Answer:I think being honest with them just tell them how you really feel not because just they ask and you just say I am fine how are you just tell how you really feel about that day. Be honest ...
Step-by-step explanation:
How I've been today? Quite magnificent. Thank thou for your generosity.
Which number is less than it’s square?
9/10
12/11
15/16
13/13
The number which is lesser than its square is 12/11
What is a square number ?When a number is multiplied by itself, the result is a square number. For instance, 25 is a square number as it is composed of 5 lots of 5, or 5 × 5.
The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number may be found by looking for a number that, when squared, yields the original value. It follows that a a = b if "a" is the square root of "b." Every integer has two square roots, one of a positive value and one of a negative value, because the square of any number is always a positive number. For instance, the square roots of 4 are both 2 and -2. However, the square root of a number is typically only expressed as the positive value.
The numbers are
9/10 , 12/11 , 15/16 and 13/13
The squares are
81/100, 144,121, 225/256, 1
here
81/100 < 9/10 abd
225/256 < 15/16
144/121 > 12/11
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Guys slove this I have to sumbit my assignment
(a) -3,-11,-19, -27, -35,-43, -51, -59, -67, -75.
(b) -9,-18,-36,-72,-144,-288,-576,-1152,-2304,-4608.
(c) 2, 6, 12, 20, 30, 42, 56, 72, 90, 110.
In the provided sequence, we will find the difference between two consecutive integers.
The difference between the second and first numbers is 622=4.
The difference between the third and second numbers is 126=6.
The difference between the fourth and third numbers is =2012=8.
We can see that the difference between two consecutive integers starts at 4 and grows by 2 each time.
As a result, the supplied sequence is created by adding the difference between a number and the preceding number, as well as 2 to the number.
Using the rule, we can determine the following three words.
The difference between the fifth and fourth numbers is =8+2=10.
As a result, the fifth number of the series equals the fourth number of the sequence plus ten.
As a result, we get the fifth number from the series =20+10=30
The difference between the sixth and fifth numbers is 10+2=12.
As a result, the sixth number of the series equals the fifth number of the sequence plus twelve.
As a result, we receive the sixth number as the sequence's sixth number =30+12=42.
The difference between the seventh and sixth numbers is 12+2=14.
As a result, we get the sequence's seventh number = the sequence's sixth number + 14
As a result, we receive the seventh number as the sequence's seventh number =42+14=56.
As a result, the following three terms in the specified sequence are 30, 42, and 56.
The sequence is changed to 2, 6, 12, 20, 30, 42, 56.
The word 'prime numbers' was used in the answer. The numbers are known as prime numbers. It has just two variables, 1 and the number itself. For instance, 2 is the sum of 2 and 1. As a result, the components of 2 are 2 and 1. As a result, 2 is a prime number.
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18 is the diameter , 9 is the radius , what is the area
Answer: The area of the circle with a radius of 9 is approximately 253.94 square units.
Step-by-step explanation:
The area of a circle is given by the formula A = πr^2, where A is the area, r is the radius, and π is approximately 3.14.
Given that the radius of the circle is 9, we can substitute this value into the formula to find the area:
A = πr^2 = π(9)^2 = 3.14 * 81 = 253.94
So the area of the circle with a radius of 9 is approximately 253.94 square units.
Note that the diameter of the circle is 18, which is twice the radius. If you knew the diameter you could also use the formula A = (π/4)*D^2 to calculate the area, where D is the diameter.
Explain why “r”, the correlation coefficient, has a range from -1 to 1?
Step-by-step explanation:
Possible values of the correlation coefficient range from -1 to +1, with -1 indicating a perfectly linear negative, i.e., inverse, correlation (sloping downward) and +1 indicating a perfectly linear positive correlation (sloping upward). A correlation coefficient close to 0 suggests little, if any, correlation
Transformed functions
See image below:
A function transformation is one that converts one function or graph into another, usually related function or graph.
What is transformation of a function?Given function, f(x)
Transformed function is y = -3f(x + 2)
To find each points transformed function:
Given point (-4 , 5)After transformation the function becomes,
y = -3(-4 + 2)
y = -3 x -2
y = 6
Then the transformed points are (-4 , 6).
Point (-2,3)After transformation the function becomes,
y = -3(-2 + 2)
y = 0
Then the transformed points are (-2 , 0).
Point (0,0)After transformation the function becomes,
y = -3(0 + 2)
y = -3 x 2
y = -6
Then the transformed points are (0 , -6).
Point (1,-2)y = -3(1 + 2)
y = -3 x 3
y = -9
Then the transformed points are (1 , -9).
Point (3,-4)y = -3(3 + 2)
y = -3 x 5
y = -15
Then the transformed points are (1 , -15).
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3 + y = 18 for y help with problem
Answer: y = 15
Step-by-step explanation:
Subtract both sides by 3
3 + y = 18
y = 15
For a dinner taste testing event, a total of cases of forks and cases of spoons were ordered. Each case of forks contains packages each containing forks. Each case of spoons contains packages each containing spoons. It is planned that each guest will receive forks and spoons at the beginning of the event. At the end of the event, forks and spoons were not given out to guests. Which question about the event can be answered from the given information?
A How many dinners were offered for tasting at the event?
B How many people attended the event?
C How much was earned from the tickets sales for the event?
D How much silverware was used?
It is possible to find out the number of people who attended the event. Hence option B is correct.
What is the system of equations?
System of equations, also known as simultaneous equations, Two or more equations to be solved together in algebra (i.e., the solution must satisfy all the equations in the system). The number of equations must equal the number of unknowns for a system to have a unique solution.
Given that, a total of 24 cases of forks and each case of forks contains 36 packages each containing 12 forks.
Form about information, calculate the number of forks.
A total of 24 cases of spoons and each case of spoons contains 45 packages each containing 12 spoons.
Form about information, calculate the number of spoons.
Given that at the end of the event, 12 forks and 18 spoons were not given out to guests.
Form these we can get information that how many spoon used.
Since each guest will receive 2 forks and 3 spoons at the beginning of the event.
Using this information we can get the number of people who attend the event.
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Multiply both sides: multiply both sides by what?
-10w ( ) = -9 ( )
[tex]-10w=-9[/tex]
Divide both sides by -10(to isolate the variable):
[tex]\dfrac{-10w}{-10} =\dfrac{-9}{-10}[/tex]
[tex]=0.9[/tex]
Lauren walks to work. She walks 112
miles in 38
hour. What is her unit rate?
Answer: Lauren's unit rate is 2.95 Miles per hour (MPH)
Step-by-step explanation:
divide the distance Lauren traveled by the time it took to travel said distance
112/38 hours=2.95 mph
Answer:
2.95 miles/hour or 2.95mph
Step-by-step explanation:
112/38 = 2.94736842 ⇒ 2.95 miles/hour
How would you do this problem on a ti-84 calculator? Or could you do this by hand and get the answer.
The answer is supposed to be -64/17, but I don't know how to get that answer.
Step-by-step explanation:
(R○R)(x) = (5 - 2((5 - 2x)/x))/((5 - 2x)/x)
we simply put the original R function into the places of x.
so,
(R○R)(-6) = (5 - 2((5 - 2×-6)/-6))/((5 - 2×-6)/-6) =
= (5 - 2((5 + 12)/-6))/((5 + 12)/-6) =
= (5 - 2×17/-6)/(17/-6) =
= (5 + 17/3)/(17/-6) = (15/3 + 17/3)/(17/-6) =
= 32/3 / 17/-6 = -6×32 / (3×17) =
= -2×32 / 17 = -64/17
Answer:
-64/17
Step-by-step explanation:
Same person here who answered previous question.
(R · R)(-6)
This basically means R(R(-6))
Now, R(-6) = (5 + 12)/-6 = -17/6
Put that value again, in (5 - 2x)/x = (5 + 34/6)/(-17/6)
= (64/6)/(-17/6) = -64/17
So, the answer is correct.
If you have any questions, please leave a comment.
Otherwise, cheers
Ahigh-speed train travels 25 feet in 1/3 second. In 4 seconds, the train will have traveled ? feet
Answer: 300 ft
Step-by-step Explanation: You start by multiplying 4 by 3 to get 12 because each second is split into 3 parts. From there you just have to multiply 12 by 25 for foot per second to get 300.
Fiona is purchasing hammers and wrenches for her workshop, and she would like to
spend under $120. Each hammer costs $5, and each wrench costs $6. Let x be the
number of hammers and y be the number of wrenches.
Select the inequality that describes the situation.
O 6x + 5y< 120
5x + 6y> 120
O6x + 5y 120
5x + 6y< 120
Answer:
The inequality that describes the situation is 5x + 6y < 120
Step-by-step explanation:
This inequality states that the total cost of purchasing x hammers and y wrenches must be less than $120. Each hammer costs $5 and each wrench costs $6, so the total cost is represented by the expression 5x + 6y.
The inequality states that 5x + 6y < 120 which means for any number of hammers and wrenches she buys it should be less than 120.
The other options:
6x + 5y < 120: the coefficient of x is 6 instead of 5 and that of y is 5 instead of 6.
5x + 6y > 120: the inequality is greater than instead of less than, which means that the total cost should be greater than $120 which is not the case.
6x + 5y ≥ 120 : the inequality is greater than or equal to instead of less than, which means that the total cost should be greater than or equal to $120 which is not the case.
A high school band director is designing a marching formation. To design formations, he uses a coordinate grid with the origin representing the middle of the field. On the grid, each mark represents one yard. One band member is moving from point G(-2, -2) to point H(3, 4). Use this graph to answer the questions in this activity.
Part D
Estimate the square root of c that you found in part C to the nearest tenth.
The required distance c between the point of marching formation is given as C = √61.
What is Distance?Distance is defined as the object traveling at a particular speed in time from one point to another.
Here,
The distance formula is given as,
C = √[[x₂ - x₁]² + [y₂+ - y₁]²]
Put the given point in the above equation,
C = √[[3 + 2₁]² + [4 + 2]²]
C = √25+36
C = √61
Thus, the required distance c between the point of marching formation is given as C = √61.
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Pls help me solve this!! It’s due today!!
f(x) and g(x) are inverses using composition
How to use composition to prove that f(x) and g(x) are inverses?A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
To confirm the inverse relationship using composition.
For valid inverse f(g(x)) must be equal to g(f(x))
f(x) = ∛(x) + 13; g(x) = (x - 13)³:
f(g(x)) = f((x - 13)³)
f(g(x)) = ∛((x - 13)³) + 13
f(g(x)) = x - 13 + 13
f(g(x)) = x
g(f(x)) = g(∛(x) + 13)
g(f(x)) = (∛(x) + 13 - 13)³
g(f(x)) = (∛(x))³
g(f(x)) = x
Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse
f(x) = x³ + 1; g(x) = ∛(x - 1):
f(x) = x³ + 1; g(x) = ∛(x - 1)
f(g(x)) = f(∛(x - 1))
f(g(x)) = (∛(x - 1))³ + 1
f(g(x)) = x - 1 + 1
f(g(x)) = x
g(f(x)) = g(x³ + 1)
g(f(x)) = ∛((x³ + 1) - 1)
g(f(x)) = ∛(x³)
g(f(x)) = x
Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse
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Margie has 64 rectangular steppingstones to arrange in an array in her backyard . How many arrays can Margie make with the 64 steppingstones
If Margie has 64 rectangular steppingstones to arrange in an array in her backyard. The number of arrays that Margie can make with the 64 steppingstones is: 2 × 32, 4 ×16, 8 × 8.
How to find the number of array:Given data:
Rectangular steppingstones to arrange in an array =64
In order to determine the number of arrays we have to find the number that will give us 64 when multiply.
The number that will gives us 64 as the answer when multiply are:
2 × 32 = 64
4 ×16 = 64
8 × 8 = 64
The arrays are 3 which are:
2 × 32
4 ×16
8 × 8
Therefore we can conclude that the number of array that Margie can make with the 64 steppingstones is: 2 × 32, 4 ×16, 8 × 8.
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Choose the correct option.
Which option is most similar in relation to the following word pair?
Water: Ocean
OPTIONS
House: Bricks
Book : Library
Biscuit : Tea
Cloth: Body
Answer:
Book: Library is most similar in relation to the following word pair Water: Ocean. Both pairs are closely related and are often found together.
