The average lifetime of a set of tires is three years. The manufacturer will replace any set of tires failing within two years of the date of purchase. The lifetime of these tires is known to follow an exponential distribution. What is the probability that the tires will fail within two years of the date of purchase?

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

Then

(x - 25)/(√x - 5) = √x + 5

and as x approaches 25, we get a limit of √25 + 5 = 5 + 5 = 10.

Question:

Convert the angle θ=260° to radians.

Express your answer exactly.

θ = ___ radians

Answer:

260° = 13π/9 or 4.54 rad

Step-by-step explanation:

Given

θ=260°

Required

Convert from degree to radians

To convert an angle in degrees to radians, we simply follow the steps below.

1° = 1 * π/180 rad

Replace the 1° with x

So,

x° = x * π/180 rad.

Now, we assume that x = 260

This means that we substitute 260 for x. This gives

260° = 260 * π/180

260° = 260π/180

Divide numerator and denominator by 20

260° = 13π/9

We can leave the answer in this form or solve further.

Take π as 22/7. This gives

260° = 13/9 * 22/7

260° = 286/63

260° = 4.5396825397

260° = 4.54 rad (Approximated)

The value of an angle 260 degree into radians is,

⇒ 260 degree = 13π/9 radians

WE have to given that,

To convert an angle 260 degree into radians.

Now, WE know that;

1 degree = π/180 radians

Hence, We can convert an angle 260 degree into radians as,

1 degree = π/180 radians

260 degree = 260 x π/180 radians

260 degree = 13π/9 radians

Thus, WE get;

260 degree = 13π/9 radians

Learn more about the measurement unit visit:

https://brainly.com/question/777464

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Answer:

Step-by-step explanation: answer is 480 cubic feet. Just do 8 x 6 x 10.

Answer:

D. Observational Study

Explanation:

An observational  study is one in which all the participants are subjected to a common treatment and then compared to people who did not receive the same treatment. This is the case with the students who where subjected to the same treatment; an additional rehearsal session. They are then observed by the professor and compared to those who did not participate in the experiment.  

This is also an example of a cohort observational study. A cohort observational study is one in which all the participants have a common uniting factor. They are made to undergo a treatment and then compared to those who did not receive the treatment. This type of study  is subject to bias because a positive or negative result might be because of other factors not related to the study.

Answer:

Mean: 85 5/9

Median: 90

Mode: 95

Step-by-step explanation:

~ Part I ~

1. To find the mean, let us take the average of the numbers through the addition of these values divided by the number of numbers:

75 + 95 + 90 + 95 + 60 + 95 + 75 + 95 + 90/9 = 770/9 = 85 5/9 (85.55.....)

~ Part 2 ~

1. Now let us arrange these numbers from least to greatest:

75 , 95 , 90 , 95 , 60 , 95 , 75 , 95 , 90 ⇒ 60,75 , 75 , 90 , 90 , 95, 95, 95,95

3. The median of this set would now be the middle number, which, (in this case) is ⇒ 90

~ Part 3 ~

1. The mode is known to be the number repeated most often, and from the previous question we see the numbers arranged in a benficial manner. Now we can straight away see that the number repeated the most is ⇒ 95

Answer:mean=85 5/9 mode=95 median=90

Step-by-step explanation:

Mean=(75+95+90+95+60+95+75+95+90)➗9

mean=770 ➗ 9

Mean=85 5/9

Mode=95

To get median we first arrange in ascending order of magnitude

60,75,75,90,90,95,95,95,95

The middle number is the median which is 90

Answer: [tex]3(3-4x+2y)[/tex]

Step-by-step explanation:

[tex]9-12x+6y[/tex]

[tex]3(3-4x+2y)[/tex]

Answer:

32332

Step-by-step explanation:

Answer:

[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]

The degrees of freedom are

[tex]df=20+20-2=38[/tex]

And the p value is given by:

[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]

Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

Step-by-step explanation:

When we have two independent samples from two normal distributions with equal variances we are assuming that  

[tex]\sigma^2_1 =\sigma^2_2 =\sigma^2[/tex]

And the statistic is given by this formula:

[tex]t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}[/tex]

Where t follows a t distribution with [tex]n_1+n_2 -2[/tex] degrees of freedom and the pooled variance [tex]S^2_p[/tex] is given by this formula:

[tex]S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]

The system of hypothesis on this case are:

Null hypothesis: [tex]\mu_1 = \mu_2[/tex]

Alternative hypothesis: [tex]\mu_1 \neq \mu_2[/tex]

We have the following data given:

[tex]n_1 =20[/tex] represent the sample size for group 1

[tex]n_2 =20[/tex] represent the sample size for group 2

[tex]\bar X_1 =43.5[/tex] represent the sample mean for the group 1

[tex]\bar X_2 =40.1[/tex] represent the sample mean for the group 2

[tex]s_1=4.1[/tex] represent the sample standard deviation for group 1

[tex]s_2=3.2[/tex] represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

[tex]\S^2_p =\frac{(20-1)(4.1)^2 +(20 -1)(3.2)^2}{20 +20 -2}=13.525[/tex]

And the deviation would be just the square root of the variance:

[tex]S_p=3.678[/tex]

The statistic is givne by:

[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]

The degrees of freedom are

[tex]df=20+20-2=38[/tex]

And the p value is given by:

[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]

Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

Using the t-distribution, as we have the standard deviation for the sample, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.

At the null hypothesis, it is tested if there is no difference, that is:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypothesis, it is tested if there is a difference, that is:

[tex]H_a: \mu_1 - \mu_2 \neq 0[/tex]

For each sample, we have that they are given by

[tex]\mu_1 = 43.5, s_1 = \frac{4.1}{\sqrt{20}} = 0.9168[/tex]

[tex]\mu_2 = 40.2, s_2 = \frac{3.2}{\sqrt{20}} = 0.7155[/tex]

Hence, for the distribution of differences, the mean and the standard error are given by:

[tex]\overline{x} = \mu_1 - \mu_2 = 43.5 - 40.2 = 3.3[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.9168^2 + 0.7155^2} = 1.163[/tex]

It is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis, hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{3.3 - 0}{1.163}[/tex]

[tex]t = 2.84[/tex]

Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05 and 20 + 20 - 2 = 38 df, the critical value is of [tex]|z^{\ast}| = 2.0244[/tex].

Since the absolute value of the test statistic is greater than the critical value, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.

More can be learned about the t-distribution at https://brainly.com/question/16313918

Answer:

3 times at 3

Step-by-step explanation:

Answer:

$42,900 a year

Step-by-step explanation:

so there are 26 bi-weeks in a year. (fun fact)

you take $1,650 and multiply that biweekly to get her annual salary.

1650*26=42,900

Answer:

~ 2 kilometers in length of the actual path ~

Step-by-step explanation:

Let us plan out our steps, and solve for each:

1. Given the information, let us create a proportionality as such:

        1       =           10,000      ⇒   x - centimeters in length of actual path

       20                    x

2. Now let us cross multiply, and solve through simple algebra for x:

10,000 * 20 = x,

x = 200,000 centimeters of the width of the item in reality

3. The answer demands in km, so let us convert 200,000 cm ⇒ km:

200,000/100,000 = 2 kilometers in length of the actual path

Answer:

The mode is 21.

Step-by-step explanation:

Mode is a number than appears most frequently in a set of numbers.

Answer:

[tex]21[/tex]

Step-by-step explanation:

The Most frequently number that appears in a set of numbers is called as mode.

21 , 7 , 19 , 21 , 60 , 21 , 19

Now here we can clearly see that 21 is the most frequent number that appears in the text.

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

72.66 in³

Step-by-step explanation:

The volume of a cylinder of radius r and height h is given by V = πr²h.

Here we have  V = πr²h = π([2.8]/2 in)²(11.8 in) = π(1.96 in²)(11.8 in) = 23.1 π in³, or approximately 72.66 in³

Answer: right isosceles

Step-by-step explanation:

the angle at the bottom is right therefore you need to figure out the lengths of the sides to conclude if it is isosceles or scalene. because two of the sides are the same length and the other is not it is isosceles

Answer:

74 and 27

Step-by-step explanation:

let x and y be the numbers

x + y =101........eqn 1

x - y = 47.......eqn 2

solve simultaneously

from equation 2, make x the subject

x= 47 + y........eqn 3

put eqn 3 into eqn 1

(47+y) + y = 101

47 + 2y = 101

       2y= 101 - 47

       2y=54

         y= 54/2

         y= 27

put y=27 into eqn 3

x = 47 + 27

x = 74

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

12/-10

Step-by-step explanation:

Any multiple of a fraction is the equivalent of the original fraction, the only difference is that it wont be fully simplified. If we multiply the original fraction (6/-5) by 2, both the numerator and denominator, you will get 12/-10.

Answer:

12/-10

Step-by-step explanation:

6/-5

6×2= 12

-5×2=-10

12/-10

Answer: 5/13

Step-by-step explanation:

Answer:

5/13 is in simplest form, because it cannot be reduced any further.

Step-by-step explanation: 4/20 can be reduced to 1/5, 6/9 to 1/3, and 14/21 can be reduced to 2/3

Answer:

The claim is not true

Step-by-step explanation:

We are given that A local retailer claims that the mean waiting time is less than 8 minutes.

[tex]H_0:\mu=8[/tex]

[tex]H_a:\mu<8[/tex]

A random sample of 20 waiting times has a mean of 6.3 minutes with a standard deviation of 2.1 minutes.

[tex]\bar{x}=6.3[/tex]

s = 2.1

n = 20

Since n <30 and population standard deviation is unknown

So,we will use t test

So,[tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t=\frac{6.3-8}{\frac{2.1}{\sqrt{20}}}[/tex]

t=-3.62

α = 0.01

Degree of freedom = df=n-1=20-1=19

[tex]t_{df,\frac{\alpha}{2}}=t_{19,\frac{0.01}{2}}=2.861[/tex]

t calculated < t critical

So, we failed to reject null hypothesis

Hence the claim is not true

Answer: it is -1

Step-by-step explanation:

5*5x=25x

5*3=15

25x+15=-10

25x= -10-15

25x= -25

X=-25/25

= -1

Answer:

maybe show me a picture of what u want me to help u with and then Ill answer it

Answer:

In the figure attached, the graph of the function is shown.

1. f(9) ≈ 6 means that at t = 9 (year 1977 + 9 = 1986) the cost to produce 1 watt of solar energy was $6

2. f(4) ≈ 25, which means at year 1981 (=1977 + 4) the cost was $25 per watt  

f(3.5) ≈ 28, which means at half of year 1980 (=1977 + 3.5) the cost was $28 per watt  

3. When f(t) = 45, t is equal to 2, which means that the year wass 1979 (= 1977 + 2)

4. From the graph we can compute the following table:

x  |  y

0  |  80

1   |  60

The general exponential decay formula is:

f(x) = a*b^x

where a is the initial value and b si the decay factor. Replacing with data from the table:

f(0) = a*b^0

80  = a

f(1) = a*b^1

60/80 = b

0.75 = b

Answer:

its 40

Step-by-step explanation:

i think

Given Information:

Number of Men having normal weight = 203

Number of Women having normal weight = 270

Sample size of Men = 750

Sample size of Women = 750

Confidence level = 95%

Required Information:

Difference in the proportion of normal weighted Men and Women = ?

Answer:

We are 95% confident that the difference in the proportion of Men and Women who are normal weight is between (0.044, 0.136)

Step-by-step explanation:

The proportion of Men who are normal weight is given by

p₁ = 203/750

p₁ = 0.27

The proportion of Women who are normal weight is given by

p₂ = 270/750

p₂ = 0.36

The difference in the proportion of normal weighted Men and Women is given by

[tex](p_2- p_1) \pm z\cdot \sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}[/tex]

Where p₁ and p₂ are the proportion of Men and Women who are normal weighted.

n₁ and n₂ are the sample size of Men and Women.  

z is the value of z-score corresponding to 95% confidence level and is given by

[tex]z_{\alpha/2} = 1 - 0.95 = 0.05/2 = 0.025\\\\z_{0.025} = 1.96[/tex]

So we have z-score of 1.96 corresponding to confidence level of 95%

 So the above equation becomes

[tex](p_2- p_1) \pm z\cdot \sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}\\\\(0.36- 0.27) \pm 1.96\cdot \sqrt{\frac{0.27(1-0.27)}{750} + \frac{0.36(1-0.36)}{750}}\\\\0.09\pm 1.96\cdot (0.0238) \\\\0.09\pm 0.046 \\\\Lower \: limit = 0.09 - 0.046 = 0.044\\\\Upper \: limit = 0.09 + 0.046 = 0.136\\\\(0.044, \: 0.136)[/tex]

Therefore, we are 95% confident that the difference in the proportion of Men and Women who are normal weight is between (0.044, 0.136)

How to find  the value of z-score?

In the z-table find the probability of 0.025 and note down the value of that row it would be 1.9 and the value of column would be 0.06, therefore, the z-score is 1.9+0.06 = 1.96

Answer:

The number: 13,226

Step-by-step explanation:

1. The smallest 5-digit number possibile is: 10,000

2. The smallest 5-digit number being odd should be: 10,001

3. All factors of 6 are {1, 2, 3, 6} so that the smallest possible way to arrange these numbers would be: 11,236

4.  Now this number contains 3 prime numbers, 2 being {2 and 3}. If we were to consider another prime number, still being a factor of 6, that would be: 2. That would mean instead of the 1 being the second digit of the value 11,236 it could be 2: 12,236.

5. The digit in the thousands place (2) should be greater than the digit in the tens place (3). Let's swap these digits for now so that condition is satisfied: 13,226. 2 is the only number that has a number greater than it, besides 1, but 1 can't be a digit in the tenth place as it would make a greater 5 digit-number. Thus, provided the conditions are still satisfied, the number 13,226 is the smallest number possible.

Answer:

186m

Step-by-step explanation:

Answer:

V = 216 cm^3

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the side length

V = (6)^3

V = 216 cm^3

Answer:216 cm^3

Step-by-step explanation:

In cube, the length of all sides are equal

length of side=6cm

Volume of cube=length x length x length

Volume of cube=6 x 6 x 6

Volume of cube=216

Volume of cube=216 cm^3

Answer:

[tex]f(x)=-5x-3[/tex].

Step-by-step explanation:

From the given machine diagram it is clear that:

[tex]f(x)=-8[/tex] at [tex]x=1[/tex]

[tex]f(x)=-13[/tex] at [tex]x=2[/tex]

[tex]f(x)=-18[/tex] at [tex]x=3[/tex]

It is clear that the value of f(x) decreasing by 5 when the value of x is increasing by 1.

Since the function changing at a constant rate, therefore it represents a linear function.

If a linear function passing through two points, then the equation of line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The given linear function passes through (1,-8) and (2,-13), therefore the linear equation is

[tex]y-(-8)=\dfrac{-13-(-8)}{2-1}(x-1)[/tex]

[tex]y+8=\dfrac{-5}{1}(x-1)[/tex]

[tex]y+8=-5(x-1)[/tex]

[tex]y=-5x+5-8[/tex]

[tex]y=-5x-3[/tex]

So, the required function is [tex]f(x)=-5x-3[/tex].

Answer: .0039

Step-by-step explanation: