The rate at which her daily revenue is currently changing and the direction of the change is; Her revenue is currently increasing at $12 per day
What is the rate of change of a function?The rate of change of a function is the rate at which the output of the function changes per unit change in the input of the function.
Let x represent the number of days, therefore;
The number of T-shirts Dorothy sells, y = 40 - 4·x
The price at which she sells the T-shirts = 7 + x
Therefore, Dorothy's daily revenue, R(x) = (40 - 4·x) × (7 + x) = 12·x - 4·x² + 280
The rate of change of her daily revenue can be obtained from the derivative of the revenue function as follows;
The rate at which her daily revenue is therefore;
R'(x) = d(R(x))/dx = 12 - 8·x
The rate at which her revenue is changing currently can be obtained from the rate function by plugging in x = 0, as follows;
R'(0) = 12 - 8×0 = 12
Her revenue is changing at a rate of $+12 per day.
The positive value of the rate, 12, indicates that her revenue is increasing at $12 per day
Learn more on the rate of change of a function here: https://brainly.com/question/20066447
#SPJ1
Noah received these two
presents
for his birthday.
Which has a greater volume?
The first rectangle has 10 in 2 in and 3 1/2 second is a square it has just 8in please help will mark anyone brainlesy who answers first
second square
add up all the inches and youll see second had bigger number leading to the answer b
ben and david plot the locations of their houses and the park on the grid show below. they r planning to each start at home and travel in a straight line to the park. how many times greater is the distance ben travels to get to the park than the distance david travels?
The distance Ben travels to get to the park is approximately 2.21 times greater than the distance David travels. This is found by using the distance formula to calculate the distances each person travels and then comparing the results.
To solve this problem, we need to find the distance between each person's house and the park using the distance formula
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
For Ben
distance = √((-2 - 4)² + (-2 - 6)²) = √((-6)² + (-8)²) = √(100) = 10
For David
distance = √((-2 - (-7))² + (-2 - (-6))²) = √((5)² + (4)²) = √(41)
So the ratio of Ben's distance to David's distance is
10 / √(41) ≈ 2.21
Therefore, Ben's distance is about 2.21 times greater than David's distance.
To know more about distance:
https://brainly.com/question/30308375
#SPJ1
Find sin(π/4). Round to 3 decimal places.
Step-by-step explanation:
sin (pi/4) = sqrt(2) / 2 = .707
you either just know this after a time or you can use a calculator (in RADIAN mode)
Answer:
sin(π/4) = sin(45°) = 0.707106781186548 ≈ 0.707 (rounded to 3 decimal places)
Step-by-step explanation:
here are the steps:
Convert π/4 to degrees: π/4 * (180/π) = 45°
Use the definition of sine to find the sine of 45°:sin(45°) = opposite/hypotenuse
In a right-angled triangle with an angle of 45°, the opposite and adjacent sides are equal, so we have:sin(45°) = opposite/hypotenuse = adjacent/hypotenuse = 1/√2
Rationalize the denominator by multiplying both the numerator and denominator by √2:sin(45°) = 1/√2 * √2/√2 = √2/2
Round to 3 decimal places: sin(45°) ≈ 0.707Therefore, sin(π/4) = sin(45°) = √2/2 ≈ 0.707 (rounded to 3 decimal places).
Use the definition of Ax
to write the vector equation as a matrix equation.
The matrix equation is enter your response here
If the vector is drawn from (0,0) to (5, -1), the outcome or the required vector is drawn.
Describe vector?A mathematical concept known as a vector has both a magnitude and a direction. Physical quantities like force, velocity, and acceleration are represented by it. In the physical sciences, engineering, and computer graphics, vectors are frequently employed. They can also be used to represent abstract concepts like magnitude, directions, and other things.
Here in the question,
(0, 0) is the beginning position. There should be an arrow above each vector name listed below.
Ink a line beginning at (3, -1). A vector has an origin of (0,0) and a destination of (3, -1).
Put a line through points (2,2). The vector B has a start point of (0, 0) and an end point of (2, 2).
These two vectors add up to: a + b = (3-1) + (2,2) = (5,1) when combined.
Whatever order they are in, b + a = (2,2) + (3, -1) = (5,1) regardless.
Either way, the same conclusion is reached.
The terminal point of A + B is at (5, 1).
If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.
To know more about vector, visit:
brainly.com/question/12949818
#SPJ1
How many significant digits are there in the number 9.15 x 10000
There are four significant digits in the number 9.15 x 10⁴.
The digits that provide the number with useful information are known as the important digits.
