The rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's call the number of items sold at a price of $p as x(p).
Based on the information given, we can write an equation for x(p) as:
x(p) = 2000 - 400(p - 30)
The profit from selling the items at a price of $p is given by the product of the number of items sold and the price:
Profit(p) = x(p)×p
Taking the derivative of the profit function with respect to the price, we can find the rate of change of the profit:
dProfit/dp = dx/dp×p + x(p)
= -400 p + 400 ( 30) + 2000 - 400(p - 30)
= -400 p + 12000
When p = 30, the rate of change of the profit is:
dProfit/dp = -400(30 )+ 12000
= 3600
So the rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.
Hence, the rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
There are 17 members on a city council. At a recent city council meeting, 5 of the council members voted in favor of a budget increase. How many possible groups of council members could have voted in favor? Will the calculation involve permutations or combinations?
The number of possible groups of council members who could have voted in favor of the budget increase is 6188. The calculation involves combinations.
Since the order in which the members voted is not required, this calculation does not involve permutations. It involves combinations.
The formula for calculating combinations is: [tex]_n C_r=\frac{n !}{r ! (n-r) !}[/tex]
where n, the total number of objects = 17
r, sample size = 5
Putting the values in the equation,
The answer is 6188.
To know more about permutations and combinations,
https://brainly.com/question/28065038
F(x) = 9 - x, g(x) = x2 + x, h(x) = x - 2 Compute the following
1. f(h(-3))
2. g(h(-9))
3.f(g(x))
The values of the composite functions, obtained by evaluating the functions at a specified x value input are presented as follows;
1. f(h(-3)) = 14
2. g(h(-9)) = 110
3. f(g(x)) = 9 - x² - x
What is a composite function?A composite funtion is a function that is applied to the output of another function.
The functions are; F(x) = 9 - x, g(x) = x² + x, h(x) = x - 2
The composite functions, which are functions that have a function as an input, aere evaluated as follows
1. h(-3) = (-3) - 2 = -5
f(h(-3)) = f(-5), therefore;
f(-5) = 9 - (-5) = 9 + 5 = 14
f(-5) = 14
f(h(-3)) = 14
2. h(-9) = -9 - 2 = -11
g(h(-9)) = g(-11)
g(-11) = (-11)² + (-11) = 121 - 11 = 110
g(-11) = 110
Therefore; g(h(-9)) = g(-11) = 110
g(h(-9)) = 110
3. g(x) = x² + x
f(x) = 9 - x
Therefore, f(g(x)) = f(x² + x) = 9 - (x² + x) = 9 - x² - x
f(g(x)) = 9 - x² - x
Learn more about composite functions here: https://brainly.com/question/29048585
#SPJ1
josiah ate three-eighths of his orange before his soccer game. He ate one third of the orange durning half-time. How much of the orange did he eat in all
By adding the two given fractions we can see that Josiah ate 17/24 of his orange.
How much of the orange did he eat in all?We know that first, Josiah ate 3/8 of his orange.
Then at this point, the remaining amount is 5/8 of the orange.
Then he ates 1/3 of the orange (the total orange, not the remaining amount)
Then the total fraction of the orange that he ate is:
3/8 + 1/3
Finding a common denominator we will get:
9/24 + 8/24 = 17/24
We conclude that Josiah ate 17/24 of his orange.
Learn more about fractions at:
https://brainly.com/question/11562149
#SPJ1
Consider the hypothesis test below. The following results are for independent samples taken from the two populations. n = 200, pi = 0.28; n2 = 300, p2 = 0.18 Sample 1 Sample 2 Use pooled estimator of . a. What is the -value (to 4 decimals)? Use Table 1 from Appendix B. b. With , what is your hypothesis testing conclusion?
The p-value is 0.0062 and we reject the null hypothesis
What is the p valueFrom the question, we have the following parameters that can be used in our computation:
n = 200, pi = 0.28; n2 = 300, p2 = 0.18
The p value is calculated as
Z = (p1 - p2) - (d0 /√(p * (1 - p) * (1/n1 + 1/n2)))
Where
d0 = 0.28 - 0.18 = 0.10.
So, we have
Z = (0.28 - 0.18) - (0.10 / √(0.23 * (1 - 0.23) * (1/200 + 1/300)))
Evaluate
Z = -2.50
Uisng the z-score table, we have
p = 0.0062
What is your hypothesis testing conclusion?We reject the null hypothesis that the population proportions are equal
Read more about test of hypothesis at
https://brainly.com/question/15110538
#SPJ1
Part A create a table for values when x=0,5,8,10,30 include worked out equations used to identify the value within the table
Part B identify the altitude and after 30 minutes.Use 1-2 sentences to explain the altitude at these two times and describe what is happening to the airplane at these time intervals
The table is shown below:
x 0 5 8 10 30
y 150 125 110 100 0
The altitude after 5 minutes is 125 feet and the altitude after 30 minutes is 0 feet
How to create a table for the values?
Part A :
To create a table for values when x=0, 5 , 8, 10, 30 substitute the values into the given equation y = -5x + 150
x= 0, y = -5(0) + 150 = 150
x=5, y = -5(5) + 150 = 125
x = 8, y = -5(8) + 150 = 110
x = 10, y = -5(10) + 150 = 100
x = 30, y = -5(30) + 150 = 0
x 0 5 8 10 30
y 150 125 110 100 0
Part B:
altitude after 5 minutes is 125 feet
altitude after 30 minutes is 0 feet
The altitude after 5 minutes represent the altitude of the plane 5 minutes during descending.
The altitude after 30 minutes represent the altitude of the plane when descending is complete.
What is happening to the airplane at these time intervals is that the plane of the plane is reducing until it finally landed.
Learn more about equation on:
brainly.com/question/29330381
#SPJ1
For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms.
x=y2
Note: Each column in the table represents an ordered pair. If multiple solutions exist, you only need to identify one.
Therefore, the solutions to the equation are (0, 0), (1, 1), (-1, 1), (2, 4), (-2, 4), (3, 9), and (-3, 9).
Which equation is this?In arithmetic equations, the exact symbol (=) is used to denote the equivalence of two assertions. It is demonstrated that mathematical methods, which have acted as manifestations of reality, can be used to assess a variety of numerical factors. The equal sign actually splits the number 12 into two separate pieces, despite the fact that the result is y + 6 = 12.
Here,
We can plug in some arbitrary values for y to find the corresponding values of x:
y x
0 0
1 1
-1 1
2 4
-2 4
3 9
-3 9
Therefore, the solutions to the equation are (0, 0), (1, 1), (-1, 1), (2, 4), (-2, 4), (3, 9), and (-3, 9).
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
which of the following steps could give us the minimum point of a function f(x) that is twice differentiable and defined over the reals?
The minimum point of a function f(x) is obtained as follows:
Obtaining the derivative of the function.Obtaining the zeros of the derivative of the function.Obtaining the signal of the second derivative at each of the zeros of the first derivative.If the second derivative is positive, then the x-coordinate for which f'(x) is a minimum and thus (x, f(x)) is the minimum point.What are the requirements for the minimum point of a function?There are two requirements such that a value of x = a is a minimum point of a function f(x):
The first derivative at x = a is of zero, that is, f'(a) = 0.The second derivative at x = a is positive, that is, f''(a) > 0.More can be learned about relative extremas of a function at https://brainly.com/question/1938915
#SPJ1
The function graphed above is:
Increasing on interval(s)
Decreasing on interval(s)
The function graphed above is:
Increasing on interval: (-3 0.5),
Decreasing on interval(s): (-∞ -3) and (0.5 ∞)
What is decreasing and increasing interval?Real number intervals with growing and decreasing real-valued functions are referred to as increasing and decreasing intervals.
We apply the first-order derivative test to examine the sign of the derivative in each interval and identify the growing and decreasing intervals.
For the graph attached, the decreasing interval is
from negative infinity to -3 and 0.5 to positive infinityWhile the increasing interval is from -3 to 0.5
Learn more about increasing interval at:
https://brainly.com/question/30460486
#SPJ1
One way to pack a 100 by 100 square with 10 000 circles, each of diameter 1, is to put them in 100 rows with 100 circles in each row. If the circles are repacked so that the centres of any three tangent circles form an equilateral triangle, what is the maximum number of additional circles that can be packed?
In this configuration, the number of circles that can be packed is already at its maximum of 10,000.
What is Equilateral triangle?
All sides of an equilateral triangle are the same length. That is, all of the triangle's angles will be congruent.
It is not possible to add more circles in this configuration because the centers of the tangent circles already form an equilateral triangle, which is the most efficient way to pack circles.
In this configuration, the number of circles that can be packed is already at its maximum of 10,000.
To know more about Equilateral triangle visit,
https://brainly.com/question/17264112
#SPJ1
A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.
See picture
Part A: What is the height of the base? Show your work. (5 points)
Part B: What is the approximate amount of cardboard used to make the candy
box? Explain how you got your answer. (5 points)
PART A) The height of the base is 10cm
PART B) Aproximate amount of cardboard to make the candy box is 860cm. You add all of the totals from each side to get the grand total of 860cm.
The sides of the parallelogram in Fig. 14.6 are given in cm. 3y + 2x 5y - 8 2x + y 4x - 3 g. 14.6 Find x and y and the perimeter of the parallelogram.
The values of x and y are -1 and -5 respectively.
The perimeter is 22cm
How to determine the valuesWe have that the opposite sides of a parallelogram are equal, then, we have that;
3y + 2x = 5y - 8
collect like terms
-2y + 2x = 8
Also,
2x + y= 4x - 3
-2x + y = -3
Make 'x' the subject from equation (2)
y = -3 + 2x
Substitute the value
-2(-3+2x) + 2x = 8
expand the bracket
6 -4x + 2x = 8
collect like terms
-2x = 2
x = -1
Then, y= -3 - 2 = -5
Perimeter = 2(8 + 3)
Perimeter = 22 cm
Hence, the value is 22cm
Learn about parallelograms on:
https://brainly.com/question/10744696
#SPJ1
25 people went on a fishing trip
17 people did not catch a mackerel
of the people who caught a mackerel, 3 people did not catch a trout
6 people caught neither a mackerel nor trout
calculate the values that should replace A, B and C in the frequency tree below
Answer: We can use the information given to find the values of A, B and C.
Let A represent the number of people who caught a mackerel,
B represent the number of people who caught a trout,
and C represent the number of people who caught both a mackerel and a trout.
From the information given, we know that:
A + 17 = 25 (the total number of people who went on the fishing trip)
B + 3 = A (the number of people who caught a mackerel)
C = B (the number of people who caught both a mackerel and a trout)
A + B + C + 6 = 25 (the total number of people who caught either a mackerel, a trout or both)
Solving for A, we get:
A = 22
B = 19
C = 19
Therefore, the values that should replace A, B and C in the frequency tree are:
A = 22, B = 19, C = 19.
Step-by-step explanation:
y=15x+b what does b equal
Therefore , the solution of the given problem of equation comes out to be value of b = 0 , as it is parallel to y axis.
Equation: What is it?The identical symbol (=) is used in arithmetic equations to signify the equality of two statements. It is shown that it is possible to evaluate various numerical factors using mathematical techniques, which have served as manifestations of reality. In actuality, even though the solution is y + 6 = 12, the equal sign divides the figure 12 into two distinct parts. How many characters are also present along either end of such a character can be calculated. Conflicting sign readings are common.
Here,
Given :
=> equation y = 15x + b
Comparing to y = mx+ b
Where b is said to be intercept.
So , value of b = 0 , as it is parallel to y axis.
Therefore , the solution of the given problem of equation comes out to be value of b = 0 , as it is parallel to y axis.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
5. What percent of 68 is 17
Answer: 25%
Step-by-step explanation:
Divide 17/68 = .25
Move decimal 2 places over = 25%
19. A tree standing on a horizontal plane is leaning towards east. At two points situated at distances a and b exactly due west on it, the angles of elevation of the top of the tree are respectively a and ß. Find the height of the top of the tree from the ground.
The height of the top of the tree from the ground is h = a * b / (a / b) = a * b
How did we arrive at the value?Let's call the height of the tree "h". Then, using trigonometry, we can write two equations to describe the two angles of elevation:
tan(a) = h / a
tan(ß) = h / b
Dividing these two equations, we get:
tan(a) / tan(ß) = h / a * b
Since tan(a) / tan(ß) = a / b, we can substitute this and simplify:
h = a * b / (a / b) = a * b
learn more about trigonometry: https://brainly.com/question/13729598
#SPJ1
What is 3/50+7/10 for adding and subtracting fractions
Answer:When adding and subtracting fractions, the denominators (the bottom numbers) must be the same. To do this, we need to find a common denominator. In this case, the least common multiple of the denominators 50 and 10 is 50. To convert 7/10 to an equivalent fraction with a denominator of 50, we multiply both the numerator and denominator by 5:
7/10 x 5/5 = 35/50
Now we can add the two fractions together:
3/50 + 35/50 = 38/50
So, the answer is 38/50.
Step-by-step explanation:
In AVWX, VX is extended through
point X to point Y,
m/XVW
m/WXY
m/VWX =
m/WXY.
=
-
(3x + 13)°,
(9x - 14), and
(x+8)°. Find
Answer:
I'm sorry but your question is not clear. Can you please provide more context or clarify what you are asking?
Determine whether the following example describes accuracy, precision, neither, or both: Three friends run a 5K and their times are 20 minutes, 21 minutes, and 21 minutes. The average time is 27 minutes. a.) Precision b.) Both c.) Accuracy d.) Neither
the average time of 27 minutes is not an accurate representation of the friends' actual times, so the example describes neither accuracy nor precision.
What is precision?Precision refers to how close multiple measurements are to each other. In this example, the three friends' times are all close to each other (20 minutes, 21 minutes, and 21 minutes), so the measurements are precise.
According to question:Accuracy refers to how close a measurement is to the true or correct value. In this example, the average time of the three friends running a 5K is 27 minutes, but the actual average time should be 20.33 minutes (20 + 21 + 21 / 3). So, the measurement is not accurate.
However, the average time of 27 minutes is not an accurate representation of the friends' actual times, so the example describes neither accuracy nor precision.
To know more about average visit:
brainly.com/question/24057012
#SPJ4
A clothing business finds there is a linear relationship between the number of shirts, n , it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $20 . Find a linear equation in the form p(n)=mn+b that gives the price p they can charge for n shirts.
The linear Equation in the form of p(n)=mn+b is p(n) = -0.005n + 999.85.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
In particular, historical data shows that 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $20 .
p = price
n = number of shirts
m = slope of the line (note, the more shirts, the lower the price, so we know it's going to be negative)
b = y intercept
so, the slope is
= (20- 30)/ (3000 - 1000)
= -10 / 2000
= -0.005
and, the equation is
p - 1000 = -0.005 ( n- 30)
p- 1000 = -0.005n + 0.15
p(n) = -0.005n + 999.85
Learn more about equation here:
https://brainly.com/question/29657992
#SPJ1
Answer:
Step-by-step explanation:
Tell me weather the given number is a solution. 3/2 t + 2 = 4; 2/3
Answer:
4/3
Step-by-step explanation:
3/2 t + 2 = 4;
1.5t+2 = 4
1.5t = 2
t= 2/1.5 = 4/3
simplify 5+2/3-3-2/3
Answer:
Step-by-step explanation:
5+2/3-3-2/3
5+93439535309573092
question 8 keeping in mind there are 86400 seconds per day, write a program that calculates how many seconds there are in a week, if a week is 7 days. print the result on the screen.
There are 604800 seconds in a week having 7 days. This is solved in the presence of python code.
What is python code?The programming language Python is high-level and versatile. Its design philosophy emphasizes the importance upon code readability through usage of substantial indentation. Both Python's types and trash collection are dynamic. It is compatible with a wide range of development methodologies, including structured, object-oriented, and functional programming.
Among the simplest programming languages to learn for novices, Python is frequently cited. Python is a fantastic place to start if you want to learn how to programme. Aside from that, it's among the most popular.
Given that,
Seconds per Day = 86400 seconds
Days in a week = 7 days
To calculate
Seconds in a week = ?
Python Code
seconds Per Day = 86400
days in a week = 7
seconds in a week = days in a Week × seconds per day print (seconds in a week)
Output of the Code: 604800
There are 604800 seconds in a week having 7 days.
To know more about program refer to:
https://brainly.com/question/11023419
#SPJ4
There are 604800 seconds in a week having 7 days. This is solved in the presence of python code.
What is python code?The programming language Python is high-level and versatile. Its design philosophy emphasizes the importance upon code readability through usage of substantial indentation. Both Python's types and trash collection are dynamic. It is compatible with a wide range of development methodologies, including structured, object-oriented, and functional programming.
Among the simplest programming languages to learn for novices, Python is frequently cited. Python is a fantastic place to start if you want to learn how to programme. Aside from that, it's among the most popular.
Given that,
Seconds per Day = 86400 seconds
Days in a week = 7 days
To calculate
Seconds in a week = ?
Python Code
seconds Per Day = 86400
days in a week = 7
seconds in a week = days in a Week × seconds per day print (seconds in a week)
Output of the Code: 604800
There are 604800 seconds in a week having 7 days.
To know more about programming refer to:
brainly.com/question/28874085
#SPJ4
han types the letters a,s,d,f and then repeats them over and over what is the 5th letter diego will type
The fifth letter, Diego will type, is 'a'.
What is a sequence?An ordered list of things is a sequence (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered items (potentially infinite).
Given:
Han types the letters a, s, d, f.
And repeats the over and over.
That means,
a, s, d, f, a, s, d, f, a, s, d, f, ....
Here, the fifth letter is 'a'.
So, the Diego will type 'a'.
Hence, the fifth letter is 'a'.
To learn more about the sequence;
https://brainly.com/question/21961097
#SPJ1
Joe earns $800 each week working his full time job. His employer has a 17% tax deduction on all monies earned each week. Calculate his weekly tax deduction.
Answer: 664 (sorry if its wrong)
Step-by-step explanation:
17% of 800 is 136.
800-136=664
Step-by-step explanation:
800 ÷ 100 = 8 (1%)
8 × 17 = 136 (17%)
800-136=664
I need HELP please
Thank you
Answer:
Length NJ = x = 3
Step-by-step explanation:
Since the pentagons are similar, the ratio of each side of pentagon ABCDE to the corresponding side of pentagon JKLMN must be the same for all sides
Therefore
[tex]\dfrac{AB}{JK} = \dfrac{BC}{KL} =\dfrac{CD}{LM} = \dfrac{DE}{MN} = \dfrac{EA}{NJ}[/tex]
From the values provided for the lengths of the sides of the two pentagons this works out to:
[tex]\dfrac{2}{1} = \dfrac{3}{1.5} = \dfrac{3}{1.5} = \dfrac{2}{1} = \dfrac{6}{x}[/tex]
Each of the computable ratios = 2
This means
each side of pentagon ABCDE = 2 x each side of pentagon JKLMN
Therefore we get
EA = 2 · NJ
6 = 2 x
x2x = 6
x = 6/2
x = 3
Note
I did not have to calculate all ratios. If the pentagons are similar, the ratios of the sides must be the same and therefore I needed to calculate only one ratio.
I wanted to cover all bases and make sure you understood
Under certain air conditions, the air temperature drops about 3.8°F for each 1,000-foot rise in altitude. Complete parts (A) and (B) below.
(A) If the temperature at sea level is 63°F, write a linear equation that expresses temperature T in terms of altitude A in thousands of feet.
(B) At what altitude is the temperature 9.8°F?
***
(A) If the temperature at sea level is 63°F, write a linear equation that expresses temperature T in terms of altitude A in thousands of feet.
Answer: A) T = 63 - 3.8A (where T is the temperature in °F, A is the altitude in thousands of feet)
(B) To find the altitude when the temperature is 9.8°F, we can substitute 9.8 for T and solve for A:
9.8 = 63 - 3.8A
3.8A = 63 - 9.8
3.8A = 53.2
A = 14
Step-by-step explanation:
What is the particular integral of ODE y”+3y’+2y= 2x+1
Refer to the attached images.
61.5 km=615.00m
True or False
Answer:true
61.5 km = 61.5 x 1000 =61.500 m
Period/Bell:
1. The figure below is a square with four congruent parallelograms inside.
A
12
What is the area, in square units, of the shaded
portion?
The area of the shaded portion of the given figure is 84 sq. units.
What is meant by area?
The size of a region on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a structure or planar lamina.
From the figure, we can conclude that,
Area of the shaded portion = Area of the square - Area of the four congruent parallelograms.
Now we have to find the area of square and parallelograms separately.
Area of square
Side length l = 12
Area = l *l = 12 * 12 = 144 sq. units
Area of parallelograms
Base b = 5
Height h = 3
Area of 1 parallelogram = b.h = 5 * 3 = 15 sq. units
Since all the parallelograms are congruent,
Area of all 4 parallelograms = 15 * 4 = 60 sq. units
Hence the area of the shaded portion of the given figure = 144 - 60
= 84 sq. units
To learn more about the area, follow the link.
https://brainly.com/question/1297097
#SPJ1
If y is proportional to the square root of x and y is=21 when x=49 find y when x =144
Answer:
y = 36
Step-by-step explanation:
Because the problem says y is proportional to the square root of x, we can assume that it is directly proportional.
The general formula for direct proportionality is
[tex]y=kx[/tex], where k is the constant of proportionality.
Taking into account the square root of x, we can use the following formula to find k by plugging in x and y:
[tex]y=k\sqrt{x}\\ 21=k\sqrt{49}\\ 21=7k\\3=k[/tex]
Since we found k, we can now use this value and the x we're given for the second part of the problem to find y:
[tex]y=3\sqrt{x} \\y=3\sqrt{144}\\ y=3*12\\y=36[/tex]