A track runner counted the number of races he had during a season. The graph shows the relationship between the number of track meets, x, and the number of races, y.
coordinate plane with the x axis labeled number of track meets and the y axis labeled number of races with a line that passes through the points 0 comma 5 and 1 comma 7
Part A: Calculate the slope of the linear equation shown in the graph. Show all necessary work. (3 points)
Part B: What does the slope mean for the relationship between the number of races and the number of track meets? (3 points)
Part C: Interpret the y-intercept in the situation. (3 points)
Part D: Write the equation of the line shown on the graph in slope-intercept form. (3 points)
A. The slope of the linear function is given as follows: m = 2.
B. The slope means that the number of races increases by two when the number of track meets increases by one.
C. The y-intercept of 5 means that when there are 5 races when there are 0 track races.
D. The slope-intercept definition of the linear function is given as follows: y = 2x + 5.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the intercept, representing the value of y when x assumes a value of zero.The input and output variables for this problem are given as follows:
Input x: number of track meets.Output y: number of races.Two points in the function are given as follows:
(0,5) and (1,7).
Hence the slope and the intercept are given as follows:
Slope of 2, as when x increases by one, y increases by two.Intercept of 5, as when x = 0, y = 5.Meaning that the function is defined as follows:
y = 2x + 5.
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Solve the linear equation using equivalent equations to isolate the variable. Express your solution as an integer as a simple fraction or as a decimal number.
t-5=9
The solution to the given linear equation is t = 14
Solving Linear equationsFrom the question, we are to solve the given linear equation.
From the given information,
The given linear equation is
t - 5 = 9
To solve the equation, we will use the addition property of equality
Solving the equation
t - 5 = 9
Add 5 to both sides of the equation
t - 5 + 5 = 9 + 5
Simplify
t = 14
Hence, the solution is t = 14
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A $5000 loan at 5% dated July 5 is due to be paid on November 10.calculate the amount of interest. assuming ordinary interest
Answer:
$250
Step-by-step explanation:
because we have to do 5,000 of 5% = 250 in sale's tax or interest.
The solution is, $250 is the amount of interest.
What is interest?Interest is the outlay you pay to borrow money. Interest is often deliberated as an annual percentage of a loan amount.
here, we have,
Explanation:
given that,
A $5000 loan at 5% dated July 5 is due to be paid on November 10.
Since the borrower is to pay 5% of the money by November 10(Due time)
so, we get,
5% of the principal is simply
(5/100)* 5000
= $250
Hence, The solution is, $250 is the amount of interest.
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Classify each of the following attributes as either categorical or numerical. For those that are numerical, determine whether they are discrete or continuous.
(a)
number of students in a class of 32 who turn in a term paper before the due date
categorical
numerical (discrete)
numerical (continuous)
(b)
gender of the next baby born at a particular hospital
categorical
numerical (discrete)
numerical (continuous)
(c)
amount of fluid (in ounces) dispensed by a machine used to fill bottles with soda pop
categorical
numerical (discrete)
numerical (continuous)
(d)
thickness of the gelatin coating of a vitamin E capsule
categorical
numerical (discrete)
numerical (continuous)
(e)
birth order classification (only child, firstborn, middle child, lastborn) of a math major
categorical
numerical (discrete)
numerical (continuous)
The correct classifications for these variables are a = numerical discrete, b= categorical, c= numerical continuous, d= numerical continous, e= categorical.
What is the difference between a numerical and a categorical variable?As indicated by their name, numerical variables can be measured using numbers; here are some examples:
Weight of a person: 170 poundsDistance between two cities: 645 kilometersNumber of students in a class: 25 studentsOn the other hand, categorical variables fit into categories, for example:
Female vs Male
Dog vs cat
What is the difference between discrete and continuous?Discrete variables differ from continuous variables because they are obtained by counting, for example, the number of students in a classroom, while continuous variables need to be measured, for example, the distance.