As they add to the value of the number in this instance, the numbers 9, 1, and 5 are all important.
The exponent, 4, just instructs us on how many places to relocate the decimal point, therefore it has no bearing on the number of significant digits.
Therefore, the number 9.15 x 10⁴ has four significant digits.
Learn more about Simplification here:
https://brainly.com/question/28996879
#SPJ1
Use an array model on graph paper to solve and explain your solution to – Candy comes in 3 1/2pound bags. At a recent party, those attending ate 2 1/4 bags of candy. How many pounds of candy did they eat? Your solution should be in simplest form.
those attending the party ate 4 1/2 pounds of candy in total.
How to solve the question?
To solve this problem using an array model on graph paper, we can draw a rectangular array with 2 1/4 rows and 3 1/2 columns. Each cell in the array represents a 1/4 pound of candy. The total number of cells in the array will give us the total amount of candy eaten.
To start, we can divide each row into four equal parts to represent 1/4 pound of candy. We can also divide each column into two equal parts to represent 1/2 pound of candy. Then, we can shade in the cells that represent the amount of candy eaten.
Starting with the first row, we shade in two full rows and an additional half row, representing 2 1/2 bags of candy. Then, in the second row, we shade in two full columns and an additional half column, representing 2 1/4 bags of candy.
When we count the total number of shaded cells in the array, we see that there are 18 cells shaded. Each cell represents 1/4 pound of candy, so we can multiply 18 by 1/4 to get the total amount of candy eaten:
18 * 1/4 = 4 1/2 pounds
Therefore, those attending the party ate 4 1/2 pounds of candy in total.
To know more about graph visit :-
https://brainly.com/question/19040584
#SPJ1
An entomologist writes an article in a scientific journal which claims that fewer than 20 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. Be sure to address the original claim.
a) There is sufficient evidence to support the claim that the true proportion is less than 20 in ten thousand.
b) There is not sufficient evidence to support the claim that the true proportion is less than 20 in ten thousand.
c) There is not sufficient evidence to support the claim that the true proportion is greater than 20 in ten thousand.
d) There is sufficient evidence to support the claim that the true proportion is greater than 20 in ten thousand.
Use the definition of Ax
to write the vector equation as a matrix equation.
The vector equation written as a matrix equation is enter your response here
.
If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.
Describe vector?A mathematical concept known as a vector has both a magnitude and a direction. Physical quantities like force, velocity, and acceleration are represented by it. In the physical sciences, engineering, and computer graphics, vectors are frequently employed. They can also be used to represent abstract concepts like magnitude, directions, and other things.
Here in the question,
(0, 0) is the beginning position. There should be an arrow above each vector name listed below.
Ink a line beginning at (3, -1). A vector has an origin of (0,0) and a destination of (3, -1).
Put a line through points (2,2). The vector B has a start point of (0, 0) and an end point of (2, 2).
These two vectors add up to: a + b = (3-1) + (2,2) = (5,1) when combined.
Whatever order they are in, b + a = (2,2) + (3, -1) = (5,1) regardless.
Either way, the same conclusion is reached.
The terminal point of A + B is at (5, 1).
If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.
To know more about vector, visit:
https://brainly.com/question/12949818
#SPJ1
y=-0.8x^2 - 4x please help
The characteristics of the above quadratic unction y=-0.8x^2 - 4x are given as follows.
What are the characteristics of the above function?The vertex is (5, -22).
The axis of symmetry is x = 5.
The function is increasing when x < 5 and decreasing when x > 5.
The x-intercepts are (-5, 0) and (0, 0).
The domain is all real numbers and positive when x < 0.
The range is (-∞, -22].
The function is negative when x > -5.
The y-intercept is (0,0).
The function is negative when x is less than -5/2 and positive when x is greater than -5/2.
Learn more about Quadratic Functions;
https://brainly.com/question/27958964
#SPJ1
please help me with this question..
The possible values of a are 3 and -3.
How to find the value of a?We know that the coefficient of x⁷ in the given expression is 1215, the expression is:
[tex]x^3(ax + 3)^5[/tex]
The term with x⁷ will be:
[tex]5*(3x^7*a^4) = (15a^4)*x^7[/tex]
Then we need to solve the equation:
15a⁴ = 1215
a⁴ = 1215/15
a⁴ = 81
a = ⁴√81 = ± 3
These are the possible values of a.
Learn more about coefficients at:
https://brainly.com/question/1038771
#SPJ1
The park near Henry's house is closed before school, so he cannot ride through the park on his way to school. Complete the sentence to show which routes Henry should take to ride the least possible distance. Henry should take it on the way to school and on the way home from school. Using the routes selected in Part A, what is the total distance, in yards, that Henry will ride each day? If necessary, round the distance to the nearest hundredth. yards?
part a:
Henry should take a route that bypasses the park on the way to school and on the way home from school in order to ride the least possible distance.
He should take Route C on his way to school and Route B on his back.
part b: no values were given to calculate the distance.
What is distance?Distance is described as a numerical or occasionally qualitative measurement of how far apart objects or points are.
Since the park near Henry's house is closed before school, so he cannot ride through the park on his way to school, he should take Route C on his way to school and Route B on his back.
Learn more about distance at:
https://brainly.com/question/26550516
#SPJ1
Compare and contrast the direct write-off method and the allowance method for bad debts.
At a minimum, please consider the following in your answer:
When is the expense for uncollected accounts receivable recognized under each method?
Why is the direct write-off method not considered to follow generally accepted accounting
The direct write-off method and the allowance method are two different ways of accounting for uncollectible accounts receivable.
How do the direct write-off method and the allowance method compare ?The direct write-off method is a simple method of accounting for bad debts, where the uncollectible accounts receivable are written off as an expense at the time they are deemed uncollectible.
In contrast, the allowance method is a more complex method of accounting for bad debts, where the company estimates the amount of bad debt expense that it expects to incur over time and creates an allowance account to record this estimate.
The main difference between the two methods is the timing of the recognition of bad debt expense. Under the direct write-off method, bad debt expense is recognized only when an account is written off, whereas under the allowance method, bad debt expense is recognized in advance based on an estimate of the amount of bad debts.
The direct write-off method is not considered to follow generally accepted accounting principles (GAAP) because it violates the matching principle, which requires that expenses be matched with the revenues they generate in the same accounting period.
Find out more on the direct write-off method at https://brainly.com/question/24108628
#SPJ1
The owners of Applewood Farmstead tracked their fruit sales over the weekend. The graph below shows the relative frequencies of the sales of each fruit. Applewood Farmstand sold a total of 320 pieces of fruit over the weekend. How many of those were apples?
Applewood Farmstand sold 102 pieces of apples over the weekend.
What is graph?Graph is a data structure which consists of nodes (vertices) that are connected with each other. Graphs are used to represent relationships between different objects, such as networks, social connections, and pathways. Graphs are useful for representing data as they can provide a visual representation that is easy to interpret, and can be used to analyse patterns in the data. Graphs can also be used to represent problems such as shortest path problems, and can be used to solve problems such as finding the most efficient route between two points.
The graph shows that apples accounted for 32% of the total fruit sales. To find the exact number of apples sold, we can calculate the following:
Apples = (320 pieces of fruit) x (0.32)
Apples = 102 pieces
Therefore, Applewood Farmstand sold 102 pieces of apples over the weekend.
To know more about graph click-
http://brainly.com/question/19040584
#SPJ1
Is (3, 5) a solution to this system of equations?
y=5
y = -5/3x + 10
yes
no
what is the simplified answer to 49^{1/2}
Answer:
7
Step-by-step explanation:
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of 1650 . What was the rate charged per hour by each mechanic if the sum of the two rates was 135 per hour?
Rates of first and second mechanics are 75 and 60 per hour respectively.
What does an equation mean?A mathematical statement or relation between two or more numeric values, variable and mathematical operations via equal sign is called an Equation.
How to solve equations in Elimination Method?Elimination method is a kind of method to solve simultaneous equations in two variables. In elimination method we compare coefficient of one of two variables and in next step we eliminate that variable using addition or subtraction and form another relation with only one variable and find the value for that one variable and then substituting that value initial equation we can get the value of another variable.
Let the rate of first mechanic and second mechanic be x and y per hour respectively.
Sum of the two rates is 135 per hour. So the suitable equation will be,
x+y = 135 ............... (i)
Since they charged together 1650 after working 10 hours by first and 15 hours by second mechanics. So the suitable equation this time will be,
10x+15y = 1650
5(2x+3y) = 1650
2x+3y = 1650/5
2x+3y = 330 ............... (ii)
Multiplying 2 with equation (i) and then subtracting it from equation (ii) we get,
(2x+3y) - 2(x+y) = 330 - 2*135
2x+3y-2x-2y = 330-270
y = 60
Substituting y=60 in equation (i) we get,
x+60 = 135
x = 135-60 = 75
Hence, the rates charged per hour are 75 and 60 per hour respectively.
To know more about Elimination Method visit:
https://brainly.com/question/25427192
#SPJ1
HURRY DUE TONIGHT
Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts. What percent of the new mixture if peanuts?
A. 34%
B. 13%
The new mixture contains 34% peanuts.
The correct option is A
We have,
Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts.
First, Total weight = 4 kg + 12 kg = 16 kg
Now, Total weight in kilograms is = (4 kg) (0.16) + (12 kg) (0.40)
= 0.64 kg + 4.80 kg
= 5.44 kg.
Now, the Percent of peanuts
= (Total amount of peanuts / Total weight) x 100%
= (5.44 kg / 16 kg) x 100
= 34%
Thus, the new mixture contains 34% peanuts.
Learn more about weighted averages here : brainly.com/question/18554478
#SPJ1
how do you do this equation?
hi
First, dont keep the equation this way.
f(x) = 2 (x+2) +4x
f(x) = 2x+4+4x
f (x) = 6x+4
after :
x= 0 f(x) = 4
x= 2 f(x)= 16
x= 10 f(x) = 64
x = 30 f(x) = 94
A particle moves in the xy plane so that at any time
,
x=3sint
and
.y=t-4cost+1
What is the vertical component of the particle's location when it's horizontal component is 2?
Responses
y = -1.05
y = -1.05
y = -2.25
y = -2.25
y = -1.25
y = -1.25
y = 0.73
The vertical component of the particle's location, when its horizontal component is 2, is:
y = -1.25
How to solveTo find the vertical component of the particle's location when its horizontal component is 2, we need to first find the value of t when x = 2.
Given the equation:
x = 3sin(t)
Substitute x with 2:
2 = 3sin(t)
Now, isolate t by dividing both sides by 3:
sin(t) = 2/3
Take the inverse sine (arcsin) of both sides:
t = arcsin(2/3)
Now, plug the value of t back into the y equation:
y = t - 4cos(t) + 1
y = arcsin(2/3) - 4cos(arcsin(2/3)) + 1
Using a calculator to find the approximate value of y, we get:
y ≈ -1.25
Therefore, the vertical component of the particle's location when its horizontal component is 2 is:
y = -1.25
Read more about vertical components here:
https://brainly.com/question/25854506
#SPJ1
lo Rebecca found the length and width of the garage door. She used the measurements to find the perimeter of the garage door. Which of the following could be the perimeter of Rebecca's garage door? F 48 square feet G 48 square inches H 48 feet J 48 cubic feet
The possible values for the perimeter of Rebecca’s garage door are 48 feet or 48 inches
What is meant by perimeter?
Perimeter is the total length of the boundary of a two-dimensional shape. It is the sum of the lengths of all sides of the shape. The perimeter is commonly used to measure the distance around an object or figure and is often used in geometry to calculate the area of a shape.
According to the given information
The perimeter of a rectangle is calculated by adding the four sides of the rectangle. The formula for the perimeter of a rectangle is given as P = 2 (Length + Width) 12.
Therefore, the possible values for the perimeter of Rebecca’s garage door are 48 feet or 48 inches
Complete question is
Rebecca found the length and width of the 6. garage door. She used the measurements to find the perimeter of the garage door. Which of the following could be the perimeter of Rebecca's garage door? F 48 square feet /G 48 square inches/ H 48 feet/ J 48 cubic feet
To know more about perimeter visit
brainly.com/question/6465134
#SPJ1
Can anybody help me please
50 Points! Multiple choice algebra question. Determine which pair of functions are inverse functions. Photo attached. Thank you!
The pair of the functions that are inverse is
A. f(x) = x - 4; g(x) = (x + 4)How to find the inverse of the functionThe inverse of the function is solved by the operations as follows
f(x) = x - 4 let y = f(x)
y = x - 4
solving for x
x = y + 4
interchanging the variables
y = x + 4 (this is the inverse)
the inverse x + 4 is equal to g(x) hence they are inverse functions
Learn more about inverse functions
https://brainly.com/question/3831584
#SPJ1
HELLLPPP ME PLSSS ITS URGENT
The ratio of the volume of both spheres is: 1/(24√3)
What is the volume of the sphere?The formula for the volume of a sphere is expressed as:
V = ⁴/₃πr³
where:
r is radius
V is volume
We are told that the radii of the two spheres have a ratio of 1:2√3. Thus:
Volume of sphere A/Volume of sphere B = (1:2√3)³
= 1/(24√3)
Read more about Volume of sphere at: https://brainly.com/question/10171109
#SPJ1
Helpppp pls it’s due rnnnn
A function relating these variables is D(x) = 10 + 2x,
D(9) = 28, meaning after 9 hours of snowfall,
What is an independent variable?An independent variable is a variable that is manipulated or controlled by the researcher in an experiment to observe its effect on the dependent variable. It is the variable that is changed deliberately to see how it affects the outcome of the experiment.
The independent variable, x, represents the number of hours since snow began falling,
and the dependent variable is the total amount of snow on Jace's lawn because the amount of snow depends on the number of hours since it began to snow.
A function relating these variables is D(x) = 10 + 2x, where D(x) is the total amount of snow on Jace's lawn in inches after x hours of snowfall.
So, D(9) = 28, meaning after 9 hours of snowfall, Jace will have a total of 28 inches of snow on his lawn.
To know more about variable, visit:
https://brainly.com/question/28248724
#SPJ1
Enter the correct answer in the box.
The function f(x) = 7x + 1 is transformed to function g through a horizontal compression by a factor of What is the equation of function g?
Substitute a numerical value for k into the function equation.
Answer:
The equation of function g after horizontal compression by a factor of 3 is:
g(x) = 7(3x) + 1 = 21x + 1
To substitute a numerical value for k into the function equation, we need to know the value of k. It is not given in the question, so we cannot provide a numerical answer.
Step-by-step explanation:
When a function is horizontally compressed by a factor of k, we divide the input (x) by k to obtain the new input for the transformed function.
The equation for the horizontally compressed function is:
g(x) = f(x/k)
Substituting f(x) = 7x + 1, we get:
g(x) = 7(x/k) + 1
Simplifying, we get:
g(x) = (7/k)x + 1
Thus, the equation for the transformed function g is obtained by replacing k with the given compression factor.
For example, if the compression factor is 3, then:
g(x) = (7/3)x + 1
And to substitute a numerical value for k, we need to know the value of k. If k = 2, for example, then:
g(x) = (7/2)x + 1
Find the volume of a composite solid with a radius of 6 and a height of 12
The volume of the composite solid is 452. 160 ft³
How to determine the volumeFirst, it is important to note that the formula for calculating the volume of a cone is expressed as;
V = πr²h/3
Such that the parameters of the formula are;
V is the volumer is the radius of the cone.h is the height of the cone.From the information given,
substitute the values
Volume = 3.14 × 6² × 12/3
Divide the values
Volume = 31.4 × 36 × 4
Multiply the values
Volume = 452. 160 ft³
Learn more about cones at: https://brainly.com/question/6613758
#SPJ1
Fill in the blanks below in order to justify whether or not the mapping shown
represents a function.
Set A
co
5
H
The mapping diagram above|
Set B
✓in
-2
3
O
7
શ function since
where there
Answer:
It is not a function
Step-by-step explanation:
A function is a rule from x to y that applies to all elements of x. Every element of x should have one image only.
Here, element "1" has two images 3 and 7. Therefore it's not a function.
When making bread from scratch, the recipe calls for 3/4 cup of water. If you need to make a smaller portion of the recipe, how much water would you need in order to make only 1/9th of the recipe?
Answer:0.67
Step-by-step explanation:
2. Select all the equations that
describe the situation and then
find the solution.
Each notebook contains
60 sheets of paper. Andre
has 5 notebooks. How
many sheets of paper do
Andre's notebooks
contain?
i.y = 60÷5
ii. y = 5 times 60
iii. Y/5 = 60
iv. 5y = 60
Answer: i. y = 60÷5
Step-by-step explanation: If he has 60 sheets of paper and 5 notebooks, it would only make sense to divide the number of sheets by the number of notebooks to get the sum. Which is 12 btw! <33
PLEASE HELP PLEASE ASAP I NEED THIS NOW
The slope-intercept form of the equation is y = 18x.
What is the function in slope-intercept formTo find the function in slope-intercept form, we have to write the general form below as;
y = mx + c
m = slope
c = y-intercept
To find the slope, we need to take two points from the table given;
slope (m) = y2 - y1 / x2 - x1
m = 720 - 450 / 40- 25
m = 18
The slope of the line is 18
we can use this with any point to find the y - intercept
y = mx + c
720 = 18(40) + c
720 = 720 + c
c = 720 - 720
c = 0
The equation of the line in slope-intercept form is y = 18x
b. To determine how far he travelled with 55 gallons of gas
y = 18x
y = 18(55)
y = 990 miles
c. How many gallons will be required to cover 630 miles
y = 18x
630 = 18x
x = 630 / 18
x = 35 gallons
Learn more on slope-intercept form here;
https://brainly.com/question/4074386
#SPJ1