The coach of an age group swim team needs to assign swimmers to a 200-yard medley relay team to send to the Junior Olympics. Since most of his best swimmers are very fast in more than one stroke, it is not clear which swimmer should be assigned to each of the four strokes. The five fastest swimmers and the best times (in seconds) they have achieved in each of the strokes (for 50 yards) are

Answer:

9

Step-by-step explanation:

6+x, when x = 3

6+(3)

6+3=9

Answer:

9

Step-by-step explanation:

6 + x, when x = 3

So, 6 + 3 = answer

So, 6 + 3 = 9

Stay Safe, Stay at Home!! Lots of Love <3 <3 =) :3

Answer:

The Laplace transform of f(t) = 1 is given by

F(s) = (1/s) for all s>0

Step-by-step explanation:

Laplace transform of a function f(t) is given as

F(s) = ∫∞₀ f(t) e⁻ˢᵗ dt

Find the Laplace transform for when f(t) = 1

F(s) = ∫∞₀ 1.e⁻ˢᵗ dt

F(s) = ∫∞₀ e⁻ˢᵗ dt = (1/s) [-e⁻ˢᵗ]∞₀

= -(1/s) [1/eˢᵗ]∞₀

Note that e^(∞) = ∞

F(s) = -(1/s) [(1/∞) - (1/e⁰)]

Note that (1/∞) = 0

F(s) = -(1/s) [0 - 1] = -(1/s) (-1) = (1/s)

Hope this Helps!!!

In this exercise we have to use the knowledge of the Laplace transform to calculate the total value of the given function, thus we will find that:

[tex]F(s) = (1/s) \\for \ all\ s>0[/tex]

So we have that the Laplace transform can be recognized as:

[tex]F(s) = \int\limits^\infty _0 { f(t) e^{-st} \, dt[/tex]

Find the Laplace transform for when f(t) = 1, we have that:

[tex]F(s) = \int\limits^\infty _0 { f(t) e^{-st} \, dt \\\\ F(s) = \int\limits^\infty _0 { 1 e^{-st} \, dt[/tex]

[tex]F(s) = \int\limits^\infty _0 { e^{-st} \, dt = (1/s) [-e^{-st}] \\[/tex]

[tex]F(s) = -(1/s) [(1/\infty ) - (1/e^0)] \\F(s) = -(1/s) [0 - 1] = -(1/s) (-1) = (1/s)[/tex]

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Answer:

The mean women's shoe size in U.S. units is 8.73.

The standard deviation in U.S. units is  1.40.

Step-by-step explanation:

For the women, the mean size was 38.73 with a standard deviation of 1.75.  This size is expressed in European units.

If we want to convert to US units, we have to use the equation:

[tex]US\, size=EuroSize*0.7987-22.2[/tex]

If we use the properties of the expected value, then the mean expressed in US units is:

[tex]Property: E(y)=E(ax+b)=aE(x)+b\\\\\\E(y)=0.7987E(x)-22.2\\\\E(y)=0.7987*38.73-22.2\\\\E(y)=8.73[/tex]

To calculate the standard deviation, we use the properties of variance:

[tex]Property: V(y)=V(ax+b)=a^2V(x)\\\\\sigma_y=\sqrt{a^2V(x)}=a\sigma_x\\\\\sigma_y=0.7987*1.75=1.40[/tex]

Answer:

Check the explanation

Step-by-step explanation:

Let

  \(W(t) = W_1 + W_2 + ... + W_n\)  

where W_i denotes the individual fare of the customer.

All W_i are independent of each other.

By formula for random sums,

E(W(t)) = E(Wi) * E(n)

  \(E(Wi) = \mu_G\)  

Mean inter arrival time =    \(\mu_F\)  

Therefore, mean number of customers per unit time =    \(1 / \mu_F\)  

=> mean number of customers in t time =    \(t / \mu_F\)  

=>    \(E(n) = t / \mu_F\)  

Answer:

Given:

P=950

r=0.07

t=8

F=950(1.07)^8

= 1632.28 (total amount)

Interest = total amount - principal

=1632.28 - 950

=682.28

Step-by-step explanation:

The formula is:

Future value = accumulated amount, F = P(1+r)^t

P=principal

r=annual interest rate [compounded annually]

t=number of years of loan

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

SST = 1800

SSR = 1512.376

SSE = 287.624

b

coefficient of determination  is [tex]r^2 \approx 0.8402[/tex]

What this is telling us is that 84.02% variation in dependent variable y can be fully explained by variation in the independent variable x

c

The correlation coefficient is   [tex]r = 0.917[/tex]

Step-by-step explanation:

The table shown the calculated mean is shown on the second uploaded image

Let first define some term

SST (sum of squares total) : This is the difference between the noted dependent variable and the mean of this noted dependent variable

SSR(sum of squared residuals) : this can defined as a predicted shift from the actual observed values of the data  

SSE (sum of squared estimate of errors): this can be defined as the  sum of the square difference between the observed value and its mean

From the table

  [tex]SST = SS_{yy} = 1800[/tex]

  [tex]SSR = \frac{SS^2_{xy}}{SS_{xx}} = \frac{4755^2}{14950} = 1512.376[/tex]

  [tex]SSE =SST-SSR[/tex]

          [tex]=1800 - 1512.376[/tex]

           [tex]= 287.62[/tex]

The coefficient of determination is mathematically represented as

               [tex]r^2 = \frac{SSR}{SST}[/tex]

                    [tex]= 1-\frac{SSE}{SST}[/tex]

                   [tex]r^2= 1-\frac{287.6237}{1800}[/tex]

                  [tex]r^2 \approx 0.8402[/tex]

The correlation coefficient is mathematically represented as

           [tex]r = \pm\sqrt{r^2}[/tex]

Substituting values

            [tex]r = \sqrt{0.84020}[/tex]

               [tex]r = 0.917[/tex]

this value is + because the value of the coefficient of x in estimated regression equation([tex]24.9 + 0.301x,[/tex]) is positive

To compute SST, SSR, and SSE, we calculate the variability of the dependent variable around the mean, the variability explained by the regression model, and the variability not explained by the regression model.

To compute SST, SSR, and SSE, we need to understand what each of them represents. SST (the total sum of squares) measures the total variability of the dependent variable (overall score) around the mean. SSR (the regression sum of squares) measures the amount of variability in the dependent variable that is explained by the regression model. Finally, SSE (the error sum of squares) measures the amount of variability in the dependent variable that is not explained by the regression model.

To compute these values:

Hence, SST = 5424, SSR = 10435.558, and SSE = 171.442.

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Step-by-step explanation:

For the charges that have same sign of charges will repel each other while for the charges that have different charges will attract each other. So, we can say that like charges repel and unlike charges attract each other.

The Coulomb's law of attraction of repulsion states that force between charges is directly proportion to the product of charges and inversely proportional to the square of distance between them. Mathematically, it is given by :

[tex]F=\dfrac{kq_1q_2}{r^2}[/tex]

Hence, all the given statements are true.

Answer:

64

Step-by-step explanation:

The answer is 64, because 4 to the 3rd power is 64.  When finding the volume of a cube, find the length of one side to the 3rd.

The average number of people per car visiting the national park is approximately 2.91.

In order to find the average number of people per car, you would first multiply the number of cars by the number of people in each.

Therefore, 57 cars had 4 people (57*4=228), 61 cars had 2 people (61*2=122), 9 cars had 1 person (9*1=9), and 5 cars had 5 people (5*5=25). After this, add all the results (228+122+9+25 = 384).

The total number of cars is the sum of all cars, which is (57+61+9+5 = 132).

Now, to find the average number of people per car, you would divide the total number of people, which is 384 by the total number of cars, which is 132. Therefore, the average number of people per car is 384 / 132 = about 2.91 people per car.

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Answer:

Where's the triangle?

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

Answer:

  40 square inches

Step-by-step explanation:

The shaded area is the area of a triangle with base 10 in and height 8 in. It is given by the area formula ...

  A = (1/2)bh = (1/2)(10 in)(8 in) = 40 in²

The shaded area is 40 square inches.

Answer:

B. The mean amount of [tex]CO_2[/tex] emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg

Step-by-step explanation:

A Type II error is the failure to reject a false null hypothesis.

Given the null and alternate hypothesis of a fuel company which wants to test a new type of gasoline designed to have lower [tex]CO_2[/tex] emissions.:

[tex]H_0: \mu = 8.9 kg\\H_a: \mu < 8.9 kg \\\text{ (where \mu is the mean amount of CO_2 emitted by burning one gallon of this new gasoline)}[/tex]

where [tex]\mu[/tex] is the mean amount of [tex]CO_2[/tex] emitted by burning one gallon of this new gasoline.

If the null hypothesis is false, then:

[tex]H_a: \mu < 8.9 kg[/tex]

A rejection of the alternate hypothesis above will be a Type II error.

Therefore:

The Type II error is: (B) The mean amount of [tex]CO_2[/tex]  emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg.

You can use the definition of type 2 error to find out which of the given option describes the type 2 error.

The Option which indicates Type II error is:

Option B. The mean amount of CO2 emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg.

Firstly the whole story starts from hypotheses. The null hypothesis is tried to reject and we try to accept the alternate hypothesis.

The negative is just like the doctor's test getting negative means no disease. Similarly, if we conclude null hypothesis negative means it is accepted. If it is accepted wrongly means the negative test result was false, thus called false negative. This error is called type II error.

Since the null hypothesis here is [tex]H_0: \text{typically emitted } {\rm CO_2} = 8.9 \: \rm kg[/tex],

Thus the type II error would be when we fail to reject that CO2 emission is 8.9 kg (or say  we accept that CO2 emission is 8.9 kg generally) but the actual amount was lower than 8.9 kg(the alternate hypothesis was true)

Thus,

The Option which indicates Type II error is:

Option B. The mean amount of CO2 emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg.

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Answer:

0.1056 = 10.56% probability that the concentration exceeds 0.60

Step-by-step explanation:

Problems of normally distributed samples are solved using 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.

In this problem, we have that:

[tex]\mu = 0.5, \sigma = 0.08[/tex]

What is the probability that the concentration exceeds 0.60?

This is 1 subtracted by the pvalue of Z when X = 0.6. So

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

[tex]Z = \frac{0.6 - 0.5}{0.08}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.8944

1 - 0.8944 = 0.1056

0.1056 = 10.56% probability that the concentration exceeds 0.60

Answer:

It will take 41.3 minutes for the element to decay to 40 grams

Step-by-step explanation:

The amount of element after t minute is given by the following equation:

[tex]x(t) = x(0)e^{-rt}[/tex]

In which x(0) is the initial amount and r is the rate that it decreases.

Element X decays radioactively with a half life of 9 minutes.

This means that [tex]x(9) = 0.5x(0)[/tex]. We use this to find r. So

[tex]x(t) = x(0)e^{-rt}[/tex]

[tex]0.5x(0) = x(0)e^{-9r}[/tex]

[tex]e^{-9r} = 0.5[/tex]

[tex]\ln{e^{-9r}} = \ln{0.5}[/tex]

[tex]-9r = \ln{0.5}[/tex]

[tex]9r = -\ln{0.5}[/tex]

[tex]r = -\frac{\ln{0.5}}{9}[/tex]

[tex]r = 0.077[/tex]

So

[tex]x(t) = x(0)e^{-0.077t}[/tex]

There are 960 grams of Element X

This means that [tex]x(0) = 960[/tex]

[tex]x(t) = 960e^{-0.077t}[/tex]

How long, to the nearest tenth of a minute, would it take the element to decay to 40 grams?

This is t when [tex]x(t) = 40[/tex]. So

[tex]x(t) = 960e^{-0.077t}[/tex]

[tex]40 = 960e^{-0.077t}[/tex]

[tex]e^{-0.077t} = \frac{40}{960}[/tex]

[tex]\ln{e^{-0.077t}} = \ln{\frac{40}{960}}[/tex]

[tex]-0.077t = \ln{\frac{40}{960}}[/tex]

[tex]0.077t = -\ln{\frac{40}{960}}[/tex]

[tex]t = -\frac{\ln{\frac{40}{960}}}{0.077}[/tex]

[tex]t = 41.3[/tex]

It will take 41.3 minutes for the element to decay to 40 grams

Answer:

(a) 1/3

(b) 1/15

Step-by-step explanation:

(a)Let X denote the waiting time in minutes. It is given that X follows a uniform distribution, and since the variable being measured is time,  we assume it to be a continuous uniform distribution.

[tex] \[f_X(x) =\begin{cases} \frac{1}{30} & 0\leqx\leq 30\\ 0 & otherwise \end{cases}\][/tex]

Now

[tex] P(X>20) = \int_{20}^{30}f_X(x) = \frac{1}{30} \times 10 = \frac{1}{3}[/tex].

Jack or Rose arriving first is equally likely, therefore the probability of Jack waiting is just the half of the above obtained probability i.e [tex]\frac{1}{6}[/tex]

(b)Using the formula for the expectation of a uniform continuous distribution,

[tex] E(X) = \frac{30+0}{2} = 15[/tex]

Answer: 10 by 16

Step-by-step explanation:

Answer: the resale value would be $791 after 4 years

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

y = b(1 - r)^x

Where

y represents the value of the laptop computer after x years.

x represents the number of years.

b represents the initial value of the laptop computer.

r represents rate of decay.

From the information given,

P = $2500

x = 4

r = 25% = 25/100 = 0.25

Therefore,

y = 2500(1 - 0.25)^4

y = 2500(0.75)^4

y = $791

Answer:

1.25

Step-by-step explanation:

Answer:

A is correct, "All numbers bigger than -3 and smaller than 3"

Step-by-step explanation:

The open circle means greater than, if it was filled in, it would be greater than or equal to. And the black line connecting each shows its more than -3 and less than 3. Hope this helps! Please rate brainliest if it does :)

Answer:

The 99% confidence interval for the mean number of computer games purchased each year is between 7.3 and 7.5 games.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{1.4}{\sqrt{1233}} = 0.1[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 7.4 - 0.1 = 7.3.

The upper end of the interval is the sample mean added to M. So it is 7.4 + 0.1 = 7.5

The 99% confidence interval for the mean number of computer games purchased each year is between 7.3 and 7.5 games.

Answer: = ( 7.3, 7.5)

Therefore at 99% confidence interval (a,b) = ( 7.3, 7.5)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean gain x = 7.4

Standard deviation r = 1.4

Number of samples n = 1233

Confidence interval = 99%

z(at 99% confidence) = 2.58

Substituting the values we have;

7.4+/-2.58(1.4/√1233)

7.4+/-2.58(0.03987)

7.4+/-0.1028

7.4+/-0.1

= ( 7.3, 7.5)

Therefore at 99% confidence interval (a,b) = ( 7.3, 7.5)

Answer:

It will take 55 years for the account value to reach 38200 dollars

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex].

In this problem, we ahve that:

[tex]T = 38200, P = 7500, I = 0.075[/tex]

So

First we find how much we have to earn in interest.

[tex]38200 = E + 7500[/tex].

[tex]E = 38200 - 7500[/tex]

[tex]E = 30700[/tex]

How much time to earn this interest?

[tex]E = P*I*t[/tex]

[tex]30700 = 7500*0.075*t[/tex]

[tex]t = \frac{30700}{7500*0.075}[/tex]

[tex]t = 54.6[/tex]

Rounding up

It will take 55 years for the account value to reach 38200 dollars

Answer:

It will take approximately 53 years for the account value to reach 38200 dollars

Step-by-step explanation:

Given the following parameters:

Principal P = 7500

Interest Rate R = 7.75% = 0.0775

Let us find the simple interest for the first year

Simple Interest, I = PRT

with T = 1 year = 12 months

I = 7500 × 0.0775 × 1

= 581.25

The amount for the first year is the addition of the principal and simple interest.

Amount, A = 7500 + 581.25 = 8081.25.

Now, we want to find the time T when Amount A = 38200

Given A = P + I

And I = PRT

A = P + PRT

= P(1 + RT)

Let us make T the subject of the formula.

Dividing both sides by P

A/P = 1 + RT

A/P - 1 = RT

T = ((A/P) - 1)/R

T = ((38200/7500) - 1)/0.0775

= (307/75)/0.0775

= 52.8172043

≈ 53 years.

Please consider the graph of the sphere.

We know that the volume of sphere is equal to [tex]\frac{4}{3}\pi r^3[/tex], where r represents radius of sphere.

We can see that diameter of sphere is 30 inches. We know that radius is half the diameter, so radius of the given sphere would be half of 30 inches that is [tex]\frac{30}{2}=15[/tex] inches.

[tex]V=\frac{4}{3}\pi r^3[/tex]

[tex]V=\frac{4}{3}\pi (15\text{ in})^3[/tex]

[tex]V=\frac{4}{3}\pi \times 3375\text{ in}^3[/tex]

[tex]V=4\times 1125\pi \text{ in}^3[/tex]

[tex]V=4500\pi \text{ in}^3[/tex]

Therefore, the volume of the given sphere is [tex]4500\pi\text{ in}^3[/tex] and option B is the correct choice.

Answer:

1. 5000 = N

2. 50 = σ

3. 95% = confidence level (1-α)

4. α = 0.05

5. α/2=0.025=2.5%

6. z_(α/2)=-1.96

1. Width of confidence interval UL-LL=20

Step-by-step explanation:

We have to calculate a 95% confidence interval for the mean (average number of gallons of gas bought per month by the residents of this town).

The margin of error has to be below 10 gallons/month.

The population standard deviation is considered 50 gallons/month.

1. 5000 = N.

This is the population size N for this study, as this is the total population of the town.

2. 50 = σ

This is the value of the population standard deviation σ, as it is estimated from other studies.

3. 95% = (1-α)

This is the confidence level of the interval, and is equal to 1 less the significance level α.

4. α = 0.05

This is calculated from the confidence level. As the confidence level is 95%, the level of significance is 5%.

[tex]1-\alpha=0.95\\\\\alpha=1-0.95\\\\\alpha=0.05[/tex]

5. α/2=0.05/2=0.025=2.5%

6. The value os z_α/2 is obtained from a standard normal distribution table, where:

[tex]P(z<z_{\alpha/2})=0.025\\\\z_{\alpha/2}=-1.96[/tex]

z_α/2=-1.96

1. As the margin of error is 10 (maximum value), the difference between upper and lower bound is:

[tex]UL-LL=2*MOE=2*10=20[/tex]

Answer:

38

Step-by-step explanation:

An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.

Inscribed Angle =1/2 Intercepted Arc

We know the intercepted are is 76 degrees

<c = 1/2 (76) = 38

The inscribed angle = 38

Answer:

38

Step-by-step explanation:

Its definetly under 90 degrees. And it is also under 76 degress, so thatmeans it is 38 degrees

Answer:

Yes

Step-by-step explanation:

Answer:

Therefore surface integral is [tex]\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c[/tex].

Step-by-step explanation:

Given function is,

[tex]\vec{F}=\frac{bx}{a}\uvec{i}+\frac{ay}{b}\uvec{j}[/tex]

To find,

[tex]\int\int_{S}\vec{F}dS[/tex]  

where S=A=surfece of elliptic cylinder we have to apply Divergence theorem so that,

[tex]\int\int_{S}\vec{F}dS[/tex]

[tex]=\int\int\int_V\nabla.\vec{F}dV[/tex]

[tex]=\int\int\int_V(\frac{b}{a}+\frac{a}{b})dV[/tex]  

[tex]=\frac{a^2+b^2}{ab}\int\int\int_VdV[/tex]

[tex]=\frac{a^2+b^2}{ab}\times \textit{Volume of the elliptic cylinder}[/tex]

[tex]=\frac{a^2+b^2}{ab}\times \pi ab\times 2c=\pi (a^2+b^2)c[/tex]

[tex]\int\int_{S_1}\vex{F}.dS_1=\int\int_{S_1}<\frac{bx}{a}, \frac{ay}{b}, 0> . <-z_x,z_y,1>dA[/tex]      

[tex]=\int\int_{S_1}<\frac{bx}{a},\frac{ay}{b}, 0>.<0,0,1>dA=0[/tex]

[tex]\int\int_{S_2}\vex{F}.dS_2=\int\int_{S_2}<\frac{bx}{a}, \frac{ay}{b}, 0>. -<-z_x,z_y,1>dA[/tex]      

[tex]=\int\int_{S_2}<\frac{bx}{a},\frac{ay}{b}, 0>. -<0,0,1>dA=0[/tex]

Therefore surface integral without unit vector of the surface is,

[tex]\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c[/tex]

The value of ∫SF ⋅dA where F =(bx/a)i +(ay/b)j and S is the elliptic cylinder oriented away from the z-axis is 2πc(a² + b²).

From the information, F = (b/ax) + (a/by)j and S is the elliptic cylinder.

To evaluate ∫F.dA goes thus:

divF = (I'd/dx + jd/dx + kd/dx) × (b/ax)i + (a/by)j

= b/a + a/b

= (a² + b²)/ab

Using Gauss divergence theorem, this will be further solved below:

∫∫∫v(a² + b²/ab)dV

= (a² + b²/ab)∫∫∫vdV

= (a² + b²/ab) × Volume of cylinder

= (a² + b²/ab) × πab(2c)

= 2πc(a² + b²)

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Answer:

The answer is x=5, −9

Answer:

The null hypothesis is rejected (P-value=0.0 28).

There is  enough evidence to support the claim that that Company A tires outlast the tires of Company B by more than 10,000 miles.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that that Company A tires outlast the tires of Company B by more than 10,000 miles.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=10000\\\\H_a:\mu_1-\mu_2> 10000[/tex]

being μ1: average for Company A and μ2: average for Company B.

The significance level is 0.05.

The sample 1, of size n1=16 has a mean of 63,500 and a standard deviation of 4,000.

The sample 1, of size n1=12 has a mean of 49,500 and a standard deviation of 6,000.

The difference between sample means is Md=14,000.

[tex]M_d=M_1-M_2=63500-49500=14000[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{4000^2}{16}+\dfrac{6000^2}{12}}\\\\\\s_{M_d}=\sqrt{1000000+3000000}=\sqrt{4000000}=2000[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{14000-10000}{2000}=\dfrac{4000}{2000}=2[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-1=16+12-2=26[/tex]

This test is a right-tailed test, with 26 degrees of freedom and t=2, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t>2)=0.028[/tex]

As the P-value (0.028) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is  enough evidence to support the claim that that Company A tires outlast the tires of Company B by more than 10,000 miles.

In statistics, you can use a two-sample t-test to compare the lifespans of two types of tires. After setting up the null and alternative hypotheses, we use the alpha level, test statistic, and p-value to decide whether to reject the null hypothesis and accept the company's claim.

To clarify, testing this claim about tire lifespan falls under the category of hypothesis testing within statistics. In your case, you're comparing the lifespan of two types of tires which involves a two-sample t-test. Unfortunately, you've only provided raw data, but let's tackle this conceptually.

First, we set up the null and alternative hypotheses. The null hypothesis, usually denoted as H0, asserts that there's no difference between the means of the two populations. In this case, it says the lifespan of Company A's tires are the same as Company B's tires.

The alternative hypothesis, usually denoted as Ha, is the claim you're trying to test - in this case, that Company A's tires do last 10,000 miles longer than Company B's tires. In this hypothesis test, your alpha, which is the threshold of how much you're willing to be wrong, is 0.05.

After calculating the t-score and finding the p-value using statistical software or a t-distribution table, you compare the p-value to the alpha. If the p-value is less than the alpha, that means the result is statistically significant and thus you reject the null hypothesis.

Based on the decision and reason provided in your question, the conclusion would be that there is sufficient evidence at the 0.05 level to support the claim that Company A's tires outlast Company B's tires by more than 10,000 miles.

For more such questions on hypotheses, click on:

https://brainly.com/question/34171008

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