Problem 2 (D.16 Exercise 5, p 511). Forty rats are placed at random in a house having 4 rooms. There is one door between rooms 1 and 2, one door between rooms 1 and 4, one door between rooms 2 and 4, one door between rooms 2 and 3, and two doors between rooms 3 and 4 see the book for a picture). There are no doors between rooms 1 and 3. After each minute, a rat may change rooms, or stay still. All possibilities are equally likely. So, here is the transition matrix: [1/3 1/4 0 1/5 ] 1/3 1/4 1/4 1/5 0 1/4 1/4 2/5 1/3 1/4 1/2 1/5 Predict the long-term distribution of rats. What is the long-term probability that a given marked rat is in room 4? You must use the method of eigenvalues and eigenvectors.

Answer:

  A, B, C

Step-by-step explanation:

You want to find the dimensions, perimeter, and area of a foundation such that the length is 6 feet more than twice the width, and the area is 1046 more that the value of the perimeter.

We can let x and y represent the length and width, respectively. Then the given relations translate to the equation ...

  A = LW . . . . . . . area formula

  P = 2(L +W) . . . . perimeter formula

  y = 2x +6 . . . . . relation between dimensions

  xy = 2(x +y) +1046 . . . . . relation between perimeter and area

Using the first equation to substitute for y, we have ...

  x(2x +6) = 2(x +(2x +6)) +1046

  2x² +6x = 6x +1058 . . . . . . . . . . . . eliminate parentheses

  x² = 529 . . . . . . . . . . . . . subtract 6x and divide by 2

  x = √529 = 23 . . . . . . . . . width; matches B

  y = 2(23) +6 = 52 . . . . length

  area = (23)(52) = 1196 . . . area; matches A

  perimeter = 2(23 +52) = 2(75) = 150 . . . . matches C

The area is 1196 square feet. (A)

The width is 23 feet. (B)

The perimeter is 150 feet. (C)

The expressions for the total costs are 2L + 0.7L  and 2.7L

From the question, we have the following parameters that can be used in our computation:

Number of litres = 3

Regular price = L

Discount = 30%

This means that there is a discount on the third item

So, we have the following expression

Total amount = 2 * L + L * (1 - discount)

Substitute the known values in the above equation, so, we have the following representation

Total amount = 2 * L + L * (1 - 30%)

Total amount = 2 * L + L * 0.7

This gives

Total amount = 2L + 0.7L

Evaluate the sum

Total amount = 2.7L

Hence, the expression is 2.7L

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The expression for the total cost of 3 liters of shampoo is written as

Let L be the regular price of a liter bottle

The expression is written in decimal and in fraction

For the promotion buy 2 liters get 30% of 3rd liter

30% off = 0.3 off

= (1 - 0.3)

= 0.7

The total cost will be

= 2 * L + 0.7 * L

= 2L + 0.7L

= 2.7 L

The cost of three bottles of shampoo is 2.7L

In another way

= 2L + (1 - 0.3)L

= 2L + 0.7L

using fractions

= 2L + 7L/10

= 27L/10

the other way is writing in fraction

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Answer:

∠N° = 19°

∠M° = 35°

∠L° = 126°

Step-by-step explanation:

Total angle in a triangle: 180°

∠N° = x°

∠M° = ( 2x - 3 )°

∠L° = ( 7x - 7 )°

180 = N + M + L

180 = x + 2x - 3 + 7x - 7

180 = 10x - 10

10x = 180 + 10

10x = 190

Divide both side by 10

x = 19

∠N° = x° = 19°

∠M° = ( 2x - 3 )° = ( 2(19) - 3 )° = 35°

∠L° = ( 7x - 7 )° = ( 7(19) - 7 )° = 126°

The region inside the unit circle centered at the origin is 1. positive 2. positive 3. positive 4. positive 5. negative

Without calculation we need to state if the each of the integrals below are positive, negative, or zero. let d be the region inside the unit circle centered at the origin

xeˣ is positive for positive , and negative for negative , but the exponential factor makes the positive part dominating, so that the integral over D is positive overall.

The integrals over B and T are identical by symmetry, and both are equal to half the value of the integral over D, so they are both positive as well.

The integral over L is negative because it takes strictly non-positive values of x .

Similarly, the integral over R is positive because it considers non-negative values of x.

Therefore, the region inside the unit circle centered at the origin is 1. positive 2. positive 3. positive 4. positive 5. negative

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The p - value of the given hypothesis is P(2<x<6.75) is 0.49974

How to calculate p - value?

In statistics,  p-value is calculated using integral calculus from the area under the probability distribution curve for all values of statistics that are at least as far from the reference value as the observed value is, relative to the total area under the probability distribution curve.

Here we have given that an article in neurology (1998, vol. 50, pp. 1246-1252) discussed that monozygotic twins share numerous physical, psychological, and pathological traits. the investigators measured an intelligence score of 10 pairs of twins, and the data.

And we need to find the value of p from it.

Here we have the following sample data,

=>2,5.73,5.80,6.08,6.22,7.99,7.44,6.48,7.99,6.32,7.60,6.03,7.52,8.42,6.84,6.43,8.76,6.32,7.62,6.59,7.67

Through the sample data we ahve identified the following values,

Standard Deviation, σ: 1.3737491940207

Count, N: 21

Sum, Σx: 141.85

Mean, μ: 6.7547619047619

Variance, σ2:  1.8871868480726

in order to find the p-value, we have to calculate the z score for the given data,

Z score = (x - μ)/σ

=> (2 - 6.75)/ 1.37

=> -3.46715

P-value from Z-Table:

=> P(x<2) = 0.000263

=> P(x>2) = 1 - P(x<2) = 0.99974

=> P(2<x<6.75) = 0.5 - P(x<2) = 0.49974

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Answer:

(−3, 2); 2 < y < ∞

Step-by-step explanation:

It's either (−3, 2); 2 < y < ∞ or (−3, 2); −∞ ≤ y < ∞ but I'm pretty sure its (−3, 2); 2 < y < ∞

x = number of small boxes

y = number of large boxes

well, we know a total of 20 boxes, large and small were shipped, that means that whatever "x" and "y" may be, we know that x + y = 20.

so the volume of one small box is 8 ft³, so sticking to ft³, we can say that the volume of 1 box is 8(1) ft³, and the volume of 2 boxes will then be 8(2) and three is 8(3) ft³ and the volume of "x" boxes will then just be 8(x) ft³.

now, we can say the same thing about large boxes, volume of 1 is 21(1) ft³, for two is 21(2) ft³, for three 21(3) ft³, and for "y" boxes that'll just be 21(y) ft³.

that said, well hell their volume combined must be 8x + 21y, and we happen to know that's 264 ft³, namely 8x + 21y = 264.

[tex]\begin{cases} x+y=20\\\\ 8x+21y=264 \end{cases}\hspace{5em}\stackrel{\textit{using the 1st equation}}{x+y=20\implies }y=20-x \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{8x+21(\underset{y}{20-x})=264}\implies 8x+420-21x=264 \\\\\\ 8x+420=264+21x\implies 8x+156=21x\implies 156=13x \\\\\\ \cfrac{156}{13}=x\implies \boxed{12=x}\hspace{13em}\stackrel{20~~ - ~~12}{\boxed{y=8}}[/tex]

The value of the estimated standard error is 1.

The set of d (differneces) scroes: 4, 8, 4 ,4

Consider,

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

Mean of the D-score is [tex]$$\begin{aligned}\bar{d} & =\frac{1}{n} \sum d_i \end$[/tex]

[tex]=\frac{1}{4}[/tex](4+8+4+4)

=5

Standard deviation of D-score is given by [tex]$$\begin{aligned}\hat{\sigma} & =\sqrt{\frac{1}{n-1} \sum_{i=1}^n\left(d_i-\bar{d}\right)^2} \\& =\sqrt{\frac{1}{4-1}\left\{(4-5)^2+(8-5)^2+(4-5)^2+(4-5)^2\right\}} \end[/tex]

The value of the estimated standard error for the following set D scores is

[tex]$$\begin{aligned}\widehat{\mathrm{SE}(d)} & =\frac{\hat{\sigma}}{\sqrt{n}} \\& =\frac{2}{\sqrt{4}}\end{aligned}$$[/tex]

[tex]=\frac{2}{2}=1[/tex]

Therefore, the value of the estimated standard error for the following set of d scroes is 1.

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Answer:

=3−√3 (Decimal: 1.267949)

Step-by-step explanation:

3−√3

=3−√3 (Decimal: 1.267949)

This is the best I could do! hope it helps!!

Answer: 1

Step-by-step explanation: So, since this is a subtraction problem of negative numbers, we will make this an inverse operation, and make this an addition problem (It's easier to solve) So, now it will be written as -9 + 10. This is the same as 10-9, which would give us our answer; 1. I hoped this helped.

Answer:

True

Step-by-step explanation:

The general indefinite integral of ([tex]e^{x}[/tex]+ 1/8x) is ∫([tex]e^{x}[/tex]+ 1/8x) dx

= [tex]e^{x}[/tex]+ 1/4x + C

An integral is considered to be indefinite if it has no upper or lower bounds.

The most generic anti-derivative of f(x) is known as an indefinite integral and denoted, in mathematics, by F(x), which is any anti-derivative of f(x).

f(x) dx = F(x) + C

The integral of [tex]e^{x}[/tex] = [tex]e^{x}[/tex]

so ∫[tex]e^{x}[/tex] dx = [tex]e^{x}[/tex] + C

The integral of 1/8x = 1/4x,

so ∫1/8x dx = 1/4x + C

To find the integral of ([tex]e^{x}[/tex] + 1/8x), add the integrals of each term:

∫([tex]e^{x}[/tex]+ 1/8x) dx = [tex]e^{x}[/tex] + 1/4x + C

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f 57 and 63 are the 90% confidence limits for the population mean, then [60, 60] might be the 97% confidence limit.

A population is a discrete collection of things having observable traits, such humans or animals, for the purpose of analysis and data collection. It is made up of a comparable collection of species that live in a specific area and have the ability to interbreed.

The average calculated from the whole population, distribution, or group is known as the population mean. It is calculated by dividing the total number of population variables by the sum of all population variables. The population mean can be found here as. Observations in the population are added together to form X.

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Answer:

That looks correct to me!

Answer:

8x + y > 4

y > -8x + 4

Step-by-step explanation:

To find the total time required to produce each product, we can add up the machining, polishing, and assembling hours for each product. For example, for Product I, the total time required would be:

Total time for Product I = 3 hours + 1 hour + 2 hours = 6 hours

We can do this for each product to find the total time required for all four products:

Total time for Product I = 3 hours + 1 hour + 2 hours = 6 hours

Total time for Product II = 2 hours + 1 hour + 1 hour = 4 hours

Total time for Product III = 2 hours + 2 hours + 2 hours = 6 hours

Total time for Product IV = 4 hours + 3 hours + 1 hour = 8 hours

So, the total time required to produce all four products is 6 hours + 4 hours + 6 hours + 8 hours = 24 hours.

Answer:

[tex]\dfrac{x\sqrt{4-x^2}}{4-x^2}[/tex]

Step-by-step explanation:

Given:

[tex]\tan \left(\sin^{-1}\left(\dfrac{x}{2}\right)\right)[/tex]

[tex]\boxed{\begin{minipage}{5cm}\underline{Trigonometric Identity}\\\\$\tan(\arcsin(x))=\dfrac{x}{\sqrt{1-x^2}}$\\ \end{minipage}}[/tex]

Use the tan(arcsin(x)) trigonometric identity and replace x for (x/2):

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\left(\dfrac{x}{2}\right)^2}}[/tex]

Simplify the denominator:

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\dfrac{x^2}{4}}}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{\dfrac{4-x^2}{4}}}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{\sqrt{4}}}}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{2}}}[/tex]

[tex]\textsf{Apply the fraction rule}: \quad \dfrac{\frac{a}{c}}{\frac{b}{c}}=\dfrac{a}{b}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}}[/tex]

Multiply the numerator and denominator by the denominator to eliminate the radical from the denominator:

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}} \cdot \dfrac{\sqrt{4-x^2}}{\sqrt{4-x^2}}[/tex]

Simplify:

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x\sqrt{4-x^2}}{4-x^2}[/tex]

The arithmetic mean of a and b in the expression  1/a + 1/b = 1/c is 2c.

Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.

Given, An expression of the form 1/a + 1/b = 1/c.

We know average of two numbers is sum of those numbers divided by 2.

So,  {(1/a) + (a/b)}/2 = 1/c.

Now to keep the equality we also have to divide the RHS by 2.

Therefore,   {(1/a) + (a/b)}/2 = (1/c)/2.

{(1/a) + (a/b)}/2 = (1/c)×((1/2).

{(1/a) + (a/b)}/2 = 1/2c.

So, The arithmetic mean of 1/a + 1/b is 1/2c.

Now taking the reciprocal of 1/a and 1/b which is a and b the arithmetic mean is

2c.

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Answer: the test is 47 percent

Step-by-step explanation: 66 out of 140 is 47 percent so it would work

We can prove the formula given in the question as a theorem using the truth table method.

A Truth Table is referred to as a logic table that can be used to perform logic functions with some formulas. The logic functions that can be performed include Boolean algebra.

Let A, B, and C represent propositions. We construct a truth table as follows:

A B C (A → (B − C)) (B → (A → C))

T T T T T

T T F T F

T F T T T

T F F T T

F T T T T

F T F T T

F F T T T

F F F T T

From the truth table, we can see that the formula holds for all possible truth values of A, B, and C. Therefore, the formula is a theorem.

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CSC 23° can be written as sec 67° in as its cofunction.  

A branch of mathematics called trigonometry in geometry focuses on the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to angles and sides.

The six trigonometric ratios are sin, cos, tan, cot, cosec, and sec.

From Trigonometrical Ratios of (90° - θ)

=> sin (90° - θ) = cos θ

=> cos (90° - θ) = sin θ

=> tan (90° - θ) = cot θ

=> csc (90° - θ) = sec θ

=> sec (90° - θ) = csc θ

=> cot (90° - θ) = tan θ

Here we have CSC 23°

Here we need to write csc 23° into its cofunction

From Trigonometrical Ratios of (90° - θ)

csc (90° - θ) = sec θ

23° can be taken as (90 - 67)°  

=>  csc 23° = csc (90 - 67)° = sec 67°    

Therefore,

CSC 23° can be written as sec 67° in as its cofunction.

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a) The distribution of X is a discrete geometric distribution with pmf p(x) = (5/36)(1/6)^(x-1).b) The theoretical mean (mu) of X is 6.c) The theoretical variance of X is 35.d) The expected value of Y is 6 and the variance of Y is 3.875.

The distribution of X is a discrete geometric distribution, which means that the probability of X taking on any particular value is given by the formula p(x) = (5/36)(1/6)^(x-1). The theoretical mean (mu) of X is 6, which means that on average it should take 6 trials to obtain a sum of 7. The theoretical variance of X is 35, which means that there is a considerable amount of variability in the number of trials needed to obtain a sum of 7. If we consider the random variable Y, the average number of trials needed to roll a sum of 7 based on 25 trials, then the expected value of Y is 6 and the variance of Y is 3.875. This indicates that the average number of trials needed to obtain a sum of 7 is 6 and that the variability decreases as more trials are taken.

a) p(x) = (5/36)(1/6)^(x-1)

b) theoretical mean (mu) of X mu = 6

c) Var(X) = (5/36)*∑x=1∞(1/6)^(x-1)^2 - mu^2

       = (5/36)*(1-1/36^2) - 6^2

       = 35

d) The expected value of Y , E(Y) = 6

Var(Y) = Var(X/6)

       = Var(X)/6^2

       = 35/6^2

       = 3.875

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The exponential representation is a decreasing function

From the question, we have the following parameters that can be used in our computation:

y = 200(0.75)x

Rewrite properly

So, we have the following representation

y = 200(0.75)ˣ

An exponential function is represented as

y = abˣ

Where

b = rate

This means that

b = 0.75

Since b is less than 1, then the function is a decreasing function

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Answer:

D

Step-by-step explanation:

The equation is like this :

Popcorn + 5(Price of each juice bottle) = total cost

1.59 + 5j = 13.34

Subtract both sides with 1.59

5j = 11.75

A and C are obviously wrong

B is wrong because there is only one of the juice bottle in the diagram

The answer is D

By using logic gate, it can be concluded-

XOR table is used in this case?

What is logic gate?

Logic gate is a device which is used to build digital circuit.

Logic gate can make passage for a system to pass through when some logical conditions are fulfilled.

Different types of logic gates are-

AND gate, OR gate, NAND gate, XOR gate, NOR gate etc.

Here one switch is in the entrance hallway and other is in the living room.

The lights are on if the switches mismatch.

For this case, XOR table is used

A  B  Result

0  1     1

1   0    1

0  0   0

1   1    0

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The total monthly rent for these three stores is $8,786.25.

What is total ?

Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16.

The outcome of adding two or more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding two or more numbers together results in a new result or total.

The monthly cost for a square foot of rental space in each city is as follows:

   Place            Monthly Cost for a Square Foot

Los Angeles                      $5.75

San Francisco                    $6.95

   Seattle                           $4.25

It is also provided that the store in Los Angeles will be 580 square feet, the store in San Francisco will be 500 square feet, and the store in Seattle will be 465 square feet.

Compute the total monthly rent for these three stores as follows:

Total Monthly Rent = Monthly Cost for a Square Foot × Area

                 = (5.75 * 580) +(6.95 * 500) +(4.25 * 465)

                 = 3335 + 3475 + 1976.25

                 = 8786.25

Thus, the total monthly rent for these three stores is $8,786.25.

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Answer: c?

Step-by-step explanation:

this is a guess :)

Answer:

C.

Step-by-step explanation:

Since Y is confirmed to cost 18

It will cancel out Answer "A" and "D"

It says River Z costs 2 dollars per hours plus a 10 dollar deposit

So that would cancel Answer "B" because you're not removing 10 dollars from the 2 dollars per hour.

So it would be...

Y=   c = 18

X=   c = 2n + 10

the linear relationship between the SAT and ACT scores 0.6675 or 66.75% of the variation in the values of the SAT scores is accounted

Given that many high school students take either the SAT or the ACT.

However, some students take both.

Data were collected from 60 students who took both college entrance exams.

                          SAT score            ACT score with a  of 180.

Average                    912                      21

standard deviation   180                        5

Correlation between the two variables r = 0.817

WE have for two variables if we have correlation coefficient then the square of correlation coefficient gives the fraction of variation in the values of the SAT scores is accounted for by the linear relationship between the SAT and ACT scores

So we find square of r

i.e. r by the linear relationship between the SAT and ACT scores 0.6675 or 66.75% of the variation in the values of the SAT scores is accounted

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Answer:

j

Step-by-step explanation: