The linear equation representing the situation is y = 0.75x - 2.25, and according to this equation, the height of the sprout after 14 days would be 8.25 inches.
To create a linear equation that represents the relationship between the height of the bean sprout and the number of days after planting.
Therefore, the slope of the line is:
slope = change in height / change in days = (7.5 - 3) / (13 - 7) = 1.5
The intercept of the line can be found by substituting one of the data points into the point-slope form of a line:
y - y1 = m(x - x1)
where m is the slope, x1 and y1 are the coordinates of one of the data points. We choose the first data point (7, 3):
y - 3 = 1.5(x - 7)
y - 3 = 1.5x - 10.5
y = 1.5x - 7.5
Therefore, the linear equation that represents the relationship between the height of the bean sprout (y) and the number of days after planting (x) is:
y = 1.5x - 7.5
To find the height of the sprout after 14 days, we substitute x = 14 into the equation:
y = 1.5(14) - 7.5
y = 10.5
Therefore, the height of the sprout after 14 days is predicted to be 10.5 inches.
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can someone please help me
Find the area of each shaded region.
Round the answer to two decimal places.
show work
The length of the arc XY = 6.28yards
The area of shaded part = 12.57yards²
Define the term arc length of circle.The arc length of a portion of a circle's circumference is the length of the curved line that makes up that portion of the circle. Formula:
Arc length = [tex]\frac{(angle subtended by the arc)}{360}[/tex] × (circumference of the circle)
Area of portion = [tex]\frac{(angle subtended by the arc)}{360}[/tex] × (area of circle)
Part 7: Given that, r = 4yards and Ф = 90°
So, The length of the arc XY = [tex]\frac{90^{o} }{360^{o} }[/tex] × 2π × 4yards = 2π = 6.28yards
The area of shaded part = [tex]\frac{90^{o} }{360^{o} }[/tex] × π × (4yards)² = 4π = 12.57yards²
Part 8: Given that, r = 19ft and Ф = 300°
So, The length of the arc ST = [tex]\frac{300^{o} }{360^{o} }[/tex] × 2π × 19ft = [tex]\frac{95}{3}[/tex]π = 99.48ft
The area of shaded part = [tex]\frac{300^{o} }{360^{o} }[/tex] × π × (19ft)² = [tex]\frac{1805}{6}[/tex]π = 945.09ft²
Part 9: Given that, r = 4inch and Ф = 315°
So, The length of the arc EF = [tex]\frac{315^{o} }{360^{o} }[/tex] × 2π × 4inch = 7π = 21.99inch≅22inch
The area of shaded part = [tex]\frac{315^{o} }{360^{o} }[/tex] × π × (4inch)² = 14π = 43.98inch²
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4 to the 3 power, x 4 to the 4th power, divide by 4 to the 9th power
Answer:
We can simplify the expression as follows:
4^3 * 4^4 / 4^9
First, we can simplify the terms in the numerator by adding the exponents of 4:
4^3 * 4^4 = 4^(3+4) = 4^7
Now, we can substitute this value in the expression:
4^7 / 4^9
To divide powers with the same base, we can subtract their exponents:
4^(7-9) = 4^(-2)
Therefore, the simplified expression is:
4^3 * 4^4 / 4^9 = 4^(-2)
So, the final answer is 1/16 or 0.0625.
solve for x.
find m∠HJB
you'll get 50 points!!!
A bag of 100 marbles contains an equal amount of marbles that are blue, green, red, yellow, and orange. If one marble is pulled at random from the bag, the probability that it is a green marble is
Suppose you roll two number cubes and find the probability distribution for the sum of the numbers. Which two sums have the same probability distribution and would be represented with equal bars on a bar graph? 4 and 11 2 and 12 5 and 10 6 and 9
The sum of two dice has a total of 36 possible outcomes. The sum can range from 2 (rolling a 1 on each die) to 12 (rolling a 6 on each die).
To find the probability distribution, we can make a table that lists all the possible sums, the number of ways to obtain each sum, and the corresponding probability.
