How to find the inverse of this matrix
[tex]\left[\begin{array}{ccc}1&0\\0&3\\\end{array}\right][/tex]

Answers

Answer 1

Answer:

Here we have the matrix:

[tex]M = \left[\begin{array}{ccc}1&0\\0&3\end{array}\right][/tex]

And we want to find its inverse.

The inverse of a 2x2 matrix A is:

(1/det(A))*adj(A)

where det(A) is the determinant of the matrix.

Such that for a matrix:

[tex]A = \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right][/tex]

The determinant is:

det(A) = a₁₁*a₂₂ - a₁₂*a₂₁

in the case of our matrix M, the determinant is:

det(M) = 1*3 - 0*0 = 3

and adj(A) is a transposition along the diagonal, and for the other elements, we just change its sign.

Then for our matrix A we would have:

[tex]adj(A) = \left[\begin{array}{ccc}a_{22}&-a_{12}\\-a_{21}&a_{11}\end{array}\right][/tex]

Then for our matrix M, we have:

[tex]adj(M) = \left[\begin{array}{ccc}3&-0\\-0&1\end{array}\right][/tex]

Then the inverse of the matrix M is:

[tex]M^{-1} = \frac{1}{det(M)} *adj(M) = \frac{1}{3}\left[\begin{array}{ccc}3&0\\0&1\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1/3\end{array}\right][/tex]


Related Questions

What's an equivalent fraction of 3/4 that has a denominator of 32

Answers

Answer:

24/32

Step-by-step explanation:

[tex]\frac{3}{4} = \frac{x}{32}[/tex]

To get from 4 to 32, you multiply by 8

so to get from 3 to x, multiply by 8

The answer for this would be 24/32

The SAT and ACT college entrance exams are taken by thousands of students each year. The scores on the exam for any one year produce a histogram that looks very much like a normal curve. Thus, we can say that the scores are approximately normally distributed. In recent years, the SAT mathematics scores have averaged around 480 with standard deviation of 100. The ACT mathematics scores have averaged around 18 with a standard deviation of 6.
a. An engineering school sets 550 as the minimum SAT math score for new students. What percent of students would score less than 550 in a typical year?
b. What would the engineering school set as comparable standard on the ACT math test?
c. What is the probability that a randomly selected student will score over 700 on the SAT math test?

Answers

Answer:

a) 75.8% of students would score less than 550 in a typical year.

b) The comparable standard would be a minimum ACT score of 22.2.

c) 0.0139 = 1.39% probability that a randomly selected student will score over 700 on the SAT math test.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Question a:

SAT, so mean of 480 and standard deviation of 100, that is, [tex]\mu = 480, \sigma = 100[/tex]

The proportion is the p-value of Z when X = 550. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{550 - 480}{100}[/tex]

[tex]Z = 0.7[/tex]

[tex]Z = 0.7[/tex] has a p-value of 0.758.

0.758*100% = 75.8%

75.8% of students would score less than 550 in a typical year.

b. What would the engineering school set as comparable standard on the ACT math test?

ACT, with a mean of 18 and a standard deviation of 6, so [tex]\mu = 18, \sigma = 6[/tex]

The comparable score is X when Z = 0.7. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.7 = \frac{X - 18}{6}[/tex]

[tex]X - 18 = 0.7*6[/tex]

[tex]X = 22.2[/tex]

The comparable standard would be a minimum ACT score of 22.2.

c. What is the probability that a randomly selected student will score over 700 on the SAT math test?

This is 1 subtracted by the p-value of Z when X = 700, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{700 - 480}{100}[/tex]

[tex]Z = 2.2[/tex]

[tex]Z = 2.2[/tex] has a p-value of 0.9861.

1 - 0.9861 = 0.0139

0.0139 = 1.39% probability that a randomly selected student will score over 700 on the SAT math test.

The smallest whole number is _______.

Answers

Step-by-step explanation:

The smallest whole number is 0 .

Which of the following points would fall on the line produced by the point-slope form equation y - 10 = 3(x - 11) when graphed?

Answers

Answer:

(-5,-37)

(-4,-34)

(-3,-31)

(-2,-28)

(-1,-25)

(0,-22)

(1,-19)

(2,-16)

(3,-13)

(4,-10)

(5,-7)

(6,-4)

Step-by-step explanation:

y - 10 = 3(x - 11)

y - 10 = 3x - 33

y = 3x -22

Gina charges an initial fee and an hourly fee to babysit. Using the table below find the hourly fee and the initial fee that
Gina charges to babysit. Show work.

Answers

By analyzing this graph we can see that it is a linear relation. Meaning that the Rate of Change is a consistent number, in this case $7. We know its $7 because by looking at the y coordinate for all present coordinates we can see a consistent difference of $7. From this point you could work backwards. Finding the coordinates for the first hour, which by doing $26 - $7 tells us the missing number for the first coordinate pair (1,19). Then we work backwards one more time, this time subtracting $7 from $19, and this tells us the initial value (the coordinate on the y-axis), which is $12. One thing you can do to show your work is draw a straight line that intersects all the coordinates and the y-axis, the line should intersect the y-axis at these coordinates (0,12). Now I could be wrong but if there is a formula that is used to determine this answer then I am unaware of it. Hope this helps however

To study the mean respiratory rate of all people in his state, Frank samples the population by dividing the residents by towns and randomly selecting 12 of the towns. He then collects data from all the residents in the selected towns. Which type of sampling is used

Answers

Answer:

Cluster Sampling

Step-by-step explanation:

Cluster Sampling involves the random sampling of observation or subjects, which are subsets of a population. Cluster analysis involves the initial division of population subjects into a number of groups called clusters . From the divided groups or clusters , a number of groups is then selected and it's elements sampled randomly. In the scenario above, the divison of the population into towns where each town is a cluster. Then, the selected clusters (12) which are randomly chosen are analysed.

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1100 bacteria selected from this population reached the size of 1177 bacteria in three hours. Find the hourly growth rate parameter. Note: This is a continuous exponential growth model. Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.

Answers

Answer:

Rate = 10^(log[Ending Amount / Beginning Amount] ÷ time)  -1

Rate = 10^(log(1177 / 1100) ÷ time) -1

Rate = 10^(log( 1.07) ÷ 3) -1

Rate = 10^(0.029383777685 /3) -1

Rate = 10^(0.0097945926) -1

Rate = 1.0228091219 -1

Rate = .0228091219% / hour

Source http://www.1728.org/expgrwth.htm

Step-by-step explanation:

USE THE PRESENT VALUE FORMULA TO CALCULATE THE AMOUNT OF MONEY THAT MUST BE INVESTED NOW AT 9% ANNUALLY COMPOUNDED QUARTERLY TO OBTAIN 1,000 IN 4 YEARS.

Answers

Answer:

The amount of money that must be invested is $252.

Step-by-step explanation:

Present value formula:

The present value formula is given by:

[tex]P = \frac{F}{(1+r)^n}[/tex]

In which:

P is the present value.

F is the future value.

r is the interest rate.

n is the number of periods.

9% ANNUALLY

This means that [tex]r = 0.09[/tex]

COMPOUNDED QUARTERLY TO OBTAIN 1,000 IN 4 YEARS.

Obtain 1000 means that [tex]F = 1000[/tex]

Compounded quarterly in 4 years, so 4*4 = 16 periods and [tex]n = 16[/tex].

Amount of money that must be invested:

[tex]P = \frac{F}{(1+r)^n}[/tex]

[tex]P = \frac{1000}{(1+0.09)^{16}}[/tex]

[tex]P = 252[/tex]

The amount of money that must be invested is $252.

As...
Which of the following geometric series diverges?

Answers

Answer:

II and II only.

Step-by-step explanation:

The first series converges because the common ratio r is 0.8 (<1).

II diverges as |r| > 1.

III is an alternating series with r = -4 - that is |r| = 4 so it diverges.

From the given-series, the series which diverges are : (ii) 4 + 8 + 16 + 32; and (iii) 2 - 8 + 32 - 128 + ..., So, correct option is (a) (ii) and (iii) only.

In option (ii), the series 4 + 8 + 16 + 32 is a geometric series with a common ratio of 2. We see that the "common-ratio" is greater than 1, this series diverges.

In option (iii), the series 2 - 8 + 32 - 128 is a geometric series with a common-ratio of |-4| = 4. We see that the "absolute-value" of the "common-ratio" is greater than 1, this series also diverges.

But, in option (i), the series -9.2 - 7.36 - 5.888 - 4.7104 is a geometric series with a common ratio of |-0.8| = 0.8. Since the "absolute-value" of the "common-ratio" is less than 1, this series converges.

Therefore, the correct answer is (a) (ii) and (iii) only.

Learn more about Series here

https://brainly.com/question/12725407

#SPJ6

Can some please help please thank you

Answers

Answer:

D. ( f + g)(x) = 2x^3 + 3x^2 - 5x - 3

The answer to this is D

5/10+4/16 in simplest form

Answers

Answer:

3/4

Step-by-step explanation:

5/10 can be written as 8/16

8/16 + 4/16 = 12/16 or 3/4

Rearrange to make P the subject, :)..​

Answers

Answer:  [tex]P = \frac{25}{E^2}-Q\\\\[/tex]

Work Shown:

[tex]E = 5\left(\sqrt{\frac{1}{P+Q}}\right)\\\\5\left(\sqrt{\frac{1}{P+Q}}\right) = E\\\\\sqrt{\frac{1}{P+Q}} = \frac{E}{5}\\\\\frac{1}{P+Q} = \left(\frac{E}{5}\right)^2\\\\\frac{1}{P+Q} = \frac{E^2}{25}\\\\P+Q = \frac{25}{E^2}\\\\P = \frac{25}{E^2}-Q\\\\[/tex]

if qqq=90 what's qqqq+87​

Answers

Answer: [tex]90\sqrt[3]{90}+87[/tex]

Step-by-step explanation:

[tex]qqq=90\\q^3=90\\\sqrt[3]{q^3} =\sqrt[3]{90}\\q= \sqrt[3]{90}\\\\qqqq+87\\q^3q^1+87\\90\sqrt[3]{90}+87[/tex]

2. How many solutions does this system of equations have? *
y = 5x – 2
y = 5x + 7

Answers

Answer:

No solution.

Step-by-step explanation:

[tex]{ \sf{y = ±∞ \: \: and \: \: x = ±∞}}[/tex]

NO SOLUTIONS!! You’re welcome

Instructions: Find the missing side. Round your answer to the nearest tenth.
22
58°

Answers

Answer:

x = 19.2

Step-by-step explanation:

tan(58)=x/12

x=12×tan(58)

x=19.2

Answered by GAUTHMATH

Find the arc length of the 3/4 of a circle with a radius of 5

Answers

Answer:

7.5 pi

Step-by-step explanation:

The formula for arc length of a sector is denoted as

[tex]\frac{x}{360}2\pi r[/tex], where x is the central angle of the sector.

Since the sector is 3/4 of a circle, the central angle will be 3/4 of 360 degrees.

3/4 of 360 is 270, so we have our central angle. We also have our radius which we can plug into the formula.

[tex]\frac{270}{360}2(5)\pi[/tex]

2 times 5 is equal to 10, and 270/360 simplifies to 3/4. 3/4 times 10 is equal to 7.5, so the answer is 7.5 pi

Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean.

Test scores: n = 92, = 90.6, σ = 8.9; 99% confidence

Options:
A.) 88.2 < μ < 93.0
B.) 88.4 < μ < 92.8
C.) 89.1 < μ < 92.1
D.) 88.8 < μ < 92.4

Answers

Answer: Choice A.)   88.2 < μ < 93.0

=============================================================

Explanation:

We have this given info:

n = 92 = sample sizexbar = 90.6 = sample meansigma = 8.9 = population standard deviationC = 99% = confidence level

Because n > 30 and because we know sigma, this allows us to use the Z distribution (aka standard normal distribution).

At 99% confidence, the z critical value is roughly z = 2.576; use a reference sheet, table, or calculator to determine this.

The lower bound of the confidence interval (L) is roughly

L = xbar - z*sigma/sqrt(n)

L = 90.6 - 2.576*8.9/sqrt(92)

L = 88.209757568781

L = 88.2

The upper bound (U) of this confidence interval is roughly

U = xbar + z*sigma/sqrt(n)

U = 90.6 + 2.576*8.9/sqrt(92)

U = 92.990242431219

U = 93.0

Therefore, the confidence interval in the format (L, U) is approximately (88.2, 93.0)

When converted to L < μ < U format, then we get approximately 88.2 < μ < 93.0 which shows that the final answer is choice A.

We're 99% confident that the population mean mu is somewhere between 88.2 and 93.0

please can anyone help me with this question what is the probability of the spinner landing on an even number.​

Answers

1/2 chance it will land on an even number


Explanation there is 4 even numbers and 4 odd numbers meaning it’s a 50/50 chance

What is the value of the x variable in the solution to the following system of equations? (5 points) 2x − 3y = 3 5x − 4y = 4 Select one: a. −1 b. 0 c. x can be any number as there are infinitely many solutions to this system d. There is no x value as there is no solution to this system

Answers

Answer:

D. There is no x value as there is no solution to this system

Step-by-step explanation:

2x − 3y = 3                                  5x − 4y = 4

5x - 4y = 4               -4y = -5x + 4                         y = 5/4x - 1

2x - 3(5/4x - 1) = 3

2x - 15/4x + 3 = 3

-7/4x = 0

x = 0

Exercise 6.2
1.
a.
The total cost function is given by C = 100 - 5x + 7x2, find
the average cost and marginal cost.

Answers

9514 1404 393

Answer:

average cost = 7x -5 +100/xmarginal cost = 14x -5

Step-by-step explanation:

The average cost is the total cost divided by the number of units produced:

  average cost = C/x = 100/x -5 +7x

__

The marginal cost is the derivative of the total cost function.

  marginal cost = -5 +14x

1/6+4/18 in simplest form

Answers

Answer:

7/18

Step-by-step explanation:

1/6 x 3 = 3/18

3/18 + 4/18 = 7/18

Answer:

7/18

Step-by-step explanation:

Make the denominators the same!

You can turn 1/6 into 3/18 by multiplying the numerator and denominator by 3. Then you add the numerators of 3/18 and 4/18 together to get 7/18.

It can't be simplified any further :)

PLEASEEEE PLEASEEEE HELPPPP

i need an equation for a vertical line going through f(x) = 2x^2 + 6x + 2

Answers

Answer:

dont understand clearly

Step-by-step explanation:

dont understand clearly

Please use the accompanying Excel data set or accompanying Text file data set when completing the following exercise. A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected and the diameter is measured. The resulting data (in millimeters) are as follows: No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Dia. 8.23 8.16 8.23 8.25 8.26 8.23 8.20 8.26 8.19 8.23 8.20 8.28 8.24 8.25 8.24 Use the data above to calculate a 95% two-sided confidence interval on the mean rod diameter. Assume the data are normally distributed. (a) Calculate the sample mean and standard deviation. Round the sample mean and the sample standard deviation to 2 and 3 decimal places respectively (e.g. 98.76 and 98.765). (b) Calculate the 95% two-sided confidence interval on the true mean rod diameter. Round your answers to 3 decimal places (e.g. 98.765).

Answers

Answer:

(8.213 ; 8.247)

Step-by-step explanation:

Given the data :

No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Dia. 8.23 8.16 8.23 8.25 8.26 8.23 8.20 8.26 8.19 8.23 8.20 8.28 8.24 8.25 8.24

Sanple size, n = 15

Sample mean, xbar = Σx / n = 123.45 / 15 = 8.23

The sample standard deviation, s = √(x -xbar)²/n-1

Using calculator :

Sample standard deviation, s = 0.03116

s = 0.031 (3 decimal places)

The 95% confidence interval :

C.I = xbar ± (Tcritical * s/√n)

Tcritical at 95%, df = 15 - 1 = 14

Tcritical = 2.145

C.I = 8.23 ± (2.145 * 0.031/√15)

C.I = 8.23 ± 0.0171689

C.I = (8.213 ; 8.247)

State if the scenario involves a permutation or a combination. Then find the number of possibilities.

The student body of 290 students wants to elect a president and vice president.

Permutation/Combination:

Answer:

Answers

Answer:

Permutation. ; 83810 ways

Step-by-step explanation:

Permutation and combination methods refers to mathematical solution to finding the number of ways of making selection for a group of objects.

Usually, selection process whereby the order of selection does not matter are being treated using permutation, while those which takes the order of selection into cognizance are calculated using combination.

Here, selecting 2 members (president and vice president) from 290 ; since order of arrangement does not matter, we use permutation ;

Recall :

nPr = n! ÷ (n - r)!

Hence,

290P2 = 290! ÷ (290 - 2)!

290P2 = 290! ÷ 288!

290P2 = (290 * 289) = 83810 ways

Given f(x) =x^2 , after performing the following transformations: shift upward 84 units and shift 13 units to the right, the new function g(x) =

Answers

g(x) = (x - 13)^2 + 84

= x^2 - 26x + 169 + 84

= x^2 - 26x + 253

Bill wants to attend a college with a current tuition of $10,000 a year. He will graduate from high school in five years. Roughly how much will Bill need to save for one-year’s tuition to account for an annual rate of inflation of 3%?
A. $638.30
B. $667.50
C. $656.50
D. $633.30

Answers

Answer:

I think the anser is 667.50

Step-by-step explanation:

A rectangular floor is 9 yards long and 3 yards wide. What is the area

Answers

Answer:

27 yards

Step-by-step explanation:

Area = Length • Width

Area = 9 • 3

Area = 27yrds

A store surveyed their customers to find out their ages. The bar graph below shows the number of customers in each age group. What percent of customers surveyed were over 50%? Round your answer to 1 decimal place.

Answers

Bar graphs are used to represent data, where the vertical axis represents the frequency and the horizontal axis.

The percentage that is over 50 is 15.6%:

The data on the bar graph can be represented as:

Under 17 [tex]\to[/tex] 25

18 - 24 [tex]\to[/tex] 35

25 - 34 [tex]\to[/tex] 40

35 - 50 [tex]\to[/tex] 35

Over 50 [tex]\to[/tex] 25

So, the total customer surveyed are:

[tex]Total = 25 + 35 + 40 + 35 + 25[/tex]

[tex]Total = 160[/tex]

The percentage over 50 are:

[tex]\%Over\ 50 = \frac{Over\ 50}{Total } * 100\%[/tex]

[tex]\%Over\ 50 = \frac{25}{160} * 100\%[/tex]

[tex]\%Over\ 50 = 0.15625* 100\%[/tex]

[tex]\%Over\ 50 = 15.625\%[/tex]

Approximate

[tex]\%Over\ 50 = 15.6\%[/tex]

Read more at:

https://brainly.com/question/10440833

I need help ASAP please!

Answers

Answer:

Option C

We need to make the negative exponent positive.

The rule is: [tex]A^{-B} =\frac{1}{A^{B} }[/tex]

Here, A=x, B= 12

[tex]so,[/tex] [tex]x^{-12}[/tex]

[tex]=\frac{1}{x^{12} }[/tex]

OAmalOHopeO

ive gotten it wrong like 4 times n i cannot figure it out pls help

Answers

I think it would be

X= 101cos(222.2) =-74.82 or 74.82 tithe left.

I’m not sure.. hope it is right :)

Answer:

x = 74.74 m

Step-by-step explanation:

you need simple trigonometry to solve it

cosine of an angle is the ratio of the adjacent side to the hypotenuse

cos(42.2) is about 0.74

so X / Hypotenuse = 0.74

we know hypotenuse is 101 m

X / 101 = 0.74

x = 74.74 m

hope this helped!

Other Questions
explain the kinds of adjective All points of the step function f(x) are graphed.On a coordinate plane, a step graph has horizontal segments that are each 2 units long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The left-most segment goes from (negative 4, 1) to (negative 2, 1). Each segment is 1 unit higher and 2 units farther to the right than the previous segment. The right-most segment goes from (2, 4) to (4, 4).What is the domain of f(x)?{x| 4 < x 4}{x| 3 < x 4}{x| 1 < x 4}{x| 2 < x 4} awncer this question https://brainly.com/question/24294790?utm_source=android&utm_medium=share&utm_campaign=question this is the other page of this paper awncer this also plz pls pls pls help meeeeee Please help me solve for this don't report I did NOT ignore the Honor rule To qualify for a certain car loan, a customer must have a credit score of at least 600. In addition, the cost of the car must be at least $5000. Define the variables, write a system of inequalities to represent this situation, and name one possible solution. Angela works a basic week of 40 hours and her hourly rate of pay is $12.50. Calculate her weekly wage. You discover a beautiful island where you decide to build a new society. What is the first rule you put in place? . Plants prepare their food on their............(leaves\roots) Why does increasing the temperature make a solid dissolve faster?- The solvent molecules bump into the solid more often.- The solid is melted before mixing into the liquid.- The chemical bonds of the solid are broken faster.- The pressure of the solute on the solid is increased. Nould you like me to tell you un cuento? Okey, let me tell you un cuento about some naugS--some muchachos y some muchachas-- who were playing with a ball in la calle near unayou can see la casa. Mi cuento concerns estos muchachos, la pelota that they are playingventana on la segunda story de la casa.Besides being about some muchachos playing pelota en la calle near una casa with glassthis cuento is about un hombre who is el owner de la casa. This hombre is not out en la calleTranslate into English 5. Dylan walks into a video arcade with a pocketful of quarters. He spends themat a rate of nine every half hour until he runs out. If the amount of quarters Dylanhas is graphed over time, which feature of the graph corresponds to Dylan'sinitial amount of quarters, before he spends the first one?The y-interceptThe slopeThe x-interceptThe minimum value factorise: 30x^5+15xy+xy Answer this question that is given Help plz!! Trig question Angelika is the Chief Operating Officer of One Spice Inc., a firm that grows and processes the Naga Viper pepper, one of the world's hottest peppers. Angelika wants to better understand the relationship between her firm's organizational culture and the ability to achieve competitive advantage. The relationship between these two states that:______.a. having a strong culture leads to achieving a competitive advantage only when companies are pursuing a cost leadership strategy.b. a firm can achieve a competitive advantage when their organizational culture follows the VRIO principles.c. having a strong culture leads to a competitive advantage only when companies are pursuing a differentiation strategy.d. having a strong culture always leads to achieving a competitive advantage because it leads to greater employee engagement. Complete each sentence with the past simple or past continuous form of the verb in brackets The equation of the line in the xy-plane that has slope 7/6 and passes through (9.-6) isa. O 6x-7y+27 = 0b. O 7x+6y-27 = 0c. O 6x+7y-27=0d. 0 6x+7 y+27 = 0e. O -7x+6y+99 = 0f.No Answer B. Adjectives into nouns: write the appropriate noun in the second sentence, so that it has asimilar meaning to the first.1. The scene was so beautiful that it took her breath away.The _____________________ of the scene took her breath away.2. They measured how wide the road was.They measured the _______________________ of the road.3. The fact that he was thin put off directors.His _______________________ put off the directors.C. Combine the sentences replacing the adjective with a noun:1. My sister was cheerful. This made me forget all my troubles._________________________________________________________________________2. The Mosque's foundations are strong. This stopped it from collapsing in the earthquake._________________________________________________________________________3. The crate is heavy. It slowed Ram's progress._________________________________________________________________________ A landowner owned a large piece of property containing an inn and a bakery. She entered into a contract to sell the property to a purchaser for $1 million. The contract was recorded. The purchaser gave the landowner $200,000 as earnest money. The closing date was set for September 10, two months after the signing of the contract. On August 10, an arsonist set fire to the inn, which burned to the ground. On September 10, the landowner appeared at the closing and tendered the deed to the property. The buyer refused to tender the remaining $800,000 of the purchase price and demanded the return of his earnest money. The landowner sued the buyer for specific performance of the contract. The buyer countersued for the return of his earnest money. Both parties stipulate that the value of the property without the inn is $600,000, that insurance on the property had lapsed, and that the common law, unmodified by statute, applies. What is the most likely result at trial