After 5 years the depreciation cost is $7200; accumulated depreciation expense is $36000 and book value at the end of year is $4000.
Given,
Cost of auto =$40,000
Residual value =$4000
Estimated lifetime =5 years
Straight-line Method:-
Depreciation cost can be calculated by formula,
[tex]Depreciation=\frac{cost\ of\ assest-residual}{estimated\ lifetime}[/tex]
It is constant for every year.
Accumulated depreciation can be calculated by formula,
[tex]Accumulation\ Depreciation=\frac{cost\ of\ assets-residual}{estimated\ lifetime}*Number\ of\ years[/tex]
Book value at start of year is nothing the cost of asset at that year and Book value at end of year is difference between cost of asset at that year and depreciation cost.
Using the above formulas all the values for each year is caculated and formed into a table.
Year BookValue DepreciationCost Accumulation Book Value
Start End
1 $40,000 $7,200.00 $7,200 $32,800
2 $32,800 $7,200.00 $14,400 $25,600
3 $25,600 $7,200.00 $21,600 $18,400
4 $18,400 $7,200.00 $28,800 $11,200
5 $11,200 $7,200.00 $36,000 $4,000
Thus, after 5 years the depreciation cost is $7200; accumulated depreciation expense is $36000 and book value at the end of year is $4000.
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Suppose that you have data recording the body weight and the running speed for each of several different jackrabbits. To summarize this data, it suffices to note the mean and SD for each of these two variables. a. True b. False
Answer:
True.
Step-by-step explanation:
I think that it is true because it is asking for a summary of the data and finding the mean of the speeds and weight would give you the summary of all the data.
10c - cd + d^3 (if c = -6 and d= 2)
Answer:
-40
Step-by-step explanation:
Given that,
c = -6
d = 2
To find the value of the given expression, replace c & d with 6 & 2 respectively.
Let us solve it now.
10c - cd + d³
( 10 × -6 ) - ( -6 × 2 ) + 2³
- 60 - ( -12 ) + 8
- 60 + 12 + 8
- 40
for what value of x is line a parallel to line b?
Two lines are parallel : Two lines (in the same plane) are said to be parallel to each other if they never intersect no matter how far they extend to either side.
The value of x is 15° for the given lines i.e a and b are parallel to each other.
As you can see in the picture above, there are two lines , i.e. a and b are parallel to each other.
Properties of parallel lines:
If you have a horizontal line that intersects two parallel lines at two different points, it makes four angles at each point.Corresponding angles formed by two parallel lines and a transverse line are equal. The pairs of interior angles on the same side of the intersection are supplementary angles.Upper and lower diagonals and vertical angles are equal.Alternate interior/interior angles are equal.i.e. angle b° = angle f° and angle a° = angle e°
Now, we conclude that
angle (6x+3)° = angle 93°
=> 6x + 3 = 93
=> 6x = 93 - 3 = 90
=> x = 15°
Hence, the value of x is 15°.
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the subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y}, {x, y}, {w, x, y}, and { } (the empty subset). how many subsets of the set {w, x, y, z} contain w ?
Answer:
4
Four subsets of {w, x, y} contain w.
Step-by-step explanation:
There are four subsets that have w in it:
{w} has w in it.
{w, x} has w in it.
{w, y} has w in it.
{w, x, y} has w in it.
The answer is 4.
f we start at the point (1,3,2), then in what direction should we move if we want to maximize the directional derivative?
To maximize, it has positive direction at x=1 in first quadrant
What are coordinates?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).
Given function:
F=x³z - yz²
Find the following :
[tex]\partial F/\partial x+ \partial F/\partial y + \partial F/\partial z[/tex]
= 3x²z + (-z²) + (x³-2yz)
So, gradient = 3x²z -z² + x³-2yz
Find the gradient at (1,3,2):
x=1, y=3 and z=2
gradient = 3*1*2 - 9 +1 - 12 = -14
To maximize, it has positive direction at x=1 in first quadrant = 14
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If May is 15 and John is five years older than may and Jay is 15 years older than John. How old is Jay?
