A company's profit is determined by its revenue less its cost of operations.Subtract costs from revenue to get the profit function.
Find the number of units ?Let P(x) stand for the profit, R(x) for the revenue, and C(x) for the expense.Profit thus equals P(x) = R(x) -C. (x).The revenue and expense can be modeled as fixed values or as functions,
Profit = Revenue - Cost
We need to find an equation for the revenue R(x).
R(x) = number of units * unit price = x * p(x) = x(72-x) = 72x - x2
Therefore: Profit P(x) = 72x - x2 - (20 + 52x) = - x2 + 20x -20
To find max profit, run the 1st derivative test, so set P'(x) = 0 and solve for x:
P'(x) = -2x + 20
set P'(x) = 0 ----> -2x+20 = 0 ----> -2x = -20 -----> x = 10
The number of units, x, that produces the maximum profit is 10.
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Triangle X Y Z is shown. Angle X Z Y is a right angle. Angle Z X Y is 60 degrees and angle X Y Z is 30 degrees. The length of hypotenuse X Y is 4.
Given right triangle XYZ, what is the value of tan(Y)?
The value of Tan Y is 0. 8660
How to determine the identityFrom the information given, we have that;
XZY = 90 degreesZXY = 60 degreesXYZ = 30 degreesXY = 4Now, let's determine the value of the adjacent side
cos θ = adjacent/ hypotenuse
cos 60 = adjacent/ 4
Adjacent = 2
Using Pythagorean theorem
4² = 2² + c²
16 - 4 = c²
c = √12
c = 3. 5
Tan Y = 3. 5/ 4
Tan Y = 0. 8660
Hence, the value is 0. 8660
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Answer:b
Step-by-step explanation:
Biologists estimate that the number of deer in Rhode Island in 2003 was 1,028, and in 2008 it had grown to 1,488. Biologists would like to model the deer population, p, as a function of the years, t, since 2000.
(a) Represent the information we have been told as two coordinate points. Be careful to know what your values of time are for each year.
(b) Calculate ∡p ÷ ∡t from 2003 to 2008. Include proper units in your answer.
(c) Give a physical interpretation of the value you found in part (b).
(d) Determine a linear relationship between the deer population, p, and the years since 2000, t.
(e) How many deer does this model predict were in Rhode Island in the year 2000? What does this represent about the linear function?
(f) How many deer does the model predict for Rhode Island now?
a) The points are given as follows: (3, 1028) and (8, 1488).
b) The rate of change is:
c) The interpretation of the rate of change is that it gives the yearly increase in the number of deers.
d) The equation is: y = 92x + 752.
e) The prediction for the year of 2000 is the intercept of the function, which is of 752 deer.
f) The prediction for the current year of 2022 is of 2776 deer.
What is a linear function?The slope-intercept representation of a linear function is:
y = mx + b
The coefficients of the function and their meaning in the context of this problem are listed as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x increases by one. Hence, in this problem, it represents the yearly increase in the number of deer.b is the y-intercept of the function, which is the value of the function when it's graph crosses the y-axis, that is, when x = 0. Hence, in this problem, it gives the population of deer in the year of 2000.Considering the reference year 2000 as year 0, the coordinate points of the function are given as follows:
(3, 1028), (8, 1488).
Given two points, the slope of the function is given by the change in the output divided by the change in the input, hence:
m = (1488 - 1028)/(8 - 3) = 92.
Hence the function is:
y = 92x + b.
When x = 3, y = 1028, hence the intercept b is obtained as follows:
1028 = 92(3) + b
b = 1028 - 92(3)
b = 752.
Then:
y = 92x + 752.
2022 is 22 years after 2000, hence the estimate for the number of deer is given as follows:
y = 92(22) + 752 = 2776.
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I need help asap if molly buys 6 tickets and they cost 75 dollars in total how much would one cost?
y do i have to write so much for a small answer the answer is 12.5
Answer: One ticket would cost $12.50
Step-by-step explanation:
If 6 tickets cost $75, to find the cost of one ticket, we need to divide.
$75 divided by 6 is $12.5.
$12.5 is not a valid answer, so we need to show the hundredths place, which is 0. This means the answer is $12.50.
Brittany has a home-based business making corsages and boutonnieres for school dances. Last year, she sold 12 corsages and 17 boutonnieres, which brought in a total of $621. This year, she sold 19 corsages and 16 boutonnieres, for a total of $754. How much does each item sell for?
please help
Each corsages sell for $22. And Each boutonnieres sell for $21.
Brittany sold 12 corsages and 17 boutonnieres last year in total of $621.
And she sold 19 corsages and 16 boutonnieres this year for a total of $754.
First, we will create the system of equation from given information
So, the equations are
12x+17y=621..…(1)
19x+16y=754..…(2)
Where,
X=cost of one corsage
Y=cost of one boutonniere
Make y the subject of equation (1)
y=(621-12x)/17
Put this value of y in equation (2)
Therefore
19x+16((621-12x)/17)=754
19x+(9936-192x)/17=754
(323x+9936-192x)/17=754
131x+9936=12818
131x=12818-9936
131x=2882
x=2882/131
x=22
So, the cost of one corsage is $22.
Now, put this value of x in equation (1)
12×22+17y=621
264+17y=621
17y=621-264
y=357/17
y=21
The cost of one boutonniere is $21.
Thus, the cost of each corsages and boutonnieres are $22 and $21.
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Choose the solution to this inequality.
3.5≥b+1.8
Answer:
[tex]1.7\geq b[/tex]
Step-by-step explanation:
3.5>=b+1.8
-1.8. -1.8
1.7>=b
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Answer question in picture
The given graph can be expressed as an equation of f(x) = -2cos(-x).
What is a graph of a trigonometric function?
In these trigonometry graphs, the x-axis values of the angles are in radians, and the y-axis value of the function at each given angle is taken as f(x).
The given graph is of a negative angle of a negative cosine.
So if we draw the graph of the negative angle of a negative cosine, the graph will pass through the origin, but
If we multiply 2 from the graph of the negative angle of a negative cosine then we will get the same graph as shown in the given figure.
So the equation would be f(x) = -2cos(-x).
Hence, the equation of the graph will be f(x) = -2cos(-x).
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The individual times of four members of a 4×400 m relay team are shown below find the teams total waste time in seconds
find x in angle ABC
............
Answer: The value of x in ∆ ABC is
Step-by-step explanation: By AA similarity
x² = 4* 16
x = 8
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Find the value of f(12) given the following arithmetic sequence of f(3) = -3 and f(6) = 8.
The value of f(12) in the arithmetic sequence is 30.
How to solve arithmetic sequence?Arithmetic sequence formula can be represented as follows;
aₙ = a + (n - 1)d
where
d = common differencea = first termn = number of termTherefore,
f(3) = - 3
f(6) = 8
Hence, let's find f(12).
-3 = a + 2d
8 = a + 5d
3d = 11
d = 11 / 3
a = -3 - 2(11 / 3)
a = - 3 - 22 / 3
a = - 31 / 3
Hence,
a₁₂ = a + 11d
a₁₂ = - 31 / 3 + 11(11 / 3)
a₁₂ = - 31 / 3 + 121 / 3
a₁₂ = 90 / 3
a₁₂ = 30
Therefore,
f(12) = 30
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A box of candy had 8 cherry pieces for every 3 lemon pieces. If the box had 30 lemon pieces how many cherry pieces would there be
Answer:
240
Step-by-step explanation:
30 X 8
Pls help me fast rapidly on khan academy:
Answer:
This triangle is obtuse and isosceles
Step-by-step explanation:
An obtuse triangle is a triangle in which one of the angles is greater than 90°. You can clearly see that angle NPO is greater than a right angle.
An isosceles triangle is a triangle in which two sides are equal and two angles are equal. Sides NP and PO are equal because they both measure 4m, which necessarily means that the angles opposite them are congruent (angles PNO and NOP).
Answer:
ΔNOP is obtuse triangle and isosceles triangle.
