a. The total revenue function is R(x) = 2x(x²+28,000)^(1/3) + 29,222 - 240(120)^(1/3).
b. At least 11 gadgets must be sold to generate a revenue of at least $40,000.
a. We are given that the marginal revenue function is R'(x) = 4x(x²+28,000)^(-2/3). We are also given that the revenue from 120 gadgets is $29,222. This means that R(120) = 29,222.
We can find the total revenue function by integrating the marginal revenue function. The integral of R'(x) is R(x) = 2x(x²+28,000)^(1/3) + C. We can find the value of C by substituting R(120) = 29,222 into the equation. This gives us C = 29,222 - 240(120)^(1/3).
Therefore, the total revenue function is R(x) = 2x(x²+28,000)^(1/3) + 29,222 - 240(120)^(1/3).
b. We are given that the revenue must be at least $40,000. We can substitute this value into the total revenue function to find the number of gadgets that must be sold. This gives us 40,000 = 2x(x²+28,000)^(1/3) + 29,222 - 240(120)^(1/3).
Solving for x, we get x = 11.63. This means that at least 11 gadgets must be sold to generate a revenue of at least $40,000.
Revenue function: R(x) = 2x(x²+28,000)^(1/3) + 29,222 - 240(120)^(1/3)
Number of gadgets to generate $40,000 revenue: 11.63
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What is the prime factorization of 97?
Answer:
97 is a prime number.
Prime[25] = 97
find a value of c so that p(z ≥ c) = 0.55.
To find a value of c such that P(z ≥ c) = 0.55, we need to use a standard normal distribution table or calculator.From the standard normal distribution table, we find that the z-score corresponding to a right-tailed area of 0.55 is approximately 0.126.
Therefore, we have:
P(z ≥ c) = 0.55
P(z ≤ c) = 1 - P(z ≥ c) = 1 - 0.55 = 0.45
Using the standard normal distribution table, we find that the z-score corresponding to a left-tailed area of 0.45 is approximately -0.126.
So, c = -0.126.
Therefore, the value of c that satisfies P(z ≥ c) = 0.55 is approximately -0.126.
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Point P(3, 9) in the coordinate plane is rotated 90 degrees counterclockwise about the origin. What are the coordinates of its image?
Please show all work and not just the answers.
Answer:
P'(-9, 3)
Step-by-step explanation:
The transformation for rotation counterclockwise about the origin by some angle α will be ...
(x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))
When the angle is α = 90°, this reduces to ...
(x, y) ⇒ (-y, x)
You have (x, y) = (3, 9), so the image point is P'(-9, 3).
__
Additional comment
The "work" is applying the right sign and choosing the right coordinate to fill in the values (-y, x). I find it easier to look up the transformations for ±90° and 180°, rather than try to derive them from first principles every time. Your text may have a list:
90° CCW or 270° CW: (x, y) ⇒ (-y, x)90° CW or 270° CCW: (x, y) ⇒ (y, -x)180°: (x, y) ⇒ (-x, -y)Un concensario de coches rebaja a 16000 un vehiculo que valia 18300 en que porcentaje lo han rebajado?
As a car dealer lowers a vehicle that was worth 18300 to 16000 by applying the formula of change in percentage we get that by 12.569 percentage (approximately) the price gets lowered .
The initial price of the car is set at P = 18300 (units)
The price after lowering drom P becomes A= 16000 (units)
Hence the change in price (or value) of the car, that is the price of the car is lowered by, C = (initial price - lowered price) = (P - A) = (18300 - 16000) units = 2300 units.
The formula for calculating percentage change is given as follows,
Change in percentage = [(Change in value)/ ( Initial value) ]*100
⇒Change in percentage = (C/ P)*100
⇒ Change in percentage =( 2300/ 18300)*100 = 12.569% (approximately)
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Solving equations and inequalities escape room
Answer:
18) 10.5
19) 45
20) 16
Step-by-step explanation:
simplified expression || hope this is what u needed
Only answer if it's 1000000000% Correct UwU
If the cost of a bat and a baseball combined is $1.10 and the bat costs $41.00 more than the ball, how much is the ball?
it is 5 cents :v
Cause I said so
Answer:
5 cents
Step-by-step explanation:
HURRYYYY
describe the end behavior of the function.
Answer:
the first one (top-most choice)
Step-by-step explanation:
the line in the graph displays an "and" function because it's got two arrows going at different directions from 1 point.
hope this helps!
Please help me solve this question.
Answer:
ZXY = KXH by reason SAA
Step-by-step explanation:
I believe that is the answer.
also, SAA stands for Side, Angle, Angle
It could also be AAS
Either one is right.
AAS or SAA
What is 7 tens + 5 ones
Answer:
\( = { \tt{(7 \times 10) + (5 \times 1)}} \\ \\ = { \tt{70 + 5}} \\ \\ { \underline{ \tt{ \: \: = 75 \: \: }}}\)
Answer:
7×10 + 5×1
70+5
=75 is the answer
Which statement describes a property of water?
O A. It is less dense as a solid than as a gas.
o B. It is less dense as a solid than as a liquid.
C. It is more dense as a gas than as a liquid.
0
D. It is more dense as a solid than as a liquid.
Answer:
the answer is D. dense means heavier, basically
Answer:
its D dense
Step-by-step explanation:
because dense means more inside
Answer the following questions a Find A b 3 whose eigenvalues are 1 and 4, and whose eigenvectors are *> respectively b Find B whose eigenvalues are 1 and 3
This gives us the equation -2x + y = 0 and 4x - 3y = 0, which has the solution x = y/2. Therefore, the eigenvector for λ = 3 is v2 = [1; 2].
a) To find matrix A with eigenvalues 1 and 4 and corresponding eigenvectors v1 and v2 respectively, we can use the formula A = PDP^-1 where P is the matrix of eigenvectors and D is the diagonal matrix of eigenvalues.
We know that v1 and v2 are eigenvectors with eigenvalues 1 and 4 respectively, so we can set up the following equations:
Av1 = 1v1 and Av2 = 4v2
Multiplying both sides of each equation by P^-1, we get:
PDv1 = v1 and PDv2 = 4v2
Therefore, P = [v1 v2] and D = [1 0; 0 4], which gives us the matrix A = PDP^-1.
b) To find matrix B with eigenvalues 1 and 3, we can use the same formula A = PDP^-1. However, we don't know the eigenvectors yet. To find them, we can use the characteristic polynomial of B, which is (1-λ)(3-λ) = 0. This gives us eigenvalues λ = 1 and λ = 3.
To find the eigenvectors for λ = 1, we need to solve the equation (B-λI)v = 0, which gives us:
(B-1I)v = 0
[0 1; 1 2][x; y] = [0; 0]
This gives us the equation x + y = 0, so the eigenvector for λ = 1 is v1 = [1; -1].
To find the eigenvectors for λ = 3, we need to solve the equation (B-λI)v = 0, which gives us:
(B-3I)v = 0
[-2 1; 4 -3][x; y] = [0; 0]
Using these eigenvectors and the formula A = PDP^-1, we can find the matrix B = PDP^-1 where P = [v1 v2] and D = [1 0; 0 3].
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Consider the absolute value functions cand d.Which statement correctly describes these functions?OA.The minimum value of d is 5 more than the maximum value of c.OB.The maximum value of dis 3 less than the minimum value of aОс.The minimum value of dis 3 more than the maximum value of c.ODThe maximum value of dis 5 less than the minimum value of a
The correct option is Option A
The minimum value of D is 2, while the maximum value of C is -3.
The minimum value of D is 5 more than the maximum value of C
Graph y=4/7x−2.
Use the line tool and select two points on the line to graph the line.
Answer:
Therefore, the answer is: The graph of the equation is a straight line passing through the points (0, -2), (7, 2), and (-7, -6).
Step-by-step explanation:
The given equation is y = (4/7)x - 2.
To graph this equation, we need to plot points on a coordinate plane. We can do this by choosing values of x and then finding the corresponding values of y using the equation.
Let's choose some values of x and find the corresponding values of y:
When x = 0, y = (4/7)(0) - 2 = -2
When x = 7, y = (4/7)(7) - 2 = 2
When x = -7, y = (4/7)(-7) - 2 = -6
We now have three points: (0, -2), (7, 2), and (-7, -6). We can plot these points on a coordinate plane and draw a line through them to get the graph of the equation.
a building is 3.1×10^2 feet high.a new roof increased its hight by 0.00005 feet how high is the building now
I’m completely lost on this, so if you have any ideas, please let me know
The number of seconds after which the ball will hit the ground will be: 0.022 seconds when rounded to the nearest tenth.
How to find the length of timeTo find the length of time, the question first requires that we obtain the values for g, Vo and H. We will proceed by using the kinematic equation that makes a relationship between the vertical displacement of an object, its initial velocity, acceleration due to gravity, and time:
y = Vo*t + (1/2)gt^2.
To obtain the value of g, we will use the value of acceleration due to gravity, which is approximately 32 ft/s^2.
Also, to find Vo, we use the initial velocity of the ball, which is 64 ft/s, and for the value of H, we use the initial vertical displacement of the ball, which is 12 ft.
When we substitute all of these figures into the first equaltion, we will have:
-12 = 64t + (1/2)gt^2
Multiplying both sides by 2 and rearranging, we get:
g*t^2 + 128t - 24 = 0
Using the quadratic formula, we get:
t = (-128 ± sqrt(128^2 - 4g(-24)))/(2*g)
t = (-128 ± sqrt(16384 + 384))/64
t = (-128 ± sqrt(16768))/64
t = (-128 ± 129.4)/64
So, t = 1.4/64 or t = -257.4/64
The negative root does not align with the value of time in reality. Therefore, the time it takes for the ball to hit the ground is: t = 1.4/64 = 0.022 seconds.
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1. Jenna measures all the angles around a point.
Her results are 23°, 145°, 23° and 69°
Explain why these results cannot be true.
Answer:
When we add 23°, 145°, 23° and 69° we get 260°
And 260° does not have defined number of sides
Step-by-step explanation:
These are the polygons with the number of sides and angles
Polygon Name | Number of Interior Angles | Sum of Interior Angles
Triangle 3 180°
Quadrilateral 4 360°
Pentagon 5 540°
Hexagon 6 720°
Septagon 7 900°
Octagon 8 1080°
Nonagon 9 1260°
Decagon 10 1440°
A stock on the New York Stock Exchanged opened at $48on Monday.During the week,the stock lost $2 ,gained $1 ,gained$3 ,lost $1 and lost $4.What was the stock worth at the close of the businesson Friday?
The stock worth at the close is $45.00
(pythagorean theorem and the coordinate plane mc) determine the length of the line segment shown. line segment from negative 3 comma 10 to 4 comma negative 1 13 units 12 units 7 units 3 units
Using Pythagorean Theorem, the length of the line segment from (-3, 10) to (4, -1) is 13 units.
Pythagorean theorem describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two other side.
c² = a² + b²
Let a = vertical distance between the two points
b = horizontal distance between the two points
c = distance between the two points / length of line segment
Hence, c² = (|y₂ - y₁|)² + (|x₂ - x₁|)².
Substitute the values of x and y and solve for c.
c² = (|y₂ - y₁|)² + (|x₂ - x₁|)²
c² = (|-1 - 10|)² + (|4 - -3|)²
c² = (|-11|)² + (|7|)²
c² = 11² + 7²
c² = 121 + 49
c² = 170
c = 13.04
length of line segment ≅ 13 units
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Please help ASAP, will give brainliest
Answer:
1/2
Step-by-step explanation:
Since there is a 100% probability (1) that the result can be either heads or tails , and since we are taking about 2 results the answer is 1/2
Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is _______.
(ii) If two angles are supplementary, then the sum of their measures is ______.
(iii) Two angles forming a linear pair are _______________.
(iv) If two adjacent angles are supplementary, they form a ___________.
(v) If two lines intersect at a point, then the vertically opposite angles are always
_____________.
(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are
acute angles, then the other pair of vertically opposite angles are __________.
Answer:
i) 90
ii) 180
iii) supplementary
iv) linear pair
v) equal
vi) obtuse
suppose we want to solve the bvp using a direct method. if we approximate as , what will the matrix be when using the direct method?
A second-order differential equation with limitations on the solution y = y(x) at two different values of x makes up a second-order boundary-value issue.
What is a differential equation?
Any equation involving the abstract representation y=f(x) including one or more of its derivatives is known as a differential equation.
A function y=f(x) that fulfills the differential equation whenever f and also its derivatives are replaced into the equation is a response to a differential equation.
A system of ordinary differential equations having a solution and derivative values defined at more than one place is referred to as a boundary value problem. A two-point boundary value problem is one where the solution and derivatives are typically provided at just two positions (the boundaries).
A second-order differential equation with limitations on the solution y = y(x) at two different values of x makes up a second-order boundary-value issue. For instance, the boundary value issue y′′ + y = 0 with y(0) = 0 and y (/6) = 4 is quite straightforward.
In light of y′(0) = 0 and y′ (/6) = 4, is y′′ + y = 0.
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what is the length of the radius of the circle 15^2
Answer:
the length of the radius of the circle = 15.
Step-by-step explanation:
Can you use a right triangle to represent the distance between any two points on the coordinate plane?.
Yes. A leg of a right triangle can indicate the distance that separates two vertical or horizontal points, and the hypotenuse can represent the distance between two non-vertical or non-horizontal points.
