue, which represents the inequality.
We see that the point (5,-5) is not on the blue.
We see that the point (1,5) is on the blue.
(-3,-3) is on the dotted line but not a solution of the inequality. The dotted line is excluded from the inequality. If it were a bold line, then it would be a solution of the inequality.
(3,-1) is also on the dotted line so it is not a solution.
Therefore, the answer is B. (1,5)
I hope that this helps!
We want to see which point is a solution for the graphed inequality.
We will find that the correct option is B, (1, 5)
Notice that the line that defines the inequality contains the points (-3, -3) and (3, -1)
Then the slope of that line is:
[tex]a = \frac{-1 -(-3)}{3 - (1)} = 1/2[/tex]
Then the line is something like:
y = (1/2)*x + b
To find the value of b, we use the fact that this line passes through the point (3, -1), then we have:
-1 = (1/2)*3 + b
-1 - 3/2 + b
-5/2 = b
So the line is:
y = (1/2)*x - 5/2
And we can see that the line is slashed, and the shaded area is above the line, then we have:
y > (1/2)*x - 5/2
Now that we have the inequality, we can just input the values of the points in the inequality and see if this is true.
First, options C and D can be discarded because these points are on the line, and the points on the line are not solutions.
So we only try with A and B.
A) x = 5
y = -5
then we have:
-5 > (1/2)*5 - 5/2
-5 > 0
Which clearly is false.
B) x = 1
y = 5
Then we have:
5 > (1/2)*1 - 5/2 = -4/2
5 > -4/2
This is true, then the point (1, 5) is a solution.
Thus the correct option is B.
If you want to learn more, you can read:
https://brainly.com/question/20383699
Andrea and Helen participated in a donut eating contest. Andrea ate six more than four times the number of donuts that Helen ate. Let d represents the number of donuts Helen ate. Write the expression that gives the number of donuts that Andrea ate.
Answer:
4d + 6
Step-by-step explanation:
Helen ate d donuts.
Andrea ate 6 more than 4 times d.
4d + 6
A function F parentheses X is graft what is the slope of the function what is the Y intercept of the function which equation represents the graph of the function
Answer:
5
Step-by-step explanation:
I NEED HELP PLEASE, THANKS! :)
While doing bicep curls, Tamara applies 155 Newtons of force to lift the dumbbell. Her forearm is 0.366 meters long and she begins the bicep curl with her elbow bent at a 15° angle below the horizontal, in the direction of the positive x-axis. Determine the magnitude of the torque about her elbow. (Show work)
Answer:
54.8 N·m
Step-by-step explanation:
The horizontal distance from the dumbbell to the elbow is ...
(0.366 m)cos(15°) ≈ 0.3535 m
Then the torque due to the vertical force is ...
(155 N)(0.3535 m) = 54.8 N·m
Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high? (Round your answer to two decimal places.)
Answer:
0.45 ft/min
Step-by-step explanation:
Given:-
- The flow rate of the gravel, [tex]\frac{dV}{dt} = 35 \frac{ft^3}{min}[/tex]
- The base diameter ( d ) of cone = x
- The height ( h ) of cone = x
Find:-
How fast is the height of the pile increasing when the pile is 10 ft high?
Solution:-
- The constant flow rate of gravel dumped onto the conveyor belt is given to be 35 ft^3 / min.
- The gravel pile up into a heap of a conical shape such that base diameter ( d ) and the height ( h ) always remain the same. That is these parameter increase at the same rate.
- We develop a function of volume ( V ) of the heap piled up on conveyor belt in a conical shape as follows:
[tex]V = \frac{\pi }{12}*d^2*h\\\\V = \frac{\pi }{12}*x^3[/tex]
- Now we know that the volume ( V ) is a function of its base diameter and height ( x ). Where x is an implicit function of time ( t ). We will develop a rate of change expression of the volume of gravel piled as follows Use the chain rule of ordinary derivatives:
[tex]\frac{dV}{dt} = \frac{dV}{dx} * \frac{dx}{dt}\\\\\frac{dV}{dt} = \frac{\pi }{4} x^2 * \frac{dx}{dt}\\\\\frac{dx}{dt} = \frac{\frac{dV}{dt}}{\frac{\pi }{4} x^2}[/tex]
- Determine the rate of change of height ( h ) using the relation developed above when height is 10 ft:
[tex]h = x\\\\\frac{dh}{dt} = \frac{dx}{dt} = \frac{35 \frac{ft^3}{min} }{\frac{\pi }{4}*10^2 ft^2 } \\\\\frac{dh}{dt} = \frac{dx}{dt} = 0.45 \frac{ft}{min}[/tex]
An auto parts shop carries an oil filter for trucks. The annual demand for the oil filter is roughly 1200 units. The ordering cost per order for the auto parts shop is $80; the holding cost of carrying 1 unit is $1.2 per year. The shop has 360 working days per year. The lead time is usually 12 working days. Determine the annual total relevant, including ordering and carrying, cost._______
a) 240
b) 80
c) 480
d) 300
e) None of the above.
Answer:
Total annual inventory cost = $480
c) 480
Step-by-step explanation:
given data
annual demand for the oil filter = 1200 units
ordering cost per order S = $80
holding cost of carrying 1 unit = $1.2 per year
lead time = 12 working days
number of working days = 360 days
solution
we get here economic order quantity that is express as
economic order quantity = [tex]\sqrt{\frac{2DS}{H}}[/tex] ...............1
here D is annual demand and S is ordering cost and H is per unit cost
so put here value and we get
EOQ = [tex]\sqrt{\frac{2\times 1200 \times 80}{1.2}}[/tex]
EOQ = 400 units
and
Annual ordering cost = annual demand × ordering cost ÷ order size .........2
and here
No orders (Q) = annual demand ÷ order size ...........3
Q = 1200 ÷ 400
Q = 3 orders
so
Annual ordering cost = ordering cost × number of order ................4
put here value
Annual ordering cost = 80 × 3
Annual ordering cost = $240
and
Annual carrying cost = average inventory × per unit cost ..........5
and
average inventory = EOQ ÷ 2 ...........6
Annual carrying cost = (EOQ × H) ÷ 2
put here value and we get
Annual carrying cost = 400 × 1.2 ÷ 2
Annual carrying cost = $240
and
so here Total annual inventory cost = Annual ordering cost + Annual carrying cost .........................7
Total annual inventory cost = $240 + $240)
Total annual inventory cost = $480
From a group of graduate students including 25 men and 22 women, 37 are chosen to participate in a presentation. What is the probability that exactly 19 men and 18 women are chosen
Answer:
25.02% probability that exactly 19 men and 18 women are chosen
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the men and the women are selected is not important, so we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
19 men, from a set of 25
18 women, from a set of 22
[tex]D = C_{25,19}*C_{22,18} = \frac{25!}{19!6!}*\frac{22!}{18!4!} = 1295486500[/tex]
Total outcomes:
37 people from a set of 25 + 22 = 47. So
[tex]T = C_{47,37} = \frac{47!}{37!10!} = 5178066751[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{1295486500}{5178066751} = 0.2502[/tex]
25.02% probability that exactly 19 men and 18 women are chosen
A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use in minutes of one particular
customer for the past 20 months. Use the given data to answer parts (a) and (b).
325 517 424 395 494
396 351 379 408 426
523 421 434 373 456
535 394 437 403 513
(a) Determine the standard deviation and interquartile range of the data.
s=(Round to two decimal places as needed.)
Answer:
The answer is: 325 517 424 395 494
Step-by-step explanation:
The profit, in thousands of dollars, from the sale of x thousand candles can be estimated by P(x) = 5 x - 0.7 x ln x.
1) Find the marginal profit, P'(x).
2) Find P'(10), and explain what this number represents. What does P'(10) represent?
A. The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.
B. The additional profit, in thousands of dollars, when 10,000 candles are sold.
C. The additional cost, in thousands of dollars, to produce a thousand candles once 10,000 candles have already been sold.
D The additional cost, in thousands of dollars, to produce 10,000 candles.
C. How many thousands of candles should be sold to maximize profit?
1) The marginal profit is [tex]4.3 - 0.7 ln(x)[/tex].
2) The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.
Thus, option (A) is correct.
C) To maximize profit 462,481 thousands of candles should be sold.
Given: [tex]P(x) = 5 x - 0.7 x[/tex] [tex]{\text}ln x.[/tex]
1) Take the derivative of the profit function P(x) with respect to x.
P(x) = 5x - 0.7x ln(x)
To find P'(x), differentiate each term separately using the power rule and the derivative of ln(x):
[tex]P'(x) = 5 - 0.7(1 + ln(x))[/tex]
= [tex]5 - 0.7 - 0.7 ln(x)[/tex]
= [tex]4.3 - 0.7 ln(x)[/tex]
2) Substitute x = 10 into the derivative:
P'(10) = 4.3 - 0.7 ln(10)
= 4.3 - 0.7(2.30259)
= 4.3 - 1.61181
= 2.68819
Therefore, the additional profit for selling a thousand candles once 10,000 candles have already been sold.