Step-by-step explanation:
An acute triangle has three angles that each measure less than 90°.
An obtuse triangle is a triangle with one angle greater than 90°.
A right triangle is a triangle with one 90° angle represented by the symbol ∟.
From inspection of the triangle, it appears that angle P is greater than 90°, which means it is an obtuse triangle.
This can be confirmed by using the cosine rule to calculate angle P.
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Cosine Rule (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]
Therefore:
[tex]\implies \cos(P)=\dfrac{4^2+4^2-7^2}{2(4)(4)}[/tex]
[tex]\implies \cos(P)=-\dfrac{17}{32}[/tex]
[tex]\implies P=\cos^{-1}\left(-\dfrac{17}{32}\right)[/tex]
[tex]\implies P=122.08995...^{\circ}[/tex]
As 122.1° > 90°, this proves that triangle NOP is obtuse.
An equilateral triangle has three sides of equal length.
A scalene triangle has three sides of differing lengths.
An isosceles triangle has two sides of equal length.
Therefore, as NP = OP ≠ ON, the triangle has two sides of equal length and so it an isosceles triangle.
Write the equation of the line in fully simplified slope-intercept form.
The equation of the line as represented in the task content in fully simplified slope-intercept form is; y = -( 1/2 )x - 2.
Equation of a line in slope-intercept formIt follows from the task content that the equation of the given line in slope-intercept form is to be determined.
As evident on the graph, the y-intercept and x-intercept of the line are; (0, -1) and (-2, 0).
Therefore, the slope can be determined from the slope formula as;
m = ( 0 - (-1) ) / (-2 - 0)
m = 1 / -2 = -1 / 2.
Therefore, by simulation of the slope-intercept model of the equation of a straight line; y = mx + c where, m = slope and c = y-coordinate of the y-intercept;
The equation of the given line is;
y = -(1/2)x - 2.
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leaves Rockford, Illinois, at the rate of 70 mph, bound for Madison, Wisconsin. At the same time, a truck leaves Madison at the rate of 50 mph, bound for Rockford. If the cities are 72 miles apart, how long will it take for the car and the truck to meet?
The time taken for the car and truck to meet is 36 minutes.
What are speed and time?The relationship between the three variables is the fundamental concept of speed, time, and distance.A body's speed is defined as the distance travelled per unit of time. That is, speed = distance divided by time.The time for the car and the truck must be the same.
time = distance/rateLet "x" be the car'sdistance:
Then 72-x is the truck'sdistancetime = timeNow,
=> x/70 = (72-x)/50=> 50x = 5040-70x=>50x+70x = 5040=> 120 x = 5040=> x = 5040/120 = 42 miles.Then trucks distance:
=> 72-42=30 miles.Time is:
=> 42/70 = 0.6 hrs=> 0.6*60 = 36 minutes.Hence, the time taken for the car and truck to meet is 36 minutes.
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5x+4=2(x+2) solve for x
Answer:
Step-by-step explanation:
Answer:
7x + 8 is your answer
Step-by-step explanation:
19. MODELING In Example 6, 44% of the voters say they plan to reelect the mayor. The poll has a margin of error of ±3% percentage points. Use a model to write and solve an absolute value inequality to find the least and greatest percents of voters who plan to reelect the mayor.
The Least percentage point = 41
The Greatest percentage point = 47
What is percent?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
Given:
Percentage of voters who plan to re-elect mayor = 44%
Margin of Error in measurement = ±3 % points
The absolute value inequality to find the lowest and greatest percent of points :
X = mid value
44% = estimated percentage
≤3 = error margin
Therefore,
|mid value - estimate| ≤ error margin
|x − 44| ≤ 3
⇒ -3 ≤ x - 44 ≤ +3
Add 44 on both sides,
-3 + 44 ≤ x ≤ 3 + 44
Simplifying,
41 ≤ x ≤ 47
Hence,
The Least percentage point = 41
The Greatest percentage point = 47
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The length of a rectangle is four more than twice its width. If the perimeter of the rectangle is 56 cm, what is the width of the rectangle?
The width has a value of 8 meters
How to determine the value of the width?The mathematical statement from the question is given as
Length of a rectangle is four more than twice its width.
Mathematically, this can be represented as
Length = 2Width + 4
The perimeter is given as
Perimeter = 56 meters
The perimeter is calculated as
Perimeter = 2 x (Length + Width)
So, we have
2 x (2Width + 4 + Width) = 56
Divide by 2
2Width + 4 + Width = 28
This gives
3Width= 24
Divide by 3
Width = 8
Hence, the width is 8 meters
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In a polygon one interior angle is 25 degrees.What is the size of the exterior angle next to (adjacent)11
In a polygon, the size of the exterior angle next to the adjacent is 155°
Exterior angle:
Exterior angle means the angle between any side of a shape, and a line extended from the next side
Given,
In a polygon one interior angle is 25 degrees.
Here we need to find the exterior angle next to the adjacent.
In order to find the exterior angle, we have to do the following,
We know that each interior angle of the polygon is 25 degrees, so each exterior angle of the polygon is
=> 180 - 25
=> 155°
Therefore, the measure of the exterior angle is 155°.
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Equation for (-6,0) (0,-8)
The equation of the line passing through (-6,0) and (0,-8) will be y = -4x/3-8.
According to the question,
We have the following information:
We have two points: (-6,0) and (0,-8) and we have to find the equation.
We know that following formula is used to find the slope of the line:
m = (y2-y1)/(x2-x1)
In this case, we have x1 = -6, y1 = 0, x2 = 0 and y2 = -8.
m = (-8-0)/{0-(-6)}
m = -8/(0+6)
m = -8/6
Dividing this fraction by 2:
m = -4/3
Now, the following formula is used to find the equation of the line:
(y-y1) = m(x-x1)
y-0 = -4/3{x-(-6)}
y = -4/3(x+6)
y = -4x/3-8
Hence, the equation of the line passing through (-6,0) and (0,-8) will be y = -4x/3-8.
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8.2: Word Problems - UNDERLINE key words, set up your division sentence, then solve!
Ms. K's cooking club needs 2 1/4 cups of flour to make enough crepes for everyone in the class. The
club split into 6 smaller groups, each making their own batch. How much flour does each group
need?
Answer:
3/8
Step-by-step explanation:
hope it helps :)
What are the steps involved in the financial plann
Identify your Financial Situation,
Determine Financial Goals,
Identify Alternatives for Investment,
Evaluate Alternatives,
Put Together a Financial Plan and Implement,
Review, Re-evaluate and Monitor The Plan
What is financial planning?The process of figuring out how a corporation will be able to afford to meet its strategic goals and objectives is known as financial planning. Normally, a business develops a financial plan right away after deciding on its vision and goals. The Financial Plan details all the tasks, assets, tools, and supplies required to accomplish these goals as well as the timelines involved.
The following tasks are part of the financial planning activity:
Analyze the commercial environmentVerify the company's goals and vision.Determine the types of resources required to accomplish these goals.Measure the quantity of the resource (labor, equipment, materials)Determine the overall expense of each type of resource.Compile the expenses to make a budget.Determine any dangers and problems with the planned budget.To learn more about financial planning, refer to
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24. the numbers in a sequence
Variable
Term
Difference
Evaluate
Exponent
Answer:
34
Step-by-step explanation:
I will need a lot more info then that but i think it'll be 34
solve the absolute value equation
2 = |x|-1
If you're looking for x, then:
2 = |x|-1
lxl-1 = 2
lxl-1+1=2+1
lxl=3
so x = -3, x=3
Please help will mark Brainly
Answer:
B
Step-by-step explanation:
I did it, I know, can I have brainliest please?
URGENT! Please Help!
The values of x or y are as follows:
(a) y = 4
(b) x = -2
(c) y = 6
(d) x = 3
(a) Given, that a line passes through (-3 , y) and (-9 , -2) having slope m = 1
as, we know the formula of slope i.e. (y1 - y2)/(x1 - x2) = m
So, (y + 2)/(-3 + 9) = 1
= (y + 2)/6 = 1
= y + 2 = 6
So, y = 4
(b) Given, that a line passes through (x , -7) and (1 , 2) having slope m = 3
as, we know the formula of slope i.e. (y1 - y2)/(x1 - x2) = m
So, (-7 - 2)/(x - 1) = 3
= -9/(x - 1) = 3
= x - 1 = -3
So, x = -2
(c) Given, that a line passes through (9 , y) and (3 , 2) having slope m = 2/3
as, we know the formula of slope i.e. (y1 - y2)/(x1 - x2) = m
So, (y - 2)/(9 - 3) = 2/3
= (y - 2)/6 = 2/3
= y - 2 = 4
So, y = 6
(d) Given, that a line passes through (7 , 5) and (x , 2) having slope m = 3/4
as, we know the formula of slope i.e. (y1 - y2)/(x1 - x2) = m
So, (5 - 2)/(7 - x) = 3/4
= 3/(7 - x) = 3/4
=7 - x = 4
So, x = 3
Hence, the values of x or y are as follows:
y = 4 , x = -2 , y = 6 and x = 3.
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The Houston Armadillos, a minor-league baseball team, play their weekly games in a small stadium just outside Houston. The stadium holds 10,000 people and tickets sell for $10 each. The franchise owner estimates that the team's annual fixed expenses are $180,000, and the variable expense per ticket sold is $1. (In the following requirements, ignore income taxes.)
Answer:
Required
1. What is the break-even point in tickets?
2. How many tickets must be sold to earn a profit of $30,000?
3. How many tickets must be sold to earn a profit of $100,000?
Step-by-step explanation:
One plane can travel 10 miles per hour faster than another. One of them goes 135 miles in the same time it takes the other to go 130 miles. What are their speeds?
The speed of the slower plane is 260 mph and the speed of the faster plane is 270 mph.
What is the distance?Distance is defined as the product of speed and time.
Let the speed of the slower plane would be s
then (s+10) = speed of the faster
So time equation; time = dist/speed
130 / s = 135 / (s+10)
130(s+10) = 135s
130s + 1300 = 135s
135s - 130s = 1300
5s = 1300
s = 1300 / 5
s = 260
Since s = 260 mph is the speed of the slower plane
So, 270 mph is the speed of the faster.
Thus, the speed of the slower plane is 260 mph and the speed of the faster plane is 270 mph.
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Jamie stirred cake batter for six minutes. After each minute, she recorded how many total stirs she had made in the table at the left.
a. Does this relation form a function?
b. Based on the information in the table, what do you think may have happened between minutes 3 and 4?
A bag contains 15 green, 18 yellow, and 16 orange balls.
One ball is randomly selected. To the nearest percent, what is the probability of the event?
P(yellow)=
31%, 33%, 37%, and 42%
The probability of the event P(Yellow) is 37% , the correct option is (c) .
In the question ,
it is given that
number of green balls in the bag [tex]=[/tex] 15
number of yellow balls in the bag [tex]=[/tex] 18
number of orange balls in the bag [tex]=[/tex] 16
So , total number of balls in the bag = number of green balls + yellow balls + orange balls .
On substituting the values ,
we get
total number of balls = 15 +18 + 16 = 49
the probability of the event P(Yellow) = (number of yellow balls)/(total balls)
= 18/49
= 0.3673
= 36.73%
≈ 37%
Therefore , The probability of the event P(Yellow) is 37% .
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Simplify
this question
Answer:
1/4
Step-by-step explanation:
[tex]\frac{6 - \sqrt{25} }{4}[/tex] =
[tex]\frac{6-5}{4}[/tex] =
[tex]\frac{1}{4}[/tex]
Convert the following equation
into standard form.
y = -7x/2 - 3
Answer:
7x + 2y = - 6
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
given
y = - [tex]\frac{7}{2}[/tex] x - 3 ( multiply through by 2 to clear the fraction )
2y = - 7x - 6 ( add 7x to both sides )
7x + 2y = - 6 ← in standard form
