The temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C.
To work out the temperature at the summit of Ben Nevis, we can use the formula:
Temperature at summit = Sea level temperature - (Altitude above sea level / 100) ×Temperature change per 100 metres
We are given that the sea level temperature is 5°C and the height of Ben Nevis is 1300 metres above sea level, and the temperature decreases by 1°C for every 100 metres above sea level.
So, after putting the values into the formula:
Temperature at summit = 5 - (1300/100) × 1 = -15°C
Therefore, the temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C
To learn more about Temperature:
https://brainly.com/question/25677592
https://brainly.com/question/1726738
Big Ideas Math:
Q1. The graph of which of the following functions does not belong with the other three?
Answer: f(x) = 3x^2 + 24x - 6
Q2. This is the only function that does not have x-intercepts at x= Response and x= Response and a vertex at (Response, Response).
Function 3x²+24x-6 does not belong with the other three
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
From the option we have to simplify each function
a. f(x)=3x²+6x-24
b. f(x)=3x²+24x-6
c. f(x)=3(x-2)(x+4)
=3(x²+4x-2x-8)
=3x²+6x-24
d. f(x)=3(x+1)²-27
3(x²+1+2x)-27
3x²+3+6x-27
3x²+6x-24
So function 3x²+24x-6 does not belong with the other three
Hence, function 3x²+24x-6 does not belong with the other three
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
A cylinder's height equals the diameter of its base. What fraction of the total surface area of the cylinder is the total area of the two bases
If the Cylinder's height equals to the diameter of its base , then the fraction of the total surface area of the cylinder to the total surface area of the two bases is 1/3 .
The curved surface area of the cylinder with height "h" and radius "r" is written as ⇒ [tex]2\pi rh[/tex] ;
the area of the top and bottom of the cylinder is ⇒ [tex]\pi r^{2} + \pi r^{2}[/tex] = [tex]2\pi r^{2}[/tex] ;
the total surface area of the cylinder will be ⇒ [tex]2\pi rh[/tex] [tex]+2\pi r^{2}[/tex] ....equation(1)
it is given that the height of cylinder is equal to the diameter of the base ,
that means ; [tex]h = 2r[/tex]
Substituting the value [tex]h = 2r[/tex] in the equation(1) ,
we get ,
total surface area of cylinder = [tex]4\pi r^{2} +2\pi r^{2}[/tex] = [tex]6\pi r^{2}[/tex]
So , the required fraction is = [tex]\frac{2\pi r^{2} }{6\pi r^{2} }[/tex] ,
On simplifying ,
we get ,
= [tex]\frac{1}{3}[/tex] .
Therefore , the fraction of two bases to the total surface area is [tex]\frac{1}{3}[/tex] .
Learn more about Cylinder here
https://brainly.com/question/23426060
#SPJ4
7. Plumber A charges $60 an hour. Plumber B charges $40 to visit your home plus $55 for each
hour. For how many hours will the total cost for each plumber be the same? How much will that
cost be? If a customer thinks they will need a plumber for 5 hours, which plumber should the
customer hire? Explain.
The total cost will be $480.
What is an Equations?
Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) symbol. It demonstrates how the expressions written on the left and right sides are equivalent. Equations can be solved to find the value of a variable that represents an unknown quantity. If there is no "equal to" symbol in a sentence, it is not an equation. It will be viewed as a phrase.
There should be two equations
For Plumber A = 60x
For Plumber B = 40 + 55x
Now in order to consider the cost to be the same we equate these two equations
60x = 40 + 55x
5x = 40
x = 8 hours
And, the total cost for plumber B is
= 40 + 55(8)
= 480
Hence, The total cost will be $480.
Learn more about equations, by the following link
brainly.com/question/2972832
#SPJ4
How do you tell if a graph is a function and inverse is a function?
If and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f has an inverse (passes the vertical line test).
What is a function?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
The function f has an inverse if and only if the result of reflecting a function's graph about the line y = x is the function's graph (passes the vertical line test).
Therefore, if and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f has an inverse (passes the vertical line test).
Know more about a function here:
https://brainly.com/question/10439235
#SPJ4
The basketball team averaged 68 points per game last season and average 77 points per game this season. What is the approximate percent of the increase
According to question we can say that the approximate percentage of the increase is 13.2352%.
What is percentage?In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Occasionally, the acronyms "pct.," "pct," and "pc" are also used. But it is commonly indicated by the percent sign, "%." The % amount has no dimensions. Percentages are essentially fractions when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it next to it. For instance, you score a 75% if you properly answer 75 out of 100 questions on a test (75/100). Divide the money by the total and multiply the result by 100 to calculate percentages. The formula for calculating the percentage is (value/total) x 100%.
Based on the given conditions, formulate: (77 —68)/ 68
e sum or difference:9/68 = 0.132352
0.132352 x100/100
=13.2352%
To know more about percentage visit:
brainly.com/question/28269290
#SPJ4
1. Calculate the unit rate if you are
shopping and you buy 10 pounds of
bananas for $8.50. What is the
cost per pound?
The cost per pound of bananas is $0.85.
To calculate the unit rate or cost per pound, we divide the total cost by the number of pounds.
You purchased 10 pounds of bananas for $8.50.
To find the cost per pound, we divide the total cost by the number of pounds:
Cost per pound = Total cost / Number of pounds
The total cost is $8.50 and the number of pounds is 10. So we can calculate the cost per pound as follows:
Cost per pound = $8.50 / 10 pounds
To perform the division, we divide the numerator ($8.50) by the denominator (10 pounds):
Cost per pound = $0.85
This means that for every pound of bananas you purchase, it will cost you $0.85.
The unit rate allows you to compare the cost of different quantities.
It tells you that if you want to know the cost of a certain number of pounds of bananas, you can multiply that number by $0.85 to find the total cost.
It's important to note that unit rates are helpful for comparing prices and making informed purchasing decisions, especially when dealing with different quantities or sizes of items.
For similar questions on cost per pound
https://brainly.com/question/23539659
#SPJ8
The cost of a certain cell phone plan can be modeled by C(m) = 2m + 15, where C(m) is the total cost for m minutes of cell phone usage. State the meaning of the slope with respect to the cost associated with the cell phone plan.
The interpretation of the slope is that the cost per minute is $2
How to determine the interpretation of the slope?From the question, we have the following parameters that can be used in our computation:
C(m) = 2m + 15
Where
m = number of minutes
C(m) = cost function
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 2
This means that the slope is 2
And it means that the cost per minute is $2
Read more about linear equations at
brainly.com/question/4074386
#SPJ1
Denise's cell phone plan is $29.95 per month plus $0.10 per minute of call time. Denise's
cell phone bill is $99.95. For how many minutes was she billed?
Answer:
700 minutes
Step-by-step explanation:
Let y represent the cost and x represent the number of minutes of call time
We have the equation
99.95 = 0.10x + 29.95
Now let's solve
99.95 = 0.10x + 29.95
70 = 0.10x
x = 700 minutes
So, she was billed for 700 minutes
If you can, please give me a Brainliest; thank you!
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
18x - 9 = 72 and x = 4.5 represents the same value as 3/5(30x - 15) =72.
What is equation?Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.
Here,
2x – 5 and 13 are expressions
The sign that connects these two expressions is “=”.
Given
x = 4.5
And equation
3/5(30x - 15) =72
Simplifying
90x/5 - 45/5 = 72
18x - 9 = 72 -----------(a)
18x = 81
x = 81/18
x = 4.5 ------------(b)
Equation (a) and (b) are among the equations given in the options.
Hence, from the above calculation equations 18x - 9 = 72 and x = 4.5 express the same value of x as 3/5(30x - 15) =72 .
Learn more about equation here:
https://brainly.com/question/29538993
#SPJ1
How do you check if a function has an inverse function?
We can check if a function has an inverse function using horizontal Line Test.
What is Function?
A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connect
horizontal Line Test
Make f a function. Any horizontal line that crosses the f graph more than once indicates that f lacks an inverse. F does have an inverse if there are no horizontal lines that cross the graph of f more than once.
To Learn more about function from the link:
https://brainly.com/question/10439235
#SPJ4
Suppose a, b, c, and d are constants such that a is not zero and the system below is consistent for all possible values of f and g . What can you say about the numbers a, b, c, and d?
Justify your answer. axı + bx2 = f cxı + dx2 = g
a and d are non-zero and ad = bc for the system to be consistent for all possible values of f and g.
By definition, a system is consistent if there exists a set of solutions that satisfy the equations. In this system, the constants a, b, c, and d are the coefficients of the two equations. Since the system is consistent for all possible values of f and g, then the coefficients must satisfy certain conditions. For example, a and d must both be non-zero in order for the equations to be solvable. Additionally, the coefficients of both equations must be in proportion to each other, meaning that ad must equal bc. This is necessary for the equations to have the same slope, which is necessary for them to be solvable. Thus, we can conclude that a and d are non-zero and ad = bc for the system to be consistent for all possible values of f and g.
Learn more about consistent here:
https://brainly.com/question/29299985
#SPJ4
1/4(12x-20)+3(3x+5) I'm extremally confused I'm supposed to simplify
Answer:
12X+10
Step-by-step explanation:
THAT IS THE SIMPLFY 1-4 x (12x-20)+3(3x+5) Facout our 4 from the expression 1-4 x4 (3x-5)+3(3x+5) Simply the expression cancel out the greatest common factor 4 remove unncessary parntheses if so collect the terms 3x 9x 12x and the solutin is 12x+10
jancie's cheerleading team designed two posters to hang around school to advertise their upcoming competition. the posters were shaped like parallelograms. the smaller of the two posters had a base of 6 1/2 feet and a total area of 16 1/4 feet. the larger poster had a base of 8 1/2 feet and a total area of 34 square feet. how much taller is the larger poster than the smaller poster?
Answer:
1.5 ft
Step-by-step explanation:
The area of a parallelogram is base times height.
So to find the height, you will need to use area/base
Small: 16.25/6.5=2.5 ft
Large: 34/8.5=4ft
4-2.5=1.5ft
All the backpacks at sports galore are on sale at 30% off the marked price. Tracy bought a backpack that was marked $60. What was the sale price?
Answer:
Step-by-step explanation:
we know the 30% off the marked price.
so the sale price is 60-60*30%=42
Answer:$42.00
Step-by-step explanation:
Find the measure of the indicated angle to the nearest degree.
Answer:
57⁰
Step-by-step explanation:
To get the indicated angle we need to use the knowledge of trigonometry.
Since the required angle has both opposite and adjacent sides we use Tangent
Tan ? = opposite/adjacent
= 37/24
= 1.5412
To get the angle we now need to to find the tan inverse of the value we found
Tan inverse of 1.5412
= 57.03⁰
to the nearest degree it will be 57⁰
The table shows pairs of values for the linear function f(x) = 3x
f(x)
-2
1
4
7
10
X
0
1
2
3
4
Which conjecture about linear functions in general is best supported by the
table?
Equal changes in the value of x
result in equal changes in the value
of y.
B. The difference between the x- ar
y-values in each ordered pair (x,
is a constant.
Answer:
the answer is. The answer is
57
Step-by-step explanation:
someone help me plsss
x2 - 3x - 5 = 0 has a unique solution of type -11, which is what the equation entails.
what is discriminant ?The "discriminant" is the value that aids in identifying the many types of solutions when using the quadratic formula to solve a problem. It is a unique function of a co-efficient in a mathematical equation (a quadratic equation), and the value it yields provides details about the roots of the equation. Calculating the discriminant involves square rooting the "b" term and subtracting four times the "a" term from the "c" term. Alongside "D," there is a (delta) that represents discrimination. A quadratic equation with two distinct real number solutions is said to have a positive discriminant. A quadratic equation with a discriminant of zero has repeated real number solutions. Both of the solutions are not real numbers, as indicated by a negative discriminant.
given
x2 - 3x - 5 = 0
D=b2−4ac
D= −32−4×1×5
D=92−20
D= −11
x2 - 3x - 5 = 0 has a unique solution of type -11, which is what the equation entails.
To know more about discriminant visit :-
https://brainly.com/question/15884086
#SPJ1
How do you know if a triangle is right acute or obtuse?
if a²+b²>c², the triangle is acute, if a²+b2²=c², the triangle is a right triangle, and if a²+b²<c², the triangle is obtuse.
where a and b are the lengths of the two shorter sides of the triangle and c is the length of the longest side.
A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle.
An acute triangle has three angles that each measure less than 90°. In an acute-angled triangle, all three internal angles of the triangle are acute, that is, they measure less than 90°.
An obtuse triangle is a triangle with one angle that is greater than 90° degrees, it is not possible for a triangle to have more than one obtuse angle.
To know more about Acute angle:
https://brainly.com/question/26990269
#SPJ4
How do you reflect over Y =- 4?
Select the equation in standard form for the line that passes through (-9, 8) and (1, -12).
A) x + 2y = -20
B) 2x + y = -13
C) 2x+y = 7
D) 2x+y = -10
E) x + 2y = 20
Answer: D
Step-by-step explanation:
Since we are given 2 points, we can use that to find slope, convert to slope-intercept form, and then manipulate it to be standard form. Standard form is ax+by=c.
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-12-8}{1-(-9)} =\frac{-20}{10} =-2[/tex]
With m=-2, we can plug it into slope-intercept form to find the y-intercept.
[tex]y=-2x+b[/tex] [plug in point]
[tex]8=-2(-9)+b[/tex] [multiply]
[tex]8=18+b[/tex] [subtract both sides by 18]
[tex]b=-10[/tex]
With m and b, we can plug in the equation.
[tex]y=-2x-10[/tex] [add both sides by 2x]
[tex]2x+y=-10[/tex]
This gives D as the answer.
How doe etimation help you place the decimal point in a product correctly?Explain
By counting the numbers of figures after the decimal points before you locate the product and shifting the decimal point from the rear to the front in the order you previously counted it after you find the product, an estimation can help you place the decimal point in a product correctly.
What is Estimation?A high number of a certain number is estimated to be the closest whole number or significant number.
When estimating, the use of decimal points aids in separating the fractional portion from the entire figure.
For instance, we have a total of three integers after the decimal point if we want to calculate the product of 4.23 and 2.1.
4.23
× 2.1
4 2 3
________
8 4 6
8 8 8 3
Therefore, we shall move the decimal point three places, working our way from the back to the front.
The result of 4.23 and 2.1 is 8.883 then.
We can therefore say that we completely understand how estimating helps you accurately set the decimal point in a product.
Therefore, by counting the numbers of figures after the decimal points before you locate the product and shifting the decimal point from the rear to the front in the order you previously counted it after you find the product, an estimation can help you place the decimal point in a product correctly.
Know more about whole number visit:
https://brainly.com/question/29766862
#SPJ4
Correct question:
How does estimation help you place the decimal Point in a product correctly?
Given: △ACE,BD¯¯¯¯¯∥AE¯¯¯¯¯ Prove: BACB=DECD A triangle with vertices labeled as A, C, and E, with base A E. Sides C A and C E contain midpoints B and D, respectively. A line segment parallel to base A E is drawn from point B to D. Angle C A E is labeled as 4 and angle C E A is labeled as 3. Angle C B D is labeled as 1 and angle C D B is labeled as 2. Drag an expression or phrase to each box to complete the proof. Statement Reason △ACE,BD¯¯¯¯¯∥AE¯¯¯¯¯ Given Response area Corresponding Angles Postulate △ACE∼△BCD Response area CACB=CECD Definition of similar triangles CA=CB+BACE=CD+DE Segment Addition Postulate CB+BACB=CD+DECD Substitution Property of Equality CBCB+BACB=CDCD+DECD Addition of fractions 1+BACB=1+DECD Simplification of fractions Response area Subtraction Property of Equality
For triangle ACE, if BD ∥AE , then BA/CB = DE/CD is proved.
For given triangle ACE,
BD || AE ...............(Given)
∠4 ≅ ∠1 and ∠3 ≅ ∠2 ..............(Corresponding Angles Postulates)
ΔACE ~ ΔBCD .............(Angle-Angle Similarity Postulate)
CA/CB = CE/CD ............(Definition of similar triangles)
CA = CB + BA, CE = CD + DE ..........(Segment Addition Postulate)
(CB + BA)/CB = (CD + DE)/CD ..........(Substitution Property of Equality)
CB/CB + BA/CB = CD/CD + DE/CD .........(Addition of Fractions)
1 + BA/CB = 1 + DE/CD .............(Siplification of fractions)
BA/CB = DE/CD ...............(Subtraction Property of equality)
Hence proved.
Learn more about triangle here:
https://brainly.com/question/22469440
#SPJ4
Exponential from Two Points (Level 1)
Write an exponential function in the form y = ab* that goes through points (0, 13)
and (2, 325).
a = 13. b^0 = 1, y=a(1), 13 = a 325 = 13(b)^2 b^2 = 325/13 = 25
b = sqr25 = 5 y=13(5)^x is the exponential equation going through the two given points
What is Exponential function?An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.The graphs of all exponential functions have these characteristics. They all contain the point (0, 1), because a0 = 1. The x-axis is always an asymptote. They are decreasing if 0 < a < 1, and increasing if 1 < a. If your function can be written in the form y = a b x , where and are constants, a ≠ 0 , b > 0 , and b ≠ 1 , then it must be exponential. In quadratic equations, your functions were always to the 2nd power. In exponential functions, the exponent is a variableTo learn more about Exponential function refers to:
brainly.com/question/30127596
#SPJ1
The scatter plot shows a hikers elevation above sea level overtime. The equation of the trend line is shown y equals 8.77x plus 686. To the nearest whole number predicted hikers elevation will be at 145 minutes
The predicted elevation of hikers at 145 minutes, based on the trend line equation, y = 8.77x + 686 is 1,958.
What is a trend line equation?A trend line equation is the equation of a linear relationship, represented as y = mx + b.
In this linear equation, y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.
Equation:y = 8.77x + 686, where x = 145 minutes
Therefore,
y = 8.77(145) + 686
y = 1,271.65 + 686
y = 1,957.65
y = 1,958
Thus, after 145 minutes of hiking, hikers' elevation will be 1,958 units.
Learn more about trend line equations at https://brainly.com/question/8241509
#SPJ1
What is the Value of P? 9=p÷9
Answer:
p = 81
Step-by-step explanation:
9 = [tex]\frac{p}{9}[/tex] Multiply both sides by 9
9(9) = [tex]\frac{p}{9}[/tex][tex](\frac{9}{1})[/tex] another name for 9 is [tex]\frac{9}{1}[/tex]
81 = p
At Clara's Beading Boutique, 9 out of the 18 beads on clearance are plastic. What percentage of beads on clearance are plastic?
The percentage of beads on clearance are plastic is 50%.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
So the percentage actually means a part per 100.
Total number of beads = 18
Number of beads which are plastic on clearance = 9
Percentage of beads which are plastic on clearance = (9 / 18) × 100
= (1/2) × 100
= 0.5 × 100
= 50%
Hence 50% of beads on clearance are plastic.
To learn more about Percentage, click here :
https://brainly.com/question/28198460
#SPJ1
a car travels at a constant speed.what does the gradient of a distance-time graph of the car's journey represent?distance the car travelled, the area under the graph,the speed of the car, the acceleration of the car
the speed of the car
=========================================================
Reason:
The term "gradient" is the same as "slope".
Recall that slope = rise/run = (change in y)/(change in x).
The change in y represents how far you travel, as the distance is along the vertical axis. The change in x is the time duration.
Then,
speed = distance/time
which helps show the slope of this distance-time graph is the speed of the car. The steeper the slope, the faster the car.
-------------
An example:
The equation y = 50x has slope 50. The x is the time and y is the distance traveled.
At time x = 0 hours, you have traveled y = 0 miles.
At time x = 1 hour, you have traveled y = 50 miles.
The two points (0,0) and (1,50) are on this line. Use the slope formula to get a slope of 50, which represents the speed of the car in miles per hour (mph). Or note that y = 50x is in the form y = mx+b
m = slope = 50
b = y intercept = 0
Give an example of a quadratic function that has a maximum value. How do you know that it has a maximum value?
An example of a quadratic function that has a maximum value is the parabola defined by the equation y = -(x-3)^2 + 4.
What is quadratic function?A quadratic function is a type of polynomial function that can be written in the form y = ax^2 + bx + c, where a, b, and c are constants and x is the variable. The graph of a quadratic function is a parabola, which can either open upward or downward depending on the value of the leading coefficient (a).
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It is usually written with an "=" sign between the two expressions, such as y = 2x + 3 or x^2 + y^2 = 1. Equations can be used to model real-world situations, and solving an equation means finding the values of the variables that make the equation true.
We can determine that this function has a maximum value by looking at the leading coefficient of the quadratic term (x^2). In this case, the coefficient is -1, which means that the parabola opens downward. Therefore, since the parabola opens downward, the vertex of the parabola is the highest point of the parabola, which means that it is a maximum point.
Also we can find the vertex of the parabola by using the formula x = -b/2a, in this case x= -0 / 2*-1 = 3/2 =1.5, and using this value in the function, we get the y value which is 4, so the vertex is (1.5,4) which confirms that the function has a maximum value at (1.5,4)
To know more about quadratic function visit:
https://brainly.com/question/18958913
#SPJ1
You have four sweaters, five pairs of pants, and three pairs of shoes. How many different combinations can you make, wearing one of each
Therefore, 60 different combinations can be made wearing one of each type
What is Fundamental Counting Principle? If an event can occur in m different ways, and another event can occur in n different ways, then the total number of occurrences of the events is m × n.This video uses manipulatives to review the five counting principles including stable order, correspondence, cardinality, abstraction, and order irrelevance. When students master the verbal counting sequence they display an understanding of the stable order of numbers.Fundamental Principle of Counting helps to determine how selection is done on the basis of available choices. Fundamental Principle of Counting simplifies the approach of selection considering all the possible choices and their combinations for calculating the ProbabilityThe fundamental counting principle states that if there are p ways to do one thing, and q ways to do another thing, then there are p×q ways to do both things. Example 1: Suppose you have 3 shirts (call them A , B , and C ), and 4 pairs of pants (call them w , x , y , and z ). Then you have. 3×4=12.To learn more about Fundamental Counting Principle refers to:
brainly.com/question/10275154
#SPJ4
Kayden has 50 m of railing.
How much more railing does Kayden need
so that he can put railing all the way around
the roof garden?
12 m
3 m
7m
10 m
20 m
10 m
Not drawn accurately
Answer: Kayden needs 12 more meters of railing.
Step-by-step explanation:
To find the perimeter of the roof garden I added up all the numbers you listed (12m+3m+7m+10m+20m+10m) to get a total perimeter of 62 meters.
Since Kayden already has 50 meters of railing we can subtract that from the total he needs to get the remaining amount needed.
62m - 50m = 12 meters of railing remaining.