Hi i need help on this im not that smart sorry, what is the x-intercept of the graph that is shown below

Hi I Need Help On This Im Not That Smart Sorry, What Is The X-intercept Of The Graph That Is Shown Below

Answers

Answer 1

Answer:

(3, 0)

Step-by-step explanation:

x-intercept is where the line touches the x-axis

It is the point on the line where y=0

Answer 2

Answer:

3,0

Step-by-step explanation:

the point where the line cuts the x axis is the x-intecept


Related Questions

Will Give Brainliest Please Answer Quick

Answers

Answer:

Option (2)

Step-by-step explanation:

If a perpendicular is drawn from the center of a circle to a chord, perpendicular divides the chord in two equal segments.

By using this property,

Segment MN passing through the center Q will be perpendicular to chords HI ans GJ.

By applying Pythagoras theorem in right triangle KNJ,

(KJ)² = (KN)² + (NJ)²

(33)² = (6√10)² + (NJ)²

NJ = [tex]\sqrt{1089-360}[/tex]

NJ = [tex]\sqrt{729}[/tex]

    = 27 units

Since, GJ = 2(NJ)

GJ = 2 × 27

GJ = 54 units

Option (2) will be the answer.

PLEASE HELPPPPP!!!!!!!!!!!!!!!Which relationships have the same constant of proportionality between y and x as the following graph?Choose two answers!!

Answers

Answer:

  B, E

Step-by-step explanation:

You can use these strategies to compare the given graph and the other representations.

  A & B) See if the point (x, y) = (8, 6) marked on the first graph works in the given equation.

A -- 6y = 8x   ⇒   6(6) = 8(8) . . . FALSE

B -- y = (3/4)x   ⇒   6 = (3/4)8 . . . True

__

  C) Compare this graph to the given graph. They don't match.

__

  D & E) Plot a point from the table on the given graph and see where it falls.

D -- The point (x, y) = (3, 4) lies above the line on the given graph.

E -- The point (x, y) = (4, 3) lies on the given graph.

_____

Choices B and E have the same constant of proportionality as shown in the given graph.

Answer:

B and E

Step-by-step explanation:

The difference between teenage female and male depression rates estimated from two samples is 0.07. The estimated standard error of the sampling distribution is 0.03. What is the 95% confidence interval

Answers

Answer:

The 95%  confidence interval is  [tex]0.0112 < \mu_m - \mu_f < 0.1288[/tex]

Step-by-step explanation:

From  the question we are told that  

      The  sample  mean difference is  [tex]\= x_m - \= x_f = 0.07[/tex]

       The  standard error  is  SE  =  0.03

Given that the confidence interval is  95% then the level of significance is mathematically evaluated as

               [tex]\alpha = 100 - 95[/tex]

               [tex]\alpha = 5\%[/tex]

               [tex]\alpha =0.05[/tex]

Next  we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

         [tex]E = Z_{\frac{ \alpha }{2} } * SE[/tex]

substituting values

         [tex]E = 1.96 * 0.03[/tex]

         [tex]E = 0.0588[/tex]

The 95% confidence interval  is mathematically represented as

      [tex](\= x_m - \= x_f ) - E < \mu_m - \mu_f <(\= x_m - \= x_f ) + E[/tex]

substituting values

     [tex]0.07 - 0.0588 < \mu_m - \mu_f <0.07 + 0.0588[/tex]

    [tex]0.0112 < \mu_m - \mu_f < 0.1288[/tex]

     

The difference between teenage female and male depression rates are given. The 95% percent confidence interval can be obtained using mean and standard error relation.

The confidence interval is (0.0016 , 0.1584).

Given:

The depression rates is [tex]0.07[/tex].

The standard error of sampling distribution is [tex]0.03[/tex].

The critical value [tex]z=1.96[/tex]

Write the relation for mean and standard error.

[tex]\mu\pm z_{\rm critical}+\rm standard\: error[/tex]

Substitute the value.

[tex]0.07\pm 1.96\times 0.03=(0.1288,\:0.0112)[/tex]

Therefore, the upper and lower boundary is [tex](0.1288,\:0.0112)[/tex]. Thus, The confidence interval is (0.0016 , 0.1584).

Learn more mean and standard error here:

https://brainly.com/question/20215215

Different varieties of field daisies have numbers of petals that follow a Fibonacci sequence. Three varieties have 13, 21, and 34 petals.

Answers

The next two petal varieties are
A. 55, 89

Answer:

A. 55, 89

Step-by-step explanation:

In a Fibonacci sequence, you start with 2 given numbers. Then each subsequent number is the sum of the last two numbers.

12, 21, 34

12 + 21 = 34

34 + 21 = 55

55 + 34 = 89

Answer: 55, 89

Find the interquartile range of the following data set.
Number of Points Scored at Ten Basketball Games
57 63 44 29 36 62 48 50 42 34
a .21
B.28
C. 6
D. 34

Answers

Answer:

b.28 its ans is no.b

Step-by-step explanation:

no point score in basketball

A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 140 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month? Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fatal Accidents 8 15 9 8 13 6 17 15 10 9 18 12

Answers

Answer:

There is enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month, as the Variance is 14 and the Standard Deviation = 4 approximately.

There is a high degree of variability in the mean of the population as explained by the Variance and the Standard Deviation.

Step-by-step explanation:

Month       No. of              Mean       Squared

           Fatal Accidents  Deviation   Difference

Jan          8                       -4                  16

Feb        15                        3                   9

Mar         9                       -3                   9

Apr         8                       -4                  16

May       13                        1                    1

Jun         6                      -6                 36

Jul         17                       5                 25

Aug       15                       3                   9

Sep       10                      -2                   4

Oct        9                       -3                   9

Nov    18                          6                 36

Dec    12                          0                   0

Total 140                                         170

Mean = 140/12 = 12    Mean of squared deviation (Variance) = 170/12 = 14.16667

Standard deviation = square root of variance = 3.76386 = 4

The fatal accidents' Variance is a measure of how spread out the fatal accident data set is. It is calculated as the average squared deviation of the number of each month's accident from the mean of the fatal accident data set.  It also shows how variable the data varies from the mean of approximately 12.

The fatal accidents' Standard Deviation is the square root of the variance, and a useful measure of variability when the distribution is normal or approximately normal.

HELP ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Option (B)

Step-by-step explanation:

The given expression is,

[tex]\sqrt{22x^6}\div\sqrt{11x^4}[/tex]

We can rewrite this expression as,

[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }[/tex]

Solving it further,

[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }=\frac{\sqrt{22(x^3)^2} }{\sqrt{11(x^2)^2} }[/tex] [Since [tex]x^3\times x^3=x^6[/tex] and [tex]x^{2}\times x^{2}=x^4[/tex]]

         [tex]=\sqrt{\frac{22(x^3)^2}{11(x^2)^2} }[/tex] [Since [tex]\frac{\sqrt{a} }{\sqrt{b} }=\sqrt{\frac{a}{b} }[/tex]]

         [tex]=\frac{x^3}{x^2}\sqrt{\frac{22}{11} }[/tex]

         [tex]=x\sqrt{2}[/tex]

Therefore, quotient will be x√2.

Option (B) will be the correct option.

A waiter earns $11.00 an hour and approximately 10% of what he serves in a shift. If he works a 6 hour shift and takes $425 in orders, his total earnings for the six hours would be:


Answers

Answer:

108.50

Step-by-step explanation:

First find the wages

11* 6 = 66 dollars

Then figure the commission

10% of 425

.10 * 425

42.5

Add the two amounts together

42.5+66

108.50

Simplify 3m2 (−6m3 )

Answers

Answer:

3m2(-6m3)

since it's a term you have to multiply it by the number in bracket

6m(-6m3)

6m(-18m)

-108m²

Mrs. Simpson’s calculus class has an exam with an average score of 80 and standard deviation of 15. Assume that exam scores are normally distributed. If Mrs. Simpson decides to give an A grade to students who score in the top 20% of the class, what exam score is needed in order to get the A grade? (3pts)

Answers

Answer:

93 is the exam score needed in order to get the A grade in Mrs Simpson’s test

Step-by-step explanation:

Let x be the score that gives an A grade

Mathematically from the z-score formula, we know that;

z-score = x-mean/SD

From the question, x = ? , mean = 80 and SD = 15

Thus;

z-score = x-80/15

But in this question, we have the probability but we do not have the z-score

So we need the z-score that is equivalent to 20%

20% is same as 0.2

Using the standard normal distribution table, a probability of 0.2 corresponds to a z-score of 0.84

Thus, mathematically;

0.84 = x-80/15

x-80 = 15(0.84)

x-80 = 12.6

x = 80 + 12.6

x = 92.6 which is approximately 93

solve for x: -3(x + 1)= -3(x + 1) - 5

Answers

Answer:

No solution : 0= -5

Step-by-step explanation:

[tex]-3\left(x+1\right)=-3\left(x+1\right)-5\\\\\mathrm{Add\:}3\left(x+1\right)\mathrm{\:to\:both\:sides}\\\\-3\left(x+1\right)+3\left(x+1\right)=-3\left(x+1\right)-5+3\left(x+1\right)\\\\\mathrm{Simplify}\\\\0=-5\\\\\mathrm{The\:sides\:are\:not\:equal}\\\\\mathrm{No\:Solution}[/tex]

Let the sample size of leg strengths to be 7 and the sample mean and sample standard deviation be 630 watts and 32 watts, respectively.

(a) Is there evidence that leg strength exceeds 600 watts at significance level 0.05? Find the P-value. There is_________ evidence that the leg strength exceeds 600 watts at ? = 0.05.

A. 0.001 < P-value < 0.005

B. 0.10 < P-value < 0.25

C. 0.010 < P-value < 0.025

D. 0.05 < P-value < 0.10

(b) Compute the power of the test if the true strength is 610 watts.

(c) What sample size would be required to detect a true mean of 610 watts if the power of the test should be at least 0.9? n=

Answers

Answer:

a. There is_sufficient evidence that the leg

C. 0.010 < P-value < 0.025

b. Power of test = 1- β=0.2066

c. So the sample size is 88

Step-by-step explanation:

We formulate the null and alternative hypotheses as

H0 : u1= u2 against Ha : u1 > u2 This is a right tailed test

Here n= 7 and significance level ∝= 0.005

Critical value for a right tailed test with 6 df is 1.9432

Sample Standard deviation = s= 32

Sample size= n= 7

Sample Mean =x`= 630

Degrees of freedom = df = n-1= 7-1= 6

The test statistic used here is

Z = x- x`/ s/√n

Z= 630-600 / 32 / √7

Z= 2.4797= 2.48

P- value = 0.0023890 > ∝ reject the null hypothesis.

so it lies between 0.010 < P-value < 0.025

b) Power of test if true strength is 610 watts.

For  a right tailed test value of z is = ± 1.645

P (type II error) β= P (Z< Z∝-x- x`/ s/√n)

Z = x- x`/ s/√n

Z= 610-630 / 32 / √7

Z=0.826

P (type II error) β= P (Z< 1.645-0.826)

= P (Z> 0.818)

= 0.7933

Power of test = 1- β=0.2066

(c)

true mean = 610

hypothesis mean = 600

standard deviation= 32

power = β=0.9

Z∝= 1.645

Zβ= 1.282

Sample size needed

n=( (Z∝ +Zβ )*s/ SE)²

n=  ((1.645+1.282) 32/ 10)²

Putting the values  and solving we get 87.69

So the sample size is 88

Which defines a line segment?
two rays with a common endpoint
O a piece of a line with two endpoints
O a piece of a line with one endpoint
all points equidistant from a given point

Answers

Answer:

O a piece of a line with two endpoints

Step-by-step explanation:

O a piece of a line with two endpoints

A piece of a line with two endpoints.

What is a line segment?

In geometry, a line segment is a part of a line this is bounded by distinct end points and includes every point on the line this is between its endpoints.

What are the examples of line segments in real life?

A ruler, a scale, a stick, a boundary line.

Learn more about line segments here https://brainly.com/question/2437195

#SPJ2

average age of 15 students of iub 11years if teacher is also included average age becomes 13 years how old is teachers

Answers

Answer: the teacher is 43

Step-by-step explanation: if you take 11 and multiply it by 15 you get 165 if you take 208 and divide it by 16 you get 13.

so basically you subtract 208 from 165 to get 43

two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 109 feet, and ball 2 is dropped from a height of 260 feet. Use the function f(t) -16t^2+h to determine the current height, f(t), of a ball from a height h, over given time t.

When does ball 1 reach the ground? Round to the nearest hundredth​

Answers

Answer:  5.22 seconds

Step-by-step explanation:

t represents time and y represents the height.

Since we want to know when the ball hits the ground, find t when y = 0

Ball 1 starts at a height of 109 --> h = 109

0 = -16t² + 109

16t² = 109

   [tex]t^2=\dfrac{109}{16}\\[/tex]

   [tex]t=\sqrt{\dfrac{109}{16}}[/tex]

   [tex]t=\dfrac{\sqrt{109}}{2}[/tex]

   t = 5.22

Answer:Let us assume "H" height here, "t" as time.

=> H = 109

=> 0 = -16t² + 109

=> 16t² = 109

=> t² = 109/16

=> t = 109/2

=> t = 5.22 sec

Therefore, 5.22 second is the answer.

Find the inverse of the following function.

Answers

Answer:

The inverse is 1/64 x^2 = y   x ≥ 0

Step-by-step explanation:

f(x) = 8 sqrt(x)

y = 8 sqrt(x)

Exchange x and y

x = 8 sqrt (y)

Solve for y

Divide each side by 8

1/8 x = sqrt(y)

Square each side

(1/8 x)^2 = (sqrt(y))^2

1/64 x^2 = y

The inverse is 1/64 x^2 = y   x ≥ 0

since x ≥0 in the original function

Answer:

[tex]\Huge \boxed{\mathrm{D}}[/tex]

Step-by-step explanation:

[tex]f(x)=8\sqrt{x}[/tex]

[tex]\sf Replace \ with \ y.[/tex]

[tex]y=8\sqrt{x}[/tex]

[tex]\sf Switch \ the \ variables.[/tex]

[tex]x= 8\sqrt{y}[/tex]

[tex]\sf Divide \ both \ sides \ of \ the \ equation \ by \ 8.[/tex]

[tex]\displaystyle \frac{x}{8} =\sqrt{y}[/tex]

[tex]\sf Square \ both \ sides \ of \ the \ equation.[/tex]

[tex]\displaystyle (\frac{x}{8} )^2 =y[/tex]

[tex]\displaystyle \frac{x^2 }{64} =y[/tex]

[tex]\displaystyle f^{-1}(x)=\frac{1}{64} x^2[/tex]

Suppose that y varies directly with x and y=20 when x=2 Find y when x=8

Answers

Answer:

80

Step-by-step explanation:

x      y

2 = 20

8 = x

cross multiply( 8*20)/2

= 4 * 20

= 80

20 POINTS ANSWER QUICK

Justine graphs the function f(x) = (x – 7)2 – 1. On the same grid, she graphs the function g(x) = (x + 6)2 – 3. Which transformation will map f(x) on to g(x)? left 13 units, down 2 units right 13 units, down 2 units left 13 units, up 2 units right 13 units, up 2 units

Answers

Answer:

Justine graphs the function f(x) = (x – 7)2 – 1. On the same grid, she graphs the function

g(x) = (x + 6)2 – 3. Which transformation will map f(x) on to g(x)?

left 13 units, down 2 units

right 13 units, down 2 units

left 13 units, up 2 units

right 13 units, up 2 units

who the hell will get that

Divide write the quotient in lowest term 1 1/3 divided by 1 3/4

Answers

Answer:

7/3  or 2 1/3

Step-by-step explanation:

1 1/3 ÷ 1  3/4

Change to improper fractions

(3*1+1)/3 ÷ (4*1+3)/4

4/3 ÷ 7/4

Copy dot flip

4/3 * 7/4

Rewriting

4/4 * 7/3

7/3

As a mixed number

2 1/3

Answer:

11/3÷13/4

11/3×4/13

44/39=

1.1282

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 53.9 for a sample of size 24 and standard deviation 5.6. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level). Assume the data is from a normally distributed population. Enter your answer as a tri-linear inequality accurate to three decimal places.

_______ < μ < _________ please teach using calculator method

Answers

Answer:

The  estimate is

             [tex]52.02 < \mu < 55.78[/tex]

Step-by-step explanation:

From the question we are told that

    The sample mean is [tex]\ = x = 53.9[/tex]

     The sample size is  n =  24

      The standard deviation is  [tex]\sigma = 5.6[/tex]

 

Given that the confidence level is  90% the level of significance is mathematically represented as

           [tex]\alpha = 100 - 90[/tex]

            [tex]\alpha = 10 \%[/tex]

            [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table.The value is  

           [tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.10 }{2} } = 1.645[/tex]

The reason we are obtaining critical value of    [tex]\frac{\alpha }{2}[/tex] instead of    [tex]\alpha[/tex] is because    [tex]\alpha[/tex]

represents the area under the normal curve where the confidence level interval (  [tex]1 - \alpha[/tex] ) did not cover which include both the left and right tail while  

[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

Generally the margin of error is mathematically represented as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]

substituting values

         [tex]E = 1.645 * \frac{5.6 }{ \sqrt{24} }[/tex]

          [tex]E = 1.880[/tex]

The  estimate of how much the drug will lower a typical patient's systolic blood pressure(using a 90% confidence level) is mathematically represented as

         [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

         [tex]53.9 - 1.880 < \mu < 53.9 + 1.880[/tex]

         [tex]52.02 < \mu < 55.78[/tex]

Let f(x) = - 4x + 5. Find and simplify f(x + 2).

Answers

Answer:

-4x - 3.

Step-by-step explanation:

f(x) = -4x + 5.

f(x + 2) = -4(x + 2) + 5

= -4x - 8 + 5

= -4x - 3.

Hope this helps!

Answer:

f(x+2)=-4x-3

Step-by-step explanation:

We are given:

[tex]f(x)= -4x+5[/tex]

and asked to find f(x+2). Therefore, we must substitute x+2 for each x in the function.

[tex]f(x+2)=-4(x+2)+5[/tex]

Now, simplify. First, distribute the -4. Multiply each term inside the parentheses by -4.

[tex]f(x+2)=(-4*x)+(-4*2)+5\\f(x+2)=-4x+(-4*2)+5\\f(x+2)=-4x-8+5[/tex]

Next, combine like terms. There are 2 constants (terms without a variable) that can be added. Add -8 and 5.

[tex]f(x+2)=-4x(-8+5)\\f(x+2)=-4x-3[/tex]

f(x+2) is -4x-3.

Charlie needs a $275,000 mortgage and he'd like to pay it off in 30 years. He is considering two banks. Bank A: 3.5% with monthly payments of $1234.87 Bank B: 4% with monthly payments of $1312.89 Charlie doesn't think a 0.5% difference is that much. What is the difference between these two bank loans with total interest paid over the life of the loan?

Answers

Answer:

Difference in interest= $41,250

Step-by-step explanation:

To calculate the interest paid on each bank loan we use the following formula

Interest = Principal * Rate * Time

For Bank A

Interest = 275,000 * 0.035 * 30

Interest = $288,750

For Bank B

Interest = 275,000 * 0.04 * 30

Interest = $330,000

Therefore

Difference in interest= 330,000 - 288,750

Difference in interest= $41,250

Therefore if the mortgage is taken from Bank B he will pay an extra $41,250 on the loan.

The 0.5% difference in rates has a large impact over the 30 year term loan

Find the product . Write your answer in exponential form 8^-2•8^-9

Answers

Answer:

  8^-11

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)(a^c) = a^(b+c)

Then we have ...

  (8^(-2))·(8^(-9)) = 8^(-2-9) = 8^-11

Please help look at the question in image

Answers

Answer:

In part 1, the value for D is given. Putting D as 1 gives us the answer 17/20

In part 2, the value of E is given as 1, putting E as 1 gives us D = 20/17

cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 6 instead, she subtracted 6 and then divided the result by 3 giving an answer of 25 what would her answer have been if she had worked the problem correctly?

Answers

The answer u been waiting for is -132

Answer:

13

Step-by-step explanation:

let the number be x

how Cindy worked it out :

(x -6) ÷ 3 = 25

x -6 = 75

x = 81

How she should have worked it out:

(x - 3) ÷ 6

(81 - 3) ÷ 6

78 ÷ 6 = 13

To which number sets of numbers does the number 3.567...belong?

Answers

Answer:

It's irrational number
Answer: irrational number set, real number set

If the decimal digits do not repeat in some known pattern, then the number is irrational. We cannot write it as a ratio or fraction of two integers. If it did have a pattern, then we can use algebra to find the fractional representation of that number. Based on what is shown, it looks like there is no pattern so that's why the value is irrational. The number is also a real number as this is the case with any number you'll encounter unless you're dealing with complex numbers (but your teacher may not have introduced that topic yet).

Find x. A. 3√3 B. 3 C. 2√3/3 D. √63

Answers

Answer:

[tex]\huge\boxed{\sf x = 3\sqrt{3}}[/tex]

Step-by-step explanation:

Cos 30 = Adjacent / Hypotenuse

Where Adjacent = x , Hypotenuse = 6

[tex]\frac{\sqrt{3} }{2}[/tex] = x / 6

x = [tex]\frac{\sqrt{3} }{2}[/tex]  * 6

[tex]\sf x = 3\sqrt{3}[/tex]

Suppose that 80% of all registered California voters favor banning the release of information from exit polls in presidential elections until after the polls in California close. A random sample of 25 registered California voters is selected.

Required:
a. Calculate the mean and standard deviation of the number of voters who favor the ban.
b. What is the probability that exactly 20 voters favor the ban?

Answers

Answer:

a. Mean = 20

Sd = 4

b. Probability of X = 20 = 0.1960

Step-by-step explanation:

we have

n = 25

p = 80% = 0.8

mean = np

= 0.8 * 25

= 20

standard deviation = √np(1-p)

= √25*0.8(1-0.8)

=√4

= 2

probability that exactly 20 favours ban

it follows a binomial distribution

= 25C20 × 0.8²⁰ × 0.2⁵

= 53130 × 0.01153 × 0.00032

= 0.1960

Probability of X = 20 = 0.1960

One more than three times a number is the same as four less than double a number

Answers

Answer:

3x + 1 = 2x - 4.  x = -5

Step-by-step explanation:

An Uber driver provides service in city A and city B only dropping off passengers and immediately picking up a new one at the same spot. He finds the following Markov dependence. For each trip, if the driver is in city A, the probability that he has to drive passengers to city B is 0.25. If he is in city B, the probability that he has to drive passengers to city A is 0.45. Required:a. What is the 1-step transition matrix? b. Suppose he is in city B, what is the probability he will be in city A after two trips? c. After many trips between the two cities, what is the probability he will be in city B?

Answers

Answer:

a.  1-step transition matrix is be expressed as:

[tex]P= \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right][/tex]

b. The probability that he will be in City A after two trips given that he is in City B  = 0.585

c. After many trips, the probability that he will be in city B = 0.3571

Step-by-step explanation:

Given that:

For each trip, if the driver is in city A, the probability that he has to drive passengers to city B is 0.25

If he is in city B, the probability that he has to drive passengers to city A is 0.45.

The objectives are to calculate the following :

a. What is the 1-step transition matrix?

To  determine the 1 -step transition matrix

Let the State ∝ and State β denotes the Uber Driver providing service in City A and City B respectively.

∴  The transition probability from state ∝ to state β is 0.25.

The transition probability from state ∝ to state ∝ is 1- 0.25 = 0.75

The transition probability from state β to state ∝ is 0.45. The transition probability from state β to state β is 1 - 0.45 = 0.55

Hence; 1-step transition matrix is be expressed as:

[tex]P= \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right][/tex]

b. Suppose he is in city B, what is the probability he will be in city A after two trips?

Consider [tex]Y_n[/tex] = ∝ or β  to represent the Uber driver is in City A or City B respectively.

∴ The probability that he will be in City A after two trips given that he is in City B

=[tex]P(Y_0 = 2, Y_2 = 1 , Y_3 = 1) + P(Y_0 = 2, Y_2 = 2 , Y_3 = 1)[/tex]

= 0.45 × 0.75 + 0.55 × 0.45

= 0.3375 + 0.2475

= 0.585

c. After many trips between the two cities, what is the probability he will be in city B?

Assuming that Ф = [ p  q ] to represent the long run proportion of time that Uber driver is in City A or City B respectively.

Then, ФP = Ф  , also  p+q = 1  , q = 1 - p  and p = 1 - q

[tex][ p\ \ \ q ] = \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right] [ p\ \ \ q ][/tex]

0.75p + 0.45q = q

-0.25p + 0.45q = 0

since p = 1- q

-0.25(1 - q) + 0.45q = 0    

-0.25 + 0.25 q + 0.45q = 0

0.7q = 0.25

q = [tex]\dfrac{0.25} {0.7 }[/tex]

q =  0.3571

After many trips, the probability that he will be in city B = 0.3571

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