To transform the graph of g(x) = lnx into the graph of of f(x) = ln(x-4) + 3 we have to translate 4 units to the right and 3 units up.
What is graph transformation?
The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.
As given in the question,
Parent function g(x)=ln x
resultant function f(x)=ln(x-4)+3
By the translation rules :
If f(x) needs to be translated in f(x-h), it mean function shifted right by h unit
and if f(x) needs to be translated in f(x)+k it mean function shifted up by k unit.
As per these rules, graph of g(x) = lnx function shifted right by 4 unit and function shifted up by 3 unit.
Therefore, Translate 4 units to the right and 3 units up.
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Determine whether a relation is a function.
Answer:
so i think id be no
Step-by-step explanation:
if each input value Leads to only one output value that Classify the Relationship as a Function tell me if im wrong
Find the exponential equation that goes through the points (-1, 2) and (2, 128) Bullet point 3
The general form of the exponential function is given by;
[tex]y=f(x)=ab^x[/tex]where a is the initial value and b is any value greater than 0.
If the exponential function goes through the points (-1, 2) and (2, 128) we have;
[tex]2=ab^{-1}\ldots\ldots\ldots\text{.}.1[/tex]And,
[tex]128=ab^2\ldots\ldots\ldots\text{.}.2[/tex]Divide [2] by [1] we have;
[tex]\frac{128}{2}=\frac{ab^2}{ab^{-1}}[/tex]Simplify
[tex]\begin{gathered} 64=\frac{b^2}{b^{-1}} \\ 64=b^2\div b^{-1} \\ 64=b^{2--1} \\ 64=b^{2+1} \\ 64=b^3 \end{gathered}[/tex]Find the cube-root of both sides
[tex]\begin{gathered} \sqrt[3]{64}=\sqrt[3]{b^3} \\ 4=b \\ \therefore b=4 \end{gathered}[/tex]Substitute the value of b = 4 in [2] we get;
[tex]\begin{gathered} 128=ab^2 \\ 128=a(4)^2 \\ 128=16a \\ \text{Divide both sides by 16} \\ \frac{128}{16}=\frac{16a}{16} \\ 8=a \\ \therefore a=8 \end{gathered}[/tex]Substitute the value of a and b in
[tex]f(x)=ab^x[/tex]then we have;
[tex]f(x)=8(4)^x[/tex]Therefore, the exponential function that goes through the points ( -1, 2) and (2, 128) is;
[tex]f(x)=8(4)^x[/tex]Using the paths shown, how long is the shortest route from Hampton to Lexington?
In this case, we have to add mixed numbers to find the shortest path from the shown alternatives. We need to work with mixed numbers, fractions, and even decimals.
To answer this question, we know that:
1. The path from Hampton to Middletown is 8 + 1/4 mi.
2. Now, we have two alternatives to go from Middletown to Campbell:
First, we have a path that is equivalent to 6 + 1/8 mi (direct). On the other path, we need to go from Middletown to Danville, and then to Campbell. The measure of the latter path is then:
[tex]3\frac{3}{8}+3\frac{3}{8}=(3+\frac{3}{8})+(3+\frac{3}{8})=(\frac{8\cdot3+3\cdot1}{8})+(\frac{8\cdot3+3\cdot1}{8})[/tex]Thus, we have:
[tex]\frac{(24+3)}{8}+\frac{(24+3)}{8}=\frac{27+27}{8}=\frac{2\cdot(27)}{8}=\frac{2}{8}\cdot27=\frac{1}{4}\cdot27=\frac{27}{4}[/tex]Which is equivalent to:
[tex]\frac{27}{4}=\frac{24}{4}+\frac{3}{4}=6+\frac{3}{4}=6\frac{3}{4}=6.75mi[/tex]If we compare the measures of the two paths, we have that:
a. The path from Middletown to Campbell (directly) is equal to:
[tex]6\frac{1}{8}=6+\frac{1}{8}=6.125mi[/tex]b. The path from Middletown to Danville, and then from Danville to Campbell is equal to 6.75 miles (it is longer).
Therefore, the shortest path, in this part of the "journey", is equal to 6.125 miles or 6 + 1/8 miles.
Now, the complete measure of the path from Hamptom to Lexington is the sum of:
1. The measure of the path from Hamptom to Middletown (8 + 1/4 miles) plus
2. The measure of the path from Middletown to Campbell (6 + 1/8 miles) (directly) plus
3. The measure of the path from Campbell to Lexington (5 + 3/4 miles).
And this is, numerically, as follows:
[tex](8+\frac{1}{4})+(6+\frac{1}{8})+(5+\frac{3}{4})=8+6+5+\frac{1}{4}+\frac{3}{4}+\frac{1}{8}[/tex][tex]19+\frac{4}{4}+\frac{1}{8}=19+1+\frac{1}{8}=20+\frac{1}{8}=20\frac{1}{8}mi[/tex]We can express the latter result as a fraction as follows:
[tex]20+\frac{1}{8}=\frac{20\cdot8+1\cdot1}{8}=\frac{160+1}{8}=\frac{161}{8}mi[/tex]Therefore, the shortest route from Hamptom to Lexington is:
1. As a fraction:
[tex]\frac{161}{8}mi[/tex]2. Or as a mixed number:
[tex]20\frac{1}{8}mi[/tex][Notice that we sum two fractions with the same denominator above:
[tex]\frac{1}{4}+\frac{3}{4}=\frac{3+1}{4}=\frac{4}{4}=1[/tex].]
What is the range of this relation?
Answer: (-9, -3, -2, 6, 8)
Step-by-step explanation:
Determine the type of triangle that is drawn below.
⇒ ΔVWX is a Scalene triangle because all the sides and all the angle are not equal.
anslating Triangle D. (2 pts.)Figure AFigure BSelect all the true statements.A. Figure A is congruent to Figure BB Figure B is a translation of Figure A.C. Triangle C is congruent to Triangle C.D. Triangle D'is congruent to Triangle D.
According to the problem, the transformation is a translation.
It is important to know that translations are rigid transformations, which means the figures won't change their shape or size. In other words, the images are congruent to the pre-images.
Hence, triangle C is congruent to triangle C', triangle D is congruent to triangle D', but the figures are not congruent because their shape is different.
Therefore, the right answers are B, C, and D.Charlie subtracts two polynomials, 5x^2 – 9x^2, and says that the difference proves that polynomials are not closed under subtraction.Kate argues that the difference does in fact show that polynomials are closed under subtraction. Who is correct? Type only 'Charlie' orKate' as your answer in the box.
Charlie
Here, we want to check if polynomials is closed under subtraction or not
To check this, we proceed either ways, if the answer is same, then it is closed. If otherwise, then it is not
We have;
[tex]\begin{gathered} 5x^2-9x^2=-4x^2 \\ \\ \text{And;} \\ \\ 9x^2-5x^2=4x^2 \end{gathered}[/tex]As we can see, both results are not equal
If subtraction was closed under polynomials, then the results of both should have been equal. This means Charlie is correct.
1.2 where was the Declaration of Independence signed
August 2, 1776, in the Pennsylvania State House.
Step-by-step explanation:After much debate, the Second Continental Congress ultimately agreed to the Declaration of Independence, and then signed it
ame of the
GXIS.
4. Practice: Organizing Information (3 points)
Fill in the blanks.
The factory is operational for at most 12 hours a day. A reasonable domain for
the graph of daily energy use would be <__x___
A domain of the situation is given by:
The factory is operational for at most 12 hours a day.
[tex]0\leq x\leq12[/tex]Answer:
[tex]0\leqslant x\leqslant12[/tex]F(x)=2x and g(x)= sqrt(x+1)Find (fg)(x)
First, let us define what (fg)(x) is:
[tex](fg)(x)=f(x)\times g(x)[/tex]Given:
[tex]f(x)=2x[/tex][tex]g(x)=\sqrt[]{x+1}[/tex]So the solution to (fg)(x) will be:
[tex]\begin{gathered} =2x\times\sqrt[]{x+1} \\ =2x\text{ }\sqrt[]{x+1} \end{gathered}[/tex]WILL GIV BRAINLIEST Fred spent $3.15 on 4 1/2 pounds of peanuts. How much did he pay for each pound of peanuts? write the number sentence that goes with the word problem. Then, write your answer.
Answer:
Fred paid 70 cents per pound.
Step-by-step explanation:
Let c = the cost of one pound of peanuts.
[tex]4.5c = 3.15[/tex]
[tex]c = .70[/tex]
Answer:0.7
Step-by-step explanation:
3.15÷4.5=0.7
Nate and his family plan to take a 2,438 mile cross-country trip this summer.if they drive 85 miles each day ,how many days will they be driving? explain your answer
28.68235294117647 days (29 days ) will be taken by nate and his family to take a cross country trip of 2438 miles .
What is division ?Divide is the polar opposite of multiply. You get four in each group when you divide twelve into three equal groups then multiply three groups of four to create twelve. Determining how many equal groups are formed or how many individuals are in each group following a fair distribution is the fundamental goal of splitting.
Calculationspeed = 85miles / day
distance = 2438
time = 2438 / 85 = 28.68235294117647 days
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Given h(x) = 4x - 4, solve for x when h(x) = 0
Answer: 1
Step-by-step explanation:
Well, what they have asked is to find the zero of this equation, or the value of the variable when the equation is equal to 0.
So, h(x) = 4x-4 = 0
4x = 4
x = [tex]\frac{4}{4}[/tex]
x = 1
1. MOVIES By the end of its first week, a
movie had grossed $2.3 million. By the
end of its sixth week, it had grossed
$6.8 million. Graph the data with the
week on the horizontal axis and the
revenue on the vertical axis, and draw a
line through the points. Then find and
interpret the slope of the line.
10
Revenue (millions of dollars)
OU
0 2 4 6 8 10
Week
A rectangular prism has a width of 4 cm, a height of 3 cm and a depth of 5 cm. What is the volume of the prism?
We have that the equation of the volume of a rectangular prism is:
[tex]V=w\cdot h\cdot d[/tex]in this case, we have the following information:
[tex]\begin{gathered} w=4\operatorname{cm} \\ h=3\operatorname{cm} \\ d=5\operatorname{cm} \end{gathered}[/tex]then, using the formula we have:
[tex]\begin{gathered} V=4\cdot3\cdot5=12\cdot5=60 \\ V=60\operatorname{cm}^3 \end{gathered}[/tex]therefore, the volume of the prism is 60 cm^3
The price for five pounds of
candy is $8. How much does it cost for
one pound?
Answer:
1.60
8/5=1.60
Step-by-step explanation:
Answer: $1.60
Step-by-step explanation: Easy, just divide 8 by 5. 8/5 = 1.6
By completing the square , solve x^2+12x-c=0 where c is a positive constant.
Give your answers in surd form in terms of c.
You must show all your working.
The roots of [tex]x^{2}[/tex] +12x -c = 0 in surd form is -6 ± [tex]\sqrt{c + 36}[/tex]
What is a quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients of [tex]x^{2}[/tex] and x respectively and c is the constant term.
[tex]x^{2}[/tex] + 12x - c = 0
taking c to the other side, we have
[tex]x^{2}[/tex] + 12x = c
adding the square of half the coefficient of x, which is 6
[tex]x^{2}[/tex] + 12x + [tex]6^{2}[/tex] = c + [tex]6^{2}[/tex]
The left side is now a perfect square which can be simplified as [tex](x + 6)^{2}[/tex]
So,
[tex](x + 6)^{2}[/tex] = c + 36
taking the square root of both sides, we have
x + 6 = [tex]\sqrt{ c + 36}[/tex]
Therefore,
x = -6 ±[tex]\sqrt{c + 36}[/tex]
In conclusion, the solution to the equation is x = -6 ±[tex]\sqrt{c + 36}[/tex]
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help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The point of maxima and minima of any function can be known by equating its derivative to zero. The rocket will take 1.5 sec to reach the maximum height and the maximum height is 27 feet.
What is differentiation?The differentiation of a function is defined as the rate change of its value at around a point. It can be written in mathematical form as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric meaning is that it is the slope of the function at a given point.
Given that,
Initial height of the launching pad is 4 feet,
Initial velocity of rocket is 48 feet/sec,
Height of the rocket as a function of time, h(t) = -16t² + 48t + 3
In order to find the time for maximum height equate h'(t) = 0 as follows,
-32t + 48 = 0
⇒ t = 48 / 32
⇒ t = 3 / 2
⇒ t = 1.5
To find the maximum height find h(t) for t = 1.5 as follows,
h(1.5) = -16 × 1.5² + 48 × 1.5 + 3
= -36 + 60 + 3
= -36 + 63
= 27
Hence, the time taken by the rocket to reach the maximum height is 1.5 sec and the maximum height reached is 27 feet.
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Can you please help me out with a question
Given ∠3≅∠13, which lines, if any, must be parallel based on the given information? Justify your conclusion. Responses a∥b, Converse of the Alternate Interior Angles Theorem a is parallel to b, , Converse of the Alternate Interior Angles Theorem c∥d, Converse of the Same-Side Interior Angles Theorem c is parallel to d, , Converse of the Same-Side Interior Angles Theorem c∥d, Converse of the Corresponding Angles Theorem c is parallel to d, , Converse of the Corresponding Angles Theorem not enough information to make a conclusion not enough information to make a conclusion Two horizontal, parallel lines, line c and line d, where line c is above line d. These lines are intersected by two diagonal parallel lines, line a and line b. Line a is to the left of line b. The angles created by each intersection are numbered. From top left, going clockwise, the angles where line a intersects line c are labeled eleven, ten, nine, and twelve. The angles where line b intersects line c are labeled seven, six, five, and eight. The angles where line a intersects line d are labeled fifteen, fourteen, thirteen and sixteen. The angles where line b intersects line d are labeled three, two, one and four.
The order of the arrangement of the angles in the question (see attached drawing based on a similar question on the website, created with MS Word) indicate that the angles ∠3 and ∠13 are congruent. The correct option is therefore;
a║b, Converse of the Alternate Interior Theorem
What are congruent angles?Congruent angles are angles that have the same measure.
The lines that must be parallel, such that ∠3 ≅ ∠13 is indicated by the definition of the relationship between ∠3 and ∠13 as follows;
Statement [tex]{}[/tex] Reason
1. ∠3 ≅ ∠13 [tex]{}[/tex] 1. Given
2. ∠3 and ∠13 are alt int. ∠s[tex]{}[/tex] between a and b 2. Definition
3. Line a is parallel to line b [tex]{}[/tex] 3. Conv of the alt int. ∠s theorem
The lines that must be parallel are line a and line bThe reason for the conclusion is based on the converse of the alternate interior angles theorem as follows;
Angle ∠3 and angle ∠13 are alternate interior angles, which are angles located on the inside and on the opposite sides of the common transversal of two lines.
The converse of the alternate interior angles theorem state that if the alternate interior angles formed between two lines, a and b and their common transversal are congruent, then the two lines, a and b are parallel (a ║ b).
The correct option is therefore;
a ║ b, Converse of the Alternate Interior Angles Theorem
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What is the area of the polygon?
A=
? square units
Answer:
30 square units.
Step-by-step explanation:
Divide the full polygon into two halves. The left half is 5 wide by 5 tall, making the area of the left 25 square units. The right half is 4 wide by 5 tall, and is perfectly cut in half. We can calculate the area normally, and then cut it in half: (5×4)/2 = 10 square units. Add the two polygons together, totalling 30 square units.
What are the rational numbers between 2 & 3
Answer:
The rational numbers between 2 & 3 include:
1. 4120
2. 4220
3. 4320
4. 4420
5. 4520
6. 4620
7. 4720
8. 4820
9. 4920
10. 5020
Step-by-step explanation:
May I have Brainliest please? I am so close to getting my next ranking! I just need 1 more to become an ACE!! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
please help asap if you help i'll give brainilist. Two pieces of metal measure one and one sixth yards and three twelfths yards each. Three times the amount of metal is needed for a project. How many total yards of metal is needed?
four and one quarter yards
four and one sixth yards
one and one quarter yards
one and ten eighteenths yards
Answer:
Step-by-step explanation:
four and one quarter yards. explanation: add 1 1/6 + 3/12 = 1 5/12. now, multiply that by 3.
Using the arithmetic operations the total yards of metal is needed 4(1/4).
What is arithmetic operation?The study and application of numbers in all other branches of mathematics is the focus of the branch of mathematics known as arithmetic operations. In essence, it consists of addition, subtraction, multiplication, and division operations.
According to the given:
First pieces of metal = 1 (1/6)
= 7/6
Then Second pieces of metal = 3/12
Adding both the pieces, we have
=7/6 + 3/12
= (14 + 3)12
= 17/12.
now multiply that by 3.
We get,
= (17/12)3
= 17/4
= 4(1/4)
Using the arithmetic operations the total yards of metal is needed 4(1/4).
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IS THE ANSWER 1, 3, 17, 57 or none of the aboveIf none of the above please write the correct answer!Please answer step by step explanation
ANSWER
None of the above.
EXPLANATION
We want to solve the equation given for x:
[tex]\sqrt[]{x-1+5}=9[/tex]First, simplify the radical:
[tex]\sqrt[]{x+4}=9[/tex]Now, find the square of both sides of the equation:
[tex]\begin{gathered} (\sqrt[]{x+4})^2=9^2 \\ x+4=81 \end{gathered}[/tex]Finally, simplify by subtracting 4 from both sides of the equation:
[tex]\begin{gathered} x=81-4 \\ x=77 \end{gathered}[/tex]Hence, the correct option is "None of the above".
If the distance a runner travels is represented by d(h) = 2√h and the associated time is t(h) = 3√/4h, what is the runner's speed?
s(h) = h√3
s(h) =1/3
s(h) = 12h
s(h) = √ 2/h
Based on the given distance and time, the speed of the runner is s(h) = 8h/√3.
Relationship between time, distance and speed:
The relationship of speed with distance and time is written as,
Speed = Distance x Time
Which describes the distance travelled divided by the time taken to cover the distance will results the speed.
Given,
Here we need to find the runner's speed when the distance a runner travels is represented by d(h) = 2√h and the associated time is t(h) = 3√/4h.
We know that the formula to calculate the speed is,
Speed = Distance / Time
Here we have the value of
distance = d(h) = 2√h
time = t(h) = √3/4h
Now, we have to apply the values on the formula, then we get,
Speed = 2√h / √3/4h
Therefore, the speed of the runner is 8h/√3.
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Please explain cos-cot equations. Then I would like to figure out the rest.If sin θ=3/5 and θ is in quadrant II, thencos(θ)=________ ;tan(θ)=________ ;cot(θ)=_________;sec(θ)=_________;csc(θ)=_________;Give exact values.
Remember that the sine of an angle in a right triangle is equal to the quotient between the side opposite to the angle and the hypotenuse of the triangle.
Since the sine of the given angle θ is equal to 3/5, we can represent θ as part of a right triangle whose hypotenuse has a measure of 5 and the side opposite to θ has a measure of 3:
The length of the side adjacent to θ must be equal to 4 in order to satisfy the Pythagorean Theorem:
[tex]3^2+4^2=5^2[/tex]On the other hand, the cosine of an angle is defined as the quotient between the side adjacent to the angle and the hypotenuse of the triangle. Then, the cosine of θ must be equal to 4/5:
[tex]\cos \theta=\frac{4}{5}[/tex]The rest of the trigonometric relations are defined in terms of the sine and the cosine as follows:
[tex]\begin{gathered} \tan \theta=\frac{\sin \theta}{\cos \theta} \\ \cot \theta=\frac{\cos \theta}{\sin \theta} \\ \sec \theta=\frac{1}{\cos \theta} \\ \csc \theta=\frac{1}{\sin \theta} \end{gathered}[/tex]Since sinθ=3/5 and cosθ=4/5, then:
[tex]\begin{gathered} \tan \theta=\frac{3}{4} \\ \cot \theta=\frac{4}{3} \\ \sec \theta=\frac{5}{4} \\ \csc \theta=\frac{5}{3} \end{gathered}[/tex]help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].
[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]
Directions: Simplify by combining like terms in each of the following expressions.
1. 10s2 + 10s2 - 13st =
2. 13st + - 2st - t2 =
3. x2+ x2 + x3 =
4. 6 x - 6 x + 2 =
5. 24x - 3s - 4t =
6. 86 + 86x - 1 =
7. 4x + 3x - 2 =
8. 7s - 4s + 3s =
9. 12 +11x - 10 x =
10. 12x + 24 x - 3 x - 4 =
11. 16t + 8t - 12t =
12. 17g + 19g - 2g +g =
13. 16 + 16 -16 + 16x =
14. 4s - 3s + 3s =
15. 12t - 11t + t =
(math is my weakest subject pls help 22 points)
A method that is frequently used to make algebraic expressions simpler.
How to simplify expressions?A method that is frequently used to make algebraic expressions simpler.
1. 10s2 + 10s2 - 13st =s*(20s-13t)
2. 13st + - 2st - t2 = 11st-t2
3. x2+ x2 + x3 = 2x2+x3
4. 6 x - 6 x + 2 =2
5. 24x - 3s - 4t =24x - 3s - 4t
6. 86 + 86x - 1 =86x+85
7. 4x + 3x - 2 = 7x-2
8. 7s - 4s + 3s = 6s
9. 12 +11x - 10 x =x+12
10. 12x + 24 x - 3 x - 4 =33x-4
11. 16t + 8t - 12t =12t
12. 17g + 19g - 2g +g =35g
13. 16 + 16 -16 + 16x = 16+16x
14. 4s - 3s + 3s =4s
15. 12t - 11t + t =2t.
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ABCD is a rhombus. Find xA) x = 3B) x = 10 D) x = 5C) x = 2
ANSWER
5
EXPLANATION
The given shape is a rhombus
The sum of interior angles of a rhombus add up to 360 degrees
The opposite angles of a rhombus are equal to each other.
hence, adding up all the interior angles, we have;
[tex]\begin{gathered} 9x+9x+135+135=360 \\ 18x+270=360 \end{gathered}[/tex]collecting like terms, we have;
[tex]\begin{gathered} 18x=360-270 \\ 18x=90 \\ x=\frac{90}{18} \\ x=5 \end{gathered}[/tex]Therefore the value of x is 5
a week before the election, based on a random sample of 1200 voters, the support rate for candidate a is 53%. can we assert, with 95% confidence, that candidate a is winning the election (in other words, his support rate is higher than 50%)?
With 95% confidence, candidate A can win the election within 50.18% and 55.82%.
Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen.
According to the question, n = 1200
The support rate for candidate A ([tex]p_{A}[/tex]) = 53% ≅ 0.53
So, [tex]z_{c}[/tex] for 95% confidence = 1.96
Confidence interval for [tex]p_{A}[/tex]
= ( [tex]p_{A}[/tex] ± [tex]z_{c}[/tex] ([tex]\sqrt{\frac{p_{A}( 1 - p_{A} ) }{n} }[/tex]) )
= ( 0.53 ± 1.96([tex]\sqrt{\frac{0.53(1-0.53)}{1200} }[/tex]) )
= ( 0.53 ± 1.96([tex]\sqrt{\frac{0.53*0.47}{1200} }[/tex]) )
= ( 0.53 ± 1.96([tex]\sqrt{\frac{0.2491}{1200} }[/tex]) )
= ( 0.53 ± 1.96([tex]\sqrt{0.0002075833}[/tex]) )
= ( 0.53 ± 1.96(0.014407751) )
= ( 0.53 ± 0.028239191 )
= ( 0.53 - 0.02823,0.53 + 0.02823 )
= ( 0.50177,0.55823 )
( 0.50177,0.55823 ) ≅ ( 50.18%,55.82%)
Candidate A can win the election between 50.18% and 55.82% with a confidence level of 95%.
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