Answers
Answer:
[tex](x-4)^2+(y+1)^2=162[/tex]
Step-by-step explanation:
Determine r² by using the equation of a circle and plugging in the center (h,k)->(4,-1) as well as (x,y)->(13,8):
[tex](x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-(-1))^2=r^2\\(13-4)^2+(8+1)^2=r^2\\9^2+9^2=r^2\\81+81=r^2\\162=r^2\\[/tex]
Hence, the equation of the circle that meets these criteria is[tex](x-4)^2+(y+1)^2=162[/tex]
Related Questions
Consider the initial value problem y⃗ ′=[33????23????4]y⃗ +????⃗ (????),y⃗ (1)=[20]. Suppose we know that y⃗ (????)=[−2????+????2????2+????] is the unique solution to this initial value problem. Find ????⃗ (????) and the constants ???? and ????.
Answers
The unique solution to the initial value problem of differential equation is y(t) = -t^2 + 2t + 3sin(3t) - 1 with e(t) = -t^2 + 2t + 3sin(3t) - 9, a = 2, and B = -21.
To find the solution to the initial value problem, we first need to solve the differential equation.
Taking the derivative of y(t), we get:
y'(t) = -2t + a
Taking the derivative again, we get:
y''(t) = -2
Substituting y''(t) into the differential equation, we get:
y''(t) + 2y'(t) + 10y(t) = 20sin(3t)
Substituting y'(t) and y(t) into the equation, we get:
-2 + 2a + 10(-2t + a) = 20sin(3t)
Simplifying, we get:
8a - 20t = 20sin(3t) + 2
Using the initial condition y(0) = 2, we get:
y(0) = -2(0) + a = 2
Solving for a, we get:
a = 2
Using the other initial condition y'(0) = 21, we get:
y'(0) = -2(0) + 2(21) + B = 21
Solving for B, we get:
B = -21
Therefore, the solution to the initial value problem is:
y(t) = -t^2 + 2t + 3sin(3t) - 1
Thus, we have e(t) = y(t) - 8, so
e(t) = -t^2 + 2t + 3sin(3t) - 9
and a = 2, B = -21.
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_____The given question is incomplete, the complete question is given below:
Consider the initial value problem >= [22. 2.1]+20). 361) = [2] Suppose we know that (t) = -2t + a 21? + is the unique solution to this initial value problem. Find e(t) and the constants and B. a = B= 8(t) =
one ticket is drawn at random from each of the two boxes below: 1 2 6 1 4 5 8 find the chance that the both numbers are even numbers.
Answers
The chance that both numbers drawn are even numbers is 8/21.
The probability refers to the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.
There are 4 even numbers and 3 odd numbers in the first box, and 2 even numbers and 1 odd number in the second box.
The probability of drawing an even number from the first box is 4/7, and the probability of drawing an even number from the second box is 2/3.
By the multiplication rule of probability, the probability of drawing an even number from both boxes is
(4/7) × (2/3) = 8/21
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solve this proportion: 5/a = 3/4
Answers
Answer:
[tex]a = \frac{20}{3}[/tex]
Step-by-step explanation:
15. Math. The poissonier receives 30 lb.. 4 oz. of
dressed mahi-mahi. After filleting and skinning.
13 lb.. 12 oz. of fillets were produced. What
is the yield percentage of the fillets? If the
whole dressed mahi-mahi was purchased
for $5.85/b.. what is the per pound cost of
the fillets?
Answers
Answer:
To find the yield percentage of the fillets, we need to divide the weight of the fillets by the weight of the dressed mahi-mahi and then multiply by 100 to get a percentage:
Yield percentage = (Weight of fillets / Weight of dressed mahi-mahi) x 100%
First, we need to convert the weights to a common unit, such as ounces:
Weight of dressed mahi-mahi = 30 lb. 4 oz. = 484 oz.
Weight of fillets = 13 lb. 12 oz. = 220 oz.
Now we can calculate the yield percentage:
Yield percentage = (220 oz. / 484 oz.) x 100% = 45.45%
So the yield percentage of the fillets is 45.45%.
To find the per pound cost of the fillets, we need to divide the total cost of the dressed mahi-mahi by its weight in pounds, and then multiply by the yield percentage to get the cost per pound of fillets:
Total cost of dressed mahi-mahi = 30.25 lb. x $5.85/b. = $176.96
Weight of dressed mahi-mahi in pounds = 30.25 lb.
Weight of fillets in pounds = 13.75 lb.
Cost per pound of fillets = (Total cost of dressed mahi-mahi / Weight of dressed mahi-mahi) x Yield percentage / 100%
Cost per pound of fillets = ($176.96 / 30.25 lb.) x 45.45% = $3.04/lb.
Therefore, the per pound cost of the fillets is $3.04/lb.
jerome haw 1,040 songs downloaded on his spotify account and 30% of the songs are country songs. How many of the songs are not country
Answers
therefore, country songs consists of 312
I will mark you brainiest!
SSS is used to prove two triangles are congruent.
A) False
B) True
Answers
Answer:
A
Step-by-step explanation:
because___________________________________
Answer:
B) True
Step-by-step explanation:
SSS or Side-Side-Side is used to prove two triangles are congruent.
Workers are preparing an athletic field by mixing soil and sand
in the correct ratio. The table shows the volume of sand to mix
with different volumes of soil. Which statement is correct?
A For 1,425 m³ of soil, the workers should use 375 m³ of sand.
B The ratio of the volume of soil to the volume of sand is 1:4.
C A graph of the relationship includes the point (900, 225).
D The equation y = 4x models the relationship.
Answers
Option B: The ratio of the volume of soil to the volume of sand is 1:4.
Looking at the table, we can see that for every 100 m³ increase in soil, the sand volume increases by 25 m³. This gives us a ratio of 4:1, which means that the volume of sand is one-fourth of the volume of soil. Therefore, option B is correct.
Option D: The equation y = 4x models the relationship.
We can see that the volume of sand is always one-fourth of the volume of soil. Therefore, we can write y = (1/4)x or y = 0.25x. This equation is the same as y = 4x. Therefore, option D is also correct.
So, the correct statements are B and D.
What is a graph?In mathematics, a graph is a visual representation of data or a mathematical function. It consists of a set of points or vertices connected by lines or curves called edges or arcs, which represent the relationships between the points. Graphs can be used to show trends, patterns, and relationships in data, and they are commonly used in fields such as statistics, economics, and computer science. Some common types of graphs include line graphs, bar graphs, pie charts, scatterplots, and network graphs.
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The table mentioned in the question has been attached below.
Assume that x and y have been defined and initialized as int values. The expression
!(!(x < y) || (y != 5))
is equivalent to which of the following?
(x < y) && (y = 5)
Answers
The expression (x < y) && (y == 5) is an alternative way of writing the original expression, and it will be true only if two conditions are met: first, x is smaller than y, and second, y is equal to 5.
The expression !(!(x < y) || (y != 5)) is equivalent to:
(x < y) && (y == 5)
To see why, let's break down the original expression:
!(!(x < y) || (y != 5))
= !(x >= y && y != 5) (by De Morgan's laws)
= (x < y) && (y == 5) (by negating and simplifying)
So, the equivalent expression is (x < y) && (y == 5). This expression is true if x is less than y and y is equal to 5.
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Complete question:
Assume that x and y have been defined and initialized as int values. The expression
!(!(x < y) || (y != 5))
is equivalent to which of the following?
(x < y) && (y = 5)
(x < y) && (y != 5)
(x >= y) && (y == 5)
(x < y) || (y == 5)
(x >= y) || (y != 5)
QUESTION THREE (30 Marks) a) For a group of 100 Kiondo weavers of Kitui, the median and quartile earnings per week are KSHs. 88.6, 86.0 and 91.8 respectively. The earnings for the group range between KShs. 80-100. Ten per cent of the group earn under KSHs. 84 per week, 13 per cent earn KSHs 94 and over and 6 per cent KShs. 96 and over. i. Put these data into the form of a frequency distribution and obtain an estimate of the mean wage. 15 Marks
Answers
Answer:
the answer would be 100 I guess
A cube of sugar is 2cm wide. Calculate the number of cube in a box 720cm³
Answers
Answer:
V=lwh
=2×2×2=8
720÷8=90
90 cubes
Lori is moving and must rent a truck. There is an initial charge of $60 for the rental plus an additional fee per mile driven. Would a linear, quadratic or exponential function be the best type of equation to model this function? Exponential Quadratic Linear
Answers
Answer:
A linear function would be the best type of equation to model this situation. The total cost of renting the truck increases linearly with the number of miles driven. The initial charge of $60 can be considered as the y-intercept of the linear function, and the additional fee per mile driven can be considered as the slope of the line. Therefore, the equation that models this situation can be written in the form y = mx + b, where y is the total cost of renting the truck, x is the number of miles driven, m is the additional fee per mile driven (the slope of the line), and b is the initial charge of $60 (the y-intercept).
Answer:
A linear function would be the best type of equation to model this function.
Step-by-step explanation:
The total cost of renting the truck is composed of two parts:
Initial charge of $60.Additional fee per mile driven.The initial charge of $60 is the fixed charge, and the additional fee is the variable charge that is proportional to the number of miles driven.
Let "x" be the number of miles driven and "y" be the total cost of the rental (in dollars), then the linear equation is:
y = mx + 60
where "m" is the additional fee (in dollars) per mile driven.
Therefore, a linear function, in the form y = mx + b, where m represents the slope or rate of change, and b represents the initial fixed charge, is the most appropriate function to model this situation.
Trains Two trains, Train A and Train B, weigh a total of 188 tons. Train A is heavier than Train B. The difference of their
weights is 34 tons. What is the weight of each train?
Answers
Step-by-step explanation:
A + B = 188
A = 188 - B - (1)
Now,
A - B = 34
188 - B - B = 34 (Substituting eqn 1 in A)
188 - 34 = 2B
154 = 2B
• B = 77 tons
Now
A = 188 - B
A = 188 - 77
A = 111 tons
Suppose you are trying to estimate the average age of the entire CSU student population. You collect a sample of size n-163, and from your data you calculate x =20.1 s 1.8 round your answers to 3 decimal places) 1. The standard error of the mean for this data set is: 2. The approximate 95% margin of error is (Use the approximation method from the notes, in which the critical value is approximately 2.) 3. The approximate 95% CI for lage is
Answers
a) The standard error of mean for this data set is approximately 0.141.
b) The approximate 95% margin of error is approximately 0.282.
c) The approximate 95% confidence interval for the population mean age is 19.824 to 20.376.
a) The standard error of mean (SEM) is given by the formula: SEM = s / sqrt(n), where s is the sample standard deviation and n is the sample size. Plugging in the values given, we have:
SEM = 1.8 / sqrt(163) ≈ 0.141
So the standard error of the mean is approximately 0.141.
b) The approximate 95% margin of error (MOE) can be calculated using the formula: MOE ≈ 2 * SEM. Plugging in the SEM value from part 1, we get:
MOE ≈ 2 * 0.141 ≈ 0.282
So the approximate 95% margin of error is approximately 0.282.
c) The approximate 95% confidence interval (CI) for the population mean age can be calculated using the formula: CI = x ± (z*SEM), where x is the sample mean, z is the critical value from the standard normal distribution corresponding to the desired level of confidence (95% in this case), and SEM is the standard error of the mean. The critical value for 95% confidence is approximately 1.96. Plugging in the values, we get
CI = 20.1 ± (1.96 * 0.141) ≈ 19.824 to 20.376
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begin by finding the area under the curve from to , . this area can be written as the definite integral
Answers
The area under the curve y = 1/ (x^2 + 6x -16) from x = t to x = 6 is 1/10( ln(4) - 1/10 ln(t+8))
To find the area under the curve y = 1/ (x^2 + 6x -16) from x = t to x = 6, where t > 2, we need to evaluate the definite integral:
∫[t,6] 1/ (x^2 + 6x -16) dx
To solve this integral, we can use partial fraction decomposition. First, we factor the denominator:
x^2 + 6x -16 = (x+8)(x-2)
Then, we can write:
1/ (x^2 + 6x -16) = A/(x+8) + B/(x-2)
Multiplying both sides by (x+8)(x-2), we get:
1 = A(x-2) + B(x+8)
Setting x = -8, we get:
1 = A(-10)
So, A = -1/10.
Setting x = 2, we get:
1 = B(10)
So, B = 1/10.
Therefore, we can write:
1/ (x^2 + 6x -16) = -1/10(x+8) + 1/10(x-2)
Substituting this into the integral, we get:
∫[t,6] 1/ (x^2 + 6x -16) dx = ∫[t,6] (-1/10(x+8) + 1/10(x-2)) dx
Integrating, we get:
= [-1/10 ln|x+8| + 1/10 ln|x-2|] from t to 6
= 1/10 ln|6-2| - 1/10 ln|t+8|
= 1/10 ln(4) - 1/10 ln(t+8)
Therefore, the area is: 1/10( ln(4) - 1/10 ln(t+8))
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_____The given question is incomplete, the complete question is given below:
begin by finding the area under the curve from to y = 1/ (x^2 + 6x -16) from x = t to x = 6, t>2 this area can be written as the definite integral
A fair coin is tossed five times. What is the theoretical probability that the coin lands on the same side every time?
A) 0.1
B) 0.5
C) 0.03125
D) 0.0625
Answers
Answer:
Step-by-step explanation:
The theoretical probability of getting the same side every time in a single coin toss is 1/2. Since we have five independent coin tosses, we can calculate the probability of getting the same side every time by multiplying the probability of getting the same side in each toss:
(1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32
Therefore, the theoretical probability of getting the same side every time in five coin tosses is 1/32, which is equivalent to 0.03125. So, the answer is (C) 0.03125.
Marcia Gadzera wants to retire in San Diego when she is 65 years old. Marcia is now 50 and believes she will need $90,000 to retire comfortably. To date, she has set aside no retirement money. If she gets interest of 10% compounded semiannually, how much must she invest today to meet her goal of $90,000?
Answers
Answer:
Step-by-step explanation:
We can use the formula for the future value of an annuity to determine how much Marcia needs to invest today to meet her retirement goal of $90,000. The formula for the future value of an annuity is:
FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)
where:
FV = future value of the annuity
PMT = payment (or deposit) made at the end of each compounding period
r = annual interest rate
n = number of compounding periods per year
t = number of years
In this case, we want to solve for the PMT (the amount Marcia needs to invest today). We know that:
Marcia wants to retire in 15 years (when she is 65), so t = 15
The interest rate is 10% per year, compounded semiannually, so r = 0.10/2 = 0.05 and n = 2
Marcia wants to have $90,000 in her retirement account
Substituting these values into the formula, we get:
$90,000 = PMT x [(1 + 0.05/2)^(2*15) - 1] / (0.05/2)
Simplifying the formula, we get:
PMT = $90,000 / [(1.025)^30 - 1] / 0.025
PMT = $90,000 / 19.7588
PMT = $4,553.39 (rounded to the nearest cent)
Therefore, Marcia needs to invest $4,553.39 today in order to meet her retirement goal of $90,000, assuming an interest rate of 10% per year, compounded semiannually.
determine if the transformation is one to one and/or onto. justify your answers. give an explanation for each of these properties.
Answers
To determine whether a transformation is one-to-one or onto, one must analyze its behavior and properties, such as passing the horizontal line test for one-to-one or checking if the range equals the codomain for onto.
In mathematical terms, a transformation refers to a function that maps elements from one set, called the domain, to another set, called the range. A transformation is said to be one-to-one if no two distinct elements in the domain are mapped to the same element in the range. This means that each element in the range is associated with a unique element in the domain.
On the other hand, a transformation is onto if every element in the range is mapped to by at least one element in the domain. In other words, for each element in the range, there exists at least one element in the domain that maps to it.
To determine whether a transformation is one-to-one or onto, one can analyze its properties and behavior. For example, a transformation is one-to-one if and only if it passes the horizontal line test. This means that no two points in the domain map to the same point on a horizontal line. To determine if a transformation is onto, one can check if the range of the transformation equals the codomain.
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The given question is incomplete, the complete question is:
How to determine the transformation is one to one and/or onto?
PLEASE HELP 30 POINTS!
Answers
Answer:
57
57
123
123
57
57
123
that's all.
Answer:
m<1 = 57°
m<2 = m<1 = 57°
m<3 = x = 123°
m<4 = x = 123°
m<5 = m<1 = 57°
m<6 = m<5 = 57°
m<7 = m<4 = 123°
Step-by-step explanation:
[tex]{ \tt{m \angle 1 + x = 180 \degree}} \\ { \colorbox{silver}{corresponding \: angles}} \\ { \tt{m \angle 1 = 180 - 123}} \\ { \tt{ \underline{ \: m \angle 1 = 57 \degree \: }}}[/tex]
Work out x. Area=194
Please help due in 2 hourss
Answers
Step-by-step explanation:
Please mark as brainliest
pls helppppppp explain !!!
Answers
Answer:
x²
Step-by-step explanation:
[tex]{ \tt{ \frac{ {x}^{ - 3} . {x}^{2} }{ {x}^{ - 3} } }} \\ \\ \dashrightarrow{ \tt{x {}^{( - 3 + 2 - ( - 3))} }} \\ \dashrightarrow{ \tt{ {x}^{( - 3 + 2 + 3)} }} \: \: \: \: \\ \dashrightarrow{ \boxed{ \tt{ \: \: \: \: {x}^{2} \: \: \: \: \: \: }}} \: \: \: \: [/tex]
A box containing 5 balls costs $8.50. If the balls are bought individually, they cost $2.00 each. How much cheaper is it, in percentage terms, to buy the box as opposed to buying 5 individual balls?
Answers
Answer: The total cost of buying 5 balls individually is $2.00 x 5 = $10.00.
The box costs $8.50, which means it is $10.00 - $8.50 = $1.50 cheaper to buy the box.
To calculate the percentage difference, we can use the formula:
% difference = (difference ÷ original value) x 100%
In this case, the difference is $1.50, and the original value is $10.00.
% difference = ($1.50 ÷ $10.00) x 100%
% difference = 0.15 x 100%
% difference = 15%
Therefore, it is 15% cheaper to buy the box than to buy 5 individual balls.
Step-by-step explanation:
A simple random sample of size n is drawn. The sample mean, x, is found to be 18.1, and the sample standard deviation, s, is found to be 4.1.
(a) Construct a 95% confidence interval about u if the sample size, n, is 34.
Lower bound: Upper bound:
(Use ascending order. Round to two decimal places as needed.)
Answers
In response to the stated question, we may state that Hence, the 95% CI function for u is (16.72, 19.48), rounded to two decimal places in increasing order.
what is function?In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v
We use the following formula to create a confidence interval around the population mean u:
CI = x ± z*(s/√n)
where x represents the sample mean, s represents the sample standard deviation, n represents the sample size, z represents the z-score associated with the desired degree of confidence, and CI represents the confidence interval.
Because the degree of confidence is 95%, we must calculate the z-score that corresponds to the standard normal distribution's middle 95%. This is roughly 1.96 and may be determined with a z-table or calculator.
CI = 18.1 ± 1.96*(4.1/√34)
CI = 18.1 ± 1.96*(0.704)
CI = 18.1 ± 1.38
Hence, the 95% CI for u is (16.72, 19.48), rounded to two decimal places in increasing order.
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Use the product of powers property to simplify the numeric expression. 2^2/5/2^1/10
Answers
Answer:
[tex] 2^\frac{3}{10} [/tex]
Step-by-step explanation:
[tex] \dfrac{2^\frac{2}{5}}{2^\frac{1}{10}} = [/tex]
[tex]= 2^{\frac{2}{5} - \frac{1}{10}}[/tex]
[tex]= 2^{\frac{4}{10} - \frac{1}{10}}[/tex]
[tex] = 2^\frac{3}{10} [/tex]
What is the correct numerical expression for "one-half the difference of 6 and 8 hundredths and 2?"
one half x (8 − 6) + 2
one half x (6 + 8 + 2)
one half x (6.08 − 2)
one half − (6.08 ÷ 2)
Answers
Answer: c
Step-by-step explanation: i dont have one
1/2 x (6.08 - 2) (6.08 - 2) is the correct numerical expression for "one-half the difference of 6 and 8 hundredths and 2 " .
what is expression ?An expression, as used in computer programming, is a grouping of values, variables, operators, and/or function calls that the computer evaluates to produce a final value. For instance, the equation 2 + 3 combines the numbers 2 and 3 using the + operator to produce the number 5. Similar to this, the equation x * (y + z) produces a value based on the current values of the variables x, y, and z by combining the variables x, y, and z with the * and + operators.
given
In terms of numbers, the phrase "one-half the difference of 6 and 8 hundredths and 2" is expressed as follows:
1/2 x (6.08 - 2) (6.08 - 2)
1/2 x (6.08 - 2) (6.08 - 2) is the correct numerical expression for "one-half the difference of 6 and 8 hundredths and 2 " .
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Find X using the picture below.
Answers
Answer: 37.5
Step-by-step explanation:
75 - 180 = 105
105 degrees = the obtuse angle, bottom triangle.
75/2= 37.5 (since both sides of the bottom triangle are equal angles)
describe all the x -values at a distance of 13 or less from the number 8 . enter your answer in interval notation.
Answers
The set of all x-values that are at a distance of 13 or less from the number 8 in the interval notation is given by [ -5, 21 ].
The distance between x and 8 is |x - 8|.
Find all the values of x such that |x - 8| ≤ 13.
This inequality can be rewritten as follow,
|x - 8| ≤ 13
⇒ -13 ≤ x - 8 ≤ 13
Now,
Adding 8 to all sides of the inequality we get,
⇒ -13 + 8 ≤ x - 8 + 8 ≤ 13 + 8
⇒ -5 ≤ x ≤ 21
Therefore, all the x-values which are at a distance of 13 or less from the number 8 represented in the interval notation as [ -5, 21 ].
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The scale on a map is 1:320000
What is the actual distance represented by 1cm?
Give your answer in kilometres.
Answers
By answering the presented question, we may conclude that Therefore, 1 expressions cm on the map corresponds to a real distance of 3.2 km.
what is expression ?In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
Scale 1:
320000 means that 1 unit on the map represents his 320000 units in the real world.
To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.
1 kilometer = 100000 cm
So,
1 unit on the map = 320000 units in the real world
1 cm on the map = (1/100000) km in the real world
Multiplying both sides by 1 cm gives:
1 cm on the map = (1/100000) km * 320000
A simplification of this expression:
1 cm on the map = 3.2 km
Therefore, 1 cm on the map corresponds to a real distance of 3.2 km.
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Find x, if √x +2y^2 = 15 and √4x - 4y^2=6
Answers
Answer:
x = 52.2
Step-by-step explanation:
Add 4x - 4y^2 = 36 and x + 2y^2 = 225
x + 2y^2 + 4x - 4y^2 = 225 + 36
5x = 261
x = 261/5=52.2
Find the product of 3√20 and √5 in simplest form. Also, determine whether the result is rational or irrational and explain your answer.
Answers
Answer:
30, rational
Step-by-step explanation:
[tex]3\sqrt{20}\cdot\sqrt{5}=3\sqrt{4}\sqrt{5}\cdot\sqrt{5}=(3\cdot2)\cdot5=6\cdot5=30[/tex]
The result is rational because it can be written as a fraction of integers.
In the year 1985, a house was valued at $108,000. By the year 2005, the value had appreciated to $148,000. What was the annual growth rate percentage between 1985 and 2005? Assume that the value continued
to grow by the same percentage. What was the value of the house in the year 2010?
Answers
Answer:
To find the annual growth rate percentage, we can use the formula:
annual growth rate = [(final value / initial value)^(1/number of years)] - 1
where "final value" is the value in the ending year, "initial value" is the value in the starting year, and "number of years" is the total number of years between the starting and ending years.
Using the given values, we have:
annual growth rate = [(148,000 / 108,000)^(1/20)] - 1
= 0.0226 or 2.26%
So the house appreciated at an annual growth rate of 2.26%.
To find the value of the house in 2010, we can use the same growth rate to project the value from 2005 to 2010:
value in 2010 = 148,000 * (1 + 0.0226)^5
= $175,465.11 (rounded to the nearest cent)
Therefore, the value of the house in the year 2010 was $175,465.11.
