Answers
On performing the given row-operation on the given augmented-matrix:
(a) multiplying row1 by -2 and adding to row2, we have [tex]\left[\begin{array}{ccc}5&-2&6\\-10&10&-15\end{array}\right][/tex],
(b) interchanging row1 and row2, we have [tex]\left[\begin{array}{ccc}0&6&-3\\5&-2&6\end{array}\right][/tex],
(c) Multiplying row1 by 2, the matrix becomes [tex]\left[\begin{array}{ccc}10&-4&12\\0&6&-3\end{array}\right][/tex].
The augmented matrix on which we have to perform the row operation is
⇒ [tex]\left[\begin{array}{ccc}5&-2&6\\0&6&-3\end{array}\right][/tex],
Part(a) : We have to multiply row1 by -2 and and add to row2,
The row-operation is performed as : [tex]\left[\begin{array}{ccc}5&-2&6\\(5\times-2)+0&(-2\times-2)+6&(6\times-2)-3\end{array}\right][/tex];
Simplifying further ,
We get,
[tex]\left[\begin{array}{ccc}5&-2&6\\-10&10&-15\end{array}\right][/tex].
Part(b) : We have to interchange the "row1" and "row2",
On interchanging,
We get,
[tex]\left[\begin{array}{ccc}0&6&-3\\5&-2&6\end{array}\right][/tex].
Part(c) : We have to multiply the elements of "row1" by 2,
So, On multiplying the "row1" by 2,
We get,
⇒ [tex]\left[\begin{array}{ccc}5\times 2&-2\times 2&6\times 2\\0&6&-3\end{array}\right][/tex]
⇒ [tex]\left[\begin{array}{ccc}10&-4&12\\0&6&-3\end{array}\right][/tex].
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Related Questions
Given: Prove: Three lines AD, CF, and BE are intersecting each other at the midpoint O Complete the proof. It is given that and . By the , . Therefore, . By the , , and by the , . After application of the ,
Answers
Answer:Given: Three lines AD, CF, and BE intersect at point O such that and
To prove: O is the midpoint of all three lines, i.e., AO = BO = CO
Proof:
Since point O lies on line AD, we can write
(1) AO + OD = AD
Similarly, since O lies on line BE, we have
(2) BO + OE = BE
Also, since O lies on line CF, we have
(3) CO + OF = CF
From the given information, we have
(4) AD = BE
Substituting (4) in (1) and (2), we get
(5) AO + OD = BO + OE
Adding (3) to (5), we get
(6) AO + BO + CO + OD + OE + OF = AD + BE + CF
From the given information, we have
(7) CF = AD + BE
Substituting (7) in (6), we get
(8) AO + BO + CO + OD + OE + OF = 2AD + 2BE
Since we know that AD = BE, we can simplify (8) as
(9) AO + BO + CO + OD + OE + OF = 4AD
Dividing both sides of (9) by 4, we get
(10) AO + BO + CO = AD
But from (4), we also know that AD = BE, so we can write
(11) AO + BO + CO = BE
Dividing both sides of (11) by 2, we get
(12) AO = BO = CO
Hence, we have proved that O is the midpoint of all three lines, i.e., AO = BO = CO.
Step-by-step explanation:
Two coins are tossed. Assume that each event is equally likely to occur.
a) Use the counting principle to determine the number of sample points in the sample space.
b) Construct a tree diagram and list the sample space.
c) Determine the probability that no tails are tossed.
d) Determine the probability that exactly one tail is tossed.
e) Determine the probability that two tails are tossed.
f) Determine the probability that at least one tail is tossed.
Question content area bottom
Part 1
a) There is/are ______sample point(s) in the sample space.
Answers
a) There are 2 x 2 = 4 sample points in the sample space
How to solve
b) Tree Diagram
O D.\nH\nHe\nT\nH\nT\n
Sample space: D. HH, HT, TH, TT
c) P(no tails) = P(HH)
= 1/4
d) P(exactly one tail) = P(HT, TH)
= 2/4
= 1/2
e) P(2 tails) = P(TT)
= 1/4
f) P(at least one tail) = P(HT, TH, TT)
= 3/4
In mathematics, tree diagrams are often used in probability and statistics to show all the possible outcomes of an event. In computer science, they are used to represent the hierarchical structure of files and directories in a file system
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Write null and alternative hypothesis, test statics, p-value, and inference.
For Climate Change Beliefs, use variables: climate change and certainty.
For Class time use, use variables: income class, and sleeping.
Answers
The value of null and alternative hypothesis are change beliefs and certainty test statics, p-value, and inference are the null hypothesis and conclude that there is insufficient evidence to suggest a significant relationship.
Climate Change Beliefs:
Null Hypothesis (H0): There is no significant relationship between climate change beliefs and certainty.
Alternative Hypothesis (Ha): There is a significant relationship between climate change beliefs and certainty.
Test Statistic: Pearson's correlation coefficient (r)
The Pearson correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, we will use it to determine the relationship between climate change beliefs and certainty.
P-Value: The p-value is the probability of obtaining a test statistic as extreme as the observed value, assuming that the null hypothesis is true.
Inference: If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is a significant relationship between climate change beliefs and certainty. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest a significant relationship.
Class Time Use:
Null Hypothesis (H0): There is no significant relationship between class time use, income class, and sleeping.
Alternative Hypothesis (Ha): There is a significant relationship between class time use, income class, and sleeping.
Test Statistic: Multiple regression analysis
Multiple regression analysis is used to determine the relationship between a dependent variable and two or more independent variables. In this case, class time use, income class, and sleeping will be the independent variables, and we will use it to determine the relationship with the dependent variable.
P-Value: The p-value is the probability of obtaining a test statistic as extreme as the observed value, assuming that the null hypothesis is true.
Inference: If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is a significant relationship between class time use, income class, and sleeping.
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Part 1
For the experiment of rolling a single fair die, find the probability of being even or divisible by 3.
Answers
The probability of rolling an even or divisible by 3 numbers is 2/3
When a single fair die is rolled, there are six possible outcomes:
1, 2, 3, 4, 5, or 6.
Of these outcomes, three are even (2, 4, and 6) and two are divisible by 3 (3 and 6). However, since the number 6 is both even and divisible by 3, we must count it only once to avoid overcounting. Thus, four outcomes are either even or divisible by 3: 2, 3, 4, and 6.
The probability of rolling an even or divisible by 3 number is the sum of the probabilities of these four outcomes, which is:
P(even or divisible by 3) = P(2) + P(3) + P(4) + P(6)
= 1/6 + 1/6 + 1/6 + 1/6
= 4/6
= 2/3
Therefore, the probability of rolling an even or divisible by 3 numbers is 2/3
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Enter the value of n so that the expression (-2y+5)+(-5y-3) is equivalent to (ny+2)
Answers
Answer:n=-7
Step-by-step explanation: (-2y+5)+(-5y-3)=-7y+2 so our answer is -7.
fill it in The value of a certain investment over time is given in the table below. Answer the questions below to determine what kind of function would best fit the data, linear or exponential.
Number of Years Since Investment Made, x
1
2
3
4
Value of Investment ($), f(x)
14,944.54
16,357.04
17,974.72
19,891.18
function would best fit the data because as x increases, the y values change
. The
of this function is approximately
.
Answers
An exponential function would be more appropriate than a linear function, as exponential growth
the best function for the dataTo determine which type of function best fits the data, we can analyze the difference in the y values (Value of Investment) as x increases.
Differences between consecutive y values:
16,357.04 - 14,944.54 = 1,412.50
17,974.72 - 16,357.04 = 1,617.68
19,891.18 - 17,974.72 = 1,916.46
The differences between consecutive y values are increasing as x increases. This suggests that an exponential function would be more appropriate than a linear function.
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College Level Trig Question Please Help!
Answers
The solution of the trigonometric problem is y = -3
How is this so ?Starting with the equation
3/2 cos^-1(y/6) = pi
First, we can simplify by dividing both sides by 3/2 ....
cos^-1(y/6) = pi / (3/2)
cos^- 1(y/6) = 2pi / 3
Next, we can take the cosine of both sides to get...
cos (cos^-1(y/6 ) )
= cos( 2pi/3)
y/6 = -1/2
y = -3
Therefore, the exact solution to the equation 3/2 cos^-1(y/6) = pi is y = -3.
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5. The Smiths took out a $155,500, 30-year mortgage. The
monthly payment was $992. What will be their total interest
charges after 30 years?
Question 6
3 pts
Answers
Answer:
$176420
Step-by-step explanation:
Monthly payment = $992
Yearly payment = 992 × 12 = $11064
Total payment = 11064 × 30 = $331920
Interest = 331920 - 155500 = $176420. The interest seems too much, are you sure there's no mistake in the question? Maybe the monthly payment is more than what you've written here?
Select the correct answer from each drop-down menu.
Rectangle ABCD is dilated by a scale factor of 1/4 to form A'B'C'D. Point T is the center of dilation and lies on line segment AB as shown. In A'B'C'D. line segment A'B has a slope of ____ and a length of _____.
Answers
In A'B'C'D, line segment A'B has a slope of 0 and a length of 5/4
Calculating the slopes and the lengths of the segment A'B'From the question, we have the following parameters that can be used in our computation:
A = (1, 4) and B = (6, 4)
The line AB is a horizontal line that passes through the point y = 4
This means that the slope of the segment A'B' is 0
The length is then calculated as
A'B' = difference in the x-coordinate * scale factor
Substitute the known values in the above equation, so, we have the following representation
A'B' = (6 - 1) * 1/4
Evaluate
A'B' = 5/4
Hence, the length A'B' is 5/4
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I can’t figure out what is correct to get about 8
Answers
Step-by-step explanation:
Going down the list :
8.98 rounds to 9
6.64 rounds to 7
7.03 rounds to 7
8.52 rounds to 9
7.59 rounds to 8
If the first number past the decimal point >= 5 round the units up
o/w leave the units as they are
Use the graph to find f(2)
Pleaaaaaaase answer ASAP
Answers
Answer:
f(2) = 3
Step-by-step explanation:
At f(2) we can notice that there is 2 y-values (one is an open circle and another is a closed circle)
But, an open circle means that the function is not defined at that point
But a closed circle means that it is defined
So we ignore the open circle and the closed circle is 3
So f(2) = 3
Write as a product 4x^2+y^2-4xy-16
PLEASEEE Help :')
Need by TONIGHT 11:59 EDT
Will give brainliest (need 2+ ppl to answer to give brainliest, I will give the first answer branliest)
Answers
Answer:
We can write 4x^2 + y^2 - 4xy - 16 as the product:
(2x - y + 4)(2x - y - 4)
Step-by-step explanation:
To write 4x^2 + y^2 - 4xy - 16 as a product, we can use the technique of completing the square. First, we can rearrange the terms to group the x terms and the y terms:
4x^2 - 4xy + y^2 - 16
Next, we can complete the square for the x terms and the y terms separately. For the x terms, we can add and subtract (2x)^2:
4x^2 - 4xy + (2x)^2 - (2x)^2 + y^2 - 16
Simplifying the first three terms gives:
(2x - y)^2 - (2x)^2 + y^2 - 16
For the y terms, we can add and subtract 16:
(2x - y)^2 - (2x)^2 + (y - 4)^2 - 16^2
Simplifying the second term gives:
-(4x^2) + 16x - (y^2) + 16y - 16^2
Therefore, we can write 4x^2 + y^2 - 4xy - 16 as the product:
(2x - y + 4)(2x - y - 4)
Answer pls my state test is cominggggg
Answers
(-3/4) x (3/4)
---When we multiply fractions, we multiply horizontally/across
(-3 x 3) / (4 x 4)
-9 / 16
Answer: -9/16
Hope this helps!
Can anyone help me answer this question?
1. What is the derivative of sin(x)cos(x)?
2. What is the derivative of sin2(x)cos2(x)?
Answers
Answer:
cos 2x
f(x)=4•sin(x)•cos(x)
Step-by-step explanation:
Reasoning What is the height of the square pyramid? Use pencil and paper. Once you know which length represents the hypotenuse, does it matter which length you substitute for a and which length you substitute for b? Explain.
Answers
The height of the square pyramid is 35.5 in.
From the given figure we can see that the figure is a pyramid.
The base of the pyramid is a square.
The each side of base square i = 24.8 in.
The slant height is = 37.6 in.
So the right angle formed in between prism has hypotenuse = 37.6 in.
one of the rest two sides = 24.8/2 = 12.4 in.
So another side is the height of the pyramid. Let that side be = x in.
By Pythagoras Theorem we get,
(12.4)² + x² = (37.6)²
153.76 + x² = 1413.76
x² = 1413.76 - 153.76
x² = 1260
x = 35.5 (rounding off to nearest tenth and neglecting the negative value obtained from square root as length cannot be negative.)
Hence the height of the square pyramid is 35.5 in.
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Please help me out it’s a new topic and I don’t know how to do it
Answers
Answer:
=x2-100
Step-by-step explanation:
When I said x2 I mean (x*x)
write the opposite of loss of 700
Answers
Answer:
gain of 700 or 700
Step-by-step explanation:
A loss of 700 would be -700 and the opposite of that is 700.
Helping in the name of Jesus.
If y varies directly as x, and y= 2 when x = 3, find y when x = 1.
a. y = 2x; y(1)=2
C.
b.
3
A
B
C
D
(1)
2
d.
4
3; P(1) - 4
3
-
2
y = x; y(1) -
3
Please select the best answer from the choices provided
2/
3
Answers
Answer:
Step-by-step explanation:
If y varies directly as x, it means that y is directly proportional to x, and we can express this relationship using a proportionality constant k:
y = kx
To find the value of k, we can use the given information that y = 2 when x = 3:
2 = k(3)
Solving for k, we get:
k = 2/3
Now that we know the value of k, we can use the formula to find y when x = 1:
y = (2/3)x
y = (2/3)(1)
y = 2/3
Therefore, when x = 1, y = 2/3.
PLEASE HELP !!! MAJOR GRADE!!!!
Column A
1. A set of two of more linear equations that contain 2 or more variables.
2. When there is no answer to a system of equations or inequalities.
3. There is only one value for the variable that makes the equation true.
4. Terms with the same variables raised to the same exponent.
5. Equation is solved for one variable and that solution is substituted into the second equation.
6. A value that makes the equation true.
7. Adding subtracting or multiplying a system of equations to help solve a system.
8. A linear equation in one variable has infinitely
many solutions.
9. A letter that represents one or more numbers.
10.This is the number in front of the variables in a term
Column B
a. Elimination
b. Substitution
c. Solution
d. Infinitely Many Solutions
e. No solutions
f. System of Equations
g. Variable
h. Like Terms
i. One solution
j. Coefficients
Answers
Answer:
1. f. System of Equations
2. e. No solutions
3. i. One solution
4. h. Like Terms
5. b. Substitution
6. c. Solution
7. a. Elimination
8. d. Infinitely Many Solutions
9. g. Variable
10. j. Coefficients
Step-by-step explanation:
Ur welcome :)
Suppose that the number of dollars spent per week on groceries are normally distributed with an unknown mean and standard deviation. A random sample of 18 grocery bills is taken and gives a sample mean of 103 dollars and a sample standard deviation of 10 dollars.
The margin of error for a 98% confidence interval estimate for the population mean using the Student's t-distribution is 6.05. Find a 98% confidence interval estimate for the population mean using the Student's t-distribution.
Round the final answers to two decimal places.
Answers
We are given that the sample size $\sf\:n = 18$, sample mean $\sf\:\bar{X} = 103$, sample standard deviation $\sf\:S = 10$, and margin of error $\sf\:E = 6.05$ for a 98% confidence interval estimate for the population mean.
Using the formula for the margin of error, we can find the value of the t-score that corresponds to a 98% confidence level with 17 degrees of freedom (since we have 18 samples):
$\sf\:t_{0.01/2, 17} \implies 2.898$
Now, we can use the formula for a confidence interval estimate to find the lower and upper bounds of the interval:
$\sf\:\bar{X} - E \implies 103 - 6.05 < \mu < \bar{X} + E \implies 103 + 6.05$
Substituting in the values we have:
$\sf\:103 - 6.05 < \mu < 103 + 6.05$
Simplifying:
$\sf\leadsto\:96.95 < \mu < 109.05$
Therefore, a 98% confidence interval estimate for the population mean is $\sf\: (96.95, 109.05)$ rounded to two decimal places.
[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
[tex]{\bigstar{\underline{\underline{\sf{\color{red}{Sumit\:Roy}}}}}}{\bigstar}\\[/tex]
Sarah is twice Jans age. Henry is 5 years younger than Jan. The sum of all their ages is 35. How old is Sarah?
Answers
Step-by-step explanation:
let the first letter of their name represent
their age
s=2j
h=j-5
s+j+h=35
replace s AND h with the values above
2j+j+j-5=35
4j=35+5
4j=40
j=10
replace j in the equation s=2j
s=2×10
s=20
replace j in the equation h=j-5
h=10-5
h=5
What are the values of x
X =
Answers
The product of the two external segments and the sum of the lengths of each segment in the circle are equal if two secants are drawn to the circle from a single shared exterior point. The x has a value of 2 units.
What is intersecting secants theorem?If two secant segments are drawn to a circle from an exterior point, the product of the measurements of one secant segment and its external secant segment is equal to the product of the measurements of the second secant segment and its external secant segment.
So, we know that:
BE * AE = CE * DE
Now, insert the values as follows:
(x+1) * (x+12) = (x+4) * (x+5)
x² + x + 12x + 12 = x² + 4x + 5x + 20
13x + 12 = 9x + 20
4x = 8x
x= 2
Then: x = 2 units
Therefore, the product of the two external segments and the sum of the lengths of each segment in the circle are equal if two secants are drawn to the circle from a single shared exterior point. The x has a value of 2 units.
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Help please connect the left to the right for each component
Answers
f(x) = the total cost for detailing the car. x = the number of minutes it takes to detail the car. m = The cost per minute for the detailing in car. b = the flat fee for detailing the car.
What is a linear equation?An algebraic equation is said to be linear if the maximum power of the variable is 1. In other words, it is an equation that, when plotted on a coordinate plane, defines a straight line. A linear equation with a single variable has the general form:
ax + b = 0, where a and b are constants and x is the variable. A single value of x that causes the equation to be true is the answer to this equation.
The given situation can be expressed in the form f(x) = mx + b.
Where,
f(x) = the total cost for detailing the car.
x = the number of minutes it takes to detail the car.
m = The cost per minute for the detailing in car.
b = the flat fee for detailing the car.
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Select all the correct answers.
If the measure of angle 0 is 2n/3, which statements are true?
Answers
The statements that are true are ;
1. tan(tetha) = -√3
2. the measure of the reference angle is 60°
What is trigonometric function?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
The value of each angle depends on the quadrant it falls on.
First quadrant = 0-90°
second quadrant = 91° -180°
third quadrant = 181-270°
fourth quadrant = 271° - 360°
pi is measurement of angle in radians which is equivalent to 180°
therefore;
2π/3 = 2 × 180/3 = 360/3
= 120°
120 falls on the second quadrant,
tan60 = √3
tan 120 = -√3
the reference angle is 60° i.e
180-120 = 60°
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divide $300 in ratio 9 : 1
Answers
Answer:
$270:$30
Step-by-step explanation:
add up the ratios = 10
then do 300/10 = 30
so 1 ratio = 30
this means the ratio will be: $270:$30
Let me know if this helped
Each number in the first table represents the points scored by a player on the Ace Academy basketball team. Make a
frequency distribution, including relative frequency (percent of total: frequency)
total
1 5 8 10 10 13
369 10 11 13
379 10 12 14
4 7 10 10 12 14
For the relative frequencies below, round to the nearest tenth.
Score Frequency Relative Frequency
1
Answers
The most common point total scored was 10 with a frequency of 9 or 25% of the total frequency.
What is the frequency distribution of points scored?To create the score frequency distribution, we have to list the unique values in the data set and count how many times each value appears.
Element Frequency Relative frequency (percent)1 1 1/24 = 0.042 = 4.2%
3 2 2/24 = 0.083 = 8.3%
4 1 1/24 = 0.042 = 4.2%
5 1 1/24 = 0.042 = 4.2%
6 1 1/24 = 0.042 = 4.2%
7 2 2/24 = 0.083 = 8.3%
8 1 1/24 = 0.042 = 4.2%
9 2 2/24 = 0.083 = 8.3%
10 6 6/24 = 0.25 = 25%
11 1 1/24 = 0.042 = 4.2%
12 2 2/24 = 0.083 = 8.3%
13 2 2/24 = 0.083 = 8.3%
14 2 2/24 = 0.083 = 8.3 %
----------
24
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On October 12, 2020, the number of new cases of Covid 19 in Milwaukee was 235. On Oct. 22, 2020, the number of new cases in Milwaukee was 395.
a. Create an exponential model for new cases in terms of days.
b. Based on your model, what would be the number of new cases on Oct. 31, 2020?
c. The actual number of new cases on Oct. 31, 2020, was 1043. How well does this fit your model?
Answers
a. To create an exponential model for new cases in terms of days, we can use the formula: y = a * b ^ x, where y is the number of new cases, x is the number of days since the first observation, and a and b are constants that we need to determine. Using the two data points given, we can set up a system of equations:
235 = a * b ^ 0
395 = a * b ^ 10
Solving for a and b, we get:
a = 235
b = (395/235)^(1/10) = 1.067
Therefore, the exponential model for new cases in Milwaukee is:
y = 235 * 1.067 ^ x
b. To find the number of new cases on Oct. 31, 2020, we need to plug in x = 19 (since Oct. 31 is 19 days after Oct. 12) into the model:
y = 235 * 1.067 ^ 19 = 1018.5
Therefore, based on the exponential model, we would expect around 1019 new cases on Oct. 31, 2020.
c. The actual number of new cases on Oct. 31, 2020, was 1043. This is higher than the predicted value of 1019, but not by a huge margin. Overall, the model seems to fit the data reasonably well, especially considering that there are many factors that can affect the number of new cases in a given area, and that the model is based on only two data points. However, it is worth noting that the exponential model assumes that the growth rate of new cases remains constant over time, which may not be a realistic assumption in the long run.
Fully factorise 27t² + 15t
Answers
Answer: 3t(9t + 5)
Step-by-step explanation:
Sure! Factoring involves breaking down an expression into simpler factors that, when multiplied together, give the original expression.
To factor 27t² + 15t, we can look for the greatest common factor (GCF) of the two terms. The GCF of 27t² and 15t is 3t, because both terms can be divided by 3t.
So we start by factoring out the 3t:
27t² + 15t = 3t(9t + 5)
Notice that we can check if the factorization is correct by using the distributive property to multiply the factor 3t by the expression inside the parentheses:
3t(9t + 5) = 3t(9t) + 3t(5) = 27t² + 15t
Therefore, 27t² + 15t can be fully factorized as 3t(9t + 5).
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n = 109, x = 65; 88% confidence
Answers
Rounding to three decimal places, the confidence interval is (0.419, 0.574).
How can a confidence interval for a sample proportion be created?The sample proportion, p′ = 0.842, which is the point estimate of the population proportion, must be determined in order to calculate the confidence interval. Given that CL = 0.95 is the requested confidence level, = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) = 0.025.
Confidence interval=proportion±margin of error
CI = p ± ME
The proportion is:
p = x / n
p = 55/110
p = 0.5
Margin of error=critical value × standard error
ME = CV × SE
n > 30, so we can approximate CV with a normal distribution.
At P=88%, CV=1.55.
SE = √(pq / n)
SE = √(0.5 (1−0.5)/110)
SE = 0.048
So the margin of error is:
ME = 1.55 × 0.048
ME = 0.074
So the confidence interval is:
CI = 0.5 ± 0.074
CI = (0.426, 0.574)
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Question:
Use the given degree of confidence and Sample data to construct income confidence interval for the population proportion p. n=110, x=55; 88% confidence
A) 0.426 B)0.442 C)0.425 D)0.421
Liz opened a savings account and deposited $1,000.00 as principal. The account earns 8% interest, compounded quarterly. What is the balance after 4 years?
Answers
After the first quarter, the interest earned would be:
$1,000.00 * 0.02 = $20.00
So the new balance would be:
$1,000.00 + $20.00 = $1,020.00
After the second quarter, the interest earned would be:
$1,020.00 * 0.02 = $20.40
So the new balance would be:
$1,020.00 + $20.40 = $1,040.40
After the third quarter, the interest earned would be:
$1,040.40 * 0.02 = $20.81
So the new balance would be:
$1,040.40 + $20.81 = $1,061.21
After the fourth quarter, the interest earned would be:
$1,061.21 * 0.02 = $21.22
So the final balance after 4 years would be:
$1,061.21 + $21.22 = $1,082.43
Therefore, the balance after 4 years would be $1,082.43.