Harriet has a square piece of paper. She folds it in half again to form a second rectangle (the high is not a square). The perimeter of the second rectangle is 30cm. What is the area of the original piece of paper?
Answer:
The area of the original piece of paper is 60cm
Answer:
the answer is 60
hope it helps :D
Step-by-step explanation:
Situation D: Suppose that, in a one-minute period during an electrical storm, the number of lightning strikes on a radar antenna follows a Poisson distribution with a mean of 2.40. Question D1: Find the probability that the antenna will be struck exactly once during this time period.
Answer:
21.77% probability that the antenna will be struck exactly once during this time period.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
In this question:
[tex]\mu = 2.40[/tex]
Find the probability that the antenna will be struck exactly once during this time period.
This is P(X = 1).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 1) = \frac{e^{-2.40}*2.40^{1}}{(1)!} = 0.2177[/tex]
21.77% probability that the antenna will be struck exactly once during this time period.
2) A bike racer completed a 20.0 kilometer race. She pedaled the first 5.0 kilometers with an average speed of 20.0 km/hr. She pedaled the next 5.0 kilometers (which were uphill) at an average speed of 10.0 km/hr. She completed the next 5.0 kilometers (which were downhill) at an average speed of 25.0 km/hr and the final 5.0 kilometers she covered at an average speed of 20.0 km/houra) (2point) How long did it take the biker to complete the race
Answer:
Step-by-step explanation:
Time = distance/speed
Considering the first stage,
Speed = 20km/hr
Distance = 5km
Time = 5/20 = 0.25 hour
Considering the second stage,
Speed = 10km/hr
Distance = 5km
Time = 5/10 = 0.5 hour
Considering the third stage,
Speed = 25km/hr
Distance = 5km
Time = 5/25 = 0.2 hour
Considering the third stage,
Speed = 20km/hr
Distance = 5km
Time = 5/20 = 0.25 hour
Therefore, the time it took the biker to complete the race is
0.25 + 0.5 + 0.2 + 0.25 = 1.2 hours
Can someone please answer this right away for me please
Answer:
45000
Step-by-step explanation:
A machine shop produces heavy duty high endurance 20-inch rods that are meant for use in a variety of military grade equipment. On occasion, the machine malfunctions and produces a groove or a chisel cut mark somewhere on the rod. If such defective rods can be cut so that there is at least 15 consecutive inches without a groove, then the rods can be salvaged for other purposes. If the location of the groove on a rod is described by a uniform distribution, what is the probability that a defective rod can be salvaged?
Answer:
The probability that a defective rod can be salvaged = 0.50
Step-by-step explanation:
Given that:
A machine shop produces heavy duty high endurance 20-inch rods
On occasion, the machine malfunctions and produces a groove or a chisel cut mark somewhere on the rod.
If such defective rods can be cut so that there is at least 15 consecutive inches without a groove.
Then; The defective rod can be salvaged if the groove lies on the rod between 0 and 5 inches i.e ( 20 - 15 )inches
Now:
P(X ≤ 5) = [tex]\dfrac{5}{20}[/tex]
= 0.25
P(X ≥ 15) = [tex]\dfrac{5}{20}[/tex]
= 0.25
The probability that a defective rod can be salvaged = P(X ≤ 5) + P(X ≥ 15)
= 0.25+0.25
= 0.50
∴ The probability that a defective rod can be salvaged = 0.50
A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by the quadratic function h(t)= -4.9t^2 + 9.8t + 1. How long does it take for the baseball to reach its maximum height? What is the maximum height obtained by the baseball?
Answer:
Step-by-step explanation:
max can be found by the formula:
t=-b/2a
t=-9.8/2*(-4.9)
t=-9.8/-9.8
t=1
1 sec
to find maximum height obtained we find the vertex:
plug in 1 for t and simply solve:
h(t)= -4.9t^2 + 9.8t + 1
h(t)= -4.9*1^2 + 9.8*1 + 1
h(t)= -4.9*1 + 9.8 + 1
h(t)= -4.9 + 10.8
h(t)= 5.9
height is 5.9
find the quotient of (5+4i)/(6+8i) ans express in simplest forms
Answer:
Your correct answer is 31/50 + -4/25 i
Step-by-step explanation:
5+4i/6+8i = 31/50 + -4/25 i
URGENT! WILL GIVE BRANLIEST!!! THX TO THOSE WHO ARE WILLING TO TAKE A LOOK. :) 3 QUESTIONS
2. Write a similarity statement comparing the two triangles
FIRST IMAGE
A) LNM-ONP
B) NML-NOP
C) MLN-PNO
3. For GH in triangle GHJ, what is the corresponding segment in triangle HIJ?
SECOND PICTURE
A) HG
B) HI
C) IJ
4. JH is the geometric mean of which two segments?
SECOND PICTURE JUST LIKE THE QUESTION ABOVE
A) GH AND HI
B) GJ AND GH
C) JI AND HI
Answer:
2. A) LNM-ONP
3. B) HI
4. A) GH AND HI
Step-by-step explanation:
2. corresponding sides of similar triangle are proportional and corresponding angles are congruent
3. it seems that triangles are 45-45-90 so GH correspondents with HI
4. JH is geometric mean of line segment making hypotenuse
so JH = [tex]\sqrt{GH*HI}[/tex]
Ron's yearly income is $44,300 and has $4,400 withheld for taxes and $2,400 for personal deductions. If he gets paid biweekly, what is his net pay for each paycheck?
Answer:
Net biweekly pay for each paycheck is [tex]\$1442[/tex]
Step-by-step explanation:
Employees paid biweekly are paid 26 times a year.
So, Required Biweekly net pay [tex]=\frac{44300-4400-2400}{26}[/tex]
[tex]\approx 1442[/tex]
Best Regards!
According to the diagram, a 13-foot ladder leans against a 12-foot wall. The distance from the base of the wall is 5 feet. Based on this information, which trigonometric ratio has the value of 12/5
Answer:
Tangent
Step-by-step explanation:
if the angle in question is the bottom of the ladder and the ground, then tangent is opposite over adjacent... or 12/5
Hope this is right
What is the solution to this equation? 4x+x-15+3-8x=13
Answer:
x = -25/3
Step-by-step explanation:
The equation simplifies to -3x - 25 = 0, so
-3x = 25 =>
x = -25/3
what set of Reflections and rotations could carry ABCD onto itself?
Reflect over y-axis,reflect over the X axis ,rotate 180°
Option D is the correct option.
Explanation:
Let's take point A which is (4,-1)
Reflection over y- axis will make this point (4,1)
Then, reflection over X axis will make this point (4,-1)
After rotation of 180 degree we will get (-4,1) .
Please see the attached picture....
Hope it helps...
Good luck on your assignment...
Answer: d) reflect over the x-axis, reflect over y-axis, rotate 180°
Step-by-step explanation:
A reflection over the x-axis and a reflection over the y-axis is the SAME as a rotation of 180°. Together they make a rotation of 360°, which results in the image staying at the same place.
Reflection over the x-axis changes the sign of the y-coordinate
Z = (x, y) → Z' = (x, -y)
Reflection over the y-axis changes the sign of the x-coordinate
Z' = (x, -y) → Z'' = (-x, -y)
Rotation of 180° changes the signs of both the x- and y-coordinates
Z'' = (-x, -y) → Z''' = (x, y)
wow I can't start typing the message an open cylindrical container has a base radius of 3.5 cm if the ratio of the area of its base to that of its curved surface is 1:6, calculate the height of the container
Answer:
height = 10.5 cm (for open-top container)
Step-by-step explanation:
The area of the base is ...
A = πr²
The lateral area is ...
A = 2πrh
We want the ratio of these to be 1:6, so we have ...
πr²/(2πrh) = 1/6
6πr² = 2πrh . . . cross multiply
h = 3r . . . . . . . divide by 2πr
h = 3(3.5 cm) = 10.5 cm
The height is 10.5 cm.
At noon, ship A is 70 km west of ship B. Ship A is sailing south at 40 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM? (Round your answer to one decimal place.)
Answer:
57.6 km per hr
Step-by-step explanation:
Let us assume the horizontal distance between the ship is constant = x
= 70 Km
The ship A sails south at 40km/h is denoted as 40t
The Ship B sails north at 20 km/h is denoted as 20t
Now the vertical distance separating the two ships is
= 20t + 40t
= 60t
And, the Distance between the ship is changing
[tex]D^2 = y^2 + x^2[/tex]
As x is constant
[tex]\frac{\partial x}{\partial t}$ = 0[/tex]
Now differentiating
[tex]2D \frac{\partial D}{\partial t}$ = 2y $\frac{\partial y}{\partial t}$[/tex]
The distance between two ships is at 4
So,
vertical distance is
[tex]= 60\times 4[/tex]
= 240
And, the horizontal distance is 70
[tex]D = \sqrt{240^2 + 70^2} = 250[/tex]
[tex]2 \times 250 \frac{\partial D}{\partial T}$ = 2 \times 240 \times 60[/tex]
So, the distance between the ships is 57.6 km per hr
Select the correct answer from each drop-down menu. Month____ Balance ($) January 45 February 10 March -15 April -35 May -5 The table shows the balance in David’s bank account for the first five months of the year. David’s balance was highest in ____ , and his debt was highest in _____
Answer:
end
January
April
1st blank might also be (account)
Answer:
January and April
Step-by-step explanation:
Fill out the tables for each scenario and answer the question that follows. Use $7.25 as the minimum wage and remember that employees in the United States must be paid time-and-a-half (1.5 times the normal hourly rate) for each hour worked over 40 hours per week
Answer:
see below for the table valuesUS labor cost: $115275 per yearStep-by-step explanation:
The labor charge is for (6 days/week). In Mongolia, the charge per laborer is then ...
(6 days/week)($1.10/day) = $6.60/week
The three laborers working 50 weeks/year will have a labor cost of ...
(3 laborers)($6.60/week/laborer)(50 weeks/year) = $990/year
__
In the US, the labor charge per person per week is ...
(14 hr/day)(6 day/week) = 84 hr/week
That's 40 hours of straight pay and 44 hours of overtime pay, or ...
7.25(40 +1.5(44)) = 7.25(106) = 768.50
For 150 person-weeks per year, the total US labor charge is ...
($768.50/person/week)(3 persons)(50 weeks/year) = $115,275/year
__
The materials cost for a year is ...
($50/rug)(12 rugs/year) = $600/year
__
The revenue is ...
($2000/rug)(12 rugs/year) = $24,000/year
Profit is the difference between revenue and the total of costs:
profit = $24,000 -($990 +600 +10000) = $12410 . . . made in Mongolia
__
So, the table gets filled as follows:
(labor, material, fixed cost, revenue, profit)
Mongolian-made
($990, $600, $10000, $24000, $12410)
US-made
($115275, $600, $10000, $24000, -$101,875)
The US labor cost would be $115,275.
_____
Comment
For the given selling price, the break-even labor cost is about $1.06 per hour (on average). At US labor rates, the break-even selling price is about $10,490 per rug.
Which is most likely the correlation coefficient for the set of data shown
Answer:
The correct answer to the following question will be "0.19".
Step-by-step explanation:
A correlation seems to be a statistical measure of how well the evidence matches the best comment. The better or larger the correlation, the stronger the match, through to 1.0 or -1.0. A positive relationship between the two indicates a growing statistical model, although a negative correlation or confidence interval suggests a down set of data.Value varies from -1.0 to 1.0. A significance level of 0.05 indicates less than -1.0 indicates that there had been a mistake throughout the calculation of correlation.So that the above seems to the right answer.
You find 20 coins consisting only of nickels, dimes, and quarters, with a face value of $2.65. However, the coins all date from 1929, and are worth considerably more than their face value. A coin dealer offers you $7 for each nickel, $5 for each dime, and $20 for each quarter, for a total of $221. How many of each type of coin did you find
Answer:
8 nickels, 5 dimes and 7 quarters
Step-by-step explanation:
Each nickel is $0.05, each dime is $0.10 and each quarter is $0.25.
So, if we have n nickes, d dimes and q quarters, we can write the system of equations:
[tex]n + d + q = 20\ (eq1)[/tex]
[tex]0.05n + 0.1d + 0.25q = 2.65\ (eq2)[/tex]
[tex]7n + 5d + 20q = 221\ (eq3)[/tex]
If we multiply (eq2) by 140 and (eq1) by 7, we have:
[tex]7n + 14d + 35q = 371\ (eq4)[/tex]
[tex]7n + 7d + 7q = 140\ (eq5)[/tex]
Now, making (eq4) - (eq3) and (eq5) - (eq3), we have:
[tex]9d + 15q = 150\ (eq6)[/tex]
[tex]2d - 13q = -81\ (eq7)[/tex]
Multiplying (eq7) by 4.5, we have:
[tex]9d - 58.5q = -364.5\ (eq8)[/tex]
Subtracting (eq6) by (eq8), we have:
[tex]73.5q = 514.5[/tex]
[tex]q = 7[/tex]
Finding 'd' using (eq6), we have:
[tex]9d + 15*7 = 150[/tex]
[tex]9d = 150 - 105[/tex]
[tex]d = 5[/tex]
Finding 'n' using (eq1), we have:
[tex]n + 5 + 7 = 20[/tex]
[tex]n = 8[/tex]
So we have 8 nickels, 5 dimes and 7 quarters.
Which equation is the inverse of y = x2 + 16? y = x2 – 16 y = plus-or-minus StartRoot x EndRoot minus 16 y = plus-or-minus StartRoot x minus 16 EndRoot y = x2 – 4
Answer:
[tex]\pm \sqrt{x-16}[/tex] is the inverse of [tex]y = x^2 + 16[/tex]
Step-by-step explanation:
Given that:
[tex]y = x^2 + 16[/tex]
Let us proceed step by step to calculate the inverse:
Step 1: Put [tex]y = f(x)[/tex]
[tex]f(x) = y=x^2 + 16[/tex]
Step 2: Interchange [tex]x[/tex] and [tex]y[/tex]:
[tex]x = y^2 + 16[/tex]
Step 3: Solve the equation to find the value of [tex]y[/tex]:
[tex]y^2 =x- 16\\\Rightarrow y =\pm \sqrt{x- 16}[/tex]
Step 4: Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]:
[tex]\Rightarrow y =f^{-1}(x)=\pm \sqrt{x- 16}[/tex]
So, the inverse of [tex]y = x^2 + 16[/tex] is [tex]\pm \sqrt{x- 16}[/tex].
The equation which is the inverse of y = x2 + 16 is; f-¹ = y = ±√(x -16)
To evaluate the inverse of the function, y = x2 + 16.
We must first make x the subject of the formula and swap x and y as follows;
x = ±√(y - 16)y = ±√(x - 16)Therefore, the inverse function is;
f-¹ = y = ±√(x -16)Read more on inverse function:
https://brainly.com/question/14391067
PLEASE ANSWER!!!!!!!! Which system of equations does this graph represent? Linear graph and parabola. They intersect at 2, negative 1 and negative 3, 4 (1 point)
A. y = x2 − 5 y = −x + 1
B. y = x2 − 5 y = −x − 1
C. y = x2 + 5 y = −x + 1
D. y = x2 + 5 y = −x − 1
Answer:
Option (A)
Step-by-step explanation:
For equation of the line,
Let the equation is, y = mx + b
Slope 'm' of the line passing through two points (-3, 4) and (2, -1),
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{4+1}{-3-2}[/tex]
= -1
y-intercept of this line, b = 1
Now we substitute these values in the equation,
y = -x + 1
Let the equation of the parabola is,
y = a(x - h)² + k
Here, (h, k) is the vertex of the parabola,
Since vertex of the given parabola is (0, -5),
then the equation will be,
y = a(x - 0)²- 5
y = ax² - 5
Since a point (2, -1) lies on this parabola,
-1 = a(2)² - 5
5 - 1 = 4a
a = 1
Equation of the parabola will be,
y = x² - 5
Therefore, Option (A) will be the answer.
How many cubes with side lengths of end fraction 1/2 cm does it take to fill the prism? btw anyone who answers this first will be marked the brainiest answer and get a thanks from me :)
The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table #7.3.8 ("SOCR data 2008," 2013). Countries that are considered high-income have a mean economic dynamism of 60.29. Do the data show that the mean economic dynamism of middle-income countries is less than the mean for high-income countries? Test at the 5% level. Table #7.3.8: Economic Dynamism of Middle Income Countries
25.8057 37.4511 51.915 43.6952 47.8506 43.7178 58.0767 41.1648 38.0793 37.7251 39.6553 42.0265 48.6159 43.8555 49.1361 61.9281 41.9543 44.9346 46.0521 48.3652 43.6252 50.9866 59.1724 39.6282 33.6074 21.6643
Answer:
No. At a significance level of 0.05, there is not enough evidence to support the claim that the mean economic dynamism of middle-income countries is less than the mean for high-income countries (60.29).
Test staitistic t= -1.02
P-value=0.159
Step-by-step explanation:
We have a sample of size n=26, with mean 43.8727 and standard deviation s=82.2857.
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{26}(25.8057+37.4511+51.915+43.6952+47.8506+. . .+21.6643)\\\\\\M=\dfrac{1140.689}{26}\\\\\\M=43.8727\\\\\\s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{25}((25.8057-43.8727)^2+. . . +(21.6643-43.8727)^2)\\\\\\s=\dfrac{2057.1431}{25}\\\\\\s=82.2857\\\\\\[/tex]
This is a hypothesis test for the population mean.
The claim is that the mean economic dynamism of middle-income countries is less than the mean for high-income countries (60.29).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=60.29\\\\H_a:\mu< 60.29[/tex]
The significance level is 0.05.
The sample has a size n=26.
The sample mean is M=43.8727.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=82.2857.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{82.2857}{\sqrt{26}}=16.138[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{43.8727-60.29}{16.138}=\dfrac{-16.42}{16.138}=-1.02[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=26-1=25[/tex]
This test is a left-tailed test, with 25 degrees of freedom and t=-1.02, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.02)=0.159[/tex]
As the P-value (0.159) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the mean economic dynamism of middle-income countries is less than the mean for high-income countries (60.29).
Please answer this correctly
Answer:
24 picked 2 or more
Step-by-step explanation:
At least 2 means 2 or more
Add up all the x's
2: 7
3: 9
4: 8
total: 24
wich of the following properties was used for 3(x+2)=3x+6
Answer:
you will want to have a good understanding of these properties to make the problems in ... Here, the same problem is worked by grouping 5 and 6 first, 5 + 6 = 11. ... “three times the variable x” can be written in a number of ways: 3x, 3(x), or 3 · x. ... Use the distributive property to evaluate the expression 5(2x – 3) when x = 2.
y
The distributive property tells us that if were given an expression such as 3(x + 2), we can multiply the 3 by both the x and the 2 to get 3x + 6.
eric has practiced more than 40 hours with his band. Write an inequality to express this situation. On the graph below, graph Erics situation
Answer:
We can call the variable e. "more than" is denoted by > so the inequality is e > 40. To graph it, draw a circle on the tick mark that has 40 underneath it but don't fill in the circle. Then, draw a continuous line to the right of the circle and draw an arrow at the end of it to show that it goes on forever.
a dock is 5 feet above water. suppose you stand on the edge of the dock and pull a rope to a boat at a constant rate of 2 ft/s. assume the boat remains at water level. at what speed is the boat approaching the dock when it is 4 feet from the dock
Answer:
The boat is approaching the dock at a speed of 3.20 ft/s when it is 4 feet from the dock.
Step-by-step explanation:
The diagram of the situation described is shown in the attached image.
The distance of the boat to the dock along the water level at any time is x
The distance from the person on the dock to the boat at any time is y
The height of the dock is 5 ft.
These 3 dimensions form a right angle triangle at any time with y being the hypotenuse side.
According to Pythagoras' theorem
y² = x² + 5²
y² = x² + 25
(d/dt) y² = (d/dt) (x² + 5²)
2y (dy/dt) = 2x (dx/dt) + 0
2y (dy/dt) = 2x (dx/dt)
When the boat is 4 ft from dock, that is x = 4 ft,
The boat is being pulled at a speed of 2 ft/s, that is, (dy/dt) = 2 ft/s
The speed with which the boat is approaching the dock = (dx/dt)
Since we are asked to find the speed with which the boat is approaching the dock when the boat is 4 ft from the dock
When the boat is 4 ft from the dock, x = 4 ft.
And we can obtain y at that point.
y² = x² + 5²
y² = 4² + 5² = 16 + 25 = 41
y = 6.40 ft.
So, to the differential equation relation
2y (dy/dt) = 2x (dx/dt)
when x = 4 ft,
y = 6.40 ft
(dy/dt) = 2 ft/s
(dx/dt) = ?
2 × 6.40 × 2 = 2 × 4 × (dx/dt)
25.6 = 8 (dx/dt)
(dx/dt) = (25.6/8) = 3.20 ft/s.
Hope this Helps!!!
Which expression is equivalent to negative 4 times 4 times 4 times 4 times 4 times 4 times 4 times 4?
Answer:
-4*4^7
Step-by-step explanation:
Answer:
-65536
Step-by-step explanation:
I do not think I understand the question but -4*4*4*4*4*4*4*4=-65536
I think there may be missing information like if the question is multiple choice.
Hope that helps
Surface area of a cylinder: S = 2ar+2arh , solve for h.
Answer:
[tex]h = \frac{s - 2ar}{2ar} \\ [/tex]
Step-by-step explanation:
[tex]s = 2ar + 2arh \\ s - 2ar = 2arh \\ \frac{s - 2ar}{2ar} = \frac{2arh}{2ar} \\ h = \frac{s - 2ar}{2ar} [/tex]
hope this helps you
brainliest appreciated
good luck! have a nice day!
An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 243 brakes using Compound 1 yields an average brake life of 37,866 miles. A sample of 268 brakes using Compound 2 yields an average brake life of 45,789 miles. Assume that the population standard deviation for Compound 1 is 4414 miles, while the population standard deviation for Compound 2 is 2368 miles. Determine the 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.
Answer:
THEREFORE THE CONFIDENCE INTERVAL from the Z table = ±1.645
Step-by-step explanation:
Confidence level = 95% = 0.95
compound 1
Number of samples ( n1 ) = 243
Average brake life ( x1 ) = 37866 miles
standard deviation ( ∝ ) = 4414 miles
compound 2
number of samples ( n2 ) = 268
Average brake life ( x2 ) = 45789 miles
standard deviation ( ∝ ) = 2368 miles
Determine the 95% confidence interval for the true difference between average lifetimes
significance level (β) = 1 - confidence level = 1 - 0.95 = 0.05
standard error = [tex]\sqrt{\frac{\alpha1^2 }{n1} + \frac{\alpha2^2}{n2} }[/tex] = [tex]\sqrt{}[/tex]( 4414^2/243) + (2368^2/268) =
critical value = 0.05/2 =Z 0.025 = 1.645
THEREFORE THE CRITICAL VALE from the Z table = ±1.645
Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the production and sale of x items. If R(x) = 6x and C(x) equals = 0.002x^2+2.2x+40, find each of the following. a. p(x) b.p(100) c. P'(x) d.P'(100)
Answer:
[tex]a.\ P(x) = - 0.002x^2+3.8x-40[/tex]
b. 320
[tex]c.\ P'(x) = -0.004 x + 3.8[/tex]
d. 3.76
Step-by-step explanation:
Given that:
Revenue function:
[tex]R(x) = 6x[/tex]
Cost Function:
[tex]C(x) = 0.002x^2+2.2x+40[/tex]
We know that,
Answer a: Profit = Revenue - Cost
[tex]\Rightarrow P(x) = R(x) - C(x)\\\Rightarrow P(x) = 6x - (0.002x^2+2.2x+40)\\\Rightarrow P(x) = - 0.002x^2+3.8x-40[/tex]
Answer b:
P(100) = ?
Putting value of x as 100 in above equation:
[tex]P(100) = - 0.002\times 100^2+3.8 \times 100-40\\\Rightarrow P(100) = -20+380 -40\\\Rightarrow P(100) = 320[/tex]
Answer c:
P'(x) = ?
Differentiating the equation [tex]P(x) = - 0.002x^2+3.8x-40[/tex]
[tex]P'(x) = -2 \times 0.002 x^{2-1} + 3.8 + 0\\P'(x) = -0.004 x + 3.8[/tex]
Answer d:
P'(100) = ?
Putting x = 100 in equation [tex]P'(x) = -0.004 x + 3.8[/tex]
[tex]P'(100) = -0.004 \times 100 + 3.8\\P'(100) = -0.4 + 3.8\\P'(100) = 3.76[/tex]