When x units are produced, the manufacturer's average cost per item can be The producer produced 200 more things this week than the previous week. The price per item reduced by $0.50 on average.
What do you meant by cost function ?Businesses frequently attempt to calculate the cost of producing a certain volume of goods. To arrive at these figures, they frequently use a cost function. A mathematical formula known as a cost function can be used to determine the total cost of production for a given quantity of goods produced. The cost function formula has the general form C(x)=F+V(x) , where x is the number of units and C(x) is the total cost of production. F and V represent the total fixed costs and variable costs, respectively.Examples of cost functions include the following:[tex]$C(x)=100,000+3.5(x)$\\[/tex][tex]$C(x)=500+25 x+2.5 x^2$\\$C(x)=1,000+0.5 x^2$[/tex]To learn more about cost function refer to :
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Lesson 4: Money and DebtsCool Down: Buying a Bike1.Clare has$150 in her bank account. She buys a bike for$200. What is Clare's accountbalance now?2.If Clare earns$75 the next week from delivering newspapers and deposits it in heraccount, what will her account balance be then?
Clare's account balance will be $25
How to determine Clare account balance?
Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Since Clare has $150 in her bank account and She buys a bike for$200. That means she overdrew and she will have an overdraft of $50. That is:
account balance now = $150 - $200 = - $50
If she earns $75 next week and then deposits it in her account.
account balance = - $50 + $75 = $25
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Marsha bought a new car for $21,152. 25.
The options she picked cost $2,150. The
sales tax was $1,007. 25. What was the base
price of Marsha's car?
If Marsha bought a new car for $21152.25 and picked cost is $2150 and sales tax is $1007.25 , then the base price of Marsha's car is $17995 .
the price that Marsha paid for the car is = $21152.25 ;
the picked cost for the car is = $2150 ;
the sales tax for the car is = $1007.25 ;
the formula to calculate the Marsha's car is = (Amount Paid) - (Picked Cost + Sales tax) ;
substituting the values ,
we get ;
= 21152.25 - (2150 + 1007.25 )
= 21152.25 - (3157.25)
= 17995 .
Therefore , the base price for the Marsha's car is $17995 .
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What is a parent function in math?
The parent function means most basic function in a family.
The term function in math is called as an equation that has only one answer for y for every x.
Here we have to define the term parent function.
The term parent function is known as the simplest function that still satisfies the definition of a certain type of function.
Here for example when we think of the linear functions which make up a family of functions, then the parent function would be y = x.
Here the given function is also known as the simplest linear function.
And these family shares the U-shaped graph called the parabola and they all have a second degree with the highest exponent.
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Perform the operation.
4 x-y/3 - x+y/2
please help!!!!will give brainlest
= (4x - y)/3 - (x + y)/2
= (4x - 3x - y + y)/6
= (x - y)/6
Answer:
18x+y
Step-by-step explanation:
[tex]4x-\frac{y}{3} - x + \frac{y}{2} \\\6(4x-\frac{y}{3} - x + \frac{y}{2})\\24x-2y-6x+3y\\18x+y[/tex]
I have no idea but I think this is what you're looking for
A toy train set includes a train station building which is a scale model of a real building. The area of the front side of the toy building is 1 square foot. The real building's front side has an area of 900 square feet. If we view the real building as a dilation of the toy, what is the scale factor?
The required scale factor between the building and toy model is given as 900.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
The area of the front side of the toy building is 1 square foot.
The real building's front side has an area of 900 square feet.
The real buildings as a dilation of the toy,
Scale factor = 900 /1
Scale factor = 900
Thus, the required scale factor between the building and the toy model is given as 900.
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Find the length s of the circular arc.
s =
The length s of the circular arc is; 27π/4
How to find the length of a circular arc?The formula for length of arc is;
L = (θ/ 360) * (2πr)
where;
θ is central angle
r is radius
From the diagram, we see that;
θ = 3π/4
r = 9
Now, 360 degrees in radians is 2π. Thus;
L = (3π/4)/(2π) * 2π(9)
L = (3π/4) * 9
L = 27π/4
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Which of the following is the value of kIf one root of the quadratic equation x²+
Kx-8=0 is - 4
The value of k If one root of the quadratic equation x²+ Kx-8=0 is - 4 should be 2.
According to the question
Given that,
A quadratic equation x²+Kx-8=0 where one root is -4
If -4 is a root of the equation x²+Kx-8=0 then if we put -4 in the pace of x we would get the final answer as 0 or in other words, -4 would satisfy the equation x²+Kx-8=0.
Hence,
⇒ x²+Kx-8=0.
⇒ (-4)²+ K(-4) - 8 = 0
⇒ 16 -4k - 8 = 0
⇒ 8 - 4k = 0.
-4k which is on the Left-Hand Side of the equation would be shifted to the Right-Hand Side of the equation and its sign would change from -4k to +4k.
⇒ 8 = 4k.
⇒ k = 2.
Thus, The value of k If one root of the quadratic equation x²+ Kx-8=0 is - 4 should be 2.
For complete question refer belowWhich of the following is the value of k If one root of the quadratic equation x²+ Kx-8=0 is - 4
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If aomeone could help me with this quick problem
Answer:
75 degrees
Step-by-step explanation:
Its an corresponding angle
The Lawn Order lawnmower factory can produce 12 lawnmowers in 8 hours. How many hours will it take the factory to produce 30 lawnmowers?
Answer:
The Lawn Order lawnmower factory can produce 12 lawnmowers in 8 hours. This means that the factory's production rate is 12 lawnmowers per 8 hours. To find how many hours it will take the factory to produce 30 lawnmowers, we can use the formula:
Time = (quantity of work to be done) / (rate of work)
In this case:
Time = 30 lawnmowers / (12 lawnmowers per 8 hours)
To solve the equation we can multiply both sides by 8/12:
Time = (30 lawnmowers * 8 hours) / (12 lawnmowers)
The result is:
Time = 20 hours
So it will take the factory 20 hours to produce 30 lawnmowers.
Answer:
45 hours.
Step-by-step explanation:
The factory makes 12 lawnmowers in 8 hours. You would divide 12 by 8 to see how many they make in 1 hour. That would be 1.5 So, you multiply 1.5 by 30 to get 45.
What is the derivative of Logbx?
The derivative of logₐ x (log x with base a) is 1/(x ln a).
Here, the interesting thing is that we have "ln" in the derivative of "log x". Note that "ln" is called the natural logarithm (or) it is a logarithm with base "e". i.e., ln = logₑ.
Further, the derivative of log x is 1/(x ln 10) because the default base of log is 10 if there is no base written.
The derivative of log x (base 10) with respect to x is denoted by d/dx (log x) or (log x)'. Thus,
d/dx(logₐ x) (or) (logₐ x)' = 1/(x ln a)
d/dx(log x) (or) (log x)' = 1/(x ln 10)
d/dx (logₐ x) = 1 / (x ln a)
Substitute a = e on both sides. Then we get:
d/dx (loge x) = 1 / (x ln e)
By the properties of natural logarithms, ln e = 1. So
d/dx (loge x) = 1 / (x · 1)
Thus, d/dx (loge x) = 1.
Replacing loge x with ln x back, we get d/dx (ln x) = 1/x.
Hence, the derivatives of logs are:
d/dx (logₐ x) = 1 / (x ln a) (this is the derivative of common logarithm)
d/dx (ln x) = 1/x (this is the derivative of natural logarithm)
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Desiree and Nick, the boy she was babysitting, were playing basketball together. Her score was 20 points, and his score was 10 points. Desiree wanted to make the game more fair, so she called a time-out and modified the rules a bit. Desiree explained that for the rest of the game she would get 3 points per basket, and Nick would get 4 points per basket. Then they played a bit longer. After a time-out, they both made the same number of baskets and ended with a tied score. How many baskets did each person make after the time-out?
After the time out each person scored 15 baskets.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Desiree's score was 20 points, and his score was 10 points. Desiree wanted to make the game fairer, so she called a time-out and modified the rules a bit. Desiree explained that for the rest of the game, she would get 3 points per basket, and Nick would get 4 points per basket.
The two equations can be written as:-
3D + 20 = 4N + 10
3D - 4N = -10
D + N = 30
Solve the above equations:-
3D - 4N = -10
4D + 4N = 120
____________
7D = 110
D = 15
Hence, the score for each person would be 15.
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As part of your retirement plan, you want to set up an annuity in which a regular payment of $25,312 is made at the end of each year. You need to determine how much money must be deposited earning 6. 2% compounded yearly in order to make the annuity payment for 20 years.
a.
$2,242. 78
c.
$285,671. 10
b.
$506,240
d.
$537,626. 90
So, the answer is $285,671.10 (Option b) that must be deposited earning 6.2% compounded yearly in order to make the annuity payment of $25,312 for 20 years.
The formula to determine the future value of an annuity is given by
FV = PV(1+r)^n + PMT( (1+r)^n - 1) / r
Where:
FV is the future value of the annuity
PV is the present value of the annuity
PMT is the payment made at the end of each period
r is the interest rate per period
n is the number of periods
We know that the payment made at the end of each period (PMT) is $25,312, the interest rate (r) is 6.2% and the number of periods (n) is 20.
We are looking for the present value of the annuity (PV)
So we can substitute the known values into the formula and solve for PV:
PV = PMT( (1+r)^n - 1) / (r (1+r)^n)
PV = $25,312 * ( (1+0.062)^20 - 1) / (0.062 (1+0.062)^20)
PV = $25,312 * (1.062^20 - 1) / (0.062 * 1.062^20)
PV = $25,312 * (1.062^20 - 1) / (0.062 * 1.062^20)
PV = $25,312 * (2.547 - 1) / (0.062 * 2.547)
PV = $25,312 * 1.547 / 0.157
PV = $285,671.10
Therefore, the answer is $285,671.10 (Option b) that must be deposited earning 6.2% compounded yearly in order to make the annuity payment of $25,312 for 20 years.
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Given the two concentric circles with center Q below,
OQ = 11.5. Find the area of the shaded region. Round
your answer to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
area of a circle formula is πr²
Find area of the larger and smaller circles and then subtract to find the shaded region. π = 3.14
area of the larger circle = π (11.5)²
3.14 (132.25)
415.265 units²
area of the smaller circle = π (5.5)²
3.14(30.25)
94.985 units²
subtract: 415.265 - 94.985 = 320.28 units²
it takes liya 7 more hours to paint a kitchen than it takes hank to complete the same job. together, they can complete the same job in 12 hours. how long does it take hank to complete the job if he works alone?
Hank has to complete the job if he works t alone by 1/12 hours.
1/t+7+1/t
=1 /12
Hank can paint a kitchen in the same amount of time in half the time it takes Liya. They can finish the same task in 12 hours if they work together.
Through multiplication by 12t(t+7),
all denominators become equal to 1, 12t + 12(t+7) = t(t+7), and
t2 = -17t -84 = 0.
(tossing out a negative solution for unit measure)
(t + 4) (t -21) = 0 (Henry's time)
Likewise,
calculating 1/28 + 1/21 = 1/12
and 49/(28 21) = 1/12
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The weight of 6 eggs is shown. Identify the constant of proportionality of total weight to number of eggs. The weight of 6 eggs is 252 g
The constant of proportionality is 42 grams per egg
How to identify the constant of proportionalityFrom the question, we have the following parameters that can be used in our computation:
The weight of 6 eggs is 252 g
The constant of proportionality can be calculated using
Constant = Weight/Number of eggs
Substitute the known values in the above equation, so, we have the following representation
Constant = 252/6
Evaluate
Constant = 42
Hence, the constant is 42 grams per egg
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How can you solve rational equations and identify extraneous solutions?
We can identify the extraneous solutions by checking if the solutions found by solving the equation make the denominator of the fraction equal to zero.
A rational equation is an equation that contains a fraction with a polynomial in the numerator and denominator.
To solve a rational equation, you can use the following steps:
Clear the fraction by multiplying both sides of the equation by the denominator of the fraction.
Solve the resulting equation for the variable.
Check your solutions by plugging them back into the original equation and making sure they are valid solutions.
Identify extraneous solutions by checking if the solutions found by solving the equation make the denominator of the fraction equal to zero. If it does, then the solutions are extraneous and should be rejected.
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how many outputs are there for each input in a function?
(x^-1/2y^4)^1/4 / x^2/3y^3/2 * x^-3/2y^1/2
Alvin wants to know what his average paddling rate was for a canoe trip to a campsite. on the way there it took him 8 hours against a river current of 3 km/ hr. on the way back, the same distance took him 3 hours with the same 3 km/hr current. let r = alvin's average paddling rate. Alvin's average paddling rate was:_____km/h.
Alvin's average paddling rate was 6.6 km/h.
We know that,
Speed= Distance/ Time (solve for distance)
Distance = Speed × Time
To Campsite against the current,
Speed=r-y ; speed=(r-3)
Time = 8 hours
Distance = (r-3)×8 (equation 1)
From Campsite with the current,
Speed = r + y ; speed=(r+3)
Time = 3 hours
Distance = (r+3)×3 (equation 2)
Equating equation 1 and equation 2 because distance is same in both case,
(r+3)×3=(r-3)×8
3r+9=8r-24
8r-3r=24+9
5r=33
r=6.6 km/hour.
What does aptitude mean upstream and downstream?
Upstream/Downstream: In the case of water, downstream refers to the direction that follows the stream. Upstream refers to the direction that runs counter to the stream. Speed downstream equals (u + v) km/hr if a boat is moving at u km/hr in still water and v km/hr in a stream.
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RIGHT ANSWER GETS 15 POINTS
In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle.
A straight line is shown and is marked with three angles. The first angle measures 60 degrees. The second angle measures 60 degrees. The third angle is labeled y. The line between the 70 degree angle and angle y extends below the straight line. The angle formed is labeled angle x.
Write and solve an equation to determine the measure of angle x. (5 points)
Your answer:
The Equation is x + 80 + 70 = 180 and the measure of x is 30 degree.
What is Vertical Angle?Horizontal Angles (Vertically Opposite Angles) The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles.
Angles that are vertically opposed to one another are equal. These are referred to as vertical angles at times.
Given:
Since x and y are vertical angles, they are the same.
Now, the equation to solve for x would be:
x + 80 + 70 = 180
Now, solving for x we get
x + 150 = 170
x= 180- 150
x= 30
Hence, the measure of x is 30.
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Ryan and Mariah are playing a game where there is a winner and a loser. Whoever wins a round gets 7 points. Whoever loses a round gets -3 points. Mariah lost the first two rounds. How many points does Ryan have after two rounds ?
Answer:14
Step-by-step explanation:
Mariah lost twice so that means she got -3 two times that goes the same for ryan he gets 7 points two times which equal 14
Answer: ryan would have 14 points and mariah would have -6 points
Step-by-step explanation:
What is the best estimate for the perimeter of the triangle?
The best estimate for the perimeter of the triangle is the sum of the length of all three sides, which would be 8+12+14 = 34 units.
The best estimate for the perimeter of the triangle can be found by adding up the length of all three sides. To begin, we will find the length of each side. Side A is 8 units, side B is 12 units, and side C is 14 units. Next, we will add up the length of all three sides, which will give us the total perimeter of the triangle. To calculate the total perimeter, we will add together 8+12+14, which will give us a total of 34 units. This is the best estimate for the perimeter of the triangle.
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how many solutions does 3+x=x+3 have
The equation has infinite solutions.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: 3+x=x+3
Clearly the two equations are equivalent and represent the exact same line
and thus the equation holds for any value of x.
The equations has infinite solutions when the graphs are the exact same line.
Hence, The solutions of the equation is infinite.
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3. A bicycle courier has a fixed delivery cost of $12.50 per day, plus a variable cost of $0.25/package. He earns $4.25 per package he delivers, in revenue. The maximum number of packages that he can deliver in a day is 27.
a. Write an equation to represent
The total cost, C, as a function of the number, p, of packages delivered.
ii. The revenue, R, as a function of the number, p, of packages delivered.
b. develop an algebraic model for the profit function
P(p) = R(p) - C(p)
c. Identify the domain and range in the context of this problem for C(p), R(p) and P(p)
The equation to represent the total cost as a function of the number of packages delivered is C(p) = 12.50 + 0.25p.
The revenue as a function of the number of packages delivered. is R(p) = 4.25p
How to write an equation to represent the total cost as a function of the number of packages delivered?a. i. The equation to represent the total cost, C, as a function of the number, p, of packages delivered is C(p) = 12.50 + 0.25p
ii. The revenue, R, as a function of the number, p, of packages delivered. is R(p) = 4.25p
b. The algebraic model for the profit function P(p) = R(p) - C(p) = 4.25p - (12.50 + 0.25p) = 4.00p - 12.50
c. i. C(p) has domain of all non-negative integers (p ≥ 0) and range of all real numbers greater than or equal to $12.50 (C(p) ≥ $12.50)
ii. R(p) has domain of all non-negative integers (p ≥ 0) and range of all real numbers greater than or equal to $0 (R(p) ≥ $0)
iii. P(p) has domain of all non-negative integers (p ≥ 0) and range of all real numbers (P(p) can be any real number)
Note: The domain of p is limited to 27 in this case as the maximum packages that can be delivered is 27.
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Part 1: Use transformations to prove congruency.
1. Given: ;
Prove: CBF EDF using isometric (rigid) transformations.
F
D
E
B
C
Outline the necessary transformations to prove CBF EDF using a paragraph proof. Be sure to name specific sides or angles used in the transformation and any congruency statements.
Part 2: Use congruency theorems to prove congruency.
1. The congruency of rMNO and rXYZ can be proven using a reflection across the line bisecting . However, this congruency can also be proven using geometric postulates, theorems, and definitions. Prove that the triangles are congruent using a two-column proof and triangle congruency theorems.
Given: M X
N Y
Prove: rMNO rXYZ
The two triangles CBF and EDF are congruent.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
The two triangles are congruent by the conditions are given;
CB // ED and both BD and CE are transversals
The point E will be the image of point C by rotation 180° around point F
The point D will be the image of point B by rotation 180° around point F
Rotation is a kind of transformation;
ΔCBF ≅ ΔEDF
Part 2;
Definition of congruent line segments;
Symmetric property of congruence;
Addition and substitution properties of equality;
Segment addition theorem;
Definition of congruent line segments;
AAS congruence postulate;
The addition property says if A=B, then A+C=B+C. The substitution property says if C=D, then A+C=B+D (D can be substituted for C). IMO, both properties are needed together to get from A=B and C=D to A+B=C+D;
Hence, the triangles CBF and EDF are congruent.
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Example 2: In a 45°–45°–90° right triangle the hypotenuse is ? times the leg. If the hypotenuse is 6 units find the length of each leg.
SN
The length of each leg is 8.46/√2 = 6 units.
In a 45-45-90 triangle, the ratio of the hypotenuse to each leg is √2: 1.
If the hypotenuse is 6 units, we can use this ratio to find the length of each leg.
6 (√2) = 6 * 1.41 = 8.46
So the length of each leg is 8.46/√2 = 6 units.
The hypotenuse is the longest side of a right triangle, and it is opposite the right angle. It is the side that is opposite the right angle and is opposite of the 90-degree angle. The two other sides of a right triangle are known as the legs. The length of the hypotenuse can be determined using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In other words, if a and b are the lengths of the legs, then the length of the hypotenuse c is given by [tex]c = √(a^2 + b^2).[/tex]
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can someone help with(2x - 4 ) + (3x - 7)
Attached is a file explaining a very complex question in which you would need to use the rules of BODMAS and DMAS.
EASY POINTS!!
Find the length of the hypotenuse in the triangle below. Round to the nearest tenth. Be sure to show your calculations and explain your answer
The length of c in the right angle triangle is 8.6 mm.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
The sides of a right angle triangle c an be found using Pythagoras's theorem as follows:
Hence,
c² = a² + b²
Hence,
a and b are the legsc is the hypotenuse sideTherefore,
c² = 5² + 7²
c² = 25 + 49
c² = 74
square root both sides
c = √74
c = 8.60232526704
Therefore,
c = 8.6 mm
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Someone help me pls!!
The graph of a function f is the set of points which satisfy the equation y = f(x). That is, the point (x, y) is on the graph of f if and only if y = f(x).
How do you transform the given graph of the parent function?Blue represents the parent function's transformation. It is a shift down of 1 unit (also known as a vertical translation down). A function is made to reflect on the x-axis by multiplying the parent function by a negative number.
The function graph "flips" over the x-axis when multiplied by a negative value. How can I find f from the graph of the function f(x)? (3). For f(3) (3), You're trying to find the output; the input is 3.
Locate the graph for the value of x equal to 3 and then move to the value of 3 on the x-axis to find the function's value at that point. At that point on the graph, determine the value of y by looking at the y-axis. The formula yields the graph of g.
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A square mural has an area of about 240 feet. What is the approximate length of one side of the mural?
(1)between 18 and 19 feet
(2)between 17 and 18 feet
(3)between 16 and 17 feet
(4)between 15 and 16 feet
(5)between 14 and 13 feet