The points that lie on the y-axis of the graph have a x-coordinate of zero.
Hence the format of the point is of:
(0,y).
How to define the ordered pair?The general format of an ordered pair is given as follows:
(x,y).
For the x-coordinate, we have that:
If it is positive, the point is x units right of the origin.If it is negative, the point is x units left of the origin.On the y-axis, the point does not move horizontally, just vertically, hence the points that lie on the y-axis of the graph have a x-coordinate of zero, and the format of the point is given as follows:
(0,y).
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Find an expression to represent the area of the triangle below
The formula for the area of a triangle is (1/4)√(105a?)
How to find the area of a triangle?By applying the triangle inequality theorem, we can verify that the given formula represents the length of the sides of a triangle. This theorem states that the sum of his two sides of a triangle must be greater than his third side.
Given the expressions 2a?, 6a + 5, and 10a?, applicable
2a? + 6a + 5 > 10a? (sum of first two pages greater than third)
2a?+10a?> 6a+5 (1st and his 3rd sides sum greater than 2nd)
6a + 5 + 10a? >2a? (sum of last 2 pages greater than first page)
Therefore, the given formula can express the length of the sides of a triangle.
According to Heron's formula, the area of a triangle with side lengths a, b, and c is
Area = √(s(s-a)(s-b)(s-c))
where s is the semicircle of the triangle and is defined as
s = (a + b + c) / 2
Replacing the given formula with a, b, c, we get:
s = (2a? + 6a + 5 + 10a?) / 2
= 6a? + 3a + 5/2
Find the value of s to calculate the area of the triangle.
Area = √((6a? + 3a + 5/2)((6a? + 3a + 5/2)-(2a? + 6a + 5))((6a? + 3a + 5/2)-(10a?)))
= √((6a? + 3a + 5/2)(2a? - 3a + 5/2)(-4a? + 3a + 5/2))
= √((15/4)(a?)(-5/4)(-a?)(-7/4)(a?))
= √(105a?/16)
= (1/4)√(105a?)
So the formula for the area of a triangle is (1/4)√(105a?).
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A ball dropped vertically fall d meter in t econd. D i directly proportional to the quare of t the ball drop 80 meter in the firt 4 econd . how far doe the ball drop in the next 8 econd
The ball will drop 320 meters in the next 8 seconds, which can be calculated using the equation d = (t^2) * k, where d is the distance (in meters) dropped, t is the time (in seconds), and k is the constant.
In the next 8 seconds, the ball will drop 320 meters. This can be calculated by using the equation [tex]d = (t^2) * k[/tex], where d is the distance (in meters) dropped, t is the time (in seconds), and k is a constant. Since the ball dropped 80 meters in the first 4 seconds, we have d = (4^2) * k, or k = (d/16). Plugging this value of k into the equation, we get d = (t^2) * (d/16), which simplifies to d = (t^2) * (80/16). In the next 8 seconds, t = 8, so d = (8^2) * (80/16) = 320 meters.
The ball will drop 320 meters in the next 8 seconds, which can be calculated using the equation d = (t^2) * k, where d is the distance (in meters) dropped, t is the time (in seconds), and k is the constant.
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Find the amount in the account for the given principal, interest rate, time, and compounding period. P = $3,650, r= 5.5%, t= 15 years; compounded monthly
Answer:
$14390.75
Step-by-step explanation:
p=3650
i = 5.5% is this annual rate or monthly rate? assuming annual rate
t=15 years compounding monthly = 15*12 = 300 periods
(1+5.5%/12)^300=3.94267155
multiply the principal 3650 *3.94267155 = $14390.75
Can someone please answer this
Answer:
X= k/2
Y= -k/2
Step-by-step explanation:
X= k/2
Y= -k/2
Set up a piece-wise function to describe the relationship between the total monthly cell phone charge and the number of minutes of use. Let y represent the total cost of the phone bill and let x represent the total number of minutes. Write a piecewise function to describe the plan
The total monthly cost of the phone bill is represented by y and the total number of minutes is represented by x. Then, a sample piece-wise function to describe their relationship is written as [tex]y(x)=\begin{cases} {{\$35\;&\mathrm{if}\;0\leq x \leq300} \\ {\$[35+(x-300)]\;&\mathrm{if}\;x > 300}} \end{cases}[/tex]
A function that is produced from bits of multiple functions over various periods is known as a piecewise function. By providing the input value, one can produce this function that operates differently.
Given the total cost of the phone bill is represented by y and the total number of minutes is represented by x. To write a piecewise function, let's consider an example of this.
For $35 per month, 300 minutes are included in a cell phone package. $0.25 will be charged for each additional minute. Then, the piecewise function for this is represented by,
[tex]y(x)=\begin{cases} {{\$35\;&\mathrm{if}\;0\leq x \leq300} \\ {\$[35+(x-300)]\;&\mathrm{if}\;x > 300}} \end{cases}[/tex]
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What would 2x - y = (-5)
Y = -x -5 be?
(Solving using substitution)
A healthy dog will drink between 50 and 60 milliliters of
water per kilogram of body weight each day.
Approximately how many fluid ounces of water will a
35-pound dog drink in a day? Express your answer as a
range of values, rounded to the nearest whole fluid
ounce.
Pls answer quickly!
The range of values for how many fluid ounces of water will a 35 pound dog will drink in a day is given as follows:
27 oz < x < 32 oz.
How to obtain the range of values?The range of values is obtained applying the proportions in the context of this problem.
The conversion of milliliters to fluid ounces is given as follows:
1 ml = 0.0338 oz.
Hence the amounts of oz per kilogram are given as follows:
50 x 0.0338 = 1.69 oz.60 x 0.0338 = 2.03 oz.The conversion of pounds to kg is given as follows:
1 kg = 2.20462 pounds.
Hence the weight in kg of the dog is given as follows:
35/2.20462 = 15.87 kg.
The bounds of the interval are given as follows:
15.87 x 1.69 = 27 oz.15.87 x 2.03 = 32 oz.More can be learned about proportions at https://brainly.com/question/24372153
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Sally has a swimming pool that needs to be drained. Her pool holds
9,774.5 gallons of water and will need to drain completely in 9.1 hours.
What is the change in the water level per hour for Sally's swimming
pool? Round your answer to the nearest hundredth.
The required change in the water level per hour for Sally's swimming pool is 1074 gallons.
What is rate change per hour?Rate of change is equal to (Change in completed assignments) / (Change in hours) Change in rate = (6-3) / (2-1) Change in rate = (3) / (1) The change rate is 3/1, or 3 assignments every hour. The rate of change is 3.0, or three assignments are completed every hour when time is measured in hours.
According to question:We have,
Her pool holds 9,774.5 gallons of water and will need to drain completely in 9.1 hours.
Number of gallons per hour are
gallons per hour = 9,774.5/9.1
gallons per hour = 1074 approx
Thus, required number of gallons per hours 1074.
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Jake earns 7.50 per hour working at a local car wash. The function f (x) = 7.50X
The inverse of the function that indicates the amount Jake earns per hour at a local car wash is [tex]\mathbf{y =\dfrac{7.50}{x}}[/tex]
What is a function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a map or transformation. Typically, these functions are identified by letters like f, g, and h. etc
A function is an operation or a relation that links each individual element of a non-empty set X, to at least one element of another non-empty set Y. In mathematics, a relation f between two sets, X and Y, is referred to as the function's domain and co-domain and can be expressed for all values of x and y as:
f = {(x,y)| for all x ∈ X, y ∈ Y}
The objective of this question is to write the inverse of the given function.
The function f(x) = 7.50x correlates Jake's pay to the number of hours he puts in the work.
The inverse of the function can be written as:
y = 7.50x
Interchange the variables
x = 7.5y
Divide both sides by 7.5
x/7.5 = 7.5y/7.5
Make y the subject of the formula:
[tex]\mathbf{y =\dfrac{7.50}{x}}[/tex]
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purchase the cat food, milk and toys for the kittens for 2 months. Each of the kitten needs a 1/2 kilogram of food and 1.5 litres of milk per week for the first month. After that each kitten will need 2.klingrams of food and 1 litre of milk for each week in the second month The table below shows the amounts charged for the cat food, milk and toys you need by three different supermarkets
Supplies A 5 kg bag of cat food. 1 litre of milk. Cat toys
Supermarket A $400 each/3 bags for. $1 100 $1900
Supermarket B $600 each/3 bags for $1660 $1 099 $2 300
Supermarket C $400 each/3 bags for $1.080 $1100 $1799
(a) Your father wants you to choose the supermarket that is giving you the best value, which supermarket is offering you the best value?
Answer: The best value for the cat food, milk and toys is Supermarket C. They are offering the 5 kg bag of cat food for $400 each/3 bags for $1,080, 1 litre of milk for $1100, and cat toys for $1799. Supermarket A is offering the 5 kg bag of cat food for $400 each/3 bags for $1,100, 1 litre of milk for $1,900, and cat toys for $1,900. Supermarket B is offering the 5 kg bag of cat food for $600 each/3 bags for $1,660, 1 litre of milk for $1,099, and cat toys for $2,300. Supermarket C has the lowest prices for all three items, so it is the best value.
Step-by-step explanation:
) Wanda, a caterer, is investing some money in equipment and employees
to help grow her business. Recently she spent $89 on equipment and hired a
server who makes $16 per hour. Wanda is hoping to make up these expense
at the next job that is scheduled, which pays a base of $90 in addition to $15
per hour that the server works. In theory, this event could pay enough to
cancel out Wanda's expenditures. How much would the job pay? How long
would the job have to be?
In theory, this event could pay enough to cancel out Wanda's expenditures the job pay 16 trips.
How much would the job pay?Establish a variable.
Utilizing the variable, write an equation.
Make the equation work.
Let C be the total cost of each transaction.
T, the quantity of slides down the water slide,
Since the price is the same regardless of how much she rides, C = 89 for the first transaction.
For the second agreement, C = 16plus T.
Set the two costs equal to one another, then use T to determine when they are equal.
89 = 16 + T + T = 18 trips.
Given that the first contract can only have a cost of $90, the price must be $15.
90 = 15 + T + T = 16 trips.
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The volume of 10 drops of a liquid is 0.1 fluid ounces.
What is the volume of 100 drops?
Answer:
1 fluid ounce
Step-by-step explanation:
if 10 drops is equal to 0.1 fl and we multiply 10 by 10 to get 100, we have to multiply 0.1 by 10 as well, which is 1 fluid ounce.
Graphing piecewise functions
The graph of the piece-wise function f(x) is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
The extreme points of the function in this problem are given as follows:
f(-1) = -1 + 3 = 2.f(2) = 2 + 3 = 5.f(2) = -2 + 9 = 7.f(6) = -6 + 9 = 3.Hence the graph of the function is composed by:
An increasing line from (-1,2) to (2,5).A decreasing line from (2,7) to (6,3).More can be learned about piece-wise functions at https://brainly.com/question/19358926
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Ella invested $4,900 in an account paying an interest rate of 3% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $5,920?
Answer:
it takes 8.8 years for the value of the account to reach $5,920.
Step-by-step explanation:
We can use the formula A = P(1+r/n)^(nt) to find the time it takes for Ella's investment to reach $5,920.
A is the future value of the investment, P is the present value (initial investment), r is the interest rate, n is the number of compounding periods per year and t is the time in years.
Plugging in the given values:
5920 = 4900(1 + 0.03/12)^(12t)
To solve for t, we need to take the natural logarithm of both sides of the equation and divide by the logarithm of (1+0.03/12)
t = ln(5920/4900)/(12*ln(1+0.03/12))
t = approximately 8.8 years (to the nearest tenth of a year)
So it takes 8.8 years for the value of the account to reach $5,920.
Solution set for the inequality for 4 - 5G greater than 39
Answer:
G < -7
Step-by-step explanation:
We can create an equation first with what the problem provides:
4 - 5G > 39
Now, since the question asks for the solution, we can solve for G:
-5G > 39-4
-5G > 35
-G > 7
Since G is still a negative, we need to switch the inequality around:
(-1)(-G) > (7)(-1) (To cancel out the negative)
G < -7
Rationalise the denominator 7/2-root 5
On rationalizing the expression 7/(2-√5) 7/(2-√5), the value is obtained as -7 (2 + √5).
What is rationalization?
In order to get rid of the irrational number in the denominator, the procedure of rationalisation is performed in elementary algebra. There are numerous rationalisation strategies that are used on the denominator.
The given expression is - 7/(2-√5).
Multiply the denominator and numerator by the (2 + √5).
= 7 × (2 + √5)/(2-√5) × (2 + √5)
= (14 + 7√5)/(2)² - (√5)²
Simplify it further -
= (14 + 7√5)/4 - 5
= (14 + 7√5)/-1
= -(14 + 7√5)
= -7 (2 + √5)
Therefore, the simplified expression is -7 (2 + √5).
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A convex pentagon has exterior angles of 83°, 83°, 26°, and 46°. What is the measure of an exterior angle at the fifth vertex?
The measure of an exterior angle at the fifth vertex is 62°.
A pentagon has 5 straight sides. The shape must also be closed.
A convex pentagon has no angles pointing inwards, and no internal angles can be more than 180°.
When all angles are equal and all sides are equal it is regular, otherwise, it is irregular.
The sum of exterior angles is 360°.
To know the angle of the fifth vertex add the remaining four vertexes and subtract from the sum of exterior angles.
Given 4 vertexes of the pentagon are 83°, 83°, 26°, and 46°.
By adding these we get a total of 238°
Fifth vertex=360°-238°
Fifth vertex=62°
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Aplicación de expresions algebraica
En la vida m cotidiana
Answer:
Aprende a leer expresiones algebraicas y comprende conceptos como variable, coeficiente u operador, entre otros.
Step-by-step explanation:
Ejemplo: la mitad de un número “x” si x= 8 x/2= 8/2= +4
Writing expressions form context of MX+B
The linear equation that represent the total cost over x GB is given as 10x + 20. The total cost when over 2 GB is $40
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
The slope intercept form of linear equation is:
y = mx + b
Where m is the rate of change and b is the initial value of y
Let y represent the total cost over x GB of data.
y = mx + b
The data plan cost $20 per month and $10 per GB over 3 GB.
Hence:
m = 10, b = 20; y = 10x + 20
Total cost when over by 2 GB = 10(2) + 20 = $40
Total cost when over by x GB = 10x + 20
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Use the figure to write a two-column proof.
Given: PSUR is a rectangle.
PQ=TU
Prove: QS=RT
*THE QUESTION IN THE PHOTO IS JUST NUMBER 10
Answer:Given Prove
PSUR is a rectangle QS = RT
PQ = TU
Proof:
Since PSUR is a rectangle, we know that opposite sides are parallel.
Therefore, PQ and TU are parallel.
Also, PSUR is a rectangle, so the angles P and R are right angles.
Therefore, angles Q and S are also right angles.
Since PQ and TU are parallel, and angles Q and S are right angles, we know that QS and RT are corresponding angles.
Therefore, QS=RT
QED.
Step-by-step explanation:
(a+√8)^2 can be written in the form c+d√2, where a c and d are integers. Find in terms of a an expression for c and an expression for d
Thank you so much
Please respond when you can in your own convenience
The expression for c and d in terms of a are c = a²+8 and d = 4a
How to write (a+√8)² in the form c+d√2?An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.
(a+√8)²can be written in the form c+d√2 by expand the bracket. That is:
(a+√8)² = (a+√8)(a+√8)
(a+√8)² = a(a+√8) + √8(a+√8)
(a+√8)² = a² + a√8) + a√8 + 8
(a+√8)² = a² + 2a√8 + 8
(a+√8)² = a² + 4a√2 + 8
(a+√8)² = (a²+8) + 4a√2
Thus, c = a²+8 and d = 4a
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How many terms are in the following Algebraic Expression? -
(7 x 6) + 8
Answer: 3
Step-by-step explanation: First you have to do 7 times 6 which is 42. Then you add 8 and get 50!
What appears to be the domain of the part of the exponential function graphed?
The domain of the function is x ≤ 1.
x ≤ 1 because your domain cannot have h(x) because that is your function and would be your range but in this case it is your domain and your domain, also known as the x coordinate, would have to be the number on the x axis that your line starts at, which would be your domain.
Your line starts on line 1 on the x axis, which would be your domain.
How do you determine a function's domain?Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
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Complete the following table.
Problem
Function
Domain Range
The number of shoes in x pairs of shoes
The cost to park in a mall garage is P 50 entry
fee plus P10 per four
A swimming pool in a hotel is draining at a rate of
3 feet per minute
please help.
For the problem , (a) The cost to park in a mall garage is $50 entry fee plus $10 per four , the function is y = 50 + 10x , the domain is (0,∞) and range is also (0,∞) .
and (b) A swimming pool in a hotel is draining at a rate of 3 feet per minute , the function is y = -3t , domain is (0,∞) and range is (0,∞) .
Part(a) ;
The cost to park in a mall garage is $50 entry fee plus $10 per four ;
the the number of hours be = "x" ;
the fixed entry fees for the mall garage is = $50 ;
the per hour charge for the garage is = $10 ;
it can be represented as : y = 50 + 10x ;
the function is : y = 50 + 10x ;
The domain of this function is (0,∞) , as the input hours can't be negative and
the range of function is (0,∞) as the charge cannot be negative
since the parking hours will be non negative .
Part(b) ,
A swimming pool is draining at the rate of 3 feet per minute.
Rate of draining is represented as "y = -3t" where t is number of minutes and
the negative sign in the function denotes the water is draining .
The domain and Range of this function is (0,∞) , as the input hours can't be negative .
The given question is incomplete , the complete question is
Find the Function , Domain and Range for the following problems :
(a) The cost to park in a mall garage is $50 entry fee plus $10 per four.
(b) A swimming pool in a hotel is draining at a rate of 3 feet per minute.
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I don't how to resolve this
[tex]\cfrac{(2x^{-1} y^2)^{\frac{1}{4}}}{(12x^2 y^{-1})^{\frac{1}{2}}}\implies \cfrac{2^{\frac{1}{4}} x^{-\frac{1}{4}} y^{\frac{2}{4}}}{12^{\frac{1}{2}} x^{\frac{2}{2}} y^{-\frac{1}{2}}}\implies \cfrac{2^{\frac{1}{4}} x^{-\frac{1}{4}} y^{\frac{1}{2}}}{12^{\frac{1}{2}} x y^{-\frac{1}{2}}}\implies \cfrac{2^{\frac{1}{4}} y^{\frac{1}{2}}y^{\frac{1}{2}}}{12^{\frac{1}{2}} xx^{\frac{1}{4}} }[/tex]
[tex]\cfrac{2^{\frac{1}{4}} y^{\frac{1}{2}+\frac{1}{2}}}{12^{\frac{1}{2}} x^{1+\frac{1}{4}} }\implies \cfrac{2^{\frac{1}{4}} y}{12^{\frac{1}{2}} x^{\frac{5}{4}} }\implies \cfrac{2^{\frac{1}{4}} y}{12^{\frac{2}{4}} x^{\frac{5}{4}} }\implies \cfrac{2^{\frac{1}{4}}}{(12^2)^{\frac{1}{4}}}\cdot \cfrac{y}{x^{\frac{5}{4}}}[/tex]
[tex]\left( \cfrac{2}{12^2} \right)^{\frac{1}{4}}\cdot \cfrac{y}{x^{\frac{5}{4}}}\implies \left( \cfrac{1}{72} \right)^{\frac{1}{4}}\cdot \cfrac{y}{x^{\frac{5}{4}}}\implies {\Large \begin{array}{llll} \cfrac{y}{(72)^{\frac{1}{4}}x^{\frac{5}{4}}} \end{array}}[/tex]
Tray earns $510 per week. He works 5 days each week and 8 hours each day.
How much money, in dollars, does Tray earn por hour?
$12.75
$39.23
$63.75
$102.00
OUTCASTS OF POKER FLAT QUESTIONS: ENGLISH
PUT THIS IN THE WRONG CATEGORY.
1. Explain three details from the story that establishes its regionalism. You must write at least three complete sentences--no sentence fragments or phrases.
2. What culture about the West does the author, Harte, convey?
3. If you were living in the East in the late 1800s, what would you find interesting about this story?
4. Although the characters in the story have little in common, they band together. Why do you think this is?
5. The circumstances these characters find themselves in seems to bring out their true characters. Which one surprised you the most? Why?
1. One detail that establishes the story's regionalism is the setting, which takes place in a small mining town in the West called Poker Flat.
2. The author, Harte, conveys a culture about the West that emphasizes the harsh and unforgiving nature of the land and its people. The characters in the story struggle against the harshness of the environment and the moral ambiguity of the mining town.
3. If you were living in the East in the late 1800s, you would find interesting the story's depiction of the West as a land of opportunity and adventure, but also one of danger and hardship. The story would also provide a glimpse into the everyday lives of people living in the West, which would likely be quite different from what they were familiar with in the East.
4. The characters band together because they are all outcasts, each in their own way, and they find comfort in each other's company. They are all looking for a sense of community and belonging that they have been denied in Poker Flat.
5. The character that surprised me the most was Mother Shipton. I was surprised by her sudden change of character when she revealed her past and her true identity as a former prostitute, which was quite different from the religious and moral woman she had pretended to be. I think this was surprising because it shows how people can hide their past and their true selves in order to fit in and be accepted by society.
What is the regionalism about?Another detail is the use of Western colloquialism and dialect in the dialogue of the characters.
Lastly, the story also includes a description of the harsh winter conditions and rugged terrain of the Sierra Nevada mountains, which is specific to that region.
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Look at the picture please (IM GIVING OUT 50 POINTS TO WHOEVER ANSWER THIS CORRECTLY AND I WILL MARK BARINLIEST)
3. Use your graph to answer the following questions
3a. If King sets the price at $2.50 per doll how many disappointing customers will each store have during the week?
3b. If King sets the price at $3.80 per doll how many unsold dolls will remain at each store at the end of the week?
3c. According to this graph, if the company could give the dolls away, how many would each door need per week?
3d. According to this graph, what price would make the doll supply so tight that the average number available to each store would be zero?
3e. Estimate the price where supply and demand will be in equilibrium
4. Complete the following using equations.
A. Use two of the points, giving to find the equation for supply (S) as a function of price (P)
B. Use two of the points given to find the equation for demand (D) as a function of price (P)
C solve the system of supply and demand equations to find the price in exact equilibrium. How does this price compare with your answer in question 4e above?
a. The number of disappointed customers is 157. b. Unsold dolls = 135. c. The dolls needed per week is 660. d. The price of $0.63 will make the supply of the doll tight. e. The price at which the demand and supply will be at equilibrium is $3.20.
What are functions?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
a. The supply and the demand associated from the graphs are:
Supply: 95(2.50) - 60 = 178
Demand: -130(2.50) + 660 = 335
Subtracting the Demand and supply:
335 - 178 = 157
The number of disappointed customers is 157.
b. For unsold dolls set the equation for supply and demand:
Supply: 95(3.80) - 60 = 301
Demand: -130(3.80) + 660 = 166
Subtract the value of demand and supply:
301 - 166 = 135
Unsold dolls = 135
c. To give the dolls away, the cost of the doll is $0.
The demand equation thus becomes:
y = -130(0) + 660
y = 660
The dolls needed per week is 660.
d. Let the supply be 0.
y = 95x - 60
0 = 95x -60
x = $0.63
The price of $0.63 will make the supply of the doll tight.
e. The supply an demand will be in equilibrium when Demand = Supply, that is:
95x - 60 = -130x + 660
95x + 130x = 720
225x = 720
x = $3.20
The price at which the demand and supply will be at equilibrium is $3.20.
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A pizza company charges $60 for 12 pizzas.
Using the above situation write a complete answer for the following questions.
li) Write the ratio
iii) Write the unit rate or m
iv)write the equation(y=Mx)
v) create a table from the above question
Answer:
Step-by-step explanation:
ii) ratio = 60:12 = 5:1
iii) unit rate is 5
iv) 60 = 12M
The following games are played with 8 cards: the four kings and the four aces. The dealer fans the cards with their back to you and asks you to take one, but not to look at it. He tells you that you will win a prize if your chosen card is an ace. There are two versions of what happens next.
In version 1, he closes up the remaining 7 cards, shuffles them and reveals to you the top card face up on the table which turns out randomly to be the King of Spades. He then deals the next card face down on the table. He then offers you the chance to trade the card you hold for the face-down card that was just dealt. So you have two choices: stay or switch. What are your chances of winning under each choice?
In version 1, if you choose to stay with the card you have initially chosen, your chances of winning are 1 in 8, since you have a 1 in 8 chance of having selected an ace initially.
If you choose to switch, your chances of winning are 7 in 8, since the card you are switching to is randomly selected from the remaining 7 cards, 4 of which are aces. However, if the card you have initially chosen is an ace, you should stay with it since you have already won the prize. If it is not an ace, it may be beneficial to switch as you have a higher chance of getting an ace with the face-down card.
In either case, the dealer has a 7-in-8 chance of winning since he has access to all the cards and can choose the card to be revealed at random. This means that he has a higher chance of winning than the player does. Overall, the game is quite balanced in terms of the chances of winning for either the player or the dealer.
The dealer has an advantage due to knowing the cards and being able to select the card to be revealed, but the player still has a chance of winning depending on their decision to switch or stay with their initial selection.
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