Need help with solving for x!

Answer:28

Step-by-step explanation: 6 x 8 = 48 6+6+8+8=28

The perimeter of rectangle is 28 inches

The formula used to calculate the perimeter of a rectangle is, perimeter of a rectangle = 2(l + w), where 'l' is the length and 'w' is the width of the rectangle.

For example

The length of a bedsheet is 120 inches and the width is 85 inches. How much lace will be needed to put around its border?

Given, length = 120 inches; width = 85 inches.

Perimeter of a rectangle = 2(l + w).

On substituting the values of length and width in this formula, we get,

Perimeter = 2(l + w) = 2(120 + 85)= 2 × 205 = 410 inches.

Let he breadth be x

length= x+ 2

Area= Perimeter + 20

x² + 2x =  4x+ 4 + 20

x² - 2x -24  =  0

x² - 2x -24  =  0

(x- 6) (x+ 4)=0

x= 6, -4

So, length= 8 inches and breadth = 6 inches.

Hence, the Perimeter of rectangle= 2( 8 +6)= 2*14= 28 inches

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Answer:

1 , - ( 3x^2/2), + (25x^4/24).

Step-by-step explanation:

We are given the following information:

y = (e^-x^2)cosx.

STEP ONE: Write out the power series out(either by deriving it or otherwise).

If you check the power series table, you will get the power series for the two functions that is cos x and e^-x^2.

e^-x^2 = 1 - (x^2) + ( x^4/2! ) - (x^6/3!) +...

Cos x = 1 - (x^2/2!) + x^4/4!) + (x^6/6!) -...

STEP TWO: Multiply both the power series of e^-x^2 and Cos x together because we are to determine or find the first three nonzero terms in the maclaurin series for the given function.

1 - (x^2) + ( x^4/2! ) - (x^6/3!) +... - 1 - (x^2/2!) + x^4/4!) + (x^6/6!) -...

= 1 - ( 3x^2/2) + (25x^4/24).

= 1, - ( 3x^2/2) , + (25x^4/24) => comma- separated list.

Answer:

dI/dt = 0.0001(2000 - I)I

I(0) = 20

[tex]I(t)=\frac{2000}{1+99e^{-0.2t}}[/tex]

Step-by-step explanation:

It is given in the question that the rate of spread of the disease is proportional to the product of the non infected and the infected population.

Also given I(t) is the number of the infected individual at a time t.

[tex]\frac{dI}{dt}\propto \textup{ the product of the infected and the non infected populations}[/tex]

Given total population is 2000. So the non infected population = 2000 - I.

[tex]\frac{dI}{dt}\propto (2000-I)I\\\frac{dI}{dt}=k (2000-I)I, \ \textup{ k is proportionality constant.}\\\textup{Since}\ k = 0.0001\\ \therefore \frac{dI}{dt}=0.0001 (2000-I)I[/tex]

Now, I(0) is the number of infected persons at time t = 0.

So, I(0) = 1% of 2000

            = 20

Now, we have dI/dt = 0.0001(2000 - I)I  and  I(0) = 20

[tex]\frac{dI}{dt}=0.0001(2000-I)I\\\frac{dI}{(2000-I)I}=0.0001 dt\\\left ( \frac{1}{2000I}-\frac{1}{2000(I-2000)} \right )dI=0.0001dt\\\frac{dI}{2000I}-\frac{dI}{2000(I-2000)}=0.0001dt\\\textup{Integrating we get},\\\frac{lnI}{2000}-\frac{ln(I-2000)}{2000}=0.0001t+k \ \ \ (k \text{ is constant})\\ln\left ( \frac{I}{I-222} \right )=0.2t+2000k[/tex]

[tex]\frac{I}{I-2000}=Ae^{0.2t}\\\frac{I-2000}{I}=Be^{-0.2t}\\\frac{2000}{I}=1-Be^{-0.2t}\\I(t)=\frac{2000}{1-Be^{-0.2t}}\textup{Now we have}, I(0)=20\\\frac{2000}{1-B}=20\\\frac{100}{1-B}=1\\B=-99\\ \therefore I(t)=\frac{2000}{1+99e^{-0.2t}}[/tex]

The required expressions are presented below:

[tex]\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)[/tex] [tex]\blacksquare[/tex]

[tex]I(0) = \frac{1}{100}[/tex] [tex]\blacksquare[/tex]

[tex]I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}[/tex] [tex]\blacksquare[/tex]

After reading the statement, we obtain the following differential equation:

[tex]\frac{dI}{dt} = k\cdot I\cdot (n-I)[/tex] (1)

Where:

Then, we solve the expression by variable separation and partial fraction integration:

[tex]\frac{1}{k} \int {\frac{dI}{I\cdot (n-I)} } = \int {dt}[/tex]

[tex]\frac{1}{k\cdot n} \int {\frac{dl}{l} } + \frac{1}{kn}\int {\frac{dI}{n-I} } = \int {dt}[/tex]

[tex]\frac{1}{k\cdot n} \cdot \ln |I| -\frac{1}{k\cdot n}\cdot \ln|n-I| = t + C[/tex]

[tex]\frac{1}{k\cdot n}\cdot \ln \left|\frac{I}{n-I} \right| = C\cdot e^{k\cdot n \cdot t}[/tex]

[tex]I(t) = \frac{n\cdot C\cdot e^{k\cdot n\cdot t}}{1+C\cdot e^{k\cdot n \cdot t}}[/tex], where [tex]C = \frac{I_{o}}{n}[/tex] (2, 3)

Note - Please notice that [tex]I_{o}[/tex] is the initial infected population.

If we know that [tex]n = 2000[/tex], [tex]k = 0.0001[/tex] and [tex]I_{o} = 20[/tex], then we have the following set of expressions:

[tex]\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)[/tex] [tex]\blacksquare[/tex]

[tex]I(0) = \frac{1}{100}[/tex] [tex]\blacksquare[/tex]

[tex]I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}[/tex] [tex]\blacksquare[/tex]

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Answer:

[tex]n = \frac{3}{5}[/tex]. Which means that Frank has been travelling out of the town 3 days for each five days.

Step-by-step explanation:

The fraction ([tex]n[/tex]) is obtained by dividing the number of days that Frank has been out of town (18 days) in the given period (30 days). That is to say:

[tex]n = \frac{t}{T}[/tex]

[tex]t[/tex] - Out-of-the-town period, measured in days.

[tex]T[/tex] - Given period, measured in days.

If [tex]t = 18\,days[/tex] and [tex]T = 30\,days[/tex], then:

[tex]n = \frac{18\,days}{30\,days}[/tex]

[tex]n = \frac{3}{5}[/tex]

Which means that Frank has been travelling out of the town 3 days for each five days.

Answer:

Step-by-step explanation:

From the summary of the given statistics;

The null and the alternative hypothesis for confirming that the new engine has a mean emission level below the current standard can be computed as follows:

Null hypothesis:

[tex]H_0: \mu = 0.60[/tex]

Alternative hypothesis:

[tex]H_a: \mu < 0.60[/tex]

Type I  error: Here, the null hypothesis which is the new engine has a mean level equal to  .6g/ml is rejected when it is true.

Type II error:  Here, the alternative hypothesis which is the new engine has a mean level less than.6g/ml is rejected when it is true.

Similarly;

From , A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4.

Sample size n = 64

sample mean [tex]\overline x[/tex] = .5 g/ml

standard deviation σ = .4

From above, the normal standard test statistics can be determined by using the formula:

[tex]z = \dfrac{\bar x- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \dfrac{0.5- 0.6}{\dfrac{0.4}{\sqrt{64}}}[/tex]

[tex]z = \dfrac{-0.1}{\dfrac{0.4}{8}}[/tex]

z = -2.00

The p-value = P(Z ≤ -2.00)

From the normal z distribution table

P -value = 0.0228

Decision Rule: At level of significance ∝ = 0.05, If P value is less than or equal to level of significance ∝ , we reject the null hypothesis.

Conclusion: SInce the p-value is less than the level of significance , we reject the null hypothesis. Therefore, we can conclude that there is enough evidence that a new engine design has reduced the emissions to a level below this standard.

Answer:

350 pairs

Step-by-step explanation:

If the ratio of Athletics, Boots, and Dress shoes is 5 to 2 to 3, it means that for every 2 pairs of Boots they have 5 pairs of Athletics shoes and 3 pairs of dress shoes.

So, if they have 70 pairs of boots, we can calculate the number of Athletics as:

[tex]\frac{5*70}{2} =175[/tex]

And if they have 70 pairs of boots, the number of dress shoes are:

[tex]\frac{3*70}{2}=105[/tex]

Finally, they have 70 pairs of boots, 175 pairs of athletics, and 105 pairs of dress shoes. It means that they have 350 pairs in total.

70 + 175 + 105 = 350

Answer:

a) The five ordered pairs are:-

(1,60) , (2,120) , (3,180) , (4,240) , (5,300)

b)When You divide the y value by x value for each ordered pair u find the slope.

c)The graph shows a proportional relationship.Because as x-value increases so does y-value.

d)Y=mx+b-->  Y=60x (No y-intercept because it starts from 0)

e)If a person hiked for 9 hours then the distance would be 540. Because If u plug in the number of hours in the x value of the equatione then u will get 540. Here's the work:-

Y=60(9)

Y=540

Step-by-step explanation:

Hope it helps u. And if u get it right pls give me brainliest.

Answer:

see below

Step-by-step explanation:

Because two sides are congruent, the triangle in the diagram is isosceles which means that angle c = angle e because of the Base Angles Theorem. We know that angle c = 63 degrees because we see that it's vertical to a 63 degree angle, and vertical angles. Since angle c = angle e, angle e = 63 degrees. Since angles e and b form a linear pair, they are supplementary, meaning that they add up to 180 degrees which means that angle b = 180 - 63 = 117 degrees. To find angle d, we notice that d and c are alternate interior angles, and since these angles are congruent in parallel lines, angle d = 63 degrees as well. To find angle a, we know that the sum of angles in a triangle is 180 degrees so angle a = 180 - 63 - 63 = 54 degrees.

See in the attachment.

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

Work Shown:

A = mass, in kg, of 1 apple

B = mass, in kg, of 1 empty basket

10A = mass of 10 apples

10A+B = mass of 10 apples and basket = 0.5

35A = mass of 35 apples

35A + B = mass of 35 apples and basket = 1.05

The system of equations we have is

[tex]\begin{cases}10A+B = 0.5\\35A+B = 1.05\end{cases}[/tex]

There are a number of ways to solve. As the top left corner of your paper indicates, we can use a matrix to solve. Either using row reduction or matrix inverse math.

We could also use elimination which I find easiest in this case. I'll use that method. Subtract the equations straight down. Note how the B terms become B-B = 0B = 0 which go away. The A terms become 10A-35A = -25A, and the terms on the right hand side become 0.5-1.05 = -0.55

--------

We're left with the equation

-25A = -0.55

Divide both sides by -25 to isolate A

A = -0.55/(-25)

A = 0.022

The mass of one apple is 0.022 kg

--------

Use this value of A to find B

10A + B = 0.5

10*0.022 + B = 0.5

0.22 + B = 0.5

B = 0.5 - 0.22

B = 0.28

Or we could use the other equation to solve for B

35A + B = 1.05

35(0.022) + B = 1.05

0.77 + B = 1.05

B = 1.05 - 0.77

B = 0.28

Either way, the empty basket's mass is 0.28 kg

Answer:

1 day.

Step-by-step explanation:

Given:

Albert's cafe uses 5 bags of coffee every day.

Required:

How many days will 5/8 bag of coffee last?

'How many days will 5/8 bag of coffee last?'

In this sentence we can see that there are 8 bags of coffee. The question in other words is Albert's Cafe is using 5 bags of coffee out of the 8 bags of coffee, and how many days will these last.

In the given we can see that the Cafe uses 5 bags of coffee per day, so the answer is 1 day.

Hope this helps ;) ❤❤❤

Step-by-step explanation:

a. The point estimate is the mean, 47 days.

b. The margin of error is the critical value times the standard error.

At 31 degrees of freedom and 98% confidence, t = 2.453.

The margin of error is therefore:

MoE = 2.453 × 10.2 / √32

MoE = 4.42

c.  The confidence interval is:

CI = 47 ± 4.42

CI = (42.58, 51.42)

d. We can conclude with 98% confidence that the true mean is between 42.58 days and 51.42 days.

e. We can reduce the margin of error by either increasing the sample size, or using a lower confidence level.

Answer: parameter: The proportion of registered voters who will vote Yes on the measure.

Sample: The 1000 registered voters who participated in the study.

Statistic: The proportion of the 1000 registered voters that were surveyed who will vote Yes on the measure.

Variable: Yes or No for each registered voter

Population: All registered voters in the US

Data: The list of Yes and No answers that were given by the 1000 participants in the study.

Step-by-step explanation:

Definitions of the given terms:

Hence, by using the above definitions, we have

Answer:

[tex]\large \boxed{\sf 15 \ \ and \ \ 24 \ \ }[/tex]

Step-by-step explanation:

Hello,

We can write the following, x being the second number.

[tex](2x-6)^2+x^2=801\\\\6^2-2\cdot 6 \cdot 2x + (2x)^2+x^2=801\\\\36-24x+4x^2+x^2=801\\\\5x^2-24x+36-801=0\\\\5x^2-24x-765=0\\\\[/tex]

Let's use the discriminant.

[tex]\Delta=b^4-4ac=24^2+4*5*765=15876=126^2[/tex]

There are two solutions and the positive one is

[tex]\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{24+126}{10}=\dfrac{150}{10}=15[/tex]

So the solutions are 15 and 15*2-6 = 30-6 = 24

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

d = 115.4 mi

Step-by-step explanation:

Since it gives us the distance in between the locations, we simply label the distances:

From the Garbage to the Hotel is 58.3 miles.

From the Hotel to the Hardware Store is 57.1 miles.

We are trying to find the distance from the Garbage to the Hardware Store, we simply add the distances between:

58.3 mi + 57.1 mi = 115.4 mi

Answer:206.703

Step-by-step explanation: you have to multiply 328.1 times 0.63 then you get your answer.

Answer:

206.703

Step-by-step explanation:

328.1 × 0.63=206.703

Answer:

b. sqrt(120)

Step-by-step explanation:

a^2+b^2=c^2

a^2+7^2=13^2

13^2-7^2=a^2

120=a^2

sqrt(120)=a

This is using Pythagorean theorem

Answer:

The answers are A. and B.

Step-by-step explanation:

Since the area of the largest square is 36. We need two numbers that equal 36. and A. had 6 and 30 so i picked it and it was right and B. is 28 and 8 which also equals 36. But, C. is 4 and 16 which is not 36. So A. and B. are the answers. Hope this helps! :)

We can use the Pythagorean theorem (a^2+b^2=c^2)(a  

2

+b  

2

=c  

2

)left parenthesis, a, squared, plus, b, squared, equals, c, squared, right parenthesis to determine possible areas of the two smaller squares.

\text{Area of a square} =\text{side}^2Area of a square=side  

2

start text, A, r, e, a, space, o, f, space, a, space, s, q, u, a, r, e, end text, equals, start text, s, i, d, e, end text, squared

So, we can substitute the areas of the squares that share side lengths with the triangle for a^2, b^2a  

2

,b  

2

a, squared, comma, b, squared and c^2c  

2

c, squared in the Pythagorean theorem.

Hint #22 / 6

For example, in the diagram above, the area of the square that shares a side with the hypotenuse is 363636 square units. So, c^2=36c  

2

=36c, squared, equals, 36.

Hint #33 / 6

Let's fill in the possible values to see if they make the equation true.

\begin{aligned} a^2 + b^2 &= c^2 \\\\ a^2 + b^2 &= 36 \\\\ 6 + 30 &\stackrel{\large?}{=}36 \\\\ 36 &\stackrel{\checkmark}{=}36\\\\ \end{aligned}  

a  

2

+b  

2

a  

2

+b  

2

6+30

36

​  

=c  

2

=36

=

?

36

=

✓

36

​  

The sum of the areas of the squares connected to the two shorter triangle sides is equal to the area of the square connected to the longest side.

So, 666 and 303030 could be the areas of the smaller squares.

Hint #44 / 6

\begin{aligned} a^2 + b^2 &= c^2 \\\\ a^2 + b^2 &= 36 \\\\ 8 + 28 &\stackrel{\large?}{=}36 \\\\ 36 &\stackrel{\checkmark}{=}36\\\\ \end{aligned}  

a  

2

+b  

2

a  

2

+b  

2

8+28

36

​  

=c  

2

=36

=

?

36

=

✓

36

​  

The sum of the areas of the squares connected to the two shorter triangle sides is equal to the area of the square connected to the longest side.

So, 888 and 282828 could be the areas of the smaller squares.

Hint #55 / 6

\begin{aligned} a^2 + b^2 &= c^2 \\\\ a^2 + b^2 &= 36 \\\\ 4 + 16 &\stackrel{\large?}{=}36 \\\\ 20 &\neq 36\\\\ \end{aligned}  

a  

2

+b  

2

a  

2

+b  

2

4+16

20

​  

=c  

2

=36

=

?

36



​  

=36

​  

The sum of the areas of the squares connected to the two shorter triangle sides is not equal to the area of the square connected to the longest side.

So, 444 and 161616 could not be the areas of the smaller squares.

Hint #66 / 6

The area of the smaller squares could be:

666 and 303030

888 and 2828

Answer:

[tex](-\infty, 0) \cup (0,2) \cup (2,\infty)[/tex]

Step-by-step explanation:

Remember that the domain of the product of functions is the intersection of domains, therefore when you intercept them you get the following interval.

[tex](-\infty, 0) \cup (0,2) \cup (2,\infty)[/tex]

Answer:

  $1025

Step-by-step explanation:

We can use the 2-point form of the equation of a line to write a function that gives Justin's salary as a function of his sales.

We start with (sales, salary) = (400, 500) and (700, 575)

__

The 2-point form of the equation of a line is ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  salary = (575 -500)/(700 -400)(sales -400) +500

  salary = 75/300(sales -400) +500

For sales of 2500, this will be ...

  salary = (1/4)(2500 -400) +500 = (2100/4) +500 = 1025

Justin's salary after selling $2500 in merchandise is $1025.

Answer:

16 flowerpots

Step-by-step explanation:

12 divided by 3/4=16

Answer:

Step-by-step explanation:

40.50/2 = 20.25

You have to divide by 2. This way both of the people will get the same amount of money.

Answer:

each friend will get

Step-by-step explanation:

20 .25

as 40 .50 ÷ 2 = 20 .25

hope this helps

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Answer:

6 2/9 miles per hour

Step-by-step explanation:

Take the miles and divide by the hours

4 2/3 ÷ 3/4

Change to an improper fraction

( 3*4+2)/3 ÷3/4

14/3 ÷3/4

Copy dot flip

14/3 * 4/3

56/9

Change back to a mixed number

9 goes into 56  6 times with 2 left over

6 2/9 miles per hour

Answer:

6 2/9 miles per hour

Step-by-step explanation:

Divide the miles by the hour.

4 2/3 ÷ 3/4

Reciprocal

4 2/3 × 4/3

Convert to improper fraction.

14/3 × 4/3

56/9

Convert to mixed fraction.

9 × 6 + 2

6 2/9

The solution to the equation above using three iterations of successive approximation is x = 25/16

The solution of an equation is the true values of the equation

The equation is given as:

[tex]5^{-x} + 7 =2x + 4[/tex]

Equate to 0

[tex]5^{-x} + 7 -2x - 4 = 0[/tex]

Write the equation as a function

[tex]f(x) = 5^{-x} + 7 -2x - 4[/tex]

The equation has a solution only when the function f(x) equals 0.

From the graph, we have:

x = 1.5

So, we have:

[tex]f(1.5) = 5^{-1.5} + 7 -2*1.5 - 4[/tex]

Evaluate

f(1.5) = 0.089

Set x to 1.52 to determine a closer value of f(x) to 0.

[tex]f(1.52) = 5^{-1.52} + 7 -2*1.52 - 4[/tex]

Evaluate

f(1.52) = 0.047

Set x to 1.54 to determine a closer value of f(x) to 0.

[tex]f(1.54) = 5^{-1.54} + 7 -2*1.54 - 4[/tex]

Evaluate

f(1.54) = 0.004

Notice that 0.004 is closer to 0 than 0.047 and 0.089

The closest value to 1.54 is 25/16 in the given options

Hence, the solution to the equation above using three iterations of successive approximation is x = 25/16

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Answer:

1. 115 chocolates were added

2. 861 visitors in September

Step-by-step explanation:

1.

Initially:

m=number of mints

60% of 230 sweets were mints  =>

m = 230*0.6 = 138 mints

initial number of chocolates, c1  =  230 - 138 = 92

Now chocolates were added

138 mints represented 40% of the total number of sweets, so

total number of sweets  = 138 / 0.4 = 345

Number of chocolates added = 345 - 230 = 115

2.

In August 36% were locals, 64% were from elsewhere.

In suptember,

locals decreassed by 25% to 36*0.75=27% (of August total)

foreigner increased by 50% to 64*1.5=96% (of August total)

Total Inrease = 96+27-100 = 23% of August total  = 161 visitors

August total = 161/0.23 = 700 visitors

September total = 700 + 161 = 861 visitors

Answer:

Step-by-step explanation:

x+y>0, x>0, when y=0

x+y<-5 x<-5 when y=0

since the sign is only< then it is dotted line, and since one is greater and is less than they actually do not intersect

Answer:

No solution with slanted lines

Step-by-step explanation:

Answer:

A 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].

Step-by-step explanation:

We are given that Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured.

For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 and For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09.

Firstly, the pivotal quantity for finding the confidence interval for the difference in population mean is given by;

                     P.Q.  =  [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]  ~  [tex]t__n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean speed for the 25-mil film = 1.15

[tex]\bar X_1[/tex] = sample mean speed for the 20-mil film = 1.06

[tex]s_1[/tex] = sample standard deviation for the 25-mil film = 0.11

[tex]s_2[/tex] = sample standard deviation for the 20-mil film = 0.09

[tex]n_1[/tex] = sample of 25-mil film = 8

[tex]n_2[/tex] = sample of 20-mil film = 8

[tex]\mu_1[/tex] = population mean speed for the 25-mil film

[tex]\mu_2[/tex] = population mean speed for the 20-mil film

Also,  [tex]s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(8-1)\times 0.11^{2}+ (8-1)\times 0.09^{2}}{8+8-2} }[/tex] = 0.1005

Here for constructing a 98% confidence interval we have used a Two-sample t-test statistics because we don't know about population standard deviations.

So, 98% confidence interval for the difference in population means, ([tex]\mu_1-\mu_2[/tex]) is;

P(-2.624 < [tex]t_1_4[/tex] < 2.624) = 0.98  {As the critical value of t at 14 degrees of

                                             freedom are -2.624 & 2.624 with P = 1%}  

P(-2.624 < [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < 2.624) = 0.98

P( [tex]-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < [tex]2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] <  ) = 0.98

P( [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ([tex]\mu_1-\mu_2[/tex]) < [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ) = 0.98

98% confidence interval for ([tex]\mu_1-\mu_2[/tex]) = [ [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] , [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ]

= [ [tex](1.15-1.06)-2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] , [tex](1.15-1.06)+2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] ]

 = [-0.042, 0.222]

Therefore, a 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].

Since the above interval contains 0; this means that decreasing the thickness of the film doesn't increase the speed of the film.