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Given Information:

Sample size = n = 25

Mean age of client = 46 years

Standard deviation of age of client = 5 years

Confidence level = 95%

Required Information:

Width of the confidence interval = ?

Answer:

[tex]$ \text {width of CI } = \pm 2.064 $\\\\[/tex]

Step-by-step explanation:

The width for the true mean client age is given by

[tex]$ \text {width of CI } =\pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $[/tex]

Where n is the sample size, s is the standard deviation of age of client, and [tex]t_{\alpha/2}[/tex] is the t-score corresponding to 95% confidence level.

The t-score corresponding to 95% confidence level is

Significance level = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 25 - 1 = 24

From the t-table at α = 0.025 and DF = 24

t-score = 2.064

[tex]$ \text {width of CI } = \pm (2.064)(\frac{5}{\sqrt{25} } ) $\\\\[/tex]

[tex]$ \text {width of CI } =\pm (2.064)(\frac{5}{5 } ) $\\\\[/tex]

[tex]$ \text {width of CI } = \pm (2.064)(1) $\\\\[/tex]

[tex]$ \text {width of CI } = \pm 2.064 $\\\\[/tex]

Therefore, width of the 95% confidence Interval for the true mean client age is approximately ±2.064.

Bonus:

The corresponding 95% confidence interval is given by

[tex]$ \text {Confidence Interval } = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $[/tex]

Where x_bar is the mean client age

[tex]$ \text {Confidence Interval } = 46 \pm 2.064 $[/tex]

[tex]$ \text {Confidence Interval } = (43.936, 48.064) $[/tex]

[tex]$ \text {Confidence Interval } = (44, 48) $[/tex]

Which means that we are 95% sure that the true mean client age is within the range of (44, 48) years.

Answer:

Mauna Kea has from the base that is to say the deepest 10 km of height that is to say 10,000 m which is equivalent to being higher than Mount Everest.jj

Step-by-step explanation:

 The main reason why we could say that Mauna Kea is the highest mountain, even surpassing Mount Everest, is because of its altitude if we compare them we see the difference; for example Mauna Kea from its base that is to say from the deepest the ocean measures 10,000 m of altitude, on the other hand the Mount Everest has an altitude of 8848 meters (29,029 ft) above sea level, that is to say from its base it measures 8848 m altitude.

Answer:

0.37

Step-by-step explanation:

As shown in table,

The probability of the fruit is orange is P(A) = 0.3

The probability of the fruit is organic is P(B)

The probability of the fruit is orange and organic is P(A⋂B) = 0.11

=> The probability that a randomly selected orange is organic is calculated by applying the conditional probability formula:

P(B|A) =P(A⋂B)/P(A) = 0.11/0.3 = 0.37

=> Option D is correct

Hope this helps!

Answer:

the anwser is in the text

Step-by-step explanation:

Answer:

0 and  -1

Step-by-step explanation:

Hello,

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

so the roots are

0 and -1 (to get x+1=0 )

do not hesitate if you need further explanation

hope this helps

Answer:

It's actually X = 0, X = - 1, with multiplicity 2, Option D, on Edge2020

Step-by-step explanation:

I just did it on edge :)

Answer:

Step-by-step explanation:

Given that :

the side of the square = 90ft

The speed of the runner = 31 ft/sec

By the time the runner is halfway to the first base;  the distance covered by the runner in time(t)  is (31 t) ft and the distance half the base = 90/2 = 45 ft

Thus; 31 t = 45

t = 45/31

From the second base ; the distance is given as:

P² = (90)² + (90 - 31t )²  

P = [tex]\sqrt{(90)^2 + (90 - 31t )^2}[/tex]

By differentiation with time;

[tex]\dfrac{dP}{dt} =\dfrac{1}{ 2 \sqrt{90^2 +(90-31t)^2} } *(0+ 2 (90-31t)(0-31))[/tex]

[tex]\dfrac{dP}{dt} =\dfrac{1}{ 2 \sqrt{90^2 +(90-31t)^2} } * 2 (-31)(90-31t)[/tex]

At t = 45/31

[tex]\dfrac{dP}{dt} =\dfrac{1}{ 2 \sqrt{90^2 +45^2} } * 2 (-31)(45)[/tex]

[tex]\dfrac{dP}{dt} =\dfrac{-35*45}{100.623}[/tex]

= - 13.86 ft/sec

Hence, we can conclude that  as soon as the runner  is halfway to the first base, the distance to the second base is therefore decreasing by 13.86 ft/sec

b) The distance from third base can be expressed by the relation:

q² = (31t)² + (90)²

[tex]q = \sqrt{(31t)^2+(90)^2}[/tex]

By differentiation with respect to time:

[tex]\dfrac{dq}{dt} = \dfrac{1}{2\sqrt{90^2 + (31)t^2} } *(0+31^2 + 2t)[/tex]

At t = 45/31

[tex]\dfrac{dq}{dt} = \dfrac{1}{2\sqrt{90^2 + 45^2} } *(0+31^2 + \frac{45}{31})[/tex]

[tex]= \dfrac{31*45}{100.623}[/tex]

[tex]= 13.86 \ ft/sec[/tex]

Thus, the rate at which the runner's distance is from the third base is increasing at the same moment of 13.86 ft/sec. So therefore; he is moving away from the third base at the same speed to the first base)

a) The distance from second base is decreasing when the batter is halfway to first base at a rate of 13.9 feet per second.

b) The distance from third base is increasing when the batter is halfway to first base at a rate of 13.9 feet per second.

a) As the batter runs towards the first base, both the distance from second base and the length of the line segment PQ decrease in time. The distance from the second base is determined by Pythagorean theorem:

[tex]QS^{2} = QP^{2}+PS^{2}[/tex] (1)

By differential calculus we derive an expression for the rate of change of the distance from second base ([tex]\dot QS[/tex]), in feet per second:

[tex]2\cdot QS \cdot \dot{QS} = 2\cdot QP\cdot \dot{QP} + 2\cdot PS\cdot \dot {PS}[/tex]

[tex]\dot{QS} = \frac{QP\cdot \dot QP + PS\cdot \dot{PS}}{QS}[/tex]

[tex]\dot {QS} = \frac{QP\cdot \dot {QP}+PS\cdot \dot {PS}}{\sqrt{QP^{2}+PS^{2}}}[/tex] (2)

If we know that [tex]QP = 0.5L[/tex], [tex]PS = L[/tex], [tex]L = 90\,ft[/tex], [tex]\dot {QP} = -31\,\frac{ft}{s}[/tex] and [tex]\dot {PS} = 0\,\frac{ft}{s}[/tex], then the rate of change of the distance from second base is:

[tex]\dot {QS} = \frac{(45\,ft)\cdot \left(-31\,\frac{ft}{s} \right)}{\sqrt{(45\,ft)^{2}+(90\,ft)^{2}}}[/tex]

[tex]\dot {QS} \approx -13.864\,\frac{ft}{s}[/tex]

The distance from second base is decreasing when the batter is halfway to first base at a rate of 13.9 feet per second.

b) As the batter runs towards the first base, both the distance from third base increases and the distance from home increase in time. The distance from the third base is determined by Pythagorean theorem:

[tex]QT^{2} = HT^{2}+QH^{2}[/tex] (3)

By differential calculus we derive an expression for the rate of change of the distance from third base ([tex]\dot QT[/tex]), in feet per second:

[tex]2\cdot QT\cdot \dot{QT} = 2\cdot HT\cdot \dot {HT} + 2\cdot QH\cdot \dot {QH}[/tex]

[tex]\dot {QT} = \frac{HT\cdot \dot {HT}+QH\cdot \dot {QH}}{QT}[/tex]

[tex]\dot {QT} = \frac{HT\cdot \dot {HT}+QH\cdot \dot {QH}}{\sqrt{HT^{2}+QH^{2}}}[/tex]

If we know that [tex]HT = 90\,ft[/tex], [tex]QH = 45\,ft[/tex], [tex]L = 90\,ft[/tex], [tex]\dot{HT} = 0\,\frac{ft}{s}[/tex] and [tex]\dot {QH} = 31\,\frac{ft}{s}[/tex], then the rate of change of the distance from third base is:

[tex]\dot{QT} = \frac{(45\,ft)\cdot \left(31\,\frac{ft}{s} \right)}{\sqrt{(90\,ft)^{2}+(45\,ft)^{2}}}[/tex]

[tex]\dot{QT} \approx 13.864\,\frac{ft}{s}[/tex]

The distance from third base is increasing when the batter is halfway to first base at a rate of 13.9 feet per second.

We kindly invite to check this question on rates of change: https://brainly.com/question/13103052

Answer:

2,210,000 different schedules

Step-by-step explanation:

Cory needs to have an equal number of piano sonatas from J. S. Bach, Haydn, and Wagner.

Since he is setting up a schedule of 9 piano sonatas to be played, he needs:

We then calculate how many different schedules are possible using combination.

Number of possible Schedules

[tex]=$ ^5C_3$ \times ^{52}C_3$ \times ^5C_3\\=10 \times 22100 \times 10\\$=2210000 ways[/tex]

There are 2,210,000 different possible schedules.

Answer:

[tex]\ S=\sqrt{\dfrac{3V}{H}}}[/tex]

Step-by-step explanation:

The opposite operation of squaring is taking the square root.

[tex]\ S=\sqrt{\dfrac{3V}{H}}}[/tex]

We know that the denominator of a fractional power is the index of the corresponding root:

[tex]\displaystyle x^\frac{1}{n}=\sqrt[n]{x}[/tex]

For n=2, we don't usually write the index in the root symbol:

[tex]x^{\frac{1}{2}}=\sqrt{x}[/tex]

In the case of this problem, ...

[tex](S^2)^{\frac{1}{2}}=\left(\dfrac{3V}{H}\right)^{\frac{1}{2}}\\\\S=\sqrt{\dfrac{3V}{H}}[/tex]

Answer:

??????

Step-by-step explanation:

Answer:

Austin's hourly wage is $8.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

Tara's hourly wage is x.

Kayte's hourly wage is y.

Austin's hourly wage is z.

Tara earns twice as much per hour as Kayte.

This means that [tex]x = 2y[/tex]

Kayte earns $3 more per hour than Austin.

This means that [tex]y = z + 3[/tex]

As a group, they earn $41 per hour.

This means that [tex]x + y + z = 41[/tex]

What is Austin's hourly wage?​

This is z.

[tex]x + y + z = 41[/tex]

[tex]y = z + 3[/tex] and [tex]x = 2y[/tex], so [tex]x = 2(z + 3) = 2z + 6[/tex]

[tex]x + y + z = 41[/tex]

[tex]2z + 6 + z + 3 + z = 41[/tex]

[tex]4z + 9 = 41[/tex]

[tex]4z = 32[/tex]

[tex]z = \frac{32}{4}[/tex]

[tex]z = 8[/tex]

Austin's hourly wage is $8.

Answer:

Austin's hourly wage is $8.

Step-by-step explanation:

We can write this problem as a system of linear equations.

We define T: Tara's hourly wage, A: Austin's hourly wage and K: Kayte's hourly wage.

Then, if Tara earns twice as much per hour as Kayte, we have:

[tex]T=2K[/tex]

If Kayte earns $3 more per hour than Austin, we have:

[tex]K=A+3[/tex]

And if they earn $41 per hour as a group, we know:

[tex]T+K+A=41[/tex]

We can use all equations to replace in the third one, as:

[tex]T+K+A=41\\\\(2K)+K+A=41\\\\3K+A=41\\\\3(A+3)+A=41\\\\3A+9+A=41\\\\4A=41-9=32\\\\A=32/4=8[/tex]

Austin's hourly wage is $8.

Answer:

11.51% probability that it will take less than 450 days to train all the contestants.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n variables, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]

In this question:

[tex]n = 100, \mu = 100*5 = 500, s = 4\sqrt{100} = 40[/tex]

Approximate the probability that it will take less than 450 days to train all the contestants.

This is the pvalue of Z when X = 450.

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

By the Central Limit Theorem

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

[tex]Z = \frac{450 - 500}{40}[/tex]

[tex]Z = -1.2[/tex]

[tex]Z = -1.2[/tex] has a pvalue of 0.1151

11.51% probability that it will take less than 450 days to train all the contestants.

Answer:

  15 cm

Step-by-step explanation:

7 cm taller than 8 cm is 15 cm tall.

Dee is 15 cm tall.

Answer:

Dee's height is

[tex]1665cm[/tex]

Step-by-step explanation:

[tex]jo = 888cm \\ dee = 777cm \: \: \: taller \: \: \: than \: \: jo \\ [/tex]

So

[tex]dee = 888 + 777 \\ = 1665cm[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

X=80

Y=9

Z=7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Consider the sets A and B

(A − (A ∩ B)) ∩ (B − (A ∩ B))

= (A ∩ (A ∩ B)c) ∩ (B ∩ (A ∩ B)c) by the set difference law

= (A ∩ (Ac ∩ B)c) ∩ (B ∩ (Ac ∩ B)c) by De Morgan's law

= {(A ∩ Ac) ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ (B ∩ Bc)} by the distributive law

= {∅ ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ ∅} by complementation

= {A ∩ Bc} ∩ {B ∩ Ac} by identity law

= (A ∩ Ac) ∩ (B ∩ Ac) by the associative law

= ∅ ∩ ∅ by complementation

= ∅ by the universal bound law

Therefore,  (A − (A ∩ B)) ∩ (B − (A ∩ B)) = ∅

Answer:

Considere los conjuntos A y B

(A − (A ∩ B)) ∩ (B − (A ∩ B))

= (A ∩ (A ∩ B)c) ∩ (B ∩ (A ∩ B)c) por la ley de diferencia establecida

= (A ∩ (Ac ∩ B)c) ∩ (B ∩ (Ac ∩ B)c) por la ley de De Morgan

= {(A ∩ Ac) ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ (B ∩ Bc)} por la ley distributiva

= {∅ ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ ∅} complementando

= {A ∩ Bc} ∩ {B ∩ Ac} por ley de identidad

= (A ∩ Ac) ∩ (B ∩ Ac) por la ley asociativa

= ∅ ∩ ∅ complementando

= ∅ por la ley universal consolidada

Step-by-step explanation:

Answer:

36 Units.

Step-by-step explanation:

In the diagram attached, K, M, P and R are points of tangency.

Theorem: Tangents to a circle from the same point are equal.

By the theorem above,

LK=LM=6 Units

NM=NP=2 Units

QP=QR=7 Units

JR=JK=3 Units

Therefore:

JL=JK+KL=3+6=9 Units

LN=LM+LN=6+2=8 Units

NQ=NP+PQ=2+7=9 Units

QJ=QR+RJ=7+3=10 Units

Therefore, the perimeter of the polygon JLNQ =9+8+9+10

=36 Units.

Note: The second diagram shows the theorem already applied.

Answer: 9%

Step-by-step explanation:

In probabilities; when two or more conditions must be met, the "and" operator is used. The probability of grey and tails is 1/12

From the attached spinner, we have:

[tex]Grey = 1[/tex]

[tex]n =6[/tex] --- partitions

So, the probability of landing on grey is:

[tex]P(Grey) = \frac{Grey}{n}[/tex]

This gives:

[tex]P(Grey) = \frac{1}{6}[/tex]

In a coin, we have:

[tex]Tail = 1[/tex]

[tex]n =2[/tex] --- faces

So, the probability of tail is:

[tex]P(Tail) = \frac{Tail}{n}[/tex]

[tex]P(Tail) = \frac{1}{2}[/tex]

The probability of grey and tail is:

[tex]Pr = P(Grey) \times P(Tail)[/tex]

[tex]Pr = \frac{1}{6} \times \frac{1}{2}[/tex]

[tex]Pr = \frac{1}{12}[/tex]

Hence, the probability of getting grey and tail is 1/12

Read more on probability at:

https://brainly.com/question/13957582

Answer:

17.52

Step-by-step explanation:

literally 11.6 x 1.51 and then round to hundredth place

Answer: pls mark me brainiest

Step-by-step explanation:

I am very sure that the answer is V≈351.86

Answer:

112π

Step-by-step explanation:

Cubic units are units when talking in the 3rd dimension

The volume of a cylinder is πr² x h

find the area of the base first.

since we can write it in terms of π, don't worry about decimals.

The radius is 4.

plug it in, the base's area is 16π. Multiply that by the height, 7.

16(7)π 

112π is the volume

Answer:

-5x^4

Step-by-step explanation:

Cube root of -125 is -5

Cube root of n^12 is n^4

Answer:

3 x (-125n^12)^1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

first you have to see itis an arithmetic or geometric sequence.

then find common difference(for A.P) or common ratio (for G.P)

c.d .=an-an-1

c.r. =an/an-1

1.G.P.

2. A.P

3.G.P

3,5,25/3,125/9,...

c.r.=5/3

or (25/3)/5=25/(3*5)=5/3

or 125/9÷25/3=125/9×3/25=(125×3)/(9×25)=5/3

Answer:

Each hiker will get 2 1/3 cups

Step-by-step explanation:

8 bags multiplied by 3.5

28 cups overall

The 28 cups is shared between 12 hikers

28/12=2 1/3 cups

Step-by-step explanation:

4y + 6 = 16

you can find y (meters)

then replace y value in every side of this shape

then plus all line you will receive the perimeter

Answer:

The probability that the mean of this sample is less than 16.1 ounces of beverage is 0.0537.

Step-by-step explanation:

We are given that the average amount of a beverage in randomly selected 16-ounce beverage can is 16.18 ounces with a standard deviation of 0.4 ounces.

A random sample of sixty-five 16-ounce beverage cans are selected

Let [tex]\bar X[/tex] = sample mean amount of a beverage

The z-score probability distribution for the sample mean is given by;

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

where, [tex]\mu[/tex] = population mean amount of a beverage = 16.18 ounces

           [tex]\sigma[/tex] = standard deviation = 0.4 ounces

           n = sample of 16-ounce beverage cans = 65

Now, the probability that the mean of this sample is less than 16.1 ounces of beverage is given by = P([tex]\bar X[/tex] < 16.1 ounces)

   P([tex]\bar X[/tex] < 16.1 ounces) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{16.1-16.18}{\frac{0.4}{\sqrt{65} } }[/tex] ) = P(Z < -1.61) = 1 - P(Z [tex]\leq[/tex] 1.61)

                                                    = 1 - 0.9463 = 0.0537

The above probability is calculated by looking at the value of x = 1.61 in the z table which has an area of 0.9591.

Answer:

If x + 5x = 90, 6x = 90 so x = 15, 5x = 75.

Answer: x= 15, 5x=75

Step-by-step explanation:

x=15                                      

x+5x=90

Add similar elements

6x=90

6x/6=90/6

x=15

5x=75

x=15

5x=15x5

15x5=75

Answer:

  £123,000

Step-by-step explanation:

Their combined income is ...

  £18,500 +22,500 = £41,000

They can borrow 3 times this amount, or ...

  3 × £41,000 = £123,000

__

Comment on this transaction

The required deposit is 5% of 130,000 = 6,500, which is more than their savings. After this down payment is made, the remaining value is £123,500, which exceeds their borrowing power. It appears that Emma and Max need to find a house with a lower price.

Answer:

x = 19

Step-by-step explanation:

In the attached file

Answer:

option b

Step-by-step explanation:

b i did it on edge

Answer:

16.25 acres

Step-by-step explanation:

If corn is 1/4 of the land and we have 65 acres, we merely multiply 1/4 to 65.

You get 16.25 acres.

Answer:

16.25acres

Step-by-step explanation:

65/4=16.25 or 16 and 1/4

Answer:

(a)[tex]E \cap F ={(2, 6),(4, 6),(6, 2),(6, 4),(6, 6)}[/tex]

(b) [tex]E^c \cap G =\{ \}[/tex]

Step-by-step explanation:

The sample space of two dice rolled is given below:

[tex]\{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5,6)\\(6, 1), (6, 2), (6, 3), (6, 4), (6,5), (6,6)\}[/tex]

For Event E (The sum is even), the outcomes are:

[tex](1, 1), (1, 3), (1, 5),(2, 2), (2, 4), (2, 6)\\(3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (4, 6)\\(5, 1),(5, 3), (5, 5), (6, 2), (6, 4), (6,6)[/tex]

For Event F (Rolling at least one six), the outcomes are:

[tex](1, 6), (2, 6), (3, 6), (4, 6),(5,6),(6, 1), (6, 2), (6, 3), (6, 4), (6,5), (6,6)[/tex]

For Event G (The sum is eight), the outcomes are:

[tex](2, 6), (3, 5),(4, 4), (5, 3),(6, 2)[/tex]

(a)[tex]E \cap F[/tex]

Therefore:

[tex]E \cap F ={(2, 6),(4, 6),(6, 2),(6, 4),(6, 6)}[/tex]

(b)[tex]E^c \cap G[/tex]

E is the event that the sum is even

Therefore: [tex]E^c$ is the event that the sum is odd.[/tex]

Since G is the event that the sum is eight( which is even), the intersection of the complement of E and G will be empty.

Therefore:

[tex]E^c \cap G =\{ \}[/tex]

Answer:

The Pareto Optimal height is  [tex]i = 100 \ inch[/tex]

Step-by-step explanation:

The Pareto Optimal height is a height  of the seawall at which an increase in wall height will exceed the amount the resident are willing to pay and a decrease will affect the protection of the city

The number of residents is [tex]n = 100[/tex]

The amount each are willing to pay is  [tex]z=[/tex]$10 per inch

 The cost of building a wall that is i inches high is given by [tex]c(i) = 6i^2.[/tex]

The total amount the residents are willing to pay is

          [tex]n = 100 * 10[/tex] =  $1000

The maximum cost  is mathematically represented as

                [tex]\frac{dc(i)}{di} = 10i[/tex]

which implies that

          1000 =  10i

Hence the Pareto Optimal height is

=>         [tex]i = \frac{1000}{10}[/tex]

             [tex]i = 100 \ inch[/tex]