Sum Ways to obtain Probability
2 1 1/36
3 2 2/36 = 1/18
4 3 3/36 = 1/12
5 4 4/36 = 1/9
6 5 5/36
7 6 6/36 = 1/6
8 5 5/36
9 4 4/36 = 1/9
10 3 3/36 = 1/12
11 2 2/36 = 1/18
12 1 1/36
From the table, we can see that the sums 6 and 9 have the same probability distribution, and would be represented with equal bars on a bar graph
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3 Find the area of the figure
below.
r = 4 in
Based on the information we can infer that the area of the image is: 50.24 in²
How to find the area of the figure?To find the area of the figure we must take into account that this figure is a circle. To find the area of this figure we must use the following mathematical formula:
A = πr²
Then we must replace the values and find the result, the formula would look like this:
A = π4²
A=3.14*4²
A=3.14*16
A = 50.24in
According to the above, the area of the circle would be 50.24 in. Additionally, we learned the formula for circle area.
Note: This question is incomplete; here is the missing information:
Find the area of the figure below.
r = 4 in
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Pack of card has 52 cards, how many cards in 36 packs?
Answer:
1872 cards
Step-by-step explanation:
1 cards=52
36×52
=1872 cards
what is the area of the figure below some help me show the work ;(!
Answer:
[tex]\large\boxed{\mathtt{Area = 586.2cm^{2}.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the area of this figure.}[/tex]
[tex]\textsf{In order to make this simpler, draw a line between the rectangle, and the semi-circle.}[/tex]
[tex]\textsf{We should identify the formulas needed for the areas of the rectangle, and semi-circle.}[/tex]
[tex]\large\underline{\textsf{For the Semi-Circle:}}[/tex]
[tex]\mathtt{Area = 1/2( pi(radius)^{2}).}[/tex]
[tex]\large\underline{\textsf{For the Rectangle:}}[/tex]
[tex]\mathtt{Area = Length \ x \ Width.}[/tex]
[tex]\textsf{Let's find the area of the Rectangle first.}[/tex]
[tex]\mathtt{Area = 15 \ x \ 24}[/tex]
[tex]\mathtt{Area = 360cm^{2}.}[/tex]
[tex]\textsf{For the Semi-Circle, the radius is 1/2 of the Diameter. (24)}[/tex]
[tex]\mathtt{Area = 1/2( pi(12)^{2}).}[/tex]
[tex]\mathtt{Area = 1/2(144 \pi).}[/tex]
[tex]\mathtt{Area = 72 \pi.}[/tex]
[tex]\mathtt{Area \approx 226.2cm^{2}.}[/tex]
[tex]\textsf{Add the areas together to represent the area of the figure.}[/tex]
[tex]\large\underline{\textsf{Add:}}[/tex]
[tex]\mathtt{360cm^{2} + 226.2cm^{2} = 586.2cm^{2}. }[/tex]
[tex]\large\boxed{\mathtt{Area = 586.2cm^{2}.}}[/tex]
Beginning inventory is &12,000 the purchase are $20,000 the ending inventory is $14,000 and other credits are $2,000 what is the actual food cost
Answer:
the actual food cost is $20,000.
Step-by-step explanation:
To calculate the actual food cost, we need to use the following formula:
Actual Food Cost = Beginning Inventory + Purchases - Ending Inventory + Other Credits
Substituting the given values in the formula, we get:
Actual Food Cost = $12,000 + $20,000 - $14,000 + $2,000
Actual Food Cost = $20,000
Therefore, the actual food cost is $20,000.
PLEASE HELP ASAP THANK YOU
On Tuesday, a local hamburger shop sold a combined total of 408
hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Tuesday?
The number of hamburger sold on Tuesday is 136.
How to find the number of hamburgers sold on Tuesday?On Tuesday, a local hamburger shop sold a combined total of 408
hamburgers and cheeseburgers. The number of cheeseburgers sold was
two times the number of hamburgers sold.
Therefore, the number of hamburger sold on Tuesday can be calculated as follows:
Let
x = number of hamburger
y =number of cheeseburger
Therefore,
x + y = 408
2x = y
x + 2x = 408
3x = 408
divide both sides by 3
x = 408 / 3
x = 136
Therefore,
number of hamburger = 136
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Find the average rate of change of the function on the interval, specified for real number b ???
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 6x^2-7 \qquad \begin{cases} x_1=1\\ x_2=b \end{cases}\implies \cfrac{f(b)-f(1)}{b - 1}[/tex]
[tex]\cfrac{[6(b)^2-7]~~ - ~~[6(1)^2-7]}{b-1}\implies \cfrac{6b^2-6}{b-1}\implies \cfrac{6(b^2-1)}{b-1}\implies \cfrac{6(b^2-1^2)}{b-1} \\\\\\ \cfrac{6(b-1)(b+1)}{b-1}\implies 6(b+1)[/tex]
3x=42 round to the nearest hundredth
Answer:
42 /3 = x
Step-by-step explanation:
it is 14 for sure.....
What is the solution?
The solution to the system of equations on the graph is (1, 5)
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have two lines that intersect at a point
Using the above as a guide, we have the following:
The point of intersection of lines in a graph is the solution to the graph
In this case, they intersect at (1, 5)
So, the solution is (1. 5)
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Complete question
Given the system of equations represented by the graph
What is the solution?
Find the difference quotient of:
f (x) = -3/√x
Therefore , the solution of the given problem of function comes out to be [-3√x + 3√(x + h)] / h / √x√(x + h).
What is function?Every subject will be covered, including created and real locations as well as algebraic variable design, in the midterm test questions. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input.
Here,
A function's difference quotient, f(x), is provided by:
=> [f(x+ h) - f(x)] / h
where h denotes a slight modification to the x-value.
The difference quotient for the function f(x) = -3/x can be calculated as follows:
=> [f(x + h) - f(x)] / h
=> [-3/√(x + h) + 3/√x] / h (substituting x + h for x in the function)
=> [-3√x + 3√(x + h)] / [h√x√(x + h)] (finding a common denominator and combining the terms)
=> [-3√x + 3√(x + h)] / h / √x√(x + h) (dividing by the denominator)
Therefore, the difference quotient of f(x) is:
=> [-3√x + 3√(x + h)] / h / √x√(x + h)
The difference fraction of f(x) is thus:
=> [-3√x + 3√(x + h)] / h / √x√(x + h)
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The width of a rectangle is 2 units less than the length. The area of the rectangle is 24 square units. What is the length, in units, of the rectangle?
The width of a rectangle is 2 units less than the length. The area of the rectangle is 24 square units. The length of the rectangle is 6 units.
Let's denote the length of the rectangle as L and the width as W. According to the given information, the width is 2 units less than the length, so we can express this relationship as:
W = L - 2
The formula for the area of a rectangle is A = L * W, and in this case, the area is given as 24 square units. Substituting the values, we have:
24 = L * (L - 2)
Expanding the equation, we get:
24 = L^2 - 2L
Rearranging the equation and setting it equal to zero, we have:
L^2 - 2L - 24 = 0
We can now factor the quadratic equation:
(L - 6)(L + 4) = 0
Setting each factor equal to zero, we have two possible solutions:
L - 6 = 0 or L + 4 = 0
Solving each equation, we find:
L = 6 or L = -4
Since the length cannot be negative, the length of the rectangle is 6 units.
The length of the rectangle is 6 units.
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please helpp!!! A sum of money was shared among three children John, Bob and Henry in the ratio 3:2:1 respectively. If Bob's share was $1 000, how much was John's share?
$1500
Step-by-step explanation:
if $1000 is equal to 2 parts then .....1 part is given by 1000÷2 =500
so John's share is given by 3x500
1500
Multiply the complex’s numbers
(7-2i)(1+3i)
The multiplicatiοn οf the cοmplex number is 13+19i.
What is cοmplex number?Cοmplex numbers are the numbers that are stated in the fοrm οf a+ib where, a,b are real numbers and I is an imaginary number termed "iοta".
Cοmplex numbers allοw sοlutiοns tο all pοlynοmial equatiοns, even thοse that have nο sοlutiοns in real numbers. Mοre precisely, the fundamental theοrem οf algebra asserts that every nοn-cοnstant pοlynοmial equatiοn with real οr cοmplex cοefficients has a sοlutiοn which is a cοmplex number.
Here the given cοmplex number is ,
=> (7-2i)(1+3i)
Nοw simplifying the expression then,
=> [tex]7\times1+7\times3i-2i \times1 -2i \times3i[/tex]
=> 7+21i-2i-[tex]6i^2[/tex]
=> 7+19i -6(-1) [[tex]i^2=1[/tex]]
=> 7+19i+6
=> 13+19i
Hence the multiplication of cοmplex number is 13+19i.
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Abdul bought 24 pounds of rice for $12. How many dollars did he pay per pound of rice?
Answer:
Abdul paid $0.50 per pound of rice ($12 divided by 24 pounds).
A quiz consists of 60 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers?
Answer: √910 . 0.5 . 0.5= √227.5≈ 15.08.
Step-by-step explanation: The number x of correct guesses in n=910
trials is a binomial random variable with probably p= 0.5 of success. The standard deviation of such a variable is √np(1 -- p ). In this case, that's √910 . 0.5 . 0.5=√227.5≈ 15.08.
Such a variable would be well modeled by a normal distribution with mean np= 910 . 0.5= 455 and standard deviation √222.75 ≈ 15. using the 68-95.99.7 rule-of-thumb , about 68% of the people who guessed on such a exam would score between 440 and 470, about 95% of such people would score between 425 and 485, and about 99.7% of such people would score between 410 and 500
(Q: 8) find the value of p in this proportion show where below answer here P=
Answer:16
Step-by-step explanation:
10/p=5/8
can be shown as
1/p=5/80
p=80/5=18
Answer:
[tex]P=16[/tex]
Step-by-step explanation:
Given
[tex]\frac{10}{P} =\frac{5}{8}[/tex]
We can use cross multiplication to find the value of [tex]P[/tex].
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
Following these steps we can evaluate [tex]P[/tex].
[tex]10*8=5P[/tex]
Multiply [tex]10[/tex] by [tex]8[/tex].
[tex]80=5P[/tex]
Divide both sides of the equation by [tex]5[/tex]. [tex]P[/tex] cancels out on the right side.
[tex]\frac{80}{5} =\frac{5P}{5}[/tex]
[tex]\frac{80}{5} =P[/tex]
Divide [tex]80[/tex] by [tex]5[/tex].
[tex]16=P[/tex]
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1. In the Khan academy video, the ratio of boys to girls is 2 : 3. What is the ratio of boys to girls if there are 40 students in the classroom?
Answer: ____
a) 8 : 12 b) 10 : 5 c) 20 : 40 d) 16 : 24
Answer:
16:24
Step-by-step explanation:
The ratio of boys to girls is 2 : 3
total of the ratio is 5
∴ fraction of the class are boys = 2/5
and the girls= 3/5
Ratio of boys =( 2/5)×40=16
Ratio of girls=3/5 ×40 =24
you draw two marbles without replacement from a bag containing 3 green marbles and 4 black marbles the number of possible outcomes in the sample spaces
The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be there are 21 pοtential οutcοmes in the sample space.
What is an unitary methοd?One may use this cοmmοn cοnvenience, already-existing variables, οr all impοrtant elements frοm the οriginal Bishοp custοmizable questiοn that adhered tο a particular methοd tο achieve the gοal. If sο, there will be anοther chance tο get in tοuch with the οbject. If it dοesn't, all οf the crucial elements that make up an expressiοn prοοf οutcοme will be lοst.
Here,
Using the fοrmula fοr the number οf cοmbinatiοns, we can determine hοw many pοssibilities are pοssible in the sample space:
=> nCk = n!/(k!*(n-k))!
where k is the number οf οbjects being selected, and n denοtes the οverall number οf οbjects in the set.
As there are 7 marbles in the cοntainer, we want tο select 2 οf them, sο n = 7 and k = 2.
the sample space has the fοllοwing amοunt οf οutcοmes that cοuld οccur:
=> 7C2 = 7! / (2! * (7-2)!)
=> 21
Therefοre, when twο marbles are drawn frοm the given bag withοut a replacement, there are 21 pοtential οutcοmes in the sample space.
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Complete Question:
'You draw two marbles without replacement from bag containing three green marbles and four black marbles_ The number of possible outcomes in the sample space is'
Find the value of an in the parallelogram shown to the right. Note that the figure is not drawn to scale.
59°
(2a+27)°
The value of a in the given parallelogram such that 2a + 27 and 59 are opposite angles is 16
Finding the value of a in the parallelogramGiven the attached parallelogram
Opposite angles in a parallelogram are equal in measure.
This property is known as the "Opposite Angles Property" or "Alternate Angles Property" of a parallelogram.
So, we have
2a + 27 = 59
Evaluating the like terms, we have
2a = 32
Divide both sides by 2
a = 16
Hence, the value of a is 16
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Please help me solve this problem
In this case, the preferred alternative is Alternative 1, since it has a present value of $60,623.
What is an investment?An investment is the use of money to buy assets or take part in activities with the expectation of a financial gain or other benefit in the future. It can take many forms, such as purchasing shares, bonds, mutual funds, real estate, artwork, or antiques.
The present value of an investment can be calculated by taking the amount of the future cash flow and discounting it by an appropriate rate of return. In this case, the appropriate rate of return is 15%. The present value of Alternative 1 can be calculated by taking the total cash flows of $105,000 and discounting them by 15%:
Present Value of Alternative 1 = $105,000 / (1 + 0.15)3 + (1 + 0.15)7 = $60,623
The present value of Alternative 2 can be calculated in the same manner:
Present Value of Alternative 2 = $8,000 / (1 + 0.15)7 = $4,923
The discounted cash flow criterion states that the preferred alternative is the one with the higher present value. Therefore, in this case, the preferred alternative is Alternative 1, since it has a present value of $60,623 compared to the present value of Alternative 2, which is $4,923.
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Based on her past experiences, a homeowner estimates that appliances lose 27% of their
resale value each year. If her estimate is accurate, how much will an appliance currently
valued at $1,128 be worth in 10 years?
Step-by-step explanation:
If the LOSE 27% per year, they RETAIN 100- 27 = 73% (.73 in decimal) per year
after ten years :
$ 1128 ( .73)^10 = $48.48
Answer:
$48.48
Step-by-step explanation:
Using compound depreciation
time
amount × percentage^
10
1128 × 0.73^ =48.477
I need help please!!!
The amount that would be in the account after 20 years would be $33,277.48.
The doubling time of the emissions would be 23.45 years
The total emissions will be higher in 2030 than 2010 by 100.96%
How to find the amount after years of investment ?To find the amount in the account after 20 years, we can use the formula:
A(t) = P(1 + r)^t
Take the 12th root of both sides:
(1 + r) = 2^(1/12)
Now find r:
r = 2^(1/12) - 1 ≈ 0.05946
Now we can find the amount in the account after 20 years with the investment of $10,000:
A(20) = 10000(1 + 0.05946)^20
A(20) = $33,277.48
How to find the doubling time ?To find the doubling time for emissions, we can use the formula:
Doubling time = ln(2) / ln(1 + r)
Doubling time = ln(2) / ln(1 + 0.03)
Doubling time = 23.45 years
To find how much higher total emissions will be in 2030 than in 2010, we can use the exponential growth formula:
E(t) = E₀(1 + r)^t
We want to find the ratio of emissions in 2030 to emissions in 2010:
E(20) / E(0) = (1 + 0.03)^20
E(20) / E(0) ≈ 2.0096
Higher emissions = E(20) / E(0) - 1
Higher emissions ≈ 1.0096
So, total emissions will be approximately 100.96% higher in 2030 than in 2010.
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Meals is making a new book cover before giving their favorite picture book to their little brother.
The width of the book cover made by Meals for his brother is 40 cm.
What is area?An area is just a surface that is free of objects. With a shape's length and breadth, one may compute the area of the object. Measured in terms of feet (ft), yards (yd), inches (in), etc., length is a one-dimensional quantity. The size of a form, however, is a two-dimensional measurement. Because of this, it is measured in square units like square inches (in2), square feet (ft 2), square yards (yd2), etc. Corners and edges are present on the majority of items and forms. Calculating the area of a certain form takes into account the length and breadth of these edges.
The area of the rectangle is:
A = lw
Given that the area is 890 cm and the height is 22 1/4 cm.
890 = (22 1/4)w
22 1/4 = (4 * 22 + 1) / 4 = 89 / 4
890 = (89 / 4)w
w = 40
Hence, the width of the book cover is 40 cm.
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The complete question is:
7. Compare the slope in each of the equations
below. Circle the equation that has a greater
rate of change. Show all work.
-9x + 3y = 27
-3x + 4y = 24
The slope of the equation -9x + 3y = 27 is greater and this line has a greater rate of change.
What is rate of change?The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one thing by the equal amount of change in another. In the slope-intercept form for a line, the rate of change m for a linear function is written as y=mx+b, whereas the rate of change of functions is defined as (f(b)-f(a))/b-a.
The standard equation of the line is given as:
y = mx + c
where, m is the slope of the line.
For the given equation of lines, transform them into standard equation:
-9x + 3y = 27
3y = 9x + 27
Divide both sides of the equation with 3:
y = 3x + 9
Here, the slope of the equation is 3.
For, -3x + 4y = 24
4y = 3x + 24
Divide both sides of the equation by 4:
y = 3/4x + 6
The slope of this line is 3/4.
Comparing the slope of the two lines we see that,
3 > 3/4
Hence, the slope of the equation -9x + 3y = 27 is greater and this line has a greater rate of change.
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b. Find the quadratic equation whose roots are aß² and a²ß. If a and b
are the roots
of the quadratic equation x^2- 3x + 2 = 0
The quadratic equation is; x^2 -6x + 8 = 0
What is a quadratic equation?A quadratic equation is a mathematical equation of the form ax^2 + bx + c = 0, where x is the unknown variable, and a, b, and c are constants (numbers). The exponent of x in the equation is 2, which means it is a second-degree polynomial equation.
We know that the solution of x^2- 3x + 2 = 0 is x = 2 and x = 1 hence;
α = 2, β = 1
We have that;
αβ^2 = 2
α^2β = (2)^2(1) = 4
The equation would now be;
x^2 - (2 + 4)x - (2 * 4) = 0
x^2 -6x + 8 = 0
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please help im begging you!
Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:
Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
.
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below.
Below given are the steps to copy the original triangle using only two of its sides and the included angle.
What is triangle?It is a fundamental geometric shape in mathematics and has many applications in science, engineering, and everyday life. They can be classified based on the lengths of their sides and the measures of their angles.
Using point E as the center, draw a circle with a radius equal to the length of n×CA that was calculated in part B.
Using point E as the vertex, draw a ray DE in the direction of one of the sides of the angle to be copied (in this case, ∠BCA).
Create an angle at point E that is equal to the measure of ∠BCA. To do this, place the point of a compass at point E and adjust the compass to the length of segment CA. Then, draw an arc that intersects both sides of the ray DE. Without changing the width of the compass, place the compass at point C and draw an arc that intersects the previous arc. Draw a line connecting point E to the intersection of the two arcs to create an angle that is equal to ∠BCA.
Draw ray ED' from point E through the intersection of the two arcs.
Locate the intersection of ray ED' and the circle drawn in step 1. Label this point F.
Draw a polygon through points D, E, and F to complete the copied triangle, which is ΔDEF.
The resulting triangle ΔDEF will be a copy of the original triangle, with side EF corresponding to the included angle and sides DE and DF corresponding to the sides used to construct the copy.
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