Based on this the correct classification is:
A. Numerical (discrete) = the number of students in a class of 32B. categorical =gender of the next baby born at a particular hospitalC. Numerical (continuous) =amount of fluid (in ounces)D. Numerical (continuous) =thickness of the gelatin coating of a vitamin E E. Categorica, =birth order classification (only child, firstborn, middle child, lastborn)Learn more about variables in: https://brainly.com/question/17344045
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Find the measurement indicated in each parallelogram
(PLEASE ANSWER THIS IS DUE SOON!!!!!!! WILL MARK BRAINLIEST!!!)
The rule of a function changes from
f(x) = x² − 4 to g(x) = -x² + 4 when it is dilated.
Which statement best describes how this dilation affects the graph of f(x)?
A. The graph is reflected across the x-axis.
B. The graph is reflected across the y-axis.
C. The graph moves up 8 units.
D. The graph moves down 8 units.
The rule for the graph changes form of the function is A)The graph is reflected across the x-axis.
What is function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). Function is a relation that connects members of one set in a certain way to those of another set. Formally speaking, a function from to is an object such that each is specifically linked to an object. Therefore, a function is a many-to-one (or occasionally, one-to-one) relation.
Here Through moving up c units, the graphs of g can be determined from the graph of f. If we subtract c from f(x), the graph shifts downward. Let h(x) = f(x)-c Shifting downward c units yields this graph of h from the graph of f.
We know that if the function reflected over x-axis then
g(x) = -f(x)
Here the given function f(x) = [tex]x^2-4[/tex] then reflection over x-axis then
=> g(x) = -f(x)
=> g(x) =-( [tex]x^2-4[/tex])
=> g(x) = [tex]-x^2+4[/tex]
Hence the correct option is A)The graph is reflected across the x-axis.
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7.4% of what number is $3.33?
Answer:
Step-by-step explanation:
A company will issue stock and bonds to raise
$35,000,000 to finance a project. The company will
need to pay specialty fees and service commission
as part of this process. 0.5% of the money raised
will be spent on specialty fees, and 2% of the
money raised will be spent on service commission.
Calculate the amount of money that will be spent
on specialty fees.
fees = $ [?]
Enter
PH
Skip
The specialty fees will of the project will be $175,000.
What is specialty fee in a project?
Specialty fee of a project is associated with the cost or money that is given for some special task for e.g. hiring a architect or other specialist.
To calculate the amount of money that will be spent on specialty fees, we need to multiply the total amount of money raised (35,000,000) by the specialty fee percentage (0.5%).
specialty fees = 35,000,000 * 0.005 = 175,000
So, $175,000 will be spent on specialty fees.
Also, To calculate the amount of money that will be spent on service commission, we need to multiply the total amount of money raised (35,000,000) by the service commission percentage (2%).
service commission = 35,000,000 * 0.02 = 700,000
So, $700,000 will be spent on service commission.
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To raise $35,000,000 for a project's financing, a corporation will issue shares and bonds. The project's specialist fees will be $175,000 in total.
What is specialty fee in a project?The cost or amount paid for a project's specialty work, such as employing an architect or another specialist, is known as the specialty fee. We must multiply the entire cash raised ($35,000,000) by the proportion of speciality fees ($0.5%) to determine the amount that will be used for fees.
35,000,000 * 0.005 = 175,000 in specialist fees.As a result, specialist fees will cost $175,000. Additionally, we must multiply the total sum of funds raised (35,000,000) by the service commission rate (2%), in order to get the amount that will be used for service commission. service commission: 35,000,000 * 0.02 = 700,000 , The service commission will therefore receive $700,000.
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3.5% as a fraction or mixed number
Answer:
[tex]3.5\% = \frac{3.5}{100} = \frac{35}{10} (fraction) = 3 \frac{5}{10} (mixed)[/tex]
4x-3 =3x + y. 3x+y =2y+5x-12
simultaneous equation
pls help
Answer: To solve these simultaneous equations, we can substitute one equation into the other.
4x-3 = 3x + y.
3x+y =2y+5x-12
If we substitute the first equation into the second equation, we get:
3(4x-3) + y = 2y+5x-12
12x -9 + y = 2y+5x-12
Now we can solve the system of equations by isolating one of the variables and then substituting it back in one of the equations.
12x - 9 + y = 2y + 5x - 12
y = -9 + 2y + 5x -12
y = 2y + 5x -21
y - 2y = 5x -21 -9
-y = 5x -30
y = -5x + 30
Now we can substitute the value of y back into one of the original equations, we have:
4x-3 = 3x + (-5x + 30)
4x-3 = -2x + 30
4x-3+2x = 30
6x -3 = 30
6x = 33
x = 5.5
Now we can substitute the value of x back into one of the original equations to find the value of y:
4x -3 = 3x + y
4(5.5) -3 = 3(5.5) + y
22 - 3 = 16.5 + y
19 = 16.5 + y
y = 2.5
So the solution to the system of equations is x = 5.5 and y = 2.5.
Step-by-step explanation:
a) Choose two vectors vw in R2 and a third vector b also in R2, and express b as a linear combination of v,w by finding scalars c₁,c2 such that c₁v + c₂w = b. Sketch the situation in R2 with an illustration that uses the parallelogram rule. (b) Repeat part (a) with vectors in R3 such that the augmented matrix [v w | b] gives a consistent system, again illustrating by graphing but this time in R3. (c) Why is it harder to find a consistent system for part (b) compared to part (a)? Explain your idea clearly using complete sentences.
Previous question
Next q
a) The linear combination of v, w by finding scalars c₁, c₂ such that c₁v + c₂w = b is [v w | b]
b) The graph of the equation is attached below.
c) The matrix representation is a useful tool for finding linear combinations of vectors, but it becomes more complex as the number of dimensions increase.
A linear combination of two vectors is when a third vector is expressed as a sum of the two vectors multiplied by scalars.
In R2, this can be represented using a parallelogram, where the vectors are drawn and the third vector is the diagonal of the parallelogram.
To find the scalars, we use the matrix representation [v w | b]. If the matrix gives a consistent system, it means that the third vector b can be expressed as a linear combination of the two vectors v and w.
In R3, the matrix representation is still used but it becomes more challenging to find a consistent system because there are more variables involved.
The vectors are graphed in 3D, and the third vector is found as the diagonal of a parallelogram that is now a parallelepiped.
However, it may not always be possible to find a consistent system in R3, as the third vector may not lie in the plane formed by the two vectors.
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Part 1 of 2
Evaluate the function f(x)=x-7 at the given value of the variable.
a. f(13)
b. f(3)
Answer:
a)
b)-4
Step-by-step explanation:
a) f(13) = 13-7=
b) f(3)= 3-7= -4
Which graph represents the solution to the following equation?
[tex]|x| \ \textless \ 3[/tex]
Answer:
a
Step-by-step explanation:
|x|<a means -a<x<a
or x lies between -3 and 3
15. Rahj owns a hardware store. For every increase of 10¢ in the price A of a package of batteries, he estimates that sales decrease by 10 packages per day. The store normally sells 700 packages of batteries per day, at $5.00 per package. a) Determine an equation for the revenue, y, when x packages of batteries are sold. b) What is the maximum daily revenue that Rahj can expect from battery sales? How many packages of batteries are sold when the revenue is at a maximum? also,how to get the zeros and the equation
Answer:
a) To determine an equation for the revenue, y, when x packages of batteries are sold, we need to know the price of each package of batteries.
Since the price of a package of batteries is $5.00, the revenue, y, when x packages of batteries are sold is given by y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.
b) To find the maximum daily revenue that Rahj can expect from battery sales, we need to find the value of x that maximizes y = 5x.
Given that for every increase of 10¢ in the price A of a package of batteries, sales decrease by 10 packages per day. And the store normally sells 700 packages of batteries per day, at $5.00 per package.
It means that the store will sell a maximum number of batteries when the price is at $5.00
And the maximum daily revenue will be $5 * 700 = $3500.
So the maximum daily revenue that Rahj can expect from battery sales is $3500. And the number of packages of batteries sold when the revenue is at a maximum is 700.
The equation is y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.
The zeroes of the equation are the points at which the function crosses the x and y-axis.
The x-intercept is the point at which the function crosses the x-axis. It happens when y = 0. So the x-intercept of this equation is (0,0)
The y-intercept is the point at which the function crosses the y-axis. It happens when x = 0. So the y-intercept of this equation is (0,0)
Step-by-step explanation:
