Answer:
Tom will pay a total of $58,064 in interest over the 30 year loan.
Step-by-step explanation:
The purchase price of the home is $144,000, and Tom will make a down payment of 10%, or $144,000 * 10/100 = $14,400.
Therefore, Tom borrows $144,000 - $14,400 = $129,600.
Next, we need to calculate the total number of payments he will make over the 30 year loan. Since the loan is for 30 years and the payments are made monthly, there will be 30 years * 12 months/year = <<30*12=360>>360 payments.
Finally, we can use the mortgage formula to calculate the total amount of interest Tom will pay over the loan:
I = P * r * t
Where:
I is the total interest
P is the principal (the amount borrowed)
r is the annual interest rate (in decimal form)
t is the number of payments
Plugging in the values, we get:
I = $129,600 * 0.045 * 360 payments
= $58,064
Question 8 options:
Given the coordinates below, determine if ΔFGH and ΔJKL are congruent. If they are, give the reason, if they aren't choose "not congruent".
F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)
FG =
GH =
FH =
JK =
KL =
JL =
Are the triangles congruent?
In the box enter one of the following:
SSS
SAS
Not Congruent
Hence, the three side length of two triangles are same so they are congurent.
What is the congurency?
Two shapes are congruent if they are the same (shape and size)- in other words, if the lengths of the sides and the angles are the same.
It is often useful to know when two triangles are congruent.
Here given coordinates of the triangle [tex]FGH[/tex] and triangle [tex]JKL[/tex] are
[tex]F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)[/tex].
So, the distance formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Distance between [tex]FG[/tex] is
[tex]d=\sqrt{(-2-(-5))^2+(2-10)^2}\\\\d=\sqrt{(-2+5)^2+(2-10)^2}\\\\d=\sqrt{(3)^2+(-8)^2}\\\\d=\sqrt{9+64}\\\\d=\sqrt{73}[/tex]
Distance between [tex]GH[/tex] is
[tex]d=\sqrt{(-9-(-2))^2+(10-(-7))^2}\\\\d=\sqrt{(-9+2)^2+(10+7)^2}\\\\d=\sqrt{(-7)^2+(-9)^2}\\\\d=\sqrt{49+81}\\\\d=\sqrt{130}[/tex]
Distance between [tex]HF[/tex] is
[tex]d=\sqrt{(-5-(-9))^2+(10-(-7))^2}\\\\d=\sqrt{(-5+9)^2+(10+7)^2}\\\\d=\sqrt{(4)^2+(17)^2}\\\\d=\sqrt{16+289}\\\\d=\sqrt{305}[/tex]
Distance between [tex]JK[/tex] is
[tex]d=\sqrt{(9-0)^2+(2-(-5))^2}\\\\d=\sqrt{(9)^2+(2+5)^2}\\\\d=\sqrt{(9)^2+(7)^2}\\\\d=\sqrt{81+49}\\\\d=\sqrt{130}[/tex]
Distance between [tex]KL[/tex] is
[tex]d=\sqrt{(-8-9)^2+(-2-2)^2}\\\\d=\sqrt{(-17)^2+(-4)^2}\\\\d=\sqrt{289+16}\\\\d=\sqrt{305}[/tex]
Distance between [tex]LJ[/tex] is
[tex]d=\sqrt{(0-(-8))^2+(-5-(-2))^2}\\\\d=\sqrt{(8)^2+(-5+2)^2}\\\\d=\sqrt{(8)^2+(-3)^2}\\\\d=\sqrt{64+9}\\\\d=\sqrt{73}[/tex]
Since, [tex]FG[/tex]≅[tex]LJ-GH[/tex]≅[tex]JK-HF[/tex]≅[tex]KL[/tex]
Hence, the three side length of two triangles are same so they are congurent.
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sine rule find the length of ac
The length AC of the triangle ABC is approximately 12.083 centimeters.
How to use the law of sine
The law of sine is a relationship between the sides and the angles of the triangle, which is defined below:
AB / sin C = AC / sin B = BC / sin A
Where:
AB, AC, BC - SidesA, B, C - AnglesFirst, determine the measure of angle C:
AB / sin C = BC / sin A
sin C = (AB / BC) · sin A
sin C = (8.2 / 13.5) · sin 81°
C ≈ 36.865°
Second, determine the measure of angle B:
B = 180° - A - C
B = 180° - 81° - 36.865°
B = 62.135°
Third, determine the length of side AC:
AC / sin B = BC / sin A
AC = BC · (sin B / sin A)
AC = 13.5 · (sin 62.135° / sin 81°)
AC ≈ 12.083 cm
The length AC is approximately equal to 12.083 centimeters.
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Can anyone solve this question ignore the 10. Find:
Part (a)
[tex]\angle CDA=\angle CBA[/tex][tex]AB=AD[/tex][tex]AC=AC[/tex]Part (b)
Yes, the triangles are congruent by RHS.
Which ordered pair below is not a solution to f(x) = x² - 3x + 4?
(1) (0,4)
(2) (1.5,1.75)
(3) (5,14)
(4) (-1,6)
Answer:
(4) (-1,6)
Step-by-step explanation:
f(x) = x² - 3x + 4
1) (0,4) ==>x=0 and f(x)=4
4 = 0² - 3(0) + 4
4 = 0 + 4
4 = 4 ==> true X
2) (1.5,1.75)==> x=1.5 and f(x)=1.75
1.75 = (1.5)² - 3(1.5) + 4
1.75 = 2.25 - 4.5 + 4
1.75 = 2.25 - 0.5
1.75 = 1.75 ==> true X
3) (5,14)
14 = (5)² - 3(5) + 4
14 = 25 - 15 + 4
14 = 10 + 4
14 = 14 ==> true X
4) (-1,6)
6 = (-1)² - 3(-1) + 4
6 = (|-1|)² - (-3) + 4 ==> the square of a negative number is equal to the square
of the absolute value of that number since the square of
a real number is always positive
6 = (1)²+ 3 + 4 ==> subtracting a negative number is equivalent to adding
the positive number
6 = 1 + 3 + 4
6 = 4 + 4
6 = 8 ==> false √√
Hence, the answer is (4) (-1,6).
assuming that workers' salaries in your company are uniformly distributed between $10,000 and $60,000 per year, find the probability that a randomly chosen worker earns an annual salary between $45,000 and $50,000.
According to the uniform distribution, there is a 0.1= 10% chance that a worker selected at random will have an annual wage between $45,000 and $60,000.
Uniform Distribution:
In statistics, uniform distribution refers to a type of probability distribution in which all outcomes are equally likely. A deck of cards has within it uniform distributions because the likelihood of drawing a heart, a club, a diamond, or a spade is equally likely.
An uniform distribution has two bounds, a and b.
The probability of finding a value between c and d is:
P(c ≤ X ≤ d) = [tex]\frac{d-c}{b-a}[/tex]
given that , workers' salaries in your company are uniformly distributed between $10,000 and $60,000 per year
a = 10,000 , b= 60,000 , c = 45,000 and d = 50,000
The probability is
P(45,000 ≤ X ≤ 50,000) = [tex]\frac{50,000-45,000}{60,000-10,000}[/tex]
= 0.1
0.1 = 10% probability that a randomly chosen worker earns an annual salary between $45,000 and $60,000
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work out the angle of def
Answer: The ∠DEF= 75°
Step-by-step explanation:
The angle subtended by circumference is half of the angle subtended at the center by the same arc.
So , ∠DEF= 75°
Linear Inequality Word Problems Harder Kyle has $50 to spend on sandwiches and chips for a picnic. He already bought chips for $2 and will buy sandwiches for $4 each. How many sandwiches can he buy?
in triangle ABC , seg XY || sideAC , If 2AX = 3BX and XY = 9 , then find the value of AC
The value of AC is 22.5
The property of three parallel lines and their transversals is used to solve this sum. The property explains that if the ratio of the corresponding intercepts made on any other transversal by the same parallel lines is the same as the ratio of the intercepts made on a transversal formed by three parallel lines.
XY ║seg AC
2AX = 3BX
XY = 9
Since, 2AX =3BX
∴ AX÷ BX = 3÷2
AX + BX÷ BX = 3+2÷2
AB ÷ BX = 5÷2
Δ BCA ~ ΔBYX (SAS test of similarity)
( The SAS similarity test determines whether two triangles are similar if the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal.)
∴ BA ÷ BX = AC ÷ XY ( Corresponding sides)
∴ 5÷ 2 = AC ÷ 9
∴ AC = 22.5
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Rewrite in simplest terms: 6(0.7y+0.8z)−4z−6(−0.1z−0.6y)
Please help?
The simplified form can be written as -
7.8y + 1.4z
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
We have the following expression -
6(0.7y + 0.8z) − 4z − 6(−0.1z − 0.6y)
We have -
6(0.7y + 0.8z) − 4z − 6(−0.1z − 0.6y)
(6 x 0.7y + 6 x 0.8z) - 4z + 6 x 0.1z + 6 x 0.6y
4.2y + 4.8z - 4z + 0.6z + 3.6y
7.8y + 4.8z - 3.4z
7.8y + 1.4z
Therefor, the simplified form can be written as -
7.8y + 1.4z
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assuming that no one is born on feb. 29 (leap day), how many people should be selected to guarantee that at least 5 were born on the same day, not considering the year?
365 sets of people born on the same day, with each set containing no more than 5 people.
Assuming everybody was born on a different day, then you could have 365 people where nobody was born on the same day. the 366 person, however, would have to have been born on the same day as somebody else in the group. therefore, the minimum number of people in the group would have to be 366 to guarantee that at least 2 people were born on the same day but you wanted to guarantee that at least 6 people were born on the same day. assuming you had 5 * 365 people together, with every 5 of them being born on the same day.
you would have a total of 365 * 5 = 1825 people, with no more than 5 people being born on the same day.
Add 1 more person and you will be guaranteed that at least 6 people were born on the same day that comes out to be 1826 people.
1825 / 5 = 365 sets of people born on the same day, with each set containing no more than 5 people.
set 1 is the number of people born on day 1.
set 2 is the number of people born on day 2 etc.
that next person had to be added to one of the sets of 5 to make it a set of 6.
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How do you write 0.112 as a fraction?
Answer:
112/1000
Step-by-step explanation:
Just put 1 under decimal point and just add as many zeros as digits after that
Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces.
Which table contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces?
The table that contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces is the second table on the image given at the end of the answer.
How to obtain the viable solutions?The variables for this problem are given as follows:
The input variable b represents the number of books ordered.The output variable w represents the total weights of the books, in ounces.To obtain the viable solutions, we must consider the input variable. The number of books is a countable amount, meaning that it can only assume non-negative integer values.
Thus the first table is incorrect, as it contains a negative amount of books, and the second table is the one that contains only viable solutions in the context of this problem.
Missing InformationThe table is given by the image shown at the end of the answer.
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7. Laura is conducting an experiment in which she draws a straw. Some of the straws are short,
and some are long. For each trial, she draws a straw, records the result, and replaces the
straw. The table shows the results of 50 trials of the experiment.
Laura will conduct 10 more trials of the experiment. Based on the results in the table, how many of these additional trials will have a result of a a short straw being drawn. :)
Answer:
7
Step-by-step explanation:
Experimental probability is based on the actual results of an experiment (gathered by experimenting repeatedly).
It is calculated by dividing the recorded number of times an event happens by the total number of trials in the actual experiment:
[tex]\boxed{\textsf{Experimental Probability} = \dfrac{\textsf{Number of times an event happens}}{\textsf{Total number of trials}}}[/tex]
As the number of trials increases, we would expect for the experimental probability to get closer to the theoretical probability.
Given:
Total number of trials = 50Recorded number of short straws = 35The experimental probability of drawing a short straw is:
[tex]\implies \sf P(short\;straw)=\dfrac{35}{50}=\dfrac{7}{10}[/tex]
If Laura conducts 10 further trials of the experiment, based on the results in the table, the number of additional trials that will have a result of a short straw being drawn is:
[tex]\begin{aligned}\implies \textsf{Additional trials (short straw)} &=\sf experimental\;probability \times number\;of\;trials\\&= \sf \dfrac{7}{10} \times 10\\&= \sf 7\end{aligned}[/tex]
help me i will give brainlest
The minimum value, Q1, Median, Q3 and maximum value of the data are 2, 5, 12, 14 and 16 respectively
How to find the statistical measures and create a box and whiskers plot for the data?Given the data: 2, 4, 4, 5, 8, 10, 12, 12, 12, 13, 14, 14, 15, 16
The minimum value of the data is 2. Thus, Min = 2
The maximum value of the data is 16. Thus, Max = 16
The median is the data value in the middle.
2, 4, 4, 5, 8, 10, 12, 12, 12, 13, 14, 14, 15, 16
So the median (Q2) of the data is (12+12)/2 = 12. Thus, Med = 12
Consider the values to the left of the median with one of the median numbers included (since we have numbers in the middle):
2, 4, 4, 5, 8, 10, 12
Find the median of this set of numbers. The median is 5. Q1 = 5
Also, consider the values to the right of the median with one of the median numbers included: 12, 12, 13, 14, 14, 15, 16. The median is 5. Q3 = 14
To create a box and whiskers plot use Min, Max, Q1, Median(Q2) and Q3 (Check the attached image)
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The equation T^2 =A^3 shows the relationship between a planets orbital period, T , and the planets mean distance for the sun, A, is astronomical unit, AU. If planet Y is k times the mean distance from the sun as a planet X, by what factor is the orbital period increased
The increase in the orbital period is by a factor of k^3/2. Option D
What is the Kepler laws?From the Kepler's laws, we know that the square of the period of the planet is directly proportional to the cube of the distance of the planet from the sun. We can see that this has been typified by the expression; T^2 =A^3 where T is the period of the planet and A is the distance between the planet and the sun.
Now, we can see that from the relationship, If planet Y is k times the mean distance from the sun as a planet X then the orbital period would be increased by a factor of about k^3/2.
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2(x+ 5) = 3x +1 solve
Answer:
x= 9
Step-by-step explanation:
2(x + 5 ) = 3x + 1
expand the bracket first
2x + 10 = 3x + 1
then collect like terms
2x-3x = 1 - 10
-1x = - 9
and the last step is divide both side by -1
then x = 9
Carson owes Nigel $110. If Carson repays this debt at a rate of $15 per week, which graph best represents when, in weeks, Carson’s debt will be less than $50?
Responses
After doing the equitation the at rate of $15 per week.
How to do graph representation?
Graph representation is a way of visualizing data as a graph or chart. It is used to easily identify relationships between data points and to illustrate trends in the data. Graphs can be used to present data in a variety of ways, such as bar graphs, line graphs, pie charts, scatter plots and more. Graphs are especially useful when trying to compare two or more sets of data and to highlight any patterns or trends that may exist. Additionally, graphs are often used to represent numerical data in a more visually appealing way. By using graphs, it is easier to identify relationships, trends and outliers in the data. Graphs also help to make data easier to interpret and understand.
Carson owes = $110
At rate of $15 per week.
The graph representation will follows:
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Maya rakes up the leaves and wants to put them into bags that hold 2\3 of a cubic yard if she rakes 2 1\2 cubic yards of leaves in total how many bags of leaves will she fill.
6)write an expression to show how you can determine the answer to the question
7) draw a picture to model what is happening in the problem using a
8)method of your choice determinate how many bags of leaves that Maya will fill
The expression to determine the number of bags is 2/3 x = 2 1/2 and the number of bags requited is 3 3/4 bags
How to write the expression of the problemInformation from the problem
Maya rakes up the leaves and wants to put them into bags that hold 2\3 of a cubic yard
she rakes 2 1\2 cubic yards of leaves
one bag = 2/3 cubic yard
total leaves raked = 2 1/2 cubic yard
the number of bags required is how many 2/3 cubic yards are there in 2 1/2 cubic yard. this is solved by division
let the number of bags be x
2/3 cubic yard * x = 2 1/2 cubic yard
2/3 x = 2 1/2
x = (2 1/2) / (2/3)
x = 15/4
x = 3 3/4 bags
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Find the product with the exponent in simplest
form. Then, identify the values of x and y.
6^1/3x6^1/4=6^x/y
X= ,y=
Answer: 6^1/3x6^1/4=6^x/y
X= ,y=
Step-by-step explanation:
Answer:
x = 7 , y = 12
edge 2023
Ruby biked a trail that is 3/5 mile each way. After biking 1/4 of the trail, she stopped to rets. What fraction of a mile did Ruby bike before she stopped to rest?
Answer:
7/20 miles
Step-by-step explanation:
get a common denominator
subtract the numerators
then you have the fraction she biked
the royal fruit company produces two types of fruit drinks. the first type is 60% pure fruit juice, and the second type is 85% pure fruit juice. the company is attempting to produce a fruit drink that contains 75% pure fruit juice. how many pints of each of the two existing types of drink must be used to make 180 pints of a mixture that is 75% pure fruit juice?
The pints of each of the two existing types of drink must be used to make 180 pints of a mixture that is 75% pure fruit juice is 72 and 108 pints respectively.
Let juice A = a
60% pure fruit juice
Let juice B = b
85% pure fruit juice
We need to make 180 pints of juice from both
a + b = 180
represented in terms of pure fruit
a = 0.60; b = 0.85 ;
Our mixed fruit juice from a and b should be 75% pure fruit = 0.75
Mathematically,
0.60a+ 0.85b = 180(0.75)
0.60a + 0.85b =135
Multiply this equation by 100
60a+ 85b = 13500
Now we have two equations for two variables,
a + b = 180 and
60a+ 85b = 13500
Multiply equation 1 by 60,
we get,
60a + 60b = 10800
On solving these equations we get,
b = 108
Substitute b = 108 into the second equation
60a+ 85(108)= 13500
60a+ 9180 = 13500
a = 72
Therefore , the pints of juice A required is 72 pints and the pints of juice B required is 108 pints.
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Answer:
Step-by-step explanation:
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 75% pure fruit juice. How many pints of the two existing types of drink must be used to make 60 pints of a mixture that is 75% pure juice?
3. 128 kg x 10 hr 1 hr
Answer: 1280 Kg
Step-by-step explanation:
The weight of the object given = 128 Kg
Time 1 = 10 hr
Time 2 = 1 hr
Cancel the hours,
128×10 = 1280 Kg
Lixin can type 2400 words in 3 hours. Find how many words can he write in 40 minutes.
Answer:
533
Step-by-step explanation:
3 hours = 180 minutes
2400 : 180 = x : 40
x = 2400 * 40 / 180
x = 2400 * 4 / 18
x = 2400 * 2 /9
x = 800 * 2 / 3
x = 1600/3
x = 533.333333
x = 533
solve for x multiple choice question
Answer:
12
Step-by-step explanation:
Using the side splitter theorem, [tex]\frac{x}{32}=\frac{9}{24} \implies x=12[/tex].
The value of x is 12, option (B) is correct.
What is triangle proportionality theorem?A line parallel to one side of a triangle splits the other two sides of the triangle proportionally if the line also crosses the other two sides.
Given that,
Two lines are parallel to each other,
And length of sides are,
32 , x , 24 and 9.
By angle proportionality theorem,
32 / x = 24 / 9
x = (32 × 9) / 24
x = (4 × 9) / 3
x = 4 × 3
x = 12
The required length of x is 12.
Hence, option (B) is correct.
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How do you solve 2cos2^x = 1 ?
Answer:
Step-by-step explanation:
Solve for x:
2 cos* (2) =
Divide both sides by 2:
cost (2) =
Take the logarithm base cos(2) of both sides:
Answer:
2inn
X=
iT+ log(-cos(2))
log(2)
i7+ log(-cos(2))
for NE Z
What is the square root of "0.9"?
The value of [tex]\sqrt{0.9}[/tex] is 0.94868329805. You can't get an accurate answer since the square root is an irrational quantity. But I suppose you could just make it simpler.
The value that a number produces when it is multiplied by itself is known as the square root of the number. The square root is denoted by the radical sign. For instance, 16 Equals 4. The root symbol or surds is another name for the radical symbol.
The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number. For instance, the square of three is nine. and the square root of 9, √9 = 3.
Since, 3*3*0.1
= 9*0.1
= 0.9
[tex]\sqrt{3*3*0.1} \\[/tex]
= 3([tex]\sqrt{0.1}[/tex])
[tex]\sqrt{0.9}[/tex] ≈ 0.94868329805
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Correct Question:
What is the value of [tex]\sqrt{0.9}[/tex]
How Many Intersections Are There Of The Graphs Of The Equations Below? 3x+30y = 36 None One Two Infinitely Many
The number of points of intersection for the graphs of the equations is infinite.
Point of intersection refers to the point at which two lines intersect on a graph. The graph of the equation refers to the visual demonstration of the equation obtained by plotting all the points of an equation on a graph. If there is only one variable, the graph is on a number line. If there are two variables, the graph is on the coordinate plane. If there are three variables, the graph is in three-dimensional coordinates.
Simplifying the given equations:
i) x/2 + 5y = 6
x + 10y = 12
ii) 3x + 30y = 36
3(x + 10y) = 36
x + 10y = 12
As the equations are equal lines, they will intersect at infinite times.
Note: The question is incomplete. The complete question probably is: How many intersections are there of the graphs of the equations below? x/2 + 5y = 6 3x + 30y = 36 none one two infinitely many
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Sydney invests $100 every month into an account that pays 0.8% annual interest, compounded monthly. Benny invests $80 every month into an account that pays 2.2% interest, compounded monthly. Determine the amount In Sydney's account after l0 years.
[tex]~~~~~~~~~~~~\stackrel{\textit{\LARGE Sydney}}{\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}}}[/tex]
[tex]A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right) \\\\ \qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 100\\ r=rate\to 0.8\%\to \frac{0.8}{100}\dotfill &0.008\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &10 \end{cases}[/tex]
[tex]A=100\left[ \cfrac{\left( 1+\frac{0.008}{12} \right)^{12 \cdot 10}-1}{\frac{0.008}{12}} \right]\left(1+\frac{0.008}{12}\right) \\\\\\ A=100\left[ \cfrac{\left( \frac{1501}{1500} \right)^{120}-1}{\frac{1}{500}} \right]\left(\frac{1501}{1500}\right) \implies {\Large \begin{array}{llll} A \approx 12497.05 \end{array}}[/tex]
Which of the following is not a criteria for the construction of triangle ASA SSS AAA SAS?
Answer:
AAA
Step-by-step explanation:
There's no angle angle angle (AAA) because all triangle's angles add up to 180
Every month Ms Smith's pays her car loan through automatic payments from her savings account she's pays the same amount on her car loan each month at the end of the year her savings account balance changed by negative 3,213 from payments made on her car loan What is the change in Ms Smith's saving account balance each month due to her car payments.
The change in Ms Smith's saving account balance each month due to her car payments is of:
-$267.75.
What is a proportion?A proportion is a fraction of a total amount, and this fraction is used along with the basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.
In this problem, the monthly balance change is obtained as follows:
Monthly balance change = Yearly balance change / 12.
(as an year is composed by 12 months).
As stated in the text, the yearly balance change of Ms. Smith's account is given as follows:
-$3,213.
The payments are equal each month, hence the monthly change is of:
Monthly balance change = -3213/12 = -$267.75.
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