Answer:
Jay is 35
Step-by-step explanation:
Creating an equationLet:
x = age of mayy = age of john z = age of jayHere, we are given that
May is 15 so x = 15John is 5 years older than may or y = x + 5 Jay is 15 years older than john or z = y + 15Solving for the agesGiven that x = 15 , y = x + 5 and z = y = 15
We can firstly find the age of john or "y" as we are given the value of x
y = x + 5
==> plug in x = 15
y = 15 + 5
==> add 15 and 5
y = 20
So John is 20
Now that we have the value of y we can easily find Jay's age or the value of z
z = y + 15
==> y = 20
z = 20 + 15
==> add 20 and 15
z = 35
Hence, Jay is 35
Answer:
35
Step-by-step explanation:
i did the math and also try adding them together?
There are 28
students in a class. 12
of them are girls and
the rest are boys.
What percent are
boys? Round to a
tenth of a percent
Answer:
The percentage of boys is 57.1%.
Step-by-step explanation:
I don't have to explain.
Hope this just helps!
Have a great day/night!
From 2006-2018 Jeff Bezo's net worth increased by 127 billion dollars. During that time Mr. Bezos paid 1.4 million in federal taxes. What percentage of that increase in worth was paid to the federal government in form of taxes? ALL WORK MUST BE SHOWN IN SCIENTIFIC NOTATION.
He paid 0.0012% of his total wealth increase as federal tax.
What is a expression? What is a mathematical equation? What is Equation Modelling? What is differentiation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. We can write -
y = f(x)
y' = dy/dx = (d/dx)[f(x)]
We have Mr. Bezos, who paid 1.4 million in federal taxes between 2006 -2018. His net worth increased by 127 billion dollars during this time span.
Assume that he paid [x]% of money to federal taxes. Then, we can write -
1.4 x 1,000,000 = (x/100) x 127 x 1000,000,000
1.4 = (x/100) x 127000
x = (1.4 x 100)/(127000)
x = 1.4/1270
x = 14/12700
x = 0.0012%
Therefore, he paid 0.0012% of his total wealth increase as federal tax.
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The ratio of h minus 4 to 3 is 5.
Answer:
19
Step-by-step explanation:
therefore the answer is 19
o build a robust distributed system, you must know what kinds of failures can occur. a. list three possible types of failure in a distributed system. b. specify which of the entries in your list also are applicable to a centralized system
Three common failures in a distributed system include
network link failure host failurestorage medium failureHost failure and storage medium failure are failures that could also occur in a centralized system, whereas a network link failure can occur only in a networked-distributed system.
CENTRALIZED SYSTEMS
Centralized systems are systems that use client/server architecture where one or more client nodes are directly connected to a central server. This is the most commonly used type of system in many organizations where a client sends a request to a company server and receives the response.
DECENTRALIZED SYSTEMS
These are other types of systems that have been gaining a lot of popularity, primarily because of the massive hype of Bitcoin.
In decentralized systems, every node makes its own decision. The final behavior of the system is the aggregate of the decisions of the individual nodes.
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Ezra applied the distributive property to the expression 8(y+2). He then used the commutative property.
Drag and drop expressions to the boxes to correctly complete the statements. Need help fast!!!!!!!!!!!
Put responses in the correct input to answer the question. Select a reply, navigate to the desired information and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button, or touchpad. Responses can also be moved by dragging with a mouse.
After applying the distributive property, Ezra's expression was the Response area.
After he used the commutative property, his expression was the Response area.
The results of the expressions after the properties are applied in this problem are given as follows:
Distributive property: 8y + 16Commutative property: 16 + 8y.What are the properties?The expression in the context of this problem is defined as follows:
8(y + 2).
The distributive property states that the outside term multiplies each of the inside terms, hence it is applied as follows:
8(y + 2) = 8 x y + 8 x 2 = 8y + 16.
The commutative property states that two terms of an addition can have the order exchanged.
The terms of the addition, after the distributive property, are 8y and 16, hence after the application of the commutative property, the expression is given as follows:
16 + 8y.
As the terms were exchanged.
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A chemical equation contains 4 hydrogen atoms and 2 oxygen atoms in the reactants. How many hydrogen and oxygen atoms should be in the products according to the law of conservation of matter? Responses 2 hydrogen atoms and 4 oxygen atoms 2 hydrogen atoms and 4 oxygen atoms 1 hydrogen atom and 1 oxygen atom 1 hydrogen atom and 1 oxygen atom, 4 hydrogen atoms and 2 oxygen atoms 4 hydrogen atoms and 2 oxygen atoms 5 hydrogen atoms and 1 oxygen atom 5 hydrogen atoms and 1 oxygen atom
The number of hydrogen and oxygen atoms that should be in the products according to the law of conservation of matter, is given as follows:
4 hydrogen atoms and 2 oxygen atoms.
What is stated by the law of conservation of matter?
The law of conservation of matter states that the amount of matter in the solution remains constant, even when the substance has a change in the format.
The amounts on the equation are given as follows:
4 hydrogen atoms.2 oxygen atoms in the reactants.The law of conservation of matter states that the amounts remain constant, hence the amounts of the solution are given as follows:
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The number of hydrogen and oxygen atoms that should be in the products according to the law of conservation of matter, is given as follows:
4 hydrogen atoms and 2 oxygen atoms.
What is stated by the law of conservation of matter?
The law of conservation of matter states that the amount of matter in the solution remains constant, even when the substance has a change in the format.
The amounts on the equation are given as follows:
4 hydrogen atoms.
2 oxygen atoms in the reactants.
The law of conservation of matter states that the amounts remain constant, hence the amounts of the solution are given as follows:
4 hydrogen atoms.
2 oxygen atoms in the reactants.
there are 6 donut with sprinkles and 7 with filling. if there are 3 donut that have both sprinkles and filling, how many have sprinkles or filling?
There are 6 donut with sprinkles and 7 with filling. if there are 3 donut that have both sprinkles and filling, 10 have sprinkles or filling
What is Venn Diagram ?Circles that overlap or do not overlap each other are used in a Venn diagram to illustrate similarities and distinctions between objects or groups of objects.Objects that share characteristics are represented as overlapping circles, whereas objects that are unique stand alone.Venn diagrams are currently utilized in many academic and business settings as demonstrations.Let S represent the set for donut with Sprinklers.
Let F represent the set for donut with Filling.
To find :- How many have sprinkles or filling?
i.e. n ( S ∪ F )
Formula,
n ( S ∪ F ) = n ( S ) + n ( F ) + n ( S ∩ F )
Given,
n ( S ) = 6
n ( F ) = 7
n ( S ∩ F ) = 3
Putting in formula
n ( S ∪ F ) = n ( S ) + n ( F ) - n ( S ∩ F )
= 6 + 7 - 3
= 10
Donuts with Sprinklers or Filling = 10
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How to Graph y=1/2x-3/2
Answer:
See below
Step-by-step explanation:
There is a great free graphing program called Desmos.
y = 1/2 x - 3/2
I highlighted 3 points for you.
The y-intercept is (0, -1.5) This is where the graph crosses the x axis. Another name for -1.5 is -3/2. That is the number that you see at the end of the equation.
The slope is 1/2. Look at the other two points on the line (-1,-2) and (1,-1) If you start at the first point and go up 1 and then 2 right you will end up at the second point. That is the slope.
if you have an unfair coin with probability p heads, what is the expected number of flips before you end up with a head?
The scenario assumed to be the number of flips until you land on a head is P(x) = 1 + (1 - p)/p.
Given info,
If you have an unfair coin with probability p heads, what is the expected number of flips before you end up with a head,
To solve the above condition, have a formula;
P(x) = 1 + ( 1 - p )/p
Hence, P(x) = 1 + ( 1 - p )/p is the case expected to number of flips before you end up with a head.
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a kite 75ft above the ground moves horizontally at a speed of 8ft/s. at what rate is the angle between the string and the horizontal decreasing when 200ft of string has been let out?
When 200ft of string has been let out, the angle is decreasing at a rate of 0.015 radians per second.
In this question, we have been given the height of the kite from the ground is y = 75 ft.
The kite moves horizontally at a speed of 8 ft/s
So, dx/dt = 8 ft/s
The length of the string is 200 ft
so, L = 200 ft
Consider the following figure for this situation.
Now consider the sine of angle theta.
sin(θ) = 75/200
sin(θ) = 3/8
Now consider the tangent of angle theta.
tan(θ) = 75/x
1 / tanθ = x/75
cot(θ) = x/75
Differentiating the above equation with respect to t.
-csc²(θ) * dθ/dt = 1/75 * dx/dt
- csc²(θ) * dθ/dt = 1/75 * 8
- csc²(θ) * dθ/dt = 8/75
We know that, csc(θ) = 1/sin(θ)
csc(θ) = 8/3
So above equation becomes,
-(8/3)² × dθ/dt = 8/75
dθ/dt = - (8/75 * 9/64)
dθ/dt = 0.015
Therefore, the angle is decreasing at a rate of 0.015 radians per second.
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suppose x is a normal random variable with and find p(x > 105.0). a) 0.9993 b) 0.9994 c) 0.9995 d) 0.0007 e) 0.0006 f) none of the above.
The value of the probability p(x > 105.0) for the given normal random variable is found as 0.6915.
Explain the term normal random variable?A randomly distributed variable with a mean of 0 and a standard deviation of 1 is referred to as a standard random variable. The letter Z will always stand in for it. regularly distributed random variable, also known as a with standard deviation, is a continuous random variable which probabilities are defined by the normal distribution of mean and standard deviation.For the stated question -
The formula for the z score -
z = (x - μ)/σ
In which,
μ = 140 and σ = 20
Put the values-
z = (150 - 140)/20
z = 0.5
p(x > 105.0) = p(z > 0.5)
p(x > 105.0) = 0.6915
Thus, the value of the probability p(x > 105.0) for the given normal random variable is found as 0.6915.
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The complete question is-
suppose x is a normal random variable with μ = 140 and σ = 20 and find p(x > 105.0).
The breaking strength of a rivet has a mean value of 10,100 psi and a standard deviation of 499 psi. (a) What is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 10,000 and 10,300? (Round your answer to four decimal places.) (b) If the sample size had been 15 rather than 40, could the probability requested in part (a) be calculated from the given information? Explain your reasoning O Yes, the probability in part (a) can still be calculated from the given information O No, n should be greater than 30 in order to apply the Central Limit Theorem. O No, n should be greater than 20 in order to apply the Central Limit Theorem. O No, n should be greater than 50 in order to apply the Central Limit Theorem. You may need to use the appropriate table in the Appendix of Tables to answer this question.
the probability that the sample mean breaking strength for a random sample of 40 rivets is between 10,000 and 10,300 P(10000 ≤ x ≤ 10300) = 0.54
We would assume a normal distribution for the breaking strength of a rivet. We would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ/√n
Where
n = number of samples
x = Breaking strengths of rivet.
µ = mean breaking strength
σ = standard deviation
From the information given,
µ = 10,100 psi
σ = 499 psi
n = 40
The probability that the sample mean breaking strength for a random sample of 40 rivets is between 10000 and 10,300 is expressed as
P(10000 ≤ x ≤ 10300)
For x = 10000,
z = (10000 - 10100)/499/√40 = - 0.13
Looking at the normal distribution table, the probability corresponding to the z score is 0.45
For x = 10300,
z = (10300 - 10100)/499/√40 = 2.54
Looking at the normal distribution table, the probability corresponding to the z score is 0.99
Therefore,
P(10000 ≤ x ≤ 10300) = 0.99 - 0.45 = 0.54
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please help!
What is/are the vertical asymptote(s) of the function?
y=3x+6x2+2x-35
Answer:
I don't think there would be any asymptotes because there are no denominators.
Step-by-step explanation:
find three vectors with which you can demonstrate that the vector cross product need not be associative, i.e., that a x (b x c) need not be the same as (a x b) x c. g
The cross product of three vectors is not associative in nature.
Considering three vectors such as : A=(2,1,3), B=(1,0,2) and C=(1,1,0)
we know that the associative law depicts that :
A x (B x C) = (A x B) x C ,while doing the operation for the considered vectors :
A x (B x C) =(2,1,3)x ((1,0,2)x (1,1,0))
=(2,1,3)x (-2,2,1)
=(-5,-8,6)
(A x B) x C= ((2,1,3)x (1,0,2))x (1,1,0)
= (2,-1,1) x (1,1,0)
=(-1,1,3)
So for this vector operation, A x (B x C) is not equal to (A x B) x C, so you can sum up that cross product of three vectors can't be associative every possible time.
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what quotients are equivalent to -48/-17
The quotient of the expression will be;
⇒ 2.823
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The equation is,
⇒ - 48 / - 17
Now,
Solve the equation as;
The equation is,
⇒ - 48 / - 17
After divide we get;
⇒ - 48 / - 17
⇒ 48 / 17
⇒ 2.823
Thus, The quotient of the expression will be;
⇒ 2.823
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A quadrilateral has 4 sides. one angle of a regular quadrilateral measures (6w 13)°. determine the value of w. round to the nearest whole number. w = 13 w = 23 w = 59 w = 90
A regular quadrilateral is one in which the lengths of all the sides and the measures of all the angles are equal. A regular quadrilateral must have all of its angles measured (6w 13°) if one of its angles does.
A quadrilateral's angles measure a total of 360 degrees. The total measure of the angles of a regular quadrilateral is 4 (6w 13)°, which equals 24w + 52°. A regular quadrilateral contains four angles, of which each measure (6w 13)°. Thus, we obtain the equation shown below:
24w + 52° = 360°
Solving for w, we get:
24w = 308°
w = 13
Consequently, w has a value of 13, and w = 13 is the right response.
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consider a population that grows according to the recursive rule p n = p n − 1 + 80 p n = p n - 1 + 80 , with initial population p 0 = 60 p 0 = 60 .
The population grows according to the recursive rule is-
Pn = 60 + n×80P100 = 8060Explain the term recursive rule?A recursive rule provides the first term and terms of the a sequence and uses a recursive equation to show how each term relates to the term(s) before it. Sequences in mathematics and geometry, for instance, can be represented recursively.For the stated question-
initial population p0 = 60recursive rule pn = p(n − 1) + 80Then,
P1 = P0 + 80
P1 = 60 + 80 = 140
P2 = P1 + 80
P2 = 140 + 80 = 220
Thus, an explicit formula for the population
Pn = P0 + n×80 = 60 + n×80
P100 = 60 + 100×80 = 8060
Thus, explicit formula for the population growth is
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The complete question is-
Consider a population that grows according to the recursive rule pn = p
(n − 1) + 80 , with initial population p0 = 60
Find an explicit formula for the population. Your formula should involve n (use lowercase n)
Pn=
Use your explicit formula to find
P100 =
What is the sequence of transformations that maps △ABC to △A′B′C′?
Select from the drop-down menus to correctly identify each step.
The transformation taking place in triangles are 90° rotation counterclockwise about origin and translation 3 units up.
What is transformation?A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.
Given that, △ ABC is transformed in to △ A′B′C′
Firstly, △ ABC is being rotated 90° counterclockwise about the origin, and then it translated 3 units up.
Hence, The transformation taking place in triangles are 90° rotation counterclockwise about origin and translation 3 units up.
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If ΔSTU ≅ ΔHIJ, then what corresponding parts are congruent?
∠I and ∠U
segment TU and segment HI
∠I and ∠S
segment US and segment JH
Segment US and segment JH are congruent is correct.
What is congruent triangles?
If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.
Given:
ΔSTU ≅ ΔHIJ
⇒ All three sides of ΔSTU are equal to all three sides of ΔHIJ.
⇒ ST ≅ HI, TU ≅ IJ and US ≅ JH.
Also all three angles of ΔSTU are same as the angles of ΔHIJ
⇒ ∠S ≅ ∠H, ∠T ≅ ∠I, and ∠U ≅ ∠J
So, from the given options segment US and segment JH are congruent is correct.
Hence, segment US and segment JH are congruent is correct.
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PLEASE HELP!! The graph g(x) is a transformation of the graph f(x)=3^x. Enter the equation of g(x) in the box.
The equation of g(x) = y=[tex]3^{x+1}[/tex]+1 is if the function f(x)=3ˣ
What is a graph?A graph is a visual depiction or diagram that organizes facts or values. The points on the graph frequently reflect the relationship between two or more objects.
A function graph is a subset of a relation. In the current foundations of mathematics, and most notably in set theory, a function is truly equivalent to its graph. However, it is frequently beneficial to consider functions as mappings, which include not only the relationship between input and output, but also which set is the domain and which set is the codomain. For example, while determining whether a function is onto (surjective) or not, the codomain must be considered. The graph of a function does not determine the codomain on its own.
The graph is as follows: f(x) =[tex]3^{x}[/tex]
The graph g(x) represents a transformation of the graph f(x).
The g(x) curve travels through (-2,2) and (-1,4).
Let (a, b) represent any point on f(x).
After translation, a new curve g(x) is obtained that is parallel to the line, y=1 or asymptode is, y=1 or the graph becomes parallel to the x axis when y reaches 1.
g(x)= y-1=[tex]3^{x+1}[/tex]
g(x) = y=[tex]3^{x+1}[/tex]+1
The graph of the translated curve is +1.
The two graphs are shown below.
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A meteor crashed onto a planet and caused crater that was 16,495.92 in deep.
Use the table of facts to find the depth of the crater In yards.
Conversion facts for length
Round your answer to the nearest tenth.
12 Inches (in) = 1 foot (ft)
3 feet (ft) = 1 yard (yd)
36 Inches (in) =
yard (yd)
5280 feet (ft) = 1 mile (mi)
1760 yards (yd) = 1 mile (mi)
yd
x5
Answer:
Step-by-step explanation:
The depth of the crater in yards is 387.2 yards
Converting Inches to yards
Since the crater is 13,937.63 in deep, we convert this to yards.
Since 36 in = 1 yard, we use this conversion factor to convert to yards
13,937.63 in × 1 yard/36 in = 387.16 yards
≅ 387.2 yards to the nearest tenth
So, the depth of the crater in yards is 387.2 yards
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The depth created by the meteor in different units will be 1,374.66 feet, 458.22 yards, and 0.26 miles.
What is conversion?Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
A meteor crashed onto a planet and caused a crater that was 16,495.92 inches deep.
The conversion ratio is given below.
12 Inches (in) = 1 foot (ft)3 feet (ft) = 1 yard (yd)36 Inches (in) = 1 yard (yd)5280 feet (ft) = 1 mile (mi)1760 yards (yd) = 1 mile (mi)⇒ 16,495.92 / 12 = 1,374.66 feet
⇒ 16,495.92 / 36 = 458.22 yards
⇒ 1,374.66 feet = 0.26 miles
The depth created by the meteor in different units will be 1,374.66 feet, 458.22 yards, and 0.26 miles.
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On the venn diagram shade the set P' ∩ ( Q ∪ R)
The desired set is shaded on the Venn Diagram given by the image at the end of the answer.
How to shade the Venn Diagram?The first step towards shading the Venn Diagram is finding the meaning of each symbol, as follows:
Symbol U: represents the union of the two sets, and the shaded elements are the elements that belong to at least one of the two sets.Inverted Symbol U: represents the intersection of two sets, and the shaded elements are the elements that belong to both sets.The negation symbol of the elements of P is given as follows:
P'.
The union is applied between the sets:
R and Q.
The intersection is then applied between:
The negative of P and the union of R and Q.
Then the shaded region is given by the elements that belong to at least one of the sets Q or R, without belonging to set P, as shown by the image presented at the end of the answer.
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a firm in a purely competitive industry is currently producing 1,000 units per day at a total cost of $700. if the firm produced 800 units per day, its total cost would be $450, and if it produced 500 units per day, its total cost would be $425.
if it produced 500 units per day, its total cost would be $425. then average total cost is $0.61
The average total cost is calculated as the total cost divided by the number of outputs. The firm's ATC at these three levels of production will be:
1. 1,000 units per day at a total cost of $700.
ATC = Total cost/output
ATC = $700/1000
ATC = $0.58
2. If the firm produced 1,000 units per day, its total cost would be $450.
ATC = Total cost/output
ATC = $450/1000
ATC = $0.45
3. If it produced 700 units per day, its total cost would be $425.
ATC = Total cost/output
ATC = $425/700
ATC = $0.61
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for question 44 is f(2pi/4) a positive or a negative number
Please help
Answer:
Amplitude = 3
Period = π
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.7cm}\underline{Standard form of a cosecant function}\\\\$y=A\csc(Bx)$\\\\where:\\\\\phantom{ww}$\bullet$ $|A|$ is the stretch factor. \\ \\\phantom{ww}$\bullet$ $\dfrac{2\pi}{|B|}$ is the period.\\\\\phantom{ww}$\bullet$ $x=\dfrac{\pi}{|B|}$ is the interval of vertical asymptotes.\\\end{minipage}}[/tex]
Given function:
[tex]f(x)=3 \csc 2x[/tex]
Therefore:
A = 3B = 2Period
[tex]\textsf{Period} = \dfrac{2 \pi}{|B|}=\dfrac{2 \pi}{|2|}=\pi[/tex]
Amplitude
The amplitude of the given function is 3, so:
minimum points are when y = 3.maximum points are when y = -3.x-values of minimum points
[tex]\begin{aligned}3\csc(2x)=3 \implies \csc(2x)&=1\\\dfrac{1}{\sin(2x)}&=1\\\sin(2x)&=1\\2x&=\dfrac{\pi}{2}+2\pi n\\x&=\dfrac{\pi}{4}+\pi n \end{aligned}[/tex]
[tex]\implies \textsf{Minimum points}: \left(\dfrac{\pi}{4}\pm \pi n,3 \right)[/tex]
x-values of maximum points
[tex]\begin{aligned}3\csc(2x)=-3 \implies \csc(2x)&=-1\\\dfrac{1}{\sin(2x)}&=-1\\\sin(2x)&=-1\\2x&=-\dfrac{\pi}{2}+2\pi n\\x&=-\dfrac{\pi}{4}+\pi n \end{aligned}[/tex]
[tex]\implies \textsf{Maximum points}: \left(-\dfrac{\pi}{4}\pm \pi n,-3 \right)[/tex]
Asymptotes:
[tex]\implies x=\dfrac{\pi}{|B|}=\dfrac{\pi}{|2|}=\dfrac{1}{2} \pi[/tex]
Therefore, there are vertical asymptotes every ¹/₂π.
To graph the given function:
[tex]\textsf{Draw vertical asymptotes at} \;\;x = 0 + \dfrac{\pi}{2} n[/tex][tex]\textsf{Plot minimum points at}\; \left(\dfrac{\pi}{4}\pm \pi n,3 \right)[/tex][tex]\textsf{Plot maximum points at}\; \left(-\dfrac{\pi}{4}\pm \pi n,-3 \right)[/tex]Draw curves between the asymptotes with the given min/max points.