The marginal revenue of the 8th item from the revenue function is 16
How to determine the marginal revenue?From the question, the revenue function is given as
R(x) = 20x - 0.25x^2
To calculate the marginal revenue, we start by differentiating the revenue function
This is calculated as follows
R(x) = 20x - 0.25x^2
Differentiate the function
R'(x) = 20 - 0.5x
The above represents the marginal revenue function
So, we have
M(x) = 20 - 0.5x
For the 8th item, we have
M(8) = 20 - 0.5 x 8
Evaluate
M(8) = 20 - 4
Evaluate
M(8) = 16
Hence, the marginal revenue is 16
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Can someone help me with this math question. I just need to see the work.
pic of question below
The polar coordinates for each point are given as follows:
a. [tex](r, \theta) = \left(2\sqrt{5}, \frac{7\pi}{4}\right)[/tex]
b. [tex](r, \theta) = \left(6, \frac{\pi}{3}\right)[/tex]
Polar coordinatesSuppose we have a point with Cartesian coordinates given as follows:
(x,y).
The polar coordinates will be found as follows:
r² = x² + y².θ = arctan(y/x).For item a), the Cartesian coordinates are as follows:
(-4, 4).
Hence the polar coordinates will be given as follows:
r² = (-4)² + (4)² -:> r = sqrt(32) = 2sqrt(5).θ = arctan(-4/4) = arctan(-1) = -45º = 2pi - pi/4 = 7pi/4.For item a), the Cartesian coordinates are as follows:
(3, 3sqrt(3)).
Hence the polar coordinates will be given as follows:
r² = (3)² + (3sqrt(3))² = 9 + 27 = 36 -> r = sqrt(36) = 6.θ = arctan(3sqrt(3)/3) = arctan(sqrt(3)) = 60º = pi/3.More can be learned about polar coordinates at https://brainly.com/question/7009095
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A triangle has squares on its three sides as shown below. What is the value of x? 4 centimeters 7 centimeters 5 centimeters 3 centimeters
find the measure of each of the other six angles
The measure of angle 1 is 71º, we can find this, because angle 1 and angle x form a straight line of 180º, so 180º - 109º = 71º
The measure of angle 2 is also 71º, we can use the vertical angles propierty, then m∠1 = m∠2
The measure of angle 3 is 109º, we can use again the vertical angles theorem to find that m∠x = m∠3
Themeasure of angle 7 is 109º. We need to use the alternating exterior angles theorem. Since angle x and angle 7 are not between the parallel lines they're exterior angles; and since they're on opposite sides of the transversal line, they're alternates. Then the theorem says that m∠x = m∠7
The measure of angle 6 is 71º, again we're using the fact that angle 7 and angle 6 forms a straight line, then m∠6 = 180º - 109º = 71º
Now we can find the lasts two measures using the vertical angles theorem.
The measure of angle 5 is 71º, because m∠6 = m∠5
The measure of angle 4 is 109º, because m∠7 = m∠4
What is the slope and y-intercept?
y=3x-2
Options:
Blank # 1
Blank # 2
The value of slope is 3 and the value of y - intercept is -2.
Slope and y intercept:
The slope refers the rate of change in y per unit change in x.
The y-intercept states the y-value when the x-value is 0.
Given,
Here we have the equation
y = 3x - 2
Now, we need to find the slope and y intercept of the equation.
We know that, the standard form of the equation of the line is,
y = mx + b
Where
m represents the slope
b represents the y-intercept.
So, we have to rewrite the given equation as,
y = 3x + (-2)
So, while comparing the given equation with standard form, then we get,
the value of the slope is 3 and the value of the y intercept is -2.
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The point P is on the unit circle. If the y-coordinate of P is −3/5, and P is in quadrant IV, then
x = _________
Answer:
[tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Knowing that [tex]{-\frac{3}{5}}^{2} + {\frac{4}{5}}^{2} = 1, {-\frac{3}{5}}^{2} + {-\frac{4}{5}}^{2} = 1[/tex],
so x can be positive or negative 4/5,
and we know that x coordinate of any point in quadrant IV is positive,
so x = 4/5.
Write an equation of variation to represent the situation and solve for the indicated information Wei received $55.35 in interest on the $1230 in her credit union account. If the interestvaries directly with the amount deposited, how much would Wei receive for the sameamount of time if she had $2000 in the account?
The diameter of the Milky Way is 2 x 10²⁰ meters. The radius of Earth is 6.37 x 10⁶meters. About how many times as great is the diameter of the Milky Way than the radius of Earth? The diameter of the Milky Way is about
Answers: 4.37 X 10¹⁴
3.1 X 10¹⁴
4.37 X 10¹³
3.1 X 10¹³
(blank) times as great as the radius of Earth.
Answer:
3.1 x [tex]10^{13}[/tex]
Step-by-step explanation:
[tex]\frac{2x10^{20} }{6.37x10^{6} }[/tex]
3/6.37 is about .31
When you are dividing with powers, you subtract the exponents
20 - 6 = 14
.31 x [tex]10^{14}[/tex] This is not in scientific notation because .31 is less than 1
3.1 x [tex]10^{-1}[/tex]x[tex]10^{14}[/tex] When we multiply powers with the same base we add the exponents
3.1 x [tex]10^{13}[/tex]
Determine the midpoint between A(2,13) and O (-4,3)
The midpoint between two points can be found by averaging their coordinates. This is done below:
[tex]\begin{gathered} x_m\text{ = }\frac{x_1+x_2}{2} \\ y_m\text{ = }\frac{y_1+y_2}{2} \end{gathered}[/tex]Using the above expressions we can apply the coordinates of the points we want to find, A(2,13) and O(-4,3).
[tex]\begin{gathered} x_m\text{ = }\frac{2\text{ -4}}{2} \\ x_m\text{ = }\frac{-2}{2} \\ x_m\text{ = -1} \end{gathered}[/tex][tex]\begin{gathered} y_m\text{ = }\frac{3+13}{2} \\ y_m\text{ = }\frac{16}{2} \\ y_m\text{ = 8} \end{gathered}[/tex]The coordinates of the midpoint are (-1,8).
he center of the circle below is at P. If arc AB measures 86 °, then what is the measure of the angle < APB ?
Answer:
D. 86°
Explanation:
Given:
• The center of the circle = P
,• The measure of arc AB = 86°
We want to find the measure of the angle APB.
By Circle's theorem: The measure of an arc is equal to the measure of the central angle subtended by the same arc.
Applying this theorem, we have that:
[tex]\begin{gathered} m\angle APB=m\widehat{AB} \\ \implies m\angle APB=86\degree \end{gathered}[/tex]The measure of the angle APB is 86 degrees.
Option D is correct.
I need help with this questions I don’t. Get it
You will need 275 ml of the 90% solution
Explanation:Let the amount of the 90% alcohol be x
Amount of the 30% alcohol solution = 385 ml
The amount of the mixture = 385 + x
(30% of 385) + (90% of x) = 55% of (385+x)
[tex]\begin{gathered} (\frac{30}{100}\times385)+(\frac{90}{100}\times x)=\frac{55}{100}\times(385+x) \\ \\ (0.3\times385)+(0.9\times x)=0.55(385+x) \\ \\ 115.5+0.9x=211.75+0.55x \\ \\ 0.9x-0.55x=211.75-115.5 \\ \\ 0.35x=96.25 \\ \\ x=\frac{96.25}{0.35} \\ \\ x=275 \\ \\ \end{gathered}[/tex]You will need 275 ml of the 90% solution
a carpentar has 16 1/2m of wood he cuts the wood into peices that are each 2 3/4m long PLSSSSS HURRY!!!!!!!!
The most appropriate choice for fraction will be given by
6 pieces of wood are cut by the carpenter
What is a fraction?
Suppose there is a collection of objects and some part of the objects are taken from the collection. The part which has been taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.
Total length of wood = [tex]16\frac{1}{2}[/tex] m
= [tex]\frac{33}{2}[/tex] m
Length of one piece of a wood = [tex]2\frac{3}{4}[/tex] m = [tex]\frac{11}{4}[/tex]
Number of pieces of wood cut by carpenter = [tex]\frac{33}{2}[/tex] ÷ [tex]\frac{11}{4}[/tex]
= [tex]\frac{33}{2}[/tex] [tex]\times \frac{4}{11}[/tex]
= 6
6 pieces of wood are cut by the carpenter
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1 Select the correct answer from each drop-down menu. 500 N 520 and = < In the figures
x = (internal angle)
y,z = (externals)
Then
Angle x= < x= 180° - 50° -45° = 85°
Angle y= 180° - (180° - Angle z =
Then answers are
Angle x= 85°
Angle y= 137°
Angle z= 128°
LanaCharles almn on the coordinate plane what is the perimeter of a ALMN round to the nearest unit
The Solution:
Given the graph below:
We are required to find the perimeter of the triangle LMN rounded to the nearest unit.
Step 1:
Find the distance LM, where L(-3,2) and M(3,5)
By the formula for distance between two points, we have
[tex]LM=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where,
[tex]\begin{gathered} x_1=-3 \\ y_1=2 \\ x_2=3 \\ y_2=5 \end{gathered}[/tex]Substituting, we get
[tex]LM=\sqrt[]{(3--3)^2+(5-2)^2}=\text{ }\sqrt[]{6^2+7^2}=\text{ }\sqrt[]{85}=9.2195[/tex]Step 2:
Find the distance LN:
[tex]LN=12[/tex]Step 3:
Find the distance MN, where M(3,5) and N(9,2)
[tex]MN=\sqrt[]{(9-3)^2+(2-5)^2}=\text{ }\sqrt[]{6^2+(-3)^2}=\text{ }\sqrt[]{45}=6.7082[/tex]Step 4:
The perimeter is:
[tex]\text{ Perimeter=LM+MN+LN=9.2195+6.7082+12=27.9277}\approx28\text{ units}[/tex]Therefore, the correct answer is 28 units.
X Y2 146 4211 77Find the constant of proportionality (r) in the equation y=rx.
From the question
We are given the equation
[tex]y=rx[/tex]We are to find r given that
When x = 2, y = 14
When x = 6, y = 42
When x = 11, y = 77
Substituting the first value, x = 2, y = 14 into the equation we get
[tex]14=r\times2[/tex]Solving for r we get
[tex]\begin{gathered} r=\frac{14}{2} \\ r=7 \end{gathered}[/tex]This is true for all values of x and y
Hence, r
Find the average rate of change of the following function from t = 1 to t=2.5h(t) = 148 – 16t
The average rate of change of the function from t=1 to t=2.5 is given by:
[tex]\frac{h(2.5)-h(1)}{2.5-1}=\frac{h(2.5)-h(1)}{1.5}[/tex]It is given that:
[tex]\begin{gathered} h(t)=148-16t \\ h(2.5)=148-16\times2.5=108 \\ h(1)=148-6=142 \end{gathered}[/tex]Substitute the values to get:
[tex]\frac{h(2.5)-h(1)}{1.5}=\frac{108-142}{1.5}=\frac{-68}{3}\approx-22.6667[/tex]Hence the rate of change is -22.6667.
PLEASE HELP ASAP! What is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola?
A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.
What is hyperbola?A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set. A hyperbola is made up of two mirror images of one another that resemble two infinite bows.These two sections are known as connected components or branches. A series of points in a plane that are equally spaced out from a directrix or focus is known as parabolas. The difference in distances between a group of points that are situated in a plane and two fixed points—which is a positive constant—is what is referred to as the hyperbola.Therefore, a hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.
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Sean, Kevin and Bill take classes at both JJC and CSU. Sean takes 8 credits at JJC and 4 credits at CSU; Kevin takes 10 credits at JJC and 6 at CSU: Bill takes 6 credits at JJC and 4 at CSU; the cost per credit at JJC is $103 and at CSU is $249. a) Write a matrix A that gives the credits each student is taking and B that gives the cost per credit at each school. b) Find the dimension of A and B. c) Find the product AB and the names of its rows and columns.
ANSWER:
a)
[tex]\begin{gathered} A=\begin{pmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{pmatrix} \\ B=\begin{pmatrix}103 \\ 249\end{pmatrix} \end{gathered}[/tex]b)
Dimension A = 3 x 2
Dimension B = 2 x 1
c)
Cost of credits
Sean $1820
Kevin $2524
Bill $1614
[tex]\begin{pmatrix}Sean \\ \: Kevin \\ \: Bill\end{pmatrix}\begin{pmatrix}1820 \\ \: 2524 \\ \: 1614\end{pmatrix}[/tex]STEP-BY-STEP EXPLANATION:
With the help of the statement, we create the matrices A and B:
[tex]\begin{gathered} A=\begin{pmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{pmatrix}\rightarrow3\times2 \\ B=\begin{pmatrix}103 \\ 249\end{pmatrix}\rightarrow2\times1 \end{gathered}[/tex]Now, we calculate the product just like this:
[tex]\begin{gathered} \text{Product }A\cdot B=\begin{pmatrix}8\cdot103+4\cdot249 \\ 10\cdot103+6\cdot249 \\ 6\cdot103+4\cdot249\end{pmatrix}=\begin{pmatrix}1820 \\ \: 2524 \\ \: 1614\end{pmatrix} \\ \text{Product }A\cdot B=\begin{pmatrix}Sean \\ Kevin \\ Bill\end{pmatrix}\begin{pmatrix}1820 \\ 2524 \\ 1614\end{pmatrix} \end{gathered}[/tex]The difference between the graph of a radical function and the graph of a rational function
The difference between the graph of a radical function and that of a rational function is:
A radical graph is drawn from a function that contains a root, it could be a square root, cube root, etc. Whenever you are graphing a radical function, we first need to consider the domain. Because of the square root sign, the domain and range are always restricted.
But a rational graph is drawn from the ratio of two polynomial functions where the function in the denominator is not equal to zero. A rational graph is characterized by asymptotes.
The major difference would be that a radical graph has a restricted domain due to the root, and usually without an asymptote, while a polynomial graph has a restricted domain and sometimes range which forms the asymptote (vertical, horizontal asymptote).
the difference of twice h and 5 is as much as the sum of h and 4
The value of h by solving the given relationship we get, h = 9
In the above question, a word problem is given with the following relations which are as
First we'll express the given word problem statements into mathematical equation expressions
Therefore, The difference of twice of h and 5 is as much as the sum of h and 4
It can be written as in mathematical equation form as
2h - 5 = h + 4
Now, we need to find the value of h by solving the above mathematical equation formed put of the given relationship
Here,
2h - 5 = h + 4
2h - h = 5 + 4
h = 9
Hence, The value of h by solving the given relationship we get, h = 9
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How many offices are between 41 and 50 meters ?
Solution
For this case we want to find the number of offices between 41 and 50 m and the answer is:
2 meters
2,000 deposit,compound interest,compounded anually,at 6% for 2 years. What is the total balance(A=Principal+Interest)?
Given a principal P, compounded anually at r% for t years. Then the
Where are all the tutors at??? Like it won’t even let me ask a tutor
The scatter plot is given and objective is to find the best line of fit for given scatter plot.
Let's take the few points of scatter plot,
(0,8) ,( -1,8) , (-4,10) ,( -8,12),(-10,14) (-12,14)
Take the line and check which graph contains most of the points of scatter plot.
[tex]1)\text{ f(x)=}\frac{-1}{2}x+8[/tex]The graph is ,
now take ,
[tex]2)\text{ f(x)=x+8}[/tex]The graph is,
This graph contains only one point of scatter plot.
Take,
[tex]3)\text{ f(x)= 10}[/tex]Now the take the last equation,
[tex]4)\text{ f(x)=-2x+14}[/tex]this graph contains no point of the scatter plot.
From all the four graph of the lines it is observed that option 1) is the best line of fit for given scatter plot. because it contains 3 points of scatter plotes . which is more than the other graph of line.
Answer: Option 1)
The point (2, 4) is reflected over the x-axis. What are its new coordinates?Use the blank grid below it it helps.-6-54-321-6ch-4-3-2.-1O3N56-1-2-3--4--5-6O (2,-4)O (-2,-4)O (4,2)O (-2,4)
Let:
[tex]\begin{gathered} A=(x1,y1)=(2,4) \\ A^{\prime}=(x1^{\prime},y1^{\prime}) \end{gathered}[/tex]After a reflection over the x-axis:
[tex]A\to(x,-y)\to A^{\prime}=(2,-4)[/tex]Answer:
(2,-4)
I need help IMMEDIATELY! I'm so confused and this is due in 7 minutes!!
I won't hesitate to give brainliest to whoever answers fastest! Please please please show work
1. Given [tex]f(x)= 2x^2-4x+2[/tex], what is the value of [tex]f(2/3)[/tex]?
2. Given [tex]f(x)= 4x^2+2x-6[/tex], what is the value of [tex]f(1/4)[/tex]?
The values of the functions are:
1. f(2/3) = 2/9
2. f(1/4) = -21/4
How to Find the Value of a Function?If we are given the a function to find the value for which x assumes a given value, substitute the given value of x into the function and solve.
1. To find the value of f(2/3), substitute x = 2/3 into the function f(x) = 2x² - 4x + 2.
f(2/3) = 2(2/3)² - 4(2/3) + 2
f(2/3) = 2(4/9) - 8/3 + 2
f(2/3) = 8/9 - 8/3 + 2
f(2/3) = (8 - 24 + 18)/9
f(2/3) = 2/9
2. To find the value of f(1/4), substitute x = 1/4 into the function f(x) = 4x² + 2x - 6.
f(1/4) = 4(1/4)² + 2(1/4) - 6
f(1/4) = 4(1/16) + 1/2 - 6
f(1/4) = 1/4 + 1/2 - 6
f(1/4) = (1 + 2 - 24)/4
f(1/4) = -21/4
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OB. 1OC.If X = 24 inches, Y = 45 inches, and Z= 51 inches, what is the tangent of ZA?OA. 19715NOD. 1B
Given that
We have a right-angled triangle and have to find angle A's tangent.
Explanation -
The triangle is shown as
Here we have,
X = 24 inches
Y = 45 inches
Z = 51 inches
Then, the tangent of angle A will be
[tex]\begin{gathered} The\text{ formula for the tangent is } \\ tan=\frac{Perpendicular}{Base} \\ \\ tan=\frac{P}{B} \\ For\text{ angle A thevalues are, P = 45 and B = 24} \\ Then, \\ tanA=\frac{45}{24} \\ \\ tanA=\frac{15}{8} \end{gathered}[/tex]So the correct option is B.
Final answer -
Therefore the final answer is 15/8i need help on number 7. Please use 4 points
In order to graph this equation, we need at least two points that are solution to the equation.
To find these points, we can choose values for x and then calculate the corresponding values of y.
Choosing the x-values of -2, -1, 0 and 1, we have:
[tex]\begin{gathered} x=-2\colon \\ y=-\frac{5}{2}\cdot(-2)-1 \\ y=5-1 \\ y=4 \\ \\ x=-1\colon \\ y=-\frac{5}{2}(-1)-1 \\ y=2.5-1 \\ y=1.5 \\ \\ x=0\colon \\ y=-\frac{5}{2}\cdot0-1 \\ y=-1 \\ \\ x=1\colon \\ y=-\frac{5}{2}\cdot1-1 \\ y=-2.5-1 \\ y=-3.5 \end{gathered}[/tex]So we have the points (-2, 4), (-1, 1.5), (0, -1) and (1, -3.5). Graphing these points and the line that passes through them, we have:
shirts are 15% off. The original price of one shirt is $20. What is the total cost, in dollars, of a shirt, at the sales price, including a 10% sales tax?
The original price of the shirt is , 20 dollar.
It is given that the shirts are 15% off.
Therefore, the price of the shirt is ,
[tex]20-20\times\frac{15}{100}=17.[/tex]The price of the shirt is, 17 dollar after 15% off.
It is also given that there are 10% sales tax.
The total cost of the shirt is determined by including the sales tax in the price of the shirt after 15% off.
[tex]17+(17\times\frac{10}{100})=18.7[/tex]Thus, The total cost of shirt is calculated as, 18.7 dollar.
I need help, I did 1-2b, but i do not mind someone answering it either way so I can double check, but I am mainly stuck with 2c and if someone can tell me the answer and as to why, it would mean a lot and you can get brainlest if it is the right answer :)(Not a multiple choice question)
Absolute Minimum: an absolute minimum point is a point where the function obtains its least possible value.
The given function :
[tex]f(x)=x^4-4x^3-x^2+12x-2[/tex]In the graph of the f(x) , the least value of x of the given curve is : (-0.939)
and the f(x) at x = (-0.939) is -10.065
The absolute minimum value is (x,y) = (-0.939, -10.065)
To round off in the nearest hundredth : (x, y) = (-0.94, -10.07)
Answer : (x, y) = (-0.94, -10.07)
Determine whether the equation represents an exponential growth function, anexponential decay function, and give the percent growth or decay.17. y = 18(1.3)^t
A exponential growth or decay function has the next general form:
[tex]y=a(1\pm r)^t[/tex]If it is :
(1+r) , (>1) the function growth
(1-r) , (<1) the function decay
------
The given equation:
[tex]y=18(1.3)^t[/tex]As the (1+r) is equal to 1.3 (> 1) then it is a exponential growth function.In (1+r) the r is the percent of growth, then for the given equation you have:
[tex]\begin{gathered} 1+r=1.3 \\ r=1.3-1 \\ \\ r=0.3 \end{gathered}[/tex]The percent of decay is 0.3 or 30%What is the slope of the line in the graph?A. 1 B. 2C. 0 D. -2
Always remember that the slope is the number of units on the Y-axis in relation to the X movement.
A horizontal line always has a slope of 0. (it is not increasing in the Y-axis)