Thus, option (A) is correct.
C) Set P'(x) = 0 and solve for x:
[tex]4.3 - 0.7 ln(x) = 0[/tex]
[tex]0.7 ln(x) = 4.3[/tex]
[tex]{\text} ln(x) = 4.3 / 0.7[/tex]
[tex]{\text} ln(x) = 6.14286[/tex]
[tex]x = e^{6.14286[/tex]
[tex]x = 462.481[/tex]
Therefore, 462,481 thousands of candles should be sold.
Learn more about Derivative here:
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1) The marginal profit, P'(x), is -0.7ln(x) + 4.3.
2) The number of thousands of candles that should be sold to maximize profit is approximately 466.9.
1) To find the marginal profit, P'(x), we need to take the derivative of the profit function, P(x), with respect to x. Using the power rule and the chain rule, we can differentiate the function:
P(x) = 5x - 0.7x ln(x)
Taking the derivative with respect to x:
P'(x) = 5 - 0.7(ln(x) + 1)
Simplifying:
P'(x) = 5 - 0.7ln(x) - 0.7
P'(x) = -0.7ln(x) + 4.3
2) To find P'(10), we substitute x = 10 into the marginal profit function:
P'(10) = -0.7ln(10) + 4.3
Using a calculator, we can evaluate this expression:
P'(10) ≈ -0.7(2.3026) + 4.3 ≈ -1.6118 + 4.3 ≈ 2.6882
The value of P'(10) is approximately 2.6882.
Now, let's interpret what P'(10) represents:
The correct interpretation is A. The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.
P'(10) represents the rate at which the profit is changing with respect to the number of candles sold when 10,000 candles have already been sold. In other words, it measures the additional profit (in thousands of dollars) for each additional thousand candles sold once 10,000 candles have already been sold.
Lastly, to determine the number of thousands of candles that should be sold to maximize profit, we need to find the critical points of the profit function P(x). This can be done by setting the derivative P'(x) equal to zero and solving for x.
-0.7ln(x) + 4.3 = 0
-0.7ln(x) = -4.3
ln(x) = 4.3 / 0.7
Using properties of logarithms:
x = e^(4.3 / 0.7)
Using a calculator, we can evaluate this expression:
x ≈ e^(6.1429) ≈ 466.9
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Write an equation that expresses the following relationship. w varies directly with u and inversely with d In your equation, use k as the constant of proportionality.
Step-by-step explanation:
solution.
if variable d increases then w reduces
w=k.u ×1/d
=ku/d
therefore w=k.u/d
If nine of every 11 trick-or-treaters that came to your house last Halloween were dressed as pirates what proportion of trick-or-treaters were not dressed as pirates
Answer:
11 - 9 = 2 trick-or-treaters out of 11 were not dressed as pirates so the proportion is 2/11.
Answer: Ratio is 2:11
Step-by-step explanation:
So your ratio of pirates to non-pirates would be 9:11
So you subtract number of pirates from total trick-or-treaters and get 2.
So the proportion of non-pirates would be 2:11.
Calculate the slope of a line passing through point A at (2, 1) and point B at (4, 2). Calculate to one decimal place.
Answer: 0.5
Step-by-step explanation:
To find the slope of a line with two given points, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
[tex]m=\frac{2-1}{4-2}=\frac{1}{2}=0.5[/tex]
The slope is 0.5.
3.
A passenger jet can fly 1,290 mil
in 3 hours with a tailwind bi
1,230 miles in 3 hours
headwind. Find the speed
the Jet in Still air and the
of the wind.
Answer:
Jet= 420 mph Wind = 10mph
Step-by-step explanation:
The speed of the plane in a tailwind can be modeled by x+y where x is the speed of the plane and y is the speed of the wind. Dividing 1290 by 3 gets you the average speed of the jet in a tailwind, which is 430.
The speed of the plane in a headwind can be modeled by x-y where x is the speed of the plane and y is the speed of the wind. Dividing 1230 by 3 gets you the average speed of the jet in a tailwind, which is 410.
This can be modeled by a system of equations, where x+y=430 and x-y=410. Solving the equation you get x=420 and y=10.
So, the speed of the jet is 420 mph and the speed of the wind is 10 mph.