A computer program has a bug that causes it to fail once in every thousand runs, on average. In an effort to find the bug, independent runs of the program will be made until the program has failed six times. What is the standard deviation of the number of runs required?

Answer:

4.875 billion hours

Step-by-step explanation:

-Let X be the total time spent on taxes and 7.8 billion (80%) is time on paper work.

#We equate and cross multiply to get the total time on taxes:

[tex]0.8=7.8\\1=X\\\\\therefore X=\frac{1\times 7.8}{0.8}\\\\\\=9.75[/tex]

-let y be the 50% amount of time spent. we equate to find it in actual hours:

[tex]1=9.75\\0.5=y\\\\y=\frac{9.75\times 0.5}{1}\\\\=4.875[/tex]

Hence, 50% of the time is equivalent to 4.875 billion hours

Answer:

  0.2036

Step-by-step explanation:

u = arcsin(0.391) ≈ 23.016737°

tan(u/2) = tan(11.508368°)

tan(u/2) ≈ 0.2036

__

You can also use the trig identity ...

  tan(α/2) = sin(α)/(1+cos(α))

and you can find cos(u) as cos(arcsin(0.391)) ≈ 0.920391

or using the trig identity ...

  cos(α) = √(1 -sin²(α)) = √(1 -.152881) = √.847119

Then ...

  tan(u/2) = 0.391/(1 +√0.847119)

  tan(u/2) ≈ 0.2036

__

Comment on the solution

These problems are probably intended to have you think about and use the trig half-angle and double-angle formulas. Since you need a calculator anyway for the roots and the division, it makes a certain amount of sense to use it for inverse trig functions. Finding the angle and the appropriate function of it is a lot easier than messing with trig identities, IMO.

Answer:

35/36

Step-by-step explanation:

total outcome: 6 x 6 = 36

getting 12: 1/36

getting less than 12: 1 - 1/36 = 35/36

Answer:

35/36

Step-by-step explanation:

The sum can be between 2 and 12.

P(sum < 12) = 1 - P(sum = 12)

Sum = 12: (6,6)

P(sum < 12) = 1 - 1/36

35/36

Answer:

2900g

Step-by-step explanation:

1kg=1000g

2.9(1000)

=2900g

Step-by-step explanation:

cosB=4/5

B=36.86°

Hope it helps u

Answer:

A   -2 to -1

Step-by-step explanation:

Answer:

the answer is C. 3(2k + 7)   i hope this helps!   :)

Step-by-step explanation:

trying to find 6k + 21

given 3(2k + 6)

distribute the 3 to both inside the parenthesis 6k + 18

given 3(k + 6)

distribute the 3 to both inside the parenthesis 3k + 18

given 3(2k + 7)

distribute the 3 again to both inside of the parenthesis 6k + 21

Answer:

C. 3(2k+7)

Step-by-step explanation:

you should mark me brainliest lol

The given 95% confidence interval of (1.6, 7.0) for the difference between the average weekly study times (mu_1 - mu_2) means we are 95% confident that students planning to attend graduate school study between 1.6 to 7 hours more per week on average than those who do not.

The teaching assistant is comparing the average weekly study times between students intending to go to graduate school and those who are not with the use of data. The relevant statistical concept in this context is the confidence interval for the difference in population means.

The given 95% confidence interval for the difference between the average weekly study times (mu_1 - mu_2) is (1.6, 7.0). This interval was calculated from the provided data, and it provides a statistical estimation that, in this context, means we are 95% sure that students who plan to attend graduate school study between 1.6 to 7 hours more per week on average compared to those who do not plan to go to graduate school.

To interpret this, you can say that we are 95% confident that the true difference in average weekly study times between the two groups falls within this interval. As the entire interval is positive, we may infer that those planning for graduate school likely study more on average than their peers not planning for graduate school.

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Answer:

50 is more than 27

Step-by-step explanation:

27 comes before 50

Answer:

The calculated chi -square  value =5.7356 Is less than12.01 at 0.1level of significance .

The null hypothesis is accepted.

The past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.

Step-by-step explanation:

Step:-(1)

Given data 28 25 29 25 32 36 27 24

Sample size 'n' = 8

mean of the sample (x⁻) = ∑x /n = [tex]\frac{28+ 25+ 29 +25 +32 +36 + 27 + 24}{8}[/tex]

mean of the sample (x⁻) =  28.25

x                           x- x⁻                         (x-x⁻ )²

28              28 - 28.25  = -0.25       0.0625    

25             25 -28.25   = -3.25       10.56

29             29-28.25    = 0.75        0.5625

25             25-28.25    = -3.25      10.56

32             32-28.25    =   3.75      14.06

36            36-28.25    =   7.75      60.06

27            27-28.25    = -1.25      1.5625

24            24-28.25    = -4.25      18.06

                                          ∑(x-x⁻)² =   115.4875    

Step:-(2)

The sample standard deviation

           S² = ∑(x-x⁻)²/n-1 = [tex]\frac{115.4875 }{7}[/tex]  = 16.49

   By using χ² distribution

                           χ²  = [tex]\frac{ns^2 }{variance}[/tex]

By above test can be applied only if the population from which sample is drawn normal.

Given data For the past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.

Population variance σ² = 23

Step:-(3)

Null hypothesis :H₀:σ² = 23

Alternative hypothesis :H₁:≠23

[tex]X^{2} = \frac{8 (16.49)}{23}=5.7356[/tex]

The calculated chi -square  value =5.7356

The degrees of freedom γ=n-1 =8-1=7

The tabulated value of chi -square = 12.01 at 0.1level of significance (check table)

The calculated chi -square  value =5.7356 Is less than12.01 at 0.1level of significance .

The null hypothesis is accepted.

Conclusion:-

The null hypothesis is accepted.

The past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.

23.27

Use a calculator

Answer:

x = -6,1

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

$6,200   i hope this helps!   :)

Step-by-step explanation:

the 4% interest of the $5000   4% of 5000 = 200

multiply by 6 for the 6 years   200 * 6 = 1200

add the 1200 to the 5000   5000 + 1200 = 6,200

Answer:

For this case we want to test that the true proportion of americans have experienced difficulty in making mortgage payments is higher than 0.28 (alternative hypothesis) and the sytem of hypotheis are:

NUll hypothesis: [tex]p \leq 0.28[/tex]

Alternative hypotheis: [tex] p >0.28[/tex]

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Solution to the problem

For this case we want to test that the true proportion of americans have experienced difficulty in making mortgage payments is higher than 0.28 (alternative hypothesis) and the sytem of hypotheis are:

NUll hypothesis: [tex]p \leq 0.28[/tex]

Alternative hypotheis: [tex] p >0.28[/tex]

Answer:

The solutions listed from the smallest to the greatest are:

x:  [tex]-\sqrt{2}[/tex]   [tex]-\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]

y:      -1         1     -1     1

Step-by-step explanation:

The slope of the tangent line at a point of the curve is:

[tex]m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]

[tex]m = -\frac{\cos 2\theta}{\sin \theta}[/tex]

The tangent line is horizontal when [tex]m = 0[/tex]. Then:

[tex]\cos 2\theta = 0[/tex]

[tex]2\theta = \cos^{-1}0[/tex]

[tex]\theta = \frac{1}{2}\cdot \cos^{-1} 0[/tex]

[tex]\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex]

[tex]\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex]

The first four solutions are:

x:   [tex]\sqrt{2}[/tex]   [tex]-\sqrt{2}[/tex]  [tex]-\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]

y:     1        -1        1     -1

The solutions listed from the smallest to the greatest are:

x:  [tex]-\sqrt{2}[/tex]   [tex]-\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]

y:      -1         1     -1     1

Using derivatives of the parametric curves and the solving a trigonometric equation, it is found that the points (x,y) are:

[tex]x = 2\cos{\left(\frac{k\pi}{4}\right)}, k = 1, 3, 5, \cdots[/tex]

[tex]y = \sin{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]

Given two parametric curves x(t) and y(t), the slope of the tangent line is given by:

[tex]m = \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]

The tangent line is horizontal for:

[tex]\frac{dy}{dt} = 0, \frac{dx}{dt} \neq 0[/tex]

In this problem, since we are working with trigonometric functions sine and cosine, they will never be simultaneously 0, hence, the equation of interest is:

[tex]\frac{dy}{dt} = 0[/tex]

Then:

[tex]y(t) = \sin{2\theta}[/tex]

[tex]\frac{dy}{d\theta} = 2cos{2\theta}[/tex]

Hence:

[tex]2\cos{2\theta} = 0[/tex]

[tex]\cos{2\theta} = 0[/tex]

[tex]\cos{2\theta} = \cos{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]

[tex]2\theta = \frac{k\pi}{2}[/tex]

[tex]\theta = \frac{k\pi}{4}, k = 1, 3, 5, \cdots[/tex]

Hence, the points (x,y) are:

[tex]x = 2\cos{\left(\frac{k\pi}{4}\right)}, k = 1, 3, 5, \cdots[/tex]

[tex]y = \sin{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]

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To test the claim that the mean difference between the prices of the two models is $10, we can use a t-test for dependent samples.

To test the claim that the mean difference between the prices of the two models is $10, we can use a t-test for dependent samples.

Answer:

$6000

Step-by-step explanation:

so she made 72000 in a year, a year as 12 months so to find the monthly rate we just need to divide 72000 by 12 which gives 6000

Answer:

The Correct answer is 6000

Step-by-step explanation:

All you do is divide all the months in a year by how much she got paid to find salary.

Answer:

8% is the final answer.

Step-by-step explanation:

(2.4/29.99)x100

=0.08x100

=8%

Answer:

B

Step-by-step explanation:

Take 2 points and use the slope formula

The 2 points: (0,0) and (5,4)

The slope formula is:

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{2} }[/tex]

We can say (0,0) is our first point, and (5,4) is our second, and substitute them in. y2 is 4, y1 is 0, x2 is 5, and x2 is 0.

[tex]m=\frac{4-0}{5-0}[/tex]

[tex]m=\frac{4}{5}[/tex]

So, the slope if 4/5, or choice B

Answer:

It takes approximately 13.737 hours for the 200 degree water to cool down to 125 degrees.

Step-by-step explanation:

Recall Newton's Law of heating and cooling for an object of initial temperature [tex]T_0[/tex], in an ambient temperature [tex]T_a[/tex]:

[tex]T(t)=T_a+(T_0-T_a)\,e^{-kt}[/tex]

where t is the time elapsed.

We know the ambient temperature and the initial temperature of the object, but we don't know the value of the constant "k" that describes the cooling process. We can obtain such value (k) by using the information that the 200 degrees water cooled 10 degrees in 1.25 hours.

In such case we have:

[tex]T(t)=T_a+(T_0-T_a)\,e^{-kt}\\200-10=75+(200-75)\,e^{-k(1.25)}\\190=75+125\,e^{-k(1.25)}\\190-75=125\,e^{-k(1.25)}\\115=125\,e^{-k(1.25)}\\\frac{115}{125}= e^{-k(1.25)}\\0.92=e^{-k(1.25)}\\ln(0.92)=-k\,(1.25)\\k=\frac{ln(0.92)}{-1.25} \\k=0.0667[/tex]

Therefore, we have now the complete expression for the cooling process:

[tex]T(t)=75+125\,e^{-0.0667\,t}[/tex]

To find the time it takes to cool the 200 degree water down to 125 degrees, we use:

[tex]125=75+125\,e^{-0.0667\,t}\\125-75=125\,e^{-0.0667\,t}\\50=125\,e^{-0.0667\,t}\\\frac{50}{125} =e^{-0.0667\,t}\\0.4=e^{-0.0667\,t}\\ln(0.4)=-0.0667\,\,t\\t=\frac{ln(0.4)}{-0.0667} \\t=13.737\,\,hours[/tex]

Answer:

Hey Tamia,

          the answer is 0.4969564

Please rate me as brainiest as the answer explanation is in attached picture, which will clear every step.

Thanks

Step-by-step explanation:

To estimate the integral within an error rate, use the power series expansion of sin(x) to construct an equivalent series for sin(x²). Add terms until the error is less than  [tex]10^{-5}[/tex]. Integrate each term from 0 to 0.5.

To estimate the value of the integral ∫ from 0 to 0.5 sin(x²) dx with an error of magnitude less than 10^-5, we can use a power series expansion of sin(x). The power series expansion is given as sin(x) = x - x³/3! + x⁵/5! - x⁷/7! + .... Now since we are interested in sin(x²), we just replace x in the above series with x²: sin(x²) = x² - (x²)³/3! + (x²)⁵/5! - (x²)⁷/7! + .... This series can be truncated at any term, and the remaining terms would represent the error in your approximation. We keep adding terms until we reach an error less than [tex]10^{-5}[/tex]. Finally, integrate term by term from 0 to 0.5 to get the approximate value of the original integral.

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Answer:

see the explanation

Step-by-step explanation:

we know that

The equation of a exponential growth function is given by

[tex]f(x)=a(b^x)[/tex]

where

a is the initial value or y-intercept

b is the factor growth (b>0)

In this problem

a=1

so

[tex]f(x)=b^x[/tex]

we know that

The graph of the function has no x-intercept

Remember that the x-intercept of a function is the value of x when the value of the function is equal to zero

That means ----> The output of the function can NEVER be equal to zero

Verify

For f(x)=0

[tex]0=b^x[/tex]

Apply log both sides

[tex]log(0)=xlog(b)[/tex]

Remember that

log 0 is undefined. It's not a real number, because you can never get zero by raising anything to the power of anything else.

Final answer:

Exponential functions with a positive base can never output zero due to their growth pattern.

Explanation:

Exponential functions of the form f(x) = b^x, where b is greater than 0, never output zero.

To verify this, consider that any positive number raised to any power will never result in zero, as it will approach zero but never reach it. For example, 2^x will grow rapidly but never touch zero. This property holds true for all exponential functions with a positive base.

Answer:    Step-by-step explanation:

Start by multiplying the ones: 6 times 28 is 168. Next, multiply the tens: 30 times 28 is 840. Add the products to get 1,008.

Answer:

Shirt: $20

Trouser: $40

Step-by-step explanation:

5x + 3y = 220

6x + 2y = 200

3x + y = 100

y = 100 - 3x

5x + 3(100 - 3x) = 220

5x + 300 - 9x = 220

4x = 80

x = 20

y = 100 - 3(20)

y = 40

The cost of a shirt is $20 and the cost of pair of a jeans is $40.

Given that, five shirts and 3 pairs of jeans cost $220. Six shirts and 2 pairs of jeans cost $200.

We need to find the cost of one shirt and the cost of pair of jeans.

A linear equation is an equation in which the highest power of the variable is always 1.

A linear equation in two variables is of the form Ax + By + C = 0, in which A, B, and C are real numbers and x and y are the two variables, each with a degree of 1. If we consider two such linear equations, they are called simultaneous linear equations.

Let the cost of a shirt be x and the cost of pair of jeans be y.

Now, five shirts and 3 pairs of jeans cost $220.

That is, 5x+3y=220------(1)

Six shirts and 2 pairs of jeans cost $200.

6x+2y=200------(2)

Multiplying the equation (1) with 2, we get 10x+6y=440------(3)

Multiplying the equation (2) with 3, we get 18x+6y=600------(4)

Now, equation (4)-(3) is 8x=160

⇒x=$20

Substitute x=20 in equation (1), we get 5(20)+3y=220

⇒y=$40

Therefore, the cost of a shirt is $20 and the cost of pair of a jeans is $40.

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Answer: 5/13

Step-by-step explanation:

I got it correct

Answer:

(0, –5)

Step-by-step explanation:

If you don't see this option there is another option, (0 , 11) is also correct.

To solve the equation -2/7x=-1/3 for x, you would divide both sides by -2/7. This translates to multiplication of -1/3 by the reciprocal of -2/7 which is -7/2. By performing this multiplication, x equals to 7/6.