We can use this theorem to calculate the distances between two locations on a coordinate grid. Consider the following example using the points:
( 3, 4 ) and ( − 2, 1 )
We can see how to make a right triangle with the hypotenuse as that of the line connecting these two spots. A right angle is formed at the coordinates ( 3, 1), where the vertical line from ( 3, 4 ) and the horizontal line from ( 2, 1 ) intersect.
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please hurry not much more time answer even if its too late somebody else can use the answer.
6. Middle school class representatives conducted a poll during lunch to see which activity students wanted for their year-end party. The results are shown in this relative frequency table below:
a) For the entire school, which was more popular, water slides or roller skating? (1 point)
THE ANSWER FOR A IS: ROLLER SKATING
b) 34% of the 6th graders and 50% of the 7th graders want to go to the water slides. What percentage of the 8th graders want to go to the water slides? (1 point)
c) Does there seem to an association between grade level and field trip choice? (2 points)
d) If this trend continued, would you expect 9th graders to prefer the water slides or roller skating? Explain your answer. (2 points)
The table of the relative frequencies show that 70% of 8th graders want the water slides.
There is an association between grade level and field trip choice with the higher grades preferring Water slides more than roller skating.
9th graders would prefer waterslides if the trend continues.
What does the frequency table show?The percentage of 8th graders who want to go to water slides is:
= 0.14 / 0.20 x 100%
= 70%
As the grades increase, less people want to go roller skating which means that should this trend continue, 9th graders would prefer water slides.
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Answer:
See below
Step-by-step explanation:
From the table:
a) roller skating is 54 percent.....slides is only 46 percent
b) 8 th graders who want water slide = .14 / ( .14 + .06) = 70 percent
c) yes higher grade, higher want water slide
d) water slides ( see answer c )
Directions- If each quadrilateral below is rectangle, find the missing measures
Answer:
1) 59
2) 31
3) 59
4) 31
5) 31
6) 59
7) 118
8) 62
9) 62
10) 118
11) 31
Step-by-step explanation:
The angle marked 59 degrees is congruent to angles 1, 3, and 6. The angle marked 59 + angle 11 is 90 degrees because the shape is a rectangle, so 90-59=31. Angle 11 is congruent to angles 2, 4, and 5. Now that we know that the triangle on the left has two angles of 59 degrees and that the angle measures of a triangle add to 180, 59+59=118 and 180-118=62, so angle 9 is 62 degrees. Angles 8 and 9 are vertical angles and therefore are congruent. To find angles 10 and 7, we can use the same method: angles 4 and 5 are both 31 degrees, 31+31=62, so we subtract 62 from 180 to get 118. Angles 7 and 10 are also vertical angles, so they are both 118 degrees. I hope this helps!
30 - 6 (x + 3) + 2x = 8
Answer:
I believe the correct answer would be the first X=1 and the second X=1
Basically they both equal 1
Answer:
X=1
Step-by-step explanation:
Select the expressions that are equivalent to 7(-7u - 4) - 5.
(-7u - 4)7 - 5
7(-8u+ u 4) - 5
-33u - 49
-7u - 33
Answer: only the first one
Step-by-step explanation:
a poster of area 11760 cm2 has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the sides. find the dimensions that maximize the printed area.
A poster of area 11760 cm2 has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the sides. The dimensions that maximize the printed area are 500 cm x 23.52 cm.
The problem can be solved using the following concept:
Suppose we have a function f(x), then at the maximum/minimum point, it holds:
f '(x) = 0
In the given problem, let:
q = length of the poster
p = width of the poster
Then,
p x q = 11760
or q = 11760/p
Let f(p,q) be the function of printed area, then:
f(p,q) = (p - 20)(q - 12)
f(p) = (p - 20) (11760/p - 12)
f(p) = -p² + 1000p - 980 x 20
At the maximum point:
f '(p) = 0
-2p + 1000 = 0
p = 500
Substitute p = 500 to get q:
q = 11760/p = 11760/500 = 23.52
Hence, the maximum printed area obtained if the dimensions are 500 cm x 23.52 cm
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QUESTION
Riley wants to order a pizza for delivery. The cost is $5 per pizza plus a $6 delivery charge. Fill in the blanks to determine the maximum number of pizzas (n) that Riley can order if she has $20 to spend.
help!
Answer:
Riley can only order 2 pizzas
Step-by-step explanation:
1. subtract delivery fee from the 20 dollars.
$20 - $6 = $14
2. Find number of pizzas with the $14 that she can use.
$14 ÷ $5 = 2 R $4
thus she can only buy 2 pizzas
and n = 2 in this case.
Find p.
Write your answer as a whole number or a decimal. Do not round.
Answer:
Is that IXL? I got the same question as well.
Step-by-step explanation: