Dada la recta L: 3x - 2y + 1 = 0, ¿cual es la pendiente de la recta L1?

Answers

Answer 1

Answer:

La pendiente de la recta L es [tex]\frac{3}{2}[/tex].

Step-by-step explanation:

La recta está presentada en su forma implícita, es decir, que está bajo la forma:

[tex]f(x,y) = 0[/tex]

Para determinar la pendiente de la recta, se debe transformarla a su forma explícita, cuya fórmula es:

[tex]y = m \cdot x + b[/tex]

Donde:

[tex]x[/tex] - Variable independiente, adimensional.

[tex]y[/tex] - Variable dependiente, adimensional.

[tex]m[/tex] - Pendiente, adimensional.

[tex]b[/tex] - Intercepto, adimensional.

Entonces:

[tex]3\cdot x - 2\cdot y + 1 = 0[/tex]

[tex]2\cdot y = 3\cdot x +1[/tex]

[tex]y = \frac{3}{2}\cdot x + \frac{1}{2}[/tex]

Por simple inspección, se determina que la pendiente de la recta L es [tex]\frac{3}{2}[/tex].


Related Questions

Robert is putting new roofing shingles on his house. Each shingle is 1 2/3 feet long. The north part of the house has a roof line that is 60 feet across. How many shingles can be placed (side by side) on the north part of the house?

Answers

Answer: 36 shingles can be placed on the north part of the house.

Step-by-step explanation:

Given: Length of each shingle = [tex]1\dfrac23[/tex] feet = [tex]\dfrac53[/tex] feet.

The north part of the house has a roof line that is 60 feet across.

Then, the number of  shingles can be placed  on the north part of the house = (Length of roof line in north part) ÷ (Length of each shingle)

[tex]=60\div \dfrac{5}{3}\\\\=60\times\dfrac{3}{5}\\\\=12\times3=36[/tex]

Hence, 36 shingles can be placed on the north part of the house.

Hey! i've been working on these questions but I have no idea how to solve this one, could anybody help me? Thanks in advance!

Answers

Answer:

1) [tex]\boxed{p(x) = x^3-x^2+x-1}[/tex]

2) [tex]\boxed{p(x) = x^2+x-2}[/tex]

3) [tex]\boxed{p(x) =- 2x^2+2x+4}[/tex]

4) [tex]\boxed{p(x) = 2x^2+x-4}[/tex]

Step-by-step explanation:

Part (1)

[tex]p(x) = x^3-x^2+x-1[/tex]

As we have to determine it by ourselves, this is the polynomial having a degree of 3. p(x) with a degree of 3 means that the highest degree/exponent of x should be 3.

Part (2)

[tex]p(x) = x^2+x-2[/tex]

This can be the polynomial having the factor x-1 because if we put:

x - 1 = 0 =>  x = 1 in the above polynomial, it gives us a result of zero which shows us that (x-1) "is" a factor of the polynomial.

Part (3)

[tex]p(x) = -2x^2+2x+4[/tex]

This can be the polynomial for which p(0) = 4 and p(-1) = 0

Let's check:

[tex]p(0) =- 2(0)^2+2(0)+4\\p(0) = 0 + 0+4\\p(0) = 4[/tex]

[tex]p(-1)= -2(-1)^2+2(-1)+4\\p(-1) = -2(1)-2+4\\p(-1) = -2-2+4\\p(-1) = 0[/tex]

So, this is the required polynomial determined by "myself".

Part (4):

[tex]p(x) = 2x^2+x-4[/tex]

This is the polynomial having a remainder 6 when divided by (x-2)

Let's check:

Let x - 2 = 0 => x = 2

Putting in the above polynomial

[tex]p(x) = 2(2)^2+(2)-4\\Given \ that \ Remainder = 6\\6 = 2(4) +2-4\\6 = 8+2-4\\6 = 10-4\\6 = 6[/tex]

So, Proved that it has a remainder of 6 when divided by (x-2)

simplify the expression 10 divided by 5 times 3

Answers

Answer:

= 2/3

Step-by-step explanation:

10 / (5*3)

= 10/15

= 2/3

Find the volume of the solid. When​ appropriate, use π=3.14 and round your answer to the nearest hundredth.

Answers

Answer:

3179.25

Step-by-step explanation:

Hello!

To find the volume of a cylinder we use the equation

[tex]V = \pi r^{2} h[/tex]

V is volume

r is radius

h is height

Put in what we know. It is says to use pi as 3.14

[tex]V = 3.14 * 7.5^{2} *18[/tex]

Solve

V = 3.14 * 56.25 * 18

V = 3179.25

Hope this Helps!

A researcher examines typing speed before a typing class begins, halfway through the class, and after the class is over. 4. Identify the number of levels: 5. Identify the type of design: 6. Identify the dependent variable:

Answers

Answer:

Number of levels = 2

Type of design = Repeated measure

Dependent variable = Typing Speed

Step-by-step explanation:

The number of levels in an experiment simply refers to the number of experimental conditions in which participants are subjected to. In the scenario above, the number of levels is 2. Which are ; Halfway through the class and After the class is over.

The type of designed employed is REPEATED MEASURE, this is because the participants all took part in each experimental condition.

The dependent variable is TYPING SPEED, which is the variable which is measured with respect to the independent variable. Hence the observed value depends on period that is (halfway through the class or after the class is over).

A graph is shown below: A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, and 10. The values on the y axis are 0, 4, 8, 12, 16, and 20. Points are shown on ordered pairs 0, 16 and 2, 12 and 4, 8 and 6, 4 and 8, 0. These points are connected by a line. What is the equation of the line in slope-intercept form?

Answers

Answer:

Graph is image, and equation is from the work result below:

Step-by-step explanation:

Take two points find the slope and y-intercept:

Slope = -2

Y-intercept = (0,16)

Equation =

y  =  − 2 x  +  16

check work for one point (to make sure equation works):

(2,12)

y = -2x + 16

12 = -2(2) + 16

12 = -4 + 16

12 = 12

The equation is correct: y  =  − 2 x  +  16

Image below are the points given:

What’s the largest fraction: 7/8, 5/8, 7/13, and 11/19

Answers

Answer:

7/8

Step-by-step explanation:

7/8 = 0.875

5/8 = 0.625

7/13 = 0.538

11/19 = 0.579

So 7/8 is the largest

The data represent the membership of a group of politicians. If we randomly select one​ politician, what is the probability of getting given that a was​ selected?

Answers

Complete Question

The data represent the membership of a group of politicians. If we randomly select one politician, what is the probability of getting a Republican given that a male was selected?    

 

        Republican      Democrat           Independent

Male           11                  6                                   0

Female       70                  17                                  7

The probability is approximately_____?

Answer:

The  probability is  [tex]P(k) = 0.647[/tex]

Step-by-step explanation:  

From the question we are told that

   The  sample size of male is  [tex]n_m = 11 + 6 =17[/tex]

     The  number of male Republican is  [tex]k = 11[/tex]  

Generally the probability of getting a Republican given that a male was selected is

            [tex]P(k) = \frac{k}{n_m}[/tex]

substituting values

          [tex]P(k) = \frac{ 11}{17}[/tex]

          [tex]P(k) = 0.647[/tex]

1. What is the value of (1/2)^3?
O A. 76
O B. 119
O C.12
O D. 18​

Answers

Answer:

1/2 to the power of 3= 1/8

Step-by-step explanation:

1/2*1/2=1/4

1/4*1/2=1/8

d?

[tex]\huge\text{Hey there!}[/tex]


[tex]\mathsf{(\dfrac{1}{2})^3}[/tex]

[tex]\mathsf{= \dfrac{1}{2}^3}[/tex]

[tex]\mathsf{= \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2}}[/tex]

[tex]\mathsf{= \dfrac{1 \times 1 \times 1}{2 \times 2 \times 2}}[/tex]

[tex]\mathsf{\mathsf{= \dfrac{1 \times 1} {4 \times 2}}}[/tex]

[tex]\mathsf{= \dfrac{1}{8}}[/tex]



[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{Option\ D.\ \dfrac{1}{8}}}\huge\checkmark[/tex]


[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]



~[tex]\frak{Amphitrite1040:)}[/tex]

Simplify (x + 4)(x2 − 6x + 3). x3 − 14x2 + 3x + 12 x3 − 6x2 − 17x + 12 x3 − 10x2 − 27x + 12 x3 − 2x2 − 21x + 12

Answers

Answer:

36 x^3 - 32 x^2 + (x + 4) (x^2 - 6 x + 3).x^3 - 62 x + 12

Step-by-step explanation:

Answer:

x^6-2x^5-21x^4+48x^3-32x^2-62x+12

Step-by-step explanation:

Mark me as brainliest!!!!

please this is easy show working out and please get correct

Answers

Answer:

$ 180,000

Step-by-step explanation:

All we are being asked to do in this question is take the simple interest, given a principle value of $100,000, with 8 percent interest each year over a course of 10 years. This is given the simple interest formula P( 1 + rt ).

Simple Interest : P( 1 + rt ),

P = $ 100,000 ; r = 8% ; t = 10 years,

100,000( 1 + 0.08( 10 ) ) = 100,000( 1 + 0.8 ) = 100,000( 1.8 ) = 180,000

Therefore you will have to pay back a total of $ 180,000

Which statement about this function is true?
O A.
The value of a is positive, so the vertex is a minimum.
OB.
The value of a is negative, so the vertex is a minimum.
OC.
The value of a is negative, so the vertex is a maximum.
OD
The value of a is positive, so the vertex is a maximum.

Answers

Answer:

b

Step-by-step explanation:

The value of a is negative, so the vertex is a minimum.

B the value of a is negative, so the vertex is a minimum

The value of y varies jointly with x and z. If y = 2 when z = 110 and x = 11, find the approximate value of y when x = 13 and z = 195.

Answers

Answer:

y = 4

Step-by-step explanation:

To find the approximate value of y when

x = 13 and z = 195 we must first find the relationship between them

The statement

y varies jointly with x and z is written as

y = kxz

where k is the constant of proportionality

From the question

y = 2

x = 11

z = 110

We have

2 = 11(110)k

2 = 1210k

Divide both sides by 1210

[tex]k = \frac{1}{605} [/tex]

So the formula for the variation is

[tex]y = \frac{1}{605} xz[/tex]

When

x = 13

z = 195

y is

[tex]y = \frac{1}{605} (13)(195)[/tex]

[tex]y = \frac{507}{121} [/tex]

y = 4.1900

We have the final answer as

y = 4

Hope this helps you

1. If a bug can flap its wings at a rate of 92 times in 6 seconds, how many times do they flap their wings in 2.34 minutes? Round to 1 decimal.

Answers

Answer:

2152.8

Step-by-step explanation:

First, 2.34 minutes is 140.4 seconds. Next, the bug can flap its wings at a pace of 15.333..... flaps per second. Multiplying this, we get 2152.8

 evaluate the expression for r=-10 -54-r=

Answers

Answer:

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

Step-by-step explanation:

Evaluate Algebraic Expressions. ... To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

A kites string is fastened to the ground. the string is 324ft long and makes an angle of 68 degrees with the ground. A model of this is shown below. use the law of sites (sin A/a=sin B/b) to determine how many feet the kite is above the ground (x). Enter the value, rounded to the nearest foot. (PLEASE)​

Answers

Answer:

x = 300 feet

Step-by-step explanation:

In the given right triangle,

Length of the string of the kite = 324 feet

Angle between the string and the ground = 68°

By applying law of Sines in the given right triangle,

[tex]\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{\text{SinC}}{c}[/tex]

Now we substitute the values of angles and sides in the formula,

[tex]\frac{\text{Sin68}}{x}=\frac{\text{Sin90}}{324}[/tex]

[tex]\frac{\text{Sin68}}{x}=\frac{1}{324}[/tex]

x = 324 × Sin(68)°

x = 300.41 feet

x ≈ 300 feet

Therefore, measure of side x = 300 feet will be the answer.

Find the area of the shaded regions:

Answers

Answer: 125.6 in^2

Step-by-step explanation:

First, we have that the radius of this circle is r = 10in

Now, we know that the area of a circle is:

A = pi*r^2

Now, if we got only a section of the circle, defined by an angle x, then the area of that region is:

A = (x/360°)*pi*r^2

Notice that if x = 360°, then the area is the same as the area of the full circle, as expected.

Then each shaded area has an angle of 72°.

A = (72°/360°)*3.14*(10in)^2 = 62.8 in^2

And we have two of those, both of them with the same angle, so the total shaded area is:

2*A = 2*62.8 in^2 = 125.6 in^2

Write the phrase "the product of 19 and a number" as a mathematical expression.
A 19 + x
B) 19/x
C) 19 x
(D) 19 -x​

Answers

Answer:

19x

Step-by-step explanation:

product means multiply

19*x

19x

Answer:

The answer is C.

Step-by-step explanation:

if a number and a variable are next to each other, it is assumed they will be multiplied.

If the item regularly cost d dollars and is discounted 12percent which of the following represents discount price dollar

Answers

Answer:

-12

Step-by-step explanation:

I need help with these

Answers

Answer:

2. 20 oranges

3. 18 yellow tulips

4. 23 students

Find the equation of the line passing through the point (–1, –2) and perpendicular to the line y = –1∕2x + 5. Question options: A) y = –1∕2x – 5∕2 B) y = 1∕2x – 5∕2 C) y = 2x D) y = –1∕2x

Answers

Answer:

The answer is option C

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question

y = - 1/2x + 5

Comparing with the general equation above

Slope / m = -1/2

Since the lines are perpendicular to each other the slope of the other line is the negative inverse of the original line

That's

Slope of the perpendicular line = 2

Equation of the line using point (–1, –2) and slope 2 is

y + 2 = 2( x + 1)

y + 2 = 2x + 2

y = 2x + 2 - 2

We have the final answer as

y = 2x

Hope this helps you

Answer:

C) y = 2x

Step-by-step explanation:

I got it right in the test !!

Chapter: Simple linear equations Answer in steps

Answers

Answer:

6x-3=21

6x=24

x=4

........

6x+27=39

6x=39-27

6x=12

x=2

........

8x-10=14

8x=24

x=3

.........

6+6x=22

6x=22-6

x=3

......

12x-2=28

12x=26

x=3

.....

8-4x=16

-4x=8

x=-2

.....

4x-24=3x-3

4x-3x=24-3

x=21

....

9x+6=6x+12

9x-6x=12-6

3x=6

x=2

Answer:

Step-by-step explanation:

1. 3(2x - 1) = 21

 = 6x - 3 = 21

 = 6x = 24

 = x = 24/6 = 4

------------------------------

2. 3(2x+9) = 39

   = 6x + 27 = 39

   = 6x = 39 - 27

   = 6x = 12

   = x = 12/6 = 2

--------------------------------

3. 2(4x - 5) = 14

  = 8x - 10 = 14

  = 8x = 14+10

 = x = 3

-------------------------------

Assume that when adults with smartphones are randomly​ selected, ​57% use them in meetings or classes. If 8 adult smartphone users are randomly​ selected, find the probability that exactly 4 of them use their smartphones in meetings or classes. The probability is

Answers

Answer:

≈ 0.2526

Step-by-step explanation:

The number of combinations of 4 out of 8:

8C4 = 8!/(4!(8-4)!)= 8*7*6*5/(1*2*3*4)= 70

Success factor is:

57% = 0.57

and failure factor is:

(100 - 57)%= 43%= 0.43

Probability:

0.57⁴*0.43⁴*70 ≈ 0.2526

if a flight to europe takes about 13 hours and you make one round trip flight per month how many total days do you travel in a year

Answers

Answer:

13 days

Step-by-step explanation:

Given that a one-way flight to europe will take 13 hours

A round trip will take = 13 hrs x 2 = 26 hours

Also given that we make one round trip per months for 12 months (1 year)

We will take a total of 12 round trips per year

Number of hours taken for 12 round trips

= 26 hours per round trip x 12 round trips

= 26 x 12

= 312 hours

Recall that there are 24 hours in a day, hence to convert 312 hours into days, we have to divide this by 24.

Number of days = number of hours ÷ 24

= 312 ÷ 24

= 13 days

This graph shows the US unemployment rate from August 2010 to November 2011.
Sample Unemployment Rate
Graph
Unemployment Rate
10%
80%
6%
Unemployment Rate
Aug 10
Jan 11
Jun 11
Nov 11
This graph suggests unemployment in the United States
O will continue to fall.
O will continue to rise.
O will remain the same.
O will only change a little.

Answers

Answer: Will continue to rise

Step-by-step explanation:

Looking at the graph one notices that after a slight dip in the unemployment rate from August 2010 to January 2011, the unemployment rate began to rise and by November 2011 was still rising.

The arrow on the graph serves to indicate the direction the unemployment rate is going and as it is pointing upwards, this means that the Unemployment rate will continue to rise.

This was down to the fact that in 2011 the US was still yet to recover from the Great Recession of 2008 - 2009.

Answer:

EDGE 2021

Step-by-step explanation:

1) 4%

2) Increase

The polynomial P(x) = 5x2(x − 1)3(x + 9) has degree ____ It has zeros 0, 1, and ____ The zero 0 has multiplicity ____ , and the zero 1 has multiplicity ____

Answers

The complete question is;

The polynomial P(x) = 5x²(x − 1)³(x + 9) has degree ____. It has zeros 0, 1, and ____. The zero 0 has multiplicity ____ , and the zero 1 has multiplicity ____

Answer:

A) degree = 6

B) -9 is also a zero of the polynomial

C) 0 has multiplicity of 2

1 has multiplicity of 3

Step-by-step explanation:

A) To find the degree of the polynomial, we will first have to identify each term [term is for example (x - 1)³]. Thus, to find the degree of each term we will add the exponents.

The terms are;

5x², (x - 1)³, (x + 9)

The exponents are, 2, 3 and 1 respectively.

Thus, degree = 2 + 3 + 1 = 6

B) A zero of a polynomial is the value of x that causes the polynomial function to equal 0.

Since 0 and 1 are zeros, looking at the polynomial P(x) = 5x²(x − 1)³(x + 9), we can tell that when the term which when x = 0 makes the polynomial 0 is 5x².

Similarly, the term which when x = 1 makes the polynomial 0 is (x - 1)³

Thus,we are left with the term (x + 9)

So for the polynomial to be zero, (x + 9) = 0

Thus,x = -9

So -9 is a zero of the polynomial

C) The zero 0 is from the term 5x².

Thus,the multiplicity is the highest power of x which is 2.

The zero 1 is from the term (x - 1)³. Thus, the multiplicity is the highest power of x which is 3

Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 18​% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Required:a. Find the probability that both generators fail during a power outage.b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital?c. Is that probability high enough for the hospital?

Answers

Answer:

a. 0.36

b. 0.1296

c. No.

Step-by-step explanation:

1. Note the probability of emergency backup generators to fail when they are needed = 18% or 0.18. Thus,

a. Probability of both emergency backup generators failing = P (G1 and G2 fails) where G represents the generators.

= P (G1 falls) x P ( G2 fails)

= 0.18 x 0.18

= 0.36

b. The probability of having a working generator in the event of a power outage = G1 fails x G2 works + G2 works x G2 fails

= 0.36 x 0.18 + 0.18 x 0.36

= 0.1296

c. Looking at the probability of any of the generators working, it is not meeting safety standards as lives could be lost if the backup generators needed to perform an emergency surgery operation fails.

A function y = g(x) is graphed below. What is the solution to the equation g(x) = 3?

Answers

Answer:

See below.

Step-by-step explanation:

From the graph, we can see that g(x)=3 is true only when x is between 3 and 5. However, note that when x=3, the point is a closed circle. When x=5, the point is an open circle. Therefore, the solution is between 3 and 5, and it includes 3 but not 5.

In set-builder notation, this is:

[tex]\{x|x\in \mathbb{R}, 3\leq x<5\}[/tex]

In interval notation, this is:

[tex][3,5)[/tex]

Essentially, these answers are saying: The solution set for g(x)=3 is all numbers between 3 and 5 including 3 and not including 5.

Design a nonlinear system that has at least two solutions. One solution must be the ordered pair: (-2, 5). Tell how you came up with your system and give the entire solution set for the system.

Answers

Answer:

[tex] \begin{cases} (x - 2)^2 + (y - 2)^2 = 25 \\ y = 5 \end{cases} [/tex]

Solutions: x = 6, y = 5   or   x = -2, y = 5

Step-by-step explanation:

Use a graph.

Plot point (-2, 5). That will be a point on a circle with radius 5.

From point (-2, 5), go right 4 and down 3 to point (2, 2). (2, 2) is the center of the circle.

You now need the equation of a circle with center (2, 2) and radius 5.

Use the standard equation of a circle:

[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]

where (h, k) is the center and 5 is the radius.

The circle has equation:

[tex] (x - 2)^2 + (y - 2)^2 = 25 [/tex]

To have a single solution, you need the equation of the line tangent to the circle at (-2, 5), but since you want more than one solution, you need the equation of a secant to the circle. For example, use the equation of the horizontal line through point (2, 5) which is y = 5.

System:

[tex] \begin{cases} (x - 2)^2 + (y - 2)^2 = 25 \\ y = 5 \end{cases} [/tex]

To solve, let y = 5 in the equation of the circle.

(x - 2)^2 + (5 - 2)^2 = 25

(x - 2)^2 + 9 = 25

(x - 2)^2 = 16

x - 2 = 4  or x - 2 = -4

x = 6 or x = -2

Solutions: x = 6, y = 5   or   x = -2, y = 5

An example of a nonlinear system that has at least two solutions, one of which is (-2,5) are,

⇒ x² + y² = 29

⇒ 3x + 4y = -2

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, This system by starting with the equation of a circle centered at the origin with radius sqrt(29), which is,

⇒ x² + y² = 29.

Then, Added a linear equation that intersects the circle at (-2,5) to create a system with two solutions.

The entire solution set for this system is: (-2, 5) and (7/5, -19/10)

Thus, An example of a nonlinear system that has at least two solutions, one of which is (-2,5) are,

⇒ x² + y² = 29

⇒ 3x + 4y = -2

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ3

A car dealer recommends that transmissions be serviced at 30,000 miles. To see whether her customers are adhering to this recommendation, the dealer selects a random sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is 1684 miles. By finding the P-­value, determine whether the owners are having their transmissions serviced at 30,000 miles. Use α = 0.10. Are the owners having their transmissions serviced at 30,000 miles?

Answers

Answer:

No, the owners are not having their transmissions serviced at 30,000 miles.

Step-by-step explanation:

We are given that a car dealer recommends that transmissions be serviced at 30,000 miles.

The car dealer selects a random sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is 1684 miles.

Let [tex]\mu[/tex] = true average mileage of the automobiles serviced.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 30,000 miles      {means that the owners are having their transmissions serviced at 30,000 miles}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 30,000 miles      {means that the owners are having their transmissions serviced at different than 30,000 miles}

The test statistics that will be used here is One-sample z-test statistics because we know about population standard deviation;

                             T.S.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~  N(0,1)

where, [tex]\bar X[/tex] = sample average mileage serviced = 30,456 miles  

            [tex]\sigma[/tex] = population standard deviation = 1684 miles

            n = sample of customers = 40

So, the test statistics =  [tex]\frac{30,456-30,000}{\frac{1684}{\sqrt{40} } }[/tex]  

                                     =  1.71

The value of z-statistics is 1.71.

Also, the P-value of the test statistics is given by;

                    P-value = P(Z > 1.71) = 1 - P(Z [tex]\leq[/tex] 1.71)

                                  = 1 - 0.9564 = 0.0436

For the two-tailed test, the P-value is calculated as = 2 [tex]\times[/tex] 0.0436 = 0.0872.

Since the P-value of our test statistics is less than the level of significance as 0.0872 < 0.10, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

Therefore, we conclude that the owners are having their transmissions serviced at different than 30,000 miles.

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