Answer:
Option C is correct.
Alex earned about $60 more than Joaquin did.
Step-by-step explanation:
The linear regression equation
y = 0.18 x + 320.22
is used to predict the weekly salary, y, of an employee who sells x dollars worth of merchandise.
Joaquin sold $1500 worth of goods. Meaning that x for that week for Joaquin is 1500.
Joaquin' s salary for that week is then given as
y = 0.18x + 320.22
y = 0.18(1500) + 320.22 = 590.22
Hence, Joaquin's salary for that week = $590.22
Alex earns $650 that week. Meaning that y for Alex in that week = 650
y = 0.18x + 320.22
650 = 0.18x + 320.22
0.18x = 650 - 320.22 = 329.78
x = (329.78/0.18) = 1832.1
Hence, Alex sold goods worth $1832.1 that week.
Joaquin sold goods worth $1500
Joaquin earned $590.22
Alex sold goods worth $1832.1
Alex earned $650
From this calculation, it is evident that 'Alex earned about $60 more than Joaquin did' is the correct option as $650 is about $60 more than $590.22
Hope this Helps!!!
Answer:
the answer is C :)
Step-by-step explanation:
Please help! Correct answer only, please! The cafeteria manager at a middle school wanted to keep track of how many student breakfast and lunches were sold on a Monday. A. B. C. D.
Answer:
Hello There Again. The Correct answer is C.
Explanation: Because it shows that the numbers need to be least median then greater of the breakfast lunch.
Hope It Helps! :)
If your customers are satisfied 11 out of 15 times how many are satisfied If 350 people come in on Black Friday
Answer:
257 people are satisfied
Step-by-step explanation:
11/15 is the fraction that are satisfied
11/15 * 350 =256.6(repeating)
Rounding to the nearest whole person
257 people are satisfied
Expression equivelent to 2/5 divided by 6
Answer:
1/15
Step-by-step explanation:
(2/5)/6 = 2/(5*6) = 2/30 = 1/15
A vertical right circular cylindrical tank measures 20 ft high and 12 ft in diameter. It is full of liquid weighing 62.4 lb divided by ft cubed. How much work does it take to pump the liquid to the level of the top of the tank?
Answer:
Step-by-step explanation:
Work done is given as the product of force and distance.
The liquid in the cylindrical tank weighs 62.4 lb/ft^3.
This means that each ft^3 of the tank has 62.4 lb of the liquid.
To find the wight of the liquid in the entire tank, we multiply 62.4 by the volume of the cylindrical tank.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r is its radius and h is its height
The radius of the tank is 6 ft (since its diameter is 12 ft) and its height is 20 ft.
Therefore, the weight of the liquid in the tank is given as:
[tex]V = \pi * 6^2 * 20 = 2261.95 lb[/tex]
This weight is a force.
The height of the tank is 20 ft.
Therefore, the work done in pumping the liquid to the top of the tank is:
W = 2261.95 * 20 = 45239 ft.lb
Draw the image of quadrilateral ABCD under the translation (x,y)→(x+4,y−3)
Answer:
The overall image would be 4 units to the right and 3 units down on the coordinate plane.
Step-by-step explanation:
We do not see an image. But that is okay. (x+4,y-3) means that the x value of each coordinate gets increased by 4 and the y value of each coordinate gets decreased by 3. The overall image would be 4 units to the right and 3 units down on the coordinate plane.
The image would be 4 units to the right and 3 units down on the coordinate plane.
What is translation?In maths, a translation moves a shape left, right, up, or down but does not turn.
Given the translation of quadrilateral ABCD
(x+4,y-3) means that the x value of each coordinate gets increased by 4 and the y value of each coordinate gets decreased by 3.
Hence, The image would be 4 units to the right and 3 units down on the coordinate plane.
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The domain of a function is
Answer:
The domain of a function is the complete set of possible values of the independent variable. In plain English, this definition means: The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
Step-by-step explanation:
I hope this helped ;)
Diego is building a fence for a rectangular garden. It needs to be at least 10 feet wide and at least 8 feet long. The fencing he uses costs $3 per foot. His budget is $120.
Answer:
240
Step-by-step explanation:
8*10=80ft *3= 240 but thats over budget
The total cost to fence the rectangular garden is $108. Diego has enough money to fence the rectangular garden.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Given that, a rectangular garden needs to be at least 10 feet wide and at least 8 feet long.
Now the perimeter of rectangular garden is
2(8+10)
= 36 feet
Total cost of fencing = 36×3
= $108
Diego's budget is $120
Therefore, Diego has enough money to fence the rectangular garden.
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there 2,500 first year students at nicks school. Nick found a brochure from the housing office thats stats 70% of students live on campus. based on the statistics how many students live on campus
Answer:
1750 Students
Step-by-step explanation:
2500*0.7
After Clara ran 8 times around a square field , she covered a distance of 288km. Calculate the area of the field.
Answer:
81 km²
Step-by-step explanation:
so the perimeter of the field is 288 : 8 = 36 km
the perimeter of square is 4 time side
4s = 36
s = 36 : 4 = 9 km
Area = side x side = s²
A = 9² = 81 km²
You are thinking about the things that can go wrong on your trip home over the Thanksgiving break. You have booked a flight with US-Scareways. You know that in 33 percent of the cases the company has canceled the flight you were on. Should such a thing occur, there would be no other air travel option home for you. As a backup, your friend Walter has offered you a ride back. However, you know that Walter only has a seat in his car for you with 88 percent probability. What is the probability of you making it home for the holidays?
Answer:
0.9604 = 96.04% probability of you making it home for the holidays
Step-by-step explanation:
We have these following probabilities:
100 - 33 = 67% probability of the flight happening.
In the 33%, that is, when the flight does not happen, there is an 88% probability that you get the ride with Walter.
What is the probability of you making it home for the holidays?
0.67 + 0.88*0.33 = 0.9604
0.9604 = 96.04% probability of you making it home for the holidays
-8+4(c-9)-5+6c+2c
plz help me out
Answer:
12c-49
Step-by-step explanation:
−8+(4)(c)+(4)(−9)+−5+6c+2c
=−8+4c+−36+−5+6c+2c
Combine Like Terms:
=−8+4c+−36+−5+6c+2c
=(4c+6c+2c)+(−8+−36+−5)
=12c−49
pls mark me brainliest
What is it ansewerr 1/5 of 45
Answer:
9
Step-by-step explanation:
Please mark me brainliest
The right answer is 9.
please see the attached picture for full solution
Good luck on your assignment
The data represents the body mass index (BMI) values for 20 females. Construct a frequency distribution beginning with a lower class limit of 15.0 and use a class width of 6.0. Does the frequency distribution appear to be roughly a normal distribution?
17.7
29.4
19.2
27.5
33.5
25.6
22.1
44.9
26.5
18.3
22.4
32.4
24.9
28.6
37.7
26.1
21.8
21.2
30.7
21.4
Body Mass Index Frequency
15.0 dash 20.9 nothing
21.0 dash 26.9 nothing
27.0 dash 32.9 nothing
Body Mass Index Frequency
33.0 dash 38.9 nothing
39.0 dash 44.9 nothing
Answer:
Given:
Body mass index values:
17.7
29.4
19.2
27.5
33.5
25.6
22.1
44.9
26.5
18.3
22.4
32.4
24.9
28.6
37.7
26.1
21.8
21.2
30.7
21.4
Constructing a frequency distribution beginning with a lower class limit of 15.0 and use a class width of 6.0.
we have:
Body Mass Index____ Frequency
15.0 - 20.9__________3( values of 17.7, 18.3, & 19.2 are within this range)
21.0 to 26.9__________8 values are within this range)
27.0 - 32.9____________ 5 values
33.0 - 38.9____________ 2 values
39.0 - 44.9 _____________2 values
The frequency distribution is not a normal distribution. Here, although the frequencies start from the lowest, increases afterwards and then a decrease is recorded again, it is not normally distributed because it is not symmetric.
The frequency distribution is not a normal distribution because it is not symmetric and this can be obtained through the given data.
Given :
The data represents the body mass index (BMI) values for 20 females.
The frequency distribution begins with a lower class limit of 15.0 and uses a class width of 6.0 are as follows:
Body Mass Index Frequency
15 - 20.9 3
21 - 26.9 8
27 - 32.9 5
33 - 38.9 2
39 - 44.9 2
The frequency distribution is not a normal distribution because it is not symmetric.
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In the previous part, we obtained dy dx = 3t2 − 27 −2t . Next, find the points where the tangent to the curve is horizontal. (Enter your answers as a comma-separated list of ordered pairs.)
x = t^3 - 3t, y = t^2 - 4
Answer:
(27.55, 7.22), (-11.3, 3.21).
Step-by-step explanation:
When is the tangent to the curve horizontal?
The tangent curve is horizontal when the derivative is zero.
The derivative is:
[tex]\frac{dy}{dx} = 3t^{2} - 2t - 27[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]3t^{2} - 2t - 27 = 0[/tex]
So
[tex]a = 3, b = -2, c = -27[/tex]
Then
[tex]\bigtriangleup = b^{2} - 4ac = (-2)^{2} - 4*3*(-27) = 328[/tex]
So
[tex]t_{1} = \frac{-(-2) + \sqrt{328}}{2*3} = 3.35[/tex]
[tex]t_{2} = \frac{-(-2) - \sqrt{328}}{2*3} = -2.685[/tex]
Enter your answers as a comma-separated list of ordered pairs.
We found values of t, now we have to replace in the equations for x and y.
t = 3.35
[tex]x = t^{3} - 3t = (3.35)^{3} - 3*3.35 = 27.55[/tex]
[tex]y = t^{2} - 4 = (3.35)^2 - 4 = 7.22[/tex]
The first point is (27.55, 7.22)
t = -2.685
[tex]x = t^{3} - 3t = (-2.685)^3 - 3*(-2.685) = -11.3[/tex]
[tex]y = t^{2} - 4 = (-2.685)^2 - 4 = 3.21[/tex]
The second point is (-11.3, 3.21).
1. Considere as funções f e g, ambas com domínio Z, dadas por f(x) = x²- 2x e g(x) = x³-1. Associe as colunas e assinale a alternativa que apresenta a sequência correta: * 1 ponto Imagem sem legenda a) C, D, A, B b) A, B, D, C c) D, C, A, B d) A, C, D, B
Answer:
(A)C,D,A,B
Step-by-step explanation:
[tex]f(x) = x^2- 2x\\g(x) = x^3-1[/tex]
a) f(-2)
[tex]f(-2) = (-2)^2- 2(-2)\\=4-(-4)\\=4+4\\=8$ (C)[/tex]
b) g(-2)
[tex]g(-2) = (-2)^3-1\\\=-8-1\\=-9 $(D)[/tex]
c) f(-1)+g(3)
[tex]f(-1) = (-1)^2- 2(-1)=1+2=3\\g(3) = (3)^3-1=27-1=26\\f(-1) + g(3)=3+26\\=29$ (A)[/tex]
d) f(5) : g(2)
[tex]f(5) = (5)^2- 2(5)=25-10=15\\g(2) = (2)^3-1=8-1=7\\f(5) :g(2)=15/7$ (B)[/tex]
Answer:
letra A confia
Step-by-step explanation:
Which represents the reference angle for 3pi/4?
a) 3pi/4
b) Pi/3
c) Pi/4
d) Pi/6
Answer:
(c) Pi/4
Step-by-step explanation:
3pi/4 = (3 x 180) / 4 = 135 degrees
135 degrees is equivalent to (180 degrees - 135 degrees) 45 degrees
45 degrees = Pi/4
Therefore, the reference angle of 3pi/4 is Pi/4
Thus, the correct option is (c) Pi/4
The reference angle for 3π/4 is π/4.
So, the correct answer is c) π/4.
Given is an angle 3π/4, we need to find its reference angle,
The reference angle is the acute angle formed between the terminal side of an angle and the x-axis in the coordinate plane.
To find the reference angle for an angle, you need to consider the position of the terminal side of the angle in the coordinate plane and determine the acute angle formed.
In this case, we are given the angle 3π/4. To find the reference angle, we need to consider the position of the terminal side of this angle.
The angle 3π/4 lies in the second quadrant of the coordinate plane, where both the x-coordinate and y-coordinate are negative.
To find the reference angle, we need to find the acute angle formed by the terminal side with the x-axis. In the second quadrant, this acute angle is formed by the vertical line connecting the terminal side to the x-axis.
If we draw a vertical line from the terminal side of 3π/4, it intersects the x-axis at π/4.
Therefore, the reference angle for 3π/4 is π/4.
So, the correct answer is c) π/4.
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PLEASE HELP ASAPPPP !!! WILL GIVE BRAINLIEST !!!
1. Find the equation of the line through point (4,−7) and parallel to y=−2/3x+3/2.
2. Find the equation of the line through point (−1,4) and parallel to 5x+y=4
3. Find the equation of the line through point (5,4) and perpendicular to y=−4/3x−2
4. Find the equation of the line through point (8,−9) and perpendicular to 3x+8y=4
Answer:
Step-by-step explanation:
Slope of parallel lines are equal.
1) m = -2/3
(4,-7)
[tex]y-y_{1}=m(x-x_{1})\\\\y-[-7]=\frac{-2}{3}(x-4)\\\\y+7=\frac{-2}{3}*x-\frac{-2}{3}*4\\\\y+7=\frac{-2}{3}x+\frac{8}{3}\\\\y=\frac{-2}{3}x+\frac{8}{3}-7\\\\y=\frac{-2}{3}x+\frac{8}{3}-\frac{7*3}{1*3}\\\\y=\frac{-2}{3}x+\frac{8}{3}-\frac{21}{3}\\\\y=\frac{-2}{3}x-\frac{13}{3}[/tex]
2) 5x + y = 4
y = -5x + 4
slope m = -5
(-1,4)
y - 4 = -5(x -[-1])
y- 4 = -5(x+1)
y - 4 = -5x - 5
y = -5x - 5 + 4
y = -5x -1
If two lines are perpendicular, m2 = -1/m1
m1 = -4/3
[tex]m_{2}=\frac{-1}{\frac{-4}{3}}=-1*\frac{-3}{4}=\frac{3}{4}\\[/tex]
(5,4)
[tex]y-4=\frac{3}{4}(x - 5)\\\\y-4=\frac{3}{4}x-\frac{3}{4}*5\\\\y-4=\frac{3}{4}x-\frac{15}{4}\\\\y=\frac{3}{4}x-\frac{15}{4}+4\\\\y=\frac{3}{4}x-\frac{15}{4}+\frac{4*4}{1*4}\\\\y=\frac{3}{4}x-\frac{15}{4}+\frac{16}{4}\\\\y=\frac{3}{4}x+\frac{1}{4}[/tex]
Answer:
3.) is y=3/4x+1/4 That's what i got but i hope this helps.
Step-by-step explanation:
*) The scale on a map is 1 : 25000
How many kilometres on the ground is represented by 9 cm on the map?
Answer:
2.25km
Step-by-step explanation:
a scale of 1 : 25000 means:
1 cm on map ------> equals 25000 cm on ground
hence,
9 cm on map ------> equals 25000 x 9 cm = 225,000 cm = 2.25km on ground
In ΔKLM, the measure of ∠M=90°, MK = 2.7 feet, and KL = 6.6 feet. Find the measure of ∠L to the nearest degree.
Answer:
24.15° = 24° to the nearest degree
Step-by-step explanation:
If we draw the triangle we would see that the KL is the longest side and the hypothenus;
Also MK would-be the height and ML is the base of the triangle.
Since L and M are the angles at the base;
From Trigonometry Sin L = MK/ KL
= 2.7/6.6
L = Sin^{-1} (2.7/6.6)
L = Sin^{-1} (0.4091)
=24.15°
Note : sin a = height/ longest side
= Opposite/hypothenus
Determine the domain of the function in the correct set notation.
f(x) = 2x+6
O {x|x € R, x*–3}
O {x|x ER, x + 3}
O {x|x € R, x† 2}
O {x|x € R, x*-2}
Answer:
{x|x[tex]\in R[/tex]}
Step-by-step explanation:
We are given that a function
[tex]f(x)=2x+6[/tex]
We have to find the domain of the function in the correct set notation.
The given function is linear polynomial .
The linear polynomial is defined for all real values of x.
Therefore, the given function is defined for values of x.
Domain of f is given by
{x|x[tex]\in R[/tex]}
Hence, the domain of the function in the correct set notation is given by
{x|x[tex]\in R[/tex]}
Which of the following describes the translation of the graph of y = x 2 to
obtain the graph of y = -x 2 - 3?
reflect over the x-axis and shift left 3
reflect over the x-axis and shift down 3
reflect over the y-axis and shift down 3
Answer:
reflect over the x-axis and shift down 3
Step-by-step explanation:
The leading coefficient of -1 means the graph is reflected over the x-axis. The addition of -3 to the function means each graphed point is shifted down 3 units from the original.
The graph of y = -x^2 -3 is the result of the transformation ...
reflect over the x-axis and shift down 3
In a missile-testing program, one random variable of interest is the distance between the point at which the missile lands and the center of the target at which the missile was aimed. If we think of the center of the target as the origin of a coordinate system, we can let Y1 denote the northsouth distance between the landing point and the target center and let Y2 denote the corresponding eastwest distance. (Assume that north and east define positive directions.) The distance between the landing point and the target center is then U=sqrt((y1)^2+(y2)^2). If Y1 and Y2 are independent, standard normal random variables, find the probability density function
Answer:
Step-by-step explanation:
From the given data
we observed that the missile testing program
Y1 and Y2 are variable, they are also independent
We are aware that
[tex](Y_1)^2 and (Y_2)^2[/tex] have [tex]x^2[/tex] distribution with 1 degree of freedom
and [tex]V=(Y_1^2)+(Y_2)^2[/tex] has x^2 with 2 degree of freedom
[tex]F_v(v)=\frac{e^{-\frac{v}{2}}}2[/tex]
Since we have to find the density formula
[tex]U=\sqrt{V}[/tex]
We use method of transformation
[tex]h(V)=\sqrt{U}\\\\=U[/tex]
There inverse function is [tex]h^-^1(U)=U^2[/tex]
We derivate the fuction above with respect to u
[tex]\frac{d}{du} (h^-^1(u))=\frac{d}{du} (u^2)\\\\=2u^2^-^1\\\\=2u[/tex]
Therefore,
[tex]F_v(u)=F_v(h-^1)(u)\frac{dh^-^1}{du} \\\\=\frac{e^-\frac{u^-^}{2} }{2} (2u)\\\\=e^-{\frac{u^2}{2} }U[/tex]
Please answer this correctly
Answer:
3769.57
Step-by-step explanation:
the perimeter of semicircle is
P = d + πd/2
251.86 = d + (3.14d/2)
multiply both side with 2
503.72 = 2d + 3.14d
503.72 = 5.14 d
d = 98 miles
d is diameter, then the radius is 98 : 2 = 49
Area of semicircle
A = ½ π r²
A = 0.5 x 3.14 x 49²
A = 3769.57 miles²
Answer: 3769.57 miles²
Step-by-step explanation:
The perimeter of the semi circle is the sum of the curve and the diameter.
Perimeter of curve
[tex]\dfrac{1}{2}C=\dfrac{1}{2}2\pi r\\\\\\.\quad =\pi r\\[/tex]
Diameter of the semi circle = 2r
[tex]P = \pi r+2r\\\\\\251.86=r(\pi +2)\\\\\\\dfrac{251.86}{\pi +2}=r\\\\\\\dfrac{251.86}{5.14}=r\\\\\\49=r[/tex]
Area of the curve
[tex]\dfrac{1}{2}A=\dfrac{1}{2}\pi r^2\\\\\\.\quad =\dfrac{1}{2}(3.14)(49)^2\\\\\\.\quad =\large\boxed{3769.57}[/tex]
Michael is making a big batch of granola bars to bring to his soccer game. The oats in the granola bars contain 568.7 grams of carbohydrates.
A 2-column table with 3 rows titled Nutritional Facts Oats (1 cup). Column 1 has entries Calories, Carbohydrates, Protein. Column 2 has entries 607, 103.4 grams, 26.3 grams.
How many cups of oats did Michael use in his recipe?
0.415 cups
0.55 cups
4.15 cups
5.5 cups
Answer:
5.5
Step-by-step explanation:
From the table; one cup of oat contains 103.4 carbohydrates.
568.7/103.4 = 5.5 cups
PLS HELP 20 POINTS
Find the volume of a pyramid with a square base, where the perimeter of the base is
19.8 m and the height of the pyramid is 24.2 m. Round your answer to the nearest
tenth of a cubic meter.
Answer:197.7m^3
Step-by-step explanation:
Area of base:
B=24.5025
h=24.2
V=1/3(24.5025)(24.2)
197.6535
V≈197.7m^3
Answer:
197.7m
Step-by-step explanation:
Help please! What is the excluded value? no excluded values x = 17 x = 0
Answer:
wrong question hai right question do
Step-by-step explanation:
0
Answer:
0
Step-by-step explanation:
Zero, because you cannot have (0/17)
7. If In 3 = 1.10 and In 6 = 1.79, then In 2
O -2.89
-0.69
O 1.63
0.61
O 0.60
Answer:
Option (2)
Step-by-step explanation:
Given in the question,
ln(3) = 1.10
ln(6) = 1.79
We have to calculate the value of ln(2).
Since ln(6) = ln(3 × 2)
= ln(3) + ln(2) [From the property of logarithm, ln(a×b) = ln(a) + ln(b)]
1.79 = 1.10 + ln(2)
ln(2) = 1.79 - 1.10
ln(2) = 0.69
Therefore, value of ln(2) will be 0.69.
Option (2) will be the answer.
Answer:
The answer is 0.69.
Step-by-step explanation:
evaluate the following expressions when x=-4 and y=4
Answer:
1025/4
Step-by-step explanation:
x^6 - x
---------------
4y
Let x =-4 and y = 4
(-4)^6 - (-4)
---------------
4*4
4096 +4
------------------
16
4100/16
1025/4
The answer is C. 1025/4
Takeisha is placing placemats around a table. Each placemat is 14 inches long and 10 inches wide. The rectangular table is 42 inches long and 48 inches wide. What is the greatest number of placemats that Takeisha can place around the table without overlapping?
welll i kinda don get ur question but ummmm if u say like the graetest number then 48
Select four statements from the invertible matrix theorem and show that all four statements are true or false
This learning module introduced the invertible matrix theorem. This theorem is a collection of 12 equivalent statements. This means that when one statement in the theorem is true, all statements in the theorem are true. Similarly, when one statement in the theorem is false, all statements are false. For your initial post, propose a specific n x n matrix A, where n >= 3. Select four statements from the invertible matrix theorem and show that all four statements are true or false, depending on the matrix you selected. Make sure to clearly explain and justify your work. Also, make sure to label your statements using the notation used in the notes (e.g., part (a), part (f), etc.).
Theorem (The Invertible Matrix Theorem): Let A be an n x n matrix. Then the following statements are equivalent:
A is an invertible matrix.
A is row equivalent to the n x n identity matrix.
A has n pivot positions.
The equation Ax = 0 has only the trivial solution.
The columns of A form a linearly independent set.
The linear transformation x à Ax is one-to-one.
There is an n x n matrix C such that CA = I.
There is an n x n matrix D such that AD = I.AT is an invertible matrix.
Answer:
A) A is an invertible matrix ( TRUE )
B) A is a row equivalent to the n x n identity matrix ( n = 3 ) ( TRUE )
C ) The equation Ax = 0 has only the trivial solution ( TRUE )
D ) The columns of A form a linearly independent set ( TRUE )
Step-by-step explanation:
Assuming a matrix A
[tex]\left[\begin{array}{ccc}1&2&1\\-1&0&3\\4&1&5\end{array}\right][/tex]
det A = 1 [ 0 -3 ] + 2 [12 + 5 ] + 1[-1]
= -3 + 34 -1 = 30 ≠ 0
THEREFORE det A = 30 ≠ 0
Attached is the detailed solution of the given statements above