Transforming the function using f(x - h) shifts its graph h units to the right. Here, we have h = -4, so the graph exists shifted 4 units to the left.
What are transforming functions?
The transformations of functions describe how to graph a function that exists moving and how its shape exists being changed. There exist basically three kinds of function transformations: translation, dilation, and reflection.
Let f(x) = x³ be the original function.
When -5 exists added to the y-value, it moves the point on the graph down 5 units. Compared to f(x), g(x) exists 5 units down.
f(x) = (x + 4)³ - 5
= [x- (- 4) ]³ - 5 (shift 4 units in the negative x direction that exists 4 units left)
Transforming the function using f(x - h) shifts its graph h units to the right. Here, we have h = -4, so the graph exists shifted 4 units to the left.
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Emily invests $x at a rate of 3% per year simple interest. After 5 years she has $20.10 interest. I Find the value of x.
The equation be 20.10 = X × 3 × 5/100 then, the value of X = 134.
How to find the value of x?To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
The formula for Simple Interest exists PTR/100,
where, P = Principal
T = Time period in years
R = Rate of interest per annum.
Simple interest = PTR / 100
20.10 = X × 3 × 5/100
simplifying the above equation, we get
20.10 = 15X / 100
15X = 20.10 × 100 = 2010
X = 2010/15 = 134
X = 134.
Therefore, the value of X exists at 134.
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if you double the side length of a cube how does it effect the volume
Step-by-step explanation:
Volume of the cube = Side
Since,
All the sides of the cube are equal
Then if the length of a side of the cube is
increased
So, the side of the cube becomes
Side of the cube = 2 × Side
Assume
Side of the cube be ‘s’
Side of the cube = 2s
Now,
Volume of the cube = 2s × 2s × 2s
Volume of the cube = (2s)
Volume of the cube = 8s
To find how many times the volume of the cube is
increased
The radius of Circle B is 4 centimeters and the
circumference of Circle A is 20 centimeters. Find CD.
[tex]CD=14.37cm.[/tex]
What is a Circle?A circle is made up of all points in the same plane that are equidistant from one another. Only the bordering points make up the circle.The following are a few examples of circles in daily life: the bicycle's wheel. Dinner dish. Coin.A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also the location of points evenly spaced apart from the center. The radius of a circle is measured from the center to the edge.Thales is thought to have developed the first circle-related theorems around 650 BC. The features of circles and issues with inscribing and describing polygons are covered in Book III of Euclid's Elements. Finding a square with the same area as a given circle was one of the issues in Greek mathematics.Find CD:
Let,
[tex]r_{1}[/tex] be a radius of Circle A
[tex]r_{2}[/tex] be a radius of Circle B
Given:
[tex]r=4cm.[/tex]
Circumference: [tex]2\pi r[/tex]
[tex]2\pi r_{1} =20[/tex]
[tex]r_{1} =\frac{10}{\pi }[/tex]
[tex]CD=D_{1} +D_{2}[/tex]
[tex]=2r_{1} +2rx_{2}[/tex]
[tex]=2*(\frac{10}{\pi } )+2*4[/tex]
[tex]CD=14.37cm.[/tex]
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A coordinate grid with 2 lines. The first line passes through (0, negative 5) and (negative 5, 0). The second line passes through (0, negative 5) and (negative 2, 1).
What is the solution to the system of equations?
Answer:
(0, -5)
Step-by-step explanation:
The two different lines have point (0, -5) in common, so the solution is (0, -5).
The probability of winning on an arcade game is 0. 659. if you play the arcade game 30 times, what is the probability of winning exactly 21 times? round your answer to two decimal places
The probability of winning exactly 21 times is:-0.32
Given,
The probability of winning on an arcade game, p = 0.659
Number of times you play arcade game, n = 30
By assuming this as a normal distribution, we get
Mean=μ=30×0.659 =19.77
Standard deviation, σ = [tex]\sqrt{np(1-p)}[/tex]
= [tex]\sqrt{30(0.659)(1-0.659)}[/tex]
≈ 2.60
Let X be a binomial variable
Then, the z score for x = 21 will be:
z = (x - μ) / σ = [tex]\frac{21-19.77}{2.60}[/tex]
≈ 0.47
Now, the probability of winning exactly 21 times
P (x ≥ z) = P (21 ≥ 0.47) = 0.32
Hence the probability of winning exactly 21 times is 0.32
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b. Write an expression equivalent to m+m+m+m that is a sum of two terms.
Type your answer in the box below.
Answer: I believe it is 4m
Step-by-step explanation:
m+m+m+m would be equivalent to 4m which is 4 times m
Step-by-step explanation:
It's like you're adding 1+1+1+1 which equals 4 so that's what I think
Find the midpoint of TU given the endpoints T(21.8, 9.3) and U(7.6, 1.7)
Answer:
Step-by-step explanation:
Remember the midpoint formula:
[tex](\frac{x2+x1}{2},\frac{y2+y1}{2} )\\[/tex]
Substitute in your values
[tex](\frac{7.6+21.8}{2},\frac{1.7+9.3}{2} )\\[/tex]
Solve
[tex](\frac{29.4}{2},\frac{11}{2} )\\(14.7,5.5)\\[/tex]
Answer: (14.7,5.5)
Step-by-step explanation: I got it right on the test...
(1+sinA)2 -(1-sinA)2=4sinA
Expand the binomials.
[tex](x+y)^2 - (x-y)^2 = (x^2 + 2xy + y^2) - (x^2 - 2xy + y^2) = 4xy[/tex]
Now let [tex]x=1[/tex] and [tex]y=\sin(A)[/tex].
20 points please help!!!!!
Answer:
a) Class A has the larger interquartile range.
b) Class A has the highest test score.
c) Class B has higher median test score.
d) Class B has smaller range of test score.
Step-by-step explanation:
a) Inter quartile range (IQR) = upper quartile - lower quartile
Class A: IQR = 79 - 65 = 14
Class B: IQR = 77 - 70 = 7
Class A has larger interquartile range.
b) Class A has the highest test score.
c) Median of class A = 70
Median of class B = 74
Class B has higher median test score.
d) Range is the difference between the highest and lowest score.
Range = highest score - lowest score
Range of Class A = 85 - 62 = 23
Range of class B = 79 - 68 = 11
Class B has smaller range of test score.
If a consumer purchases a combination of commodities x and y such that mux/px = 30 and muy/py = 40, to maximize utility, the consumers should buy.
If [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 then the consumer should buy the commodity y to maximise utility.
Given that [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 of commodities x and y.
Marginal utility is the additional utility that a consumer gets from consuming additional units of commodity. For maximising the utility of the consumer,the ratio of marginal utilities must be equal to the ratio of the products.
There can be two situations in our case:
Because [tex]MU_{x}/P_{x}[/tex]<[tex]MU_{y} /P_{y}[/tex]
So to equalise the ratio we need to reduce [tex]MU_{y} /P_{y}[/tex]. To reduce the utility of y the consumer needs to increase the consumption of y because as the consumption of commodity y increase it decreases the utility of commodity y.
Hence if [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 then the consumer should buy the commodity y to maximise utility.
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PLEASE ANSWER QUICKLY
Answer:
f(x) = 5x - 5
Step-by-step explanation:
f(x) = 5x - 5 is a linear equation as it has no power.
PLEASE HELP ASAP
18. A surveyor intends to create a bridge across a river. There is a tall tree on the other side of the river. He
measures a line down his side of the river for 125 feet. At each side of this line he uses his surveying
equipment to measure the angle to the tree on the other side of the river. At the beginning of the line, the
angle to the tree was 65°10', at the end of the line the angle to the tree is 60°10'. If he wants the bridge to go
from where he started his line to the tree, then how long will the bridge be?
The 125 feet long line and the angles 65°10', and 60°10' obtained from the surveying equipment gives the length of the bridge as approximately 1234.2 feet.
Which rule can be used to find the length of the bridge?Given;
Location of the tree = The other side of the river from the surveyor
Length of the line measured along the river, L = 125 feet
Angle to the tree from the start of the line = 65°10'
1° = 60'
10' = ((1/60)×10)° = (1/6)°
65°10' = (65 + 10/60)° = (65 + 1/6)°
Angle measured at the end of the line, E = 60°10'
Similarly;
E = 60°10' = (60 + 1/6)°
The interior angle, S, of the triangle formed by the tree and the line, at the start of the line is therefore;
Angle S = 180° - (65 + 1/6)° = (114+5/6)° (linear pair angles)
S = (114+5/6)°
From the angle sum property of a triangle, angle formed at the tree, T, is therefore;
T = 180° - ((114+5/6)° + (60 + 1/6)°) = 5°
According to the rule of sines, we have;
l/(sin T) = b/(sin E)
Where;
b = The length of the bridge
Which gives;
124/(sin 5°) = b/(sin (60 + 1/6)°)
b = (sin (60 + 1/6)°) × (124/(sin 5°)) ≈ 1234.2
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PROBLEMS TO SOLVE
Solve the following problems IN PENCIL. You must show ALL WORK. Make sure graphs
have Titles and are properly labeled WITH UNITS:
1. Graph the following sample data set showing the distance covered by a runner
during an 800 meter race.
A graph for the data (time and distance) shown in the given table is plotted in the image attached below.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
What is a linear function?A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
This ultimately implies that, the data of a linear graph are directly proportional and as such as the value on the x-axis increases or decreases, the values on the y-axis also increases or decreases.
In this exercise, you're required to plot a graph for the data (time and distance) that are recorded for an object that is starting from rest.
By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the linear function is given by:
y = 67.814x
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A density graph for all the possible heights between 0 inches and 80 inches is
rectangular. What is the height of the rectangle in this density graph?
OA. 0.04
B. 0.025
C. 0.05
D. 0.0125
Satia drives for 4 hours from a to b. angelique drives at half the speed of safia. find how many hours angelique takes to drive from a to b
Angelique takes 8 hours to drive from a to b.
What is the concept of speed, distance and time?How quickly something or someone is moving is indicated by their speed. If you know how far something travels and how long it takes, you can calculate their average speed. Speed equals distance x times time, according to the speed formula. Knowing the units for distance and time will help you determine what the units are for speed.
According to given Information:let us assume distance from a to b be x units.
let us assume speed of vehicle be y units/hour.
For case -1For Satia, speed=y units time=4 hours we know the formula of distance is:
distance=speed × time distance=(y× 4) units -------------------(1)
For case - 2Angelique :speed=y / 2 units time=?
We know the formula of distance is:
Distance=speed × time distance=(y/2)× time -------------------(2)
We can see that distance in both cases is equal,
So compare case (1) ad (2) ,
We get (y× 4)=(y/2)× time
On rearranging ,
Time= (4×2) hours=8 hours
hence,
Angelique takes 8 hours to cover the distance from a to b.
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A resource comparison of the union and confederacy during the civil war. the title is comparing resources. the data are as follows. for each category, the union percentage is listed first, the confederate percentage, second. horses, 72, 28, food crops, 72, 28, cotton, 1, 99, prewar exports, 30, 70, soldiers, 67, 33, firearm production, 97, 3, railroad tracks, 71, 29, factories, 86, 14, bank deposits, 81, 19, total population, 71, 29 public domain during the civil war, in which resource area did the confederacy hold 28 percent of the total resources? factories food crops soldiers total population
During the Civil War, the North's heavy industrialization provided an advantage.
According to the information:
The distinct economic division between the northern and southern economies played a key role in the Union's Civil War victory. First, the vast capitalist industry was expanding, with a significant concentration of salaried labor, in full force, and on the verge of the Second Industrial Revolution (to which the development of new military technologies, such as battleships and the mass production of weapons, helped to the war. These northern bourgeois sectors were represented by the liberal nationalist new Republican Party, which worked to enact protectionist laws.
On the other hand, the south remained rooted in an economic structure that was adverse to the growth of capitalism (mechanization and hiring of workers were cheaper than the maintenance of slaves). To protect slavery would be the Democratic Party. This party, which had spearheaded the nation's significant southern expansion (pro-Mexican territorial annexation movement), now served as a proxy for the region's elites, who essentially favored the growth of the slave trade and unrestricted trade in manufactured products and raw resources.
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I understand that the question you are looking for is:
A resource comparison of the Union and Confederacy during the Civil War. The title is Comparing Resources. The data are as follows. For each category, the Union percentage is listed first, the Confederate percentage, second. Horses, 72, 28, Food Crops, 72, 28, Cotton, 1, 99, Prewar Exports, 30, 70, Soldiers, 67, 33, Firearm Production, 97, 3, Railroad Tracks, 71, 29, Factories, 86, 14, Bank Deposits, 81, 19, Total Population, 71, 29. Public domain Use the graph and your knowledge of U.S. history to answer the question. Which of these explains the differences in Union vs. Confederate firearm production during the Civil War? The North had a highly skilled labor force to make them. The North's heavy industrialization provided an advantage. The South had fewer men who were trained as metalworkers. The South's means of production were destroyed by General William Tecumseh Sherman.
On the day after my birthday this year, I can truthfully say: "The day after tomoroow is Monday". ON which day is my birthday?
Answer:
Saturday
Step-by-step explanation:
2 days before (starting from Monday) is Saturday
Select the correct answer from each drop-down menu.
A cell phone tower is shown. The edge of the base is 50 feet and the height is 200 feet.
Photograph of a cell phone tower.
What shape best models the object and what is the approximate surface area of that shape?
The best shape for the model is a
.
The approximate surface area is
square feet.
A square pyramid can be defined as a type of pyramid that has a square base, four (4) triangular sides, five (5) vertices, and eight (8) edges.
In this context, we can logically deduce that the geometric shape which best models the object (cell phone tower) shown in the image attached above is a square pyramid.
How to calculate surface area of a square pyramid?Mathematically, the surface area of a square pyramid is given by this formula:
A = a² + 2a√(a²/4 + h²)
Where:
A is the surface area of a square pyramid.a represents the edge of the base.h represents the height.Given the following parameters:
Edge of the base = 50 feet.
Height = 200 feet.
Substituting the given parameters into the formula, we have;
A = 50² + 2(50)√(50²/4 + 200²)
A = 2,500 + 100√(2500/4 + 40,000)
A = 2,500 + 100√(625 + 40,000)
A = 2,500 + 100√(40,625)
A = 2,500 + 100(201.56)
A = 2,500 + 20,156
A = 22,656 ≈ 22,500 ft².
In conclusion, the best geometric shape for the model is a square pyramid and the approximate surface area is equal to 22,500 square feet.
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Answer:The best shape for the model is a square pyramid.
The approximate surface area is 22,500 square feet.
Step-by-step explanation: edmentum/plato answers
Please help me
Prove the following identity. Include a complete proof in proper form
1/1-sin x-1/1+sin x=2 tan x/COS X
By using algebra properties and trigonometric formulas we find that the trigonometric expression [tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] is equivalent to the trigonometric expression [tex]\frac{2\cdot \tan x}{\cos x}[/tex].
How to prove a trigonometric equivalence by algebraic and trigonometric proceduresIn this question we have trigonometric expression whose equivalence to another expression has to be proved by using algebra properties and trigonometric formulas, including the fundamental trigonometric formula, that is, cos² x + sin² x = 1. Now we present in detail all steps to prove the equivalence:
[tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] Given.
[tex]\frac{1 + \sin x - 1 + \sin x}{1 - \sin^{2}x}[/tex] Subtraction between fractions with different denominator / (- 1) · a = - a.
[tex]\frac{2\cdot \sin x}{\cos^{2}x}[/tex] Definitions of addition and subtraction / Fundamental trigonometric formula (cos² x + sin² x = 1)
[tex]\frac{2\cdot \tan x}{\cos x}[/tex] Definition of tangent / Result
By using algebra properties and trigonometric formulas we conclude that the trigonometric expression [tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] is equal to the trigonometric expression [tex]\frac{2\cdot \tan x}{\cos x}[/tex]. Hence, the former expression is equivalent to the latter one.
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What is the Y-Intercept of the line that has a slope of -4 and passes through the point (4,-6)
Answer:
Y-intercept = 22
Step-by-step explanation:
The equation of a line in slope-intercept format is given by the equation y=mx+c
where m is the slope and c the y-intercept.
(The y-intercept is the value of y when x = 0)
Slope given as -4
And we know it passes through the point(4,6) ie at x=4, y =6
Substitute in above equation to get value of c, the y-intercept
6 = -4(4) + c
6 = -16 + c
c = 22
And this is the y-intercept
The equation of the line is y = -4x + 22
See attached figure for graph
Point D is located at 4. Point E is 6 less than Point D. Where is E located?
Answer:
-2
Step-by-step explanation:
<________|____|___-2___|___0___|____|____|____4________>
E D
The Point E is located at -2.
Given that Point D is located at 4. Point E is 6 less than Point D.
We need to find the location of the point E.
Based on the information provided, Point D is located at 4. Now, we know that Point E is 6 less than Point D.
When we say, "less than," it means we need to subtract the given value from Point D to find the location of Point E.
If Point D is located at 4, and Point E is 6 less than Point D, then the location of Point E can be calculated as follows:
E = D - 6
Since D is 4, we can substitute that value into the equation:
E = 4 - 6
E = -2
So, Point E is located at -2.
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Canceling units is also called: a. changing the value c. multiplication b. unit analysis d. making connections
Canceling units is also called unit analysis.
This is also called dimensional analysis.
What is a unit of analysis in statistics?
The unit of analysis is the entity that you're analyzing. It's called this because it's your analysis (what you want to examine) that determines what this unit is, rather than the data itself.Because it is the analysis you do in your study that determines what the unit is. For instance, if you are comparing the children in two classrooms on achievement test scores, the unit is the individual child because you have a score for each child.For example -
1 ft = 12 in
3 ft = [tex]3 ft * \frac{12 in }{1 ft}[/tex]
3 ft = ( 3 * 12 ) in ⇒ 36 in
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ABCD is an isosceles trapezium. Prove that: (1) (2) (3) AC=BD BE = CE AE = DE
is there a picture included in this problem? if so please comment it so i can answer this problem.
Find an equation for the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0)
The equation for the plane through the points p(0, 1, 1), q(1, 0, 1) and r(1, 1, 0) is x + y + z = 2
Given,
Three points :- p(0, 1, 1), q(1, 0, 1), r(1, 1, 0)
We can take this as ([tex](x_{1} ,y _{1}, z_{1} ), (x_{2}, y_{2}, z_{2}), (x_{3}, y_{3}, z_{3})[/tex] respectively.
Thus,
The equation for the plane through the points
Here,
The formula of equation of the plane passing through three non collinear points
[tex]x-x_{1} y-y_{1} z-z_{1} \\x_{2} -x_{1} y_{2} -y_{1} z_{2} -z_{1} = 0\\x_{3} -x_{2} y_{3} -y_{2} z_{3} -z_{2}[/tex]
by substituting the values in the formula of equation of the plane
x-0 y-1 z-1
1-0 0-1 1-1 = 0
1-0 1-1 0-1
x y z
1 -1 0 = 0
1 0 -1
x(1) - (y-1)(-1) - (z-1)(-1) = 0
x + y - 1 + z - 1 = 0
x + y + z + 2 = 0
x + y + z = 2
The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2
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The equation of the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2
For given question,
We have been given three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0)
We need to find an equation for the plane through the given three points.
We know that the equation of the plane through the points [tex](x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)[/tex] is,
[tex]\begin{vmatrix}x-x_1 & y-y_1 & z-z_1\\x_2-x_1 & y_2-y_1 & z_2-z_1\\x_3-x_1 & y_3-y_1 & z_3-z_1\end{vmatrix}=0[/tex]
Assume that for given points,
[tex](x_1,y_1,z_1)=(0, 1, 1)\\\\(x_1,y_1,z_1)=(1, 0, 1)\\\\(x_1,y_1,z_1)=(1, 1, 0)[/tex]
So, the equation of the plane passing though given points would be,
[tex]\Rightarrow \begin{vmatrix}x-0 & y-1 & z-1\\1-0 & 0-1 & 1-1\\1-0 & 1-1 & 0-1\end{vmatrix}=0\\\\\\\Rightarrow \begin{vmatrix}x-0 & y-1 & z-1\\1 & -1 & 0\\1 & 0 & -1\end{vmatrix}=0\\\\\\\Rightarrow x(1-0)-(y-1)(-1-0)+(z-1)(1-0)=0\\\\\Rightarrow x+y-1+z-1=0\\\\\Rightarrow x+y+z=2[/tex]
Therefore, the equation of the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2
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Write an equation of the line that passes through the point (5, -8) with slope 5
[tex]\Large\texttt{Answer}[/tex]
[tex]equation=[/tex][tex]\bold{y=5x-33}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
⇨ Use the formula below
[tex]\bf{y-\hfill\stackrel{y \:co-ordinate}{y1}=\hfill\stackrel{slope}{m}(x-\hfill\stackrel{x\:co-ordinate}{x1)}}[/tex]
⇨ Substitute the parameters:
[tex]\bold{y-(-8)=5(x-5)}[/tex]
[tex]\bold{y+8=5x-25}[/tex]
[tex]\bold{y=5x-33}[/tex]
Hope that helped
how do you solve these two questions and what are the answers?
Answer:
a) -6/2
b) -9/2
Step-by-step explanation:
a) rearrange by making y the subject as y = mx+c
y = -6/2x-9/2
the gradient = -6/2
b) c is the y-intercept as it touch the y-axis, therefore -9/2 is where the line crosses the y-axis
Solve the que in the given picture!
Answer:
a) 20
Step-by-step explanation:
when we have an exponent of an exponent, we simply multiply them for the overall exponent.
so, we actually have
a^((1/4)×12) × b^((1/3)×12) = a³b⁴ = 5000
let's find the prime factors of 5000 :
5000 ÷ 2 = 2500
2500 ÷ 2 = 1250
1250 ÷ 2 = 625
625 ÷ 3 no
625 ÷ 5 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
so,
5000 = 2³ × 5⁴
so, a = 2, b = 5
a²b = 2²×5 = 4×5 = 20
A pizza has a diameter of 18 inches. If the pizza is
cut into 10 equal slices and 6 slices were eaten,
what is the area of the remaining pizza?
Answer:
25
Step-by-step explanation:
Find the surface area of the cylinder and round to the nearest tenth. (It is recommended that you use the π button on your calculator) (Note: Remember the radius is half of the diameter.)
If you are using a screen-reader, please consult your instructor for assistance.
The surface area of the cylinder is 18.84 square feet
How to determine the surface area?The given parameters are
Height, h = 2 ft
Diameter, d = 2 ft
The radius (r) is half of the diameter (d)
This is calculated as:
Radius = Diameter/2
So, we have:
r = d/2
Substitute 2 for d
r = 2/2
Evaluate the quotient i.e. divide 2 by 1
r = 1
The surface area is then calculated using the following formula
A = 2πr² + 2πrh
Substitute the given values in the above equation
So, we have:
A = 2 * 3.14 * 1^2 + 2 * 3.14 * 1 * 2
Evaluate the exponents
A = 2 * 3.14 * 1 + 2 * 3.14 * 1 * 2
Evaluate the products
A = 6.28 + 12.56
Evaluate the sum
A = 18.84
Hence, the surface area of the cylinder with the given height and radius is 18.84 square feet
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Select the correct choice from the drop down.
Elena drank 3 liters of water yesterday. Jada drank 34 times as much water as Elena. Lin drank twice as much water as Jada.
a. Did Jada drink more or less water than Elena?
(b)
Explain how you know Jada drank more or less water than Elena.
Using proportions, it is found that Jada drinks more water than Elena, as her proportion is 3/2 of Elena's proportion.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Jada drank 3/4 the amount x that Elena drank, hence:
J = 3x/4.
Lin drank twice as much water as Jada, hence her proportion relative to Elena is given by:
L = 2J = 2 x 3x/4 = 6x/4 = 1.5x.
1.5x = 50% more than Elena.
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