The equation at question here is -2/7x=-1/3. To solve for x, we need to isolate x on one side of the equation. To do this, we can divide both sides of the equation by -2/7, which is the coefficient of x in the equation. Performing this operation (also known as the division property of equality), we get:

When we divide by a fraction, it's the same as multiplying by its reciprocal, so:

Performing this multiplication gives x = 7/6.

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Answer:

a) 0.6062

b) 0.9505

c) 0.679

Step-by-step explanation:

The customer service center in a large new york department store has determined tha the amount of time spent with a customer about a complaint is normally distributed, with a mean of 9.3 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be

(a) less than 10 minutes?

(b) longer than 5 minutes?

(c) between 8 and 15 minutes?

a) The Z score (z) is given by the equation:

[tex]z=\frac{x-\mu}{\sigma}[/tex],

Where:

μ is the mean = 9.3 minutes,

σ is the standard deviation = 2.6 minutes and x is the raw score

[tex]z=\frac{x-\mu}{\sigma}=\frac{10-9.3}{2.6}=0.27[/tex]

From the z tables, P(X < 10) = P(z < 0.27) = 0.6062 = 60.62%

b) The Z score (z) is given by the equation:

[tex]z=\frac{x-\mu}{\sigma}[/tex],

[tex]z=\frac{x-\mu}{\sigma}=\frac{5-9.3}{2.6}=-1.65[/tex]

From the z tables, P(X > 5) = P(z > -1.65) = 1 - P(z < -1.65) = 1 - 0.0495 =  0.9505 = 95.05%

c) For 8 minutes

[tex]z=\frac{x-\mu}{\sigma}=\frac{8-9.3}{2.6}=-0.5[/tex]

For 15 minutes

[tex]z=\frac{x-\mu}{\sigma}=\frac{15-9.3}{2.6}=2.19[/tex]

From the z tables, P(8< X < 15) = P(-0.5 < z < 2.19) = P(z < 2.19) - P(z< -0.5) = 0.9875 - 0.3085 = 0.679 = 67.9%

The question pertains to finding a probability concerning the time taken to resolve a customer's complaint. The time follows a normal distribution with a mean of 9.3 minutes and a standard deviation of 2.6 minutes. We need to calculate the Z-score with the required time, mean and standard deviation, which can then be referenced on a standard normal distribution table to find the probability.

The question is about finding the probability of the time spent with a customer in a Customer Service Center of a department store in New York, given that the time that is spent follows a normal distribution with a mean of 9.3 minutes, and a standard deviation of 2.6 minutes.

To calculate this, we'll use the standard normal distribution, Z-score, which standardizes the distribution. The Z-score is a measure of how many standard deviations an element is from the mean. It can be calculated by using the formula: Z = (X - μ) / σ

where X is the time about which we want to find the probability, μ is the mean, and σ is the standard deviation.

Unfortunately, the exact time (X) you want to find the probability for was not provided in your question. However, assuming X to be a given time, t, you substitute t, 9.3 (the mean), and 2.6 (the standard deviation) into the formula to get a Z-score. Then, by referencing the Z-score on a standard normal distribution table, you can find the probability for a complaint taking at an amount of time, t, to be resolved.

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Answer:

1) 0.700

2) 0.730

3) 0.030

4) 0.959

Step-by-step explanation:

1) proportion of support for the ban with at least one child =

     [tex]\frac{no of support atleast 1 child}{Total no of atleast 1 child\\}[/tex]

   = [tex]\frac{1739}{2485}[/tex]

   = 0.700

2)  proportion of support for the ban with no child =

    = [tex]\frac{no of support with no child}{Total of no child}[/tex]

    = [tex]\frac{3089}{4231}[/tex]

    = 0.730

3) Difference in proportion of supporters for the ban between those with atleast one child and those with no child

    =  0.700 - 0.730

    = -0.03

4) Relative risk = [tex]\frac{proportion with atleast on child}{proportion with no child}[/tex]

    = [tex]\frac{0.700}{0.730}[/tex]  = 0.959