Observations on burst strength (Ib/in2) were obtained both for test nozzle closure welds and for production canister nozzle welds. Test 7200 6100 7300 7300 8000 7400 7300 7300 8000 6700 8300 5250 5625 5900 5900 5700 6050 5800 6000 5875 6100 5850 6600 Cannister A comparative boxplot is given below. Test Nozde Cannister 5000 000006000 Bunt strength (b, m Comment on interesting features (the cited article did not include such a picture, but the authors commented that they had looked at one). (Select all that apply.) The production canister welds have consistently lower burst strengths than the test nozze welds. The production canister weids have much more variable burst strengths The test nozzle welds data contain 2 outliers. test nozzle welds have much more variable burst strengths. The production canister welds have much higher burst strengths. The production canister welds data contain 2 outiers.

Answer:the term of the loan is approximately 4 months

Step-by-step explanation:

The term of the loan means the period for which the loan was given.

We would apply the formula for simple interest which is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

P = 17500

R = 6.5%

I = total amount paid - principal

I = 17,873.97 - 17,500.00 = 373.97

Therefore

373.97 = (17500 × 6.5 × T)/100

373.97 = 1137.5T

T = 373.97/1137.5

T = 0.32 years

Converting to months, it becomes

0.32 × 12 = 3.84

Approximately 4 months.

L = 0.403 is the lower end of the confidence interval

U = 0.487 is the upper end of the confidence interval

The margin of error E is

E = (U-L)/2

E = (0.487-0.403)/2

E = 0.042

Which is half the distance from the lower to upper end

---------------------------

The midpoint of the confidence interval is the value of [tex]\hat{p}[/tex] (read out as "p hat")

phat = (U+L)/2

phat = (0.487+0.403)/2

phat = 0.445

---------------------------

Answer: The confidence interval (0.403, 0.487) can be rewritten into the form [tex]0.445 \pm 0.042[/tex]

Answer:there are 11 goats and 17 ducks.

Step-by-step explanation:

Let x represent the number of goats in the field.

Let y represent the number of ducks in the field.

A farmer looks over a field and sees 28 heads and 78 feet. some are goats, some are ducks. A goat has one head and a duck also has one head. It means that

x + y = 28

A goat has 4 feets and a duck has two feets. It means that

4x + 2y = 78 - - - - - - - - - - - - - 1

Substituting x = 28 - y into equation 1, it becomes

4(28 - y) + 2y = 78

112 - 4y + 2y = 78

- 4y + 2y = 78 - 112

- 2y = - 34

y = - 34/- 2

y = 17

x = 28 - y = 28 - 17

x = 11

To find the number of goats and ducks in the field, set up a system of equations using the given information. Solve the system of equations using elimination or substitution method. After solving, you will find that there are 11 goats and 17 ducks in the field.

Let's solve this problem by setting up a system of equations. Let's assume that the number of goats is G and the number of ducks is D.

From the given information, we can set up two equations:
1) G + D = 28 (equation 1) - since the total number of heads is 28
2) 4G + 2D = 78 (equation 2) - since each goat has 4 feet and each duck has 2 feet

We can solve these equations using substitution or elimination. Let's solve by elimination method:

Multiplying equation 1 by 2, we get:
2G + 2D = 56 (equation 3)

Subtracting equation 3 from equation 2, we get:
2G = 22
G = 11

Substituting the value of G into equation 1, we get:
11 + D = 28
D = 17

Therefore, there are 11 goats and 17 ducks in the field.

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Answer:

The margin of error is of 3.97 percentage points.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence interval [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The confidence interval has the following margin of error

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence interval

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].

We also have that

[tex]n = 600, \pi = 0.56[/tex]

So, the margin of error is:

[tex]M = 1.96*\sqrt{\frac{0.56*0.44}{600}} = 0.0397[/tex]

So the margin of error is of 3.97 percentage points.

The margin of error for the 56% point estimate using a 95% confidence level is; 3.97%

Formula for margin of error here is;

M = z√(p(1 - p)/n)

Where;

z is critical value at given confidence level

p is sample proportion

n is sample size

We are given;

p = 56% = 0.56

n = 600

Confidence level = 95%

Now,from tables, the critical value at a confidence level of 95% is; z = 1.96

Thus;

M = 1.96√(0.56(1 - 0.56)/600)

M = 0.0397 or 3.97%

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Answer:

The 99% confidence interval for the mean gross earnings of all Rolling Stones concerts (in millions) is (2.5690, 3.0110).

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 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{0.47}{\sqrt{30}} = 0.2210[/tex]

The lower end of the interval is the mean subtracted by M. So it is 2.79 - 0.2210 = 2.5690 million dollars.

The upper end of the interval is the mean added to M. So it is So it is 2.79 + 0.2210 = 3.0110 million dollars.

The 99% confidence interval for the mean gross earnings of all Rolling Stones concerts (in millions) is (2.5690, 3.0110).

Answer:

D) 1/2

Step-by-step explanation:

A linear function has the following format:

[tex]y = ax + b[/tex]

In which a is the slope, that is, the rate of change of the function and b is the y-intercept, that is, the value of y when x = 0.

We have that:

Point (5,2), which means that when x = 5, y = 2. So

[tex]y = ax + b[/tex]

[tex]5a + b = 2[/tex]

Point (9,4), which means that when x = 9, y = 4. So

[tex]9a + b = 4[/tex]

I am going to write b as a function of a in the second equation, and replace on the first. So

[tex]b = 4 - 9a[/tex]

Then

[tex]5a + b = 2[/tex]

[tex]5a + 4 - 9a = 2[/tex]

[tex]-4a = -2[/tex]

[tex]4a = 2[/tex]

[tex]a = 1/2[/tex]

This means that the slope, which is the rate of change of the function, is 1/2.

So the correct answer is:

D) 1/2

Answer:

8.69% of their bulbs would they have to replace under warranty if they offered a warranty of 7200 hours.

Step-by-step explanation:

Problems of normally distributed samples can be 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 = 7500, \sigma = 220[/tex]

What percentage of their bulbs would they have to replace under warranty if they offered a warranty of 7200 hours?

This is the probability that X is lower or equal than 7200 hours. So this is the pvalue of Z when X = 7200.

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

[tex]Z = \frac{7200 - 7500}{220}[/tex]

[tex]Z = -1.36[/tex]

[tex]Z = -1.36[/tex] has a pvalue of 0.0869

So 8.69% of their bulbs would they have to replace under warranty if they offered a warranty of 7200 hours.

Final answer:

The manufacturer would need to replace approximately 8.69% of their 75-watt light bulbs under a warranty of 7200 hours, based on the given mean lifetime and standard deviation.

Explanation:

To calculate the percentage of 75-Watt light bulbs that a manufacturer would have to replace under warranty if they offered a warranty of 7200 hours, we need to use the normal distribution. The mean lifetime of the bulbs is 7500 hours with a standard deviation of 220 hours. To find the percentage of bulbs that burn out before 7200 hours, we first calculate the z-score, which is the number of standard deviations an observation is from the mean.

The z-score is calculated as:

Z = (X - μ) / σ

Where μ is the mean, σ is the standard deviation, and X is the value we are interested in (7200 hours in this case).

Plugging in the numbers:

Z = (7200 - 7500) / 220 = -300 / 220 = -1.36

Using a Z-table or a statistical calculator, we find that the probability corresponding to a Z-score of -1.36 is approximately 0.0869 or 8.69%. This means that the manufacturer would have to replace about 8.69% of their bulbs under this warranty.

Answer:

P(X > 126) = 0.2119

Step-by-step explanation:

Problems of normally distributed samples can be 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 = 110, \sigma = 20[/tex]

P(X > 126) is the 1 subtracted by the pvalue of Z when X = 126. So

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

[tex]Z = \frac{126 - 110}{20}[/tex]

[tez]Z = 0.8[/tex]

[tez]Z = 0.8[/tex] has a pvalue of 0.7881.

P(X > 126) = 1 - 0.7881 = 0.2119

The probability P(X > 126) for a normally distributed random variable X with mean μ = 110 and standard deviation σ = 20 is approximately 21.19%.

This question is about computing the probability that a normally distributed random variable X with a specified mean and standard deviation exceeds a certain value. In our case, mean μ = 110 and standard deviation σ = 20, and we want to find the probability P(X > 126).

To solve this problem, we first need to compute the Z-score, which is a measure of how many standard deviations a given data point is from the mean, using the formula: Z = (X - μ) / σ. To compute P(X > 126), therefore, we first compute Z = (126 - 110) / 20 = 0.8.

Next, we look up the probability associated with Z = 0.8 in a standard normal distribution table. However, standard normal tables usually give the probability P(Z < z). Since we are looking for P(X > 126), or equivalently P(Z > 0.8), we need to subtract the value we get from the table from 1, since the total probability under a normal curve is one. If we look up Z = 0.8 in the table, we get approximately 0.7881. Hence, P(Z > 0.8) = 1 - P(Z ≤ 0.8) = 1 - 0.7881 = 0.2119 or about 21.19%.

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Answer:

z-score = 3.5, Yes, z-score is unusual.

Step-by-step explanation:

Given information:

Population mean ; μ = 6 feet

Standard deviation ; σ = 0.2 feet

Sample mean = 6.7 feet

The formula for z-score is

[tex]z=\dfrac{\overline{X}-\mu}{\sigma}[/tex]

where, [tex]\overline{X}[/tex] is sample mean, μ is population mean and σ is standard deviation.

Substitute the given values in the above formula.

[tex]z=\dfrac{6.7-6}{0.2}[/tex]

[tex]z=\dfrac{0.7}{0.2}[/tex]

[tex]z=3.5[/tex]

The z-score is 3.5.

If a z-score is less than -2 or greater than 2, then it is known as unusual score.

3.5 >  2

It means z-score is unusual.

Since the z score is greater than 3, hence his score is unusual.]

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma} \\ \\ where\ x=raw\ score,\mu=mean\ and\ \sigma=standard\ deviation[/tex]

Given that mean = 6, standard deviation = 0.2.

For x = 6.7:

[tex]z=\frac{6.7-6}{0.2}=3.5 [/tex]

Since the z score is greater than 3, hence his score is unusual.

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Based on the information given, it should be noted that the 28 years would be considered an example of descriptive statistics.

Therefore, 28 years would be considered an example of descriptive statistics.

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The average age of 28 years in the given class is an example of a statistic, which is a numerical value calculated from a sample of a larger population.

In the context of this question from the subject of mathematics, specifically statistics, the average age of 28 years for students in a class is considered an example of a statistic. A statistic is a value calculated from a sample drawn from a larger population. In this case, the sample consists of students in this particular class, and the population could be all students taking a statistics class in the country or the world. The average (or mean) is a basic type of statistic used to summarise a set of values. It's important to note that the average is just one type of statistic - there are many others, such as median, mode, range, and standard deviation that provide different ways to summarise and represent data.

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a. The probability that the target is hit is 0.65.

b. The probability that the target is hit by exactly one shot is 0.5.

c. Given exactly one shot hits, the probability Laura hit is 0.7.

a. To find the probability that the target is hit, we can calculate the probability that at least one shot hits the target. Since the shots are independent, we can use the complement rule:

[tex]\[ P(\text{Target hit}) = 1 - P(\text{Both miss}) \][/tex]

Laura misses with probability 0.5 and Phillip misses with probability 0.7 (since the probability of hitting the target is 0.3). Therefore:

[tex]\[ P(\text{Both miss}) = 0.5 \times 0.7 = 0.35 \][/tex]

[tex]\[ P(\text{Target hit}) = 1 - 0.35 = 0.65 \][/tex]

So, the probability that the target is hit is 0.65.

b. To find the probability that the target is hit by exactly one shot, we need to consider the cases where Laura hits and Phillip misses, and where Laura misses and Phillip hits. These events are mutually exclusive, so we can add their probabilities:

[tex]\[ P(\text{Exactly one shot hits}) = P(\text{Laura hits, Phillip misses}) + P(\text{Laura misses, Phillip hits}) \][/tex]

[tex]\[ = (0.5 \times 0.7) + (0.5 \times 0.3) \][/tex]

= 0.35 + 0.15

= 0.5

So, the probability that the target is hit by exactly one shot is 0.5.

c. Given that the target was hit by exactly one shot, we need to find the probability that Laura hit the target. This is the conditional probability:

[tex]\[ P(\text{Laura hit} | \text{Exactly one shot hit}) = \frac{P(\text{Laura hit and exactly one shot hit})}{P(\text{Exactly one shot hit})} \][/tex]

From part b, we found [tex]\( P(\text{Exactly one shot hit}) = 0.5 \)[/tex]. And from part b, we found [tex]\( P(\text{Laura hit and exactly one shot hit}) = 0.35 \)[/tex].

[tex]\[ P(\text{Laura hit} | \text{Exactly one shot hit}) = \frac{0.35}{0.5} = 0.7 \][/tex]

So, the probability that Laura hit the target, given that the target was hit by exactly one shot, is 0.7.

Answer: 59.91%.

Step-by-step explanation:

We are given , that the correlation between a car’s engine size and its fuel economy (in mpg) is r = - 0.774.

Then, the fraction of the variability in fuel economy is accounted for by the engine size would be [tex]r^2=( - 0.774)^2=0.599076\approx59.91\%[/tex]

[Multiply 100 to convert a decimal into percent]

Hence, the fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.

None of the options are correct.

To solve such problems we must know about the fraction of the variability in data values or R-squared.

                                                                           = r²

The fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.

As it is given that the correlation between a car’s engine size and its fuel economy (in mpg) is r = - 0.774.

the variability in fuel economy = r²

                                                   = (-0.774)²

                                                   = 0.599076

                                                   = 59.91%

Hence, the fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.

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The question involves calculating the area between a hyperbola and a line using trigonometric substitution, yet it's more directly related to understanding hyperbola properties and standard integration techniques of hyperbolic functions rather than a straightforward trigonometric substitution problem.

The problem involves finding the area bounded by the hyperbola 25x² - 4y² = 100 and the line x = 3 using trigonometric substitution. This specific problem requires a solid understanding of calculus, particularly integration, and knowledge of hyperbolas and trigonometric identities. To solve this, we first rewrite the hyperbola in its standard form, which is √(25x²/100 - 4y²/100) = 1, simplifying to x²/4 - y²/25 = 1, indicating that a = 2 and b = 5. Using trigonometric substitution, we set x = a sec(θ) and y = b tan(θ) where a and b are the semi-major and semi-minor axes of the hyperbola, respectively. However, the given question simplifies to the computation of an area for a given range of x, particularly up to x = 3, which doesn't directly imply a need for integral computation but rather an understanding of the geometry of hyperbolas.

The straight line x = 3 intersects the hyperbola at specific points, and the area in question could be typically found using trigonometric integrals if it required finding an area under a curve or between two curves. In this context, without further details on the exact method of trigonometric substitution to be used for computing the area directly, we often rely on the integrals involving the hyperbolic trigonometric functions, using limits set by the intersections of the curve and the line. Since a direct solution involving trigonometric substitution for area calculation under these conditions is complex and not standard, it's crucial to review the application within this specific problem's context further.

Answer:

The correct answer is C. 32h = C

Step-by-step explanation:

For finding out the equation that can be used to find the total number of contestants, C, that audition in h hours. we will use these variables:

Number of contestants = C

Number of hours of auditions = h

Number of contestants that can audition per hour = 32

Now, we can affirm that the equation that can be used to find the total number of contestants, C, that audition in h hours is:

C = 32 * h

The correct answer is C. 32h = C

Convert pounds to kilograms.

1 pound = 0.4536 kg.

170 pounds x 0.4536 = 77.11 kg.

Multiply weight by grams of protein per kg.

77.11 kg x 1.4 =107.95 grams. Round answer as needed.

Viola should consume approximately 108.18 grams of protein daily based on her weight and the recommended intake for collegiate volleyball players.

To calculate the amount of protein Viola should consume daily, we need to follow these steps:

1. Convert Viola's weight from pounds to kilograms:

170 lbs / 2.2 = 77.27 kg (rounded to 2 decimal places).

2. Determine her protein needs:

77.27 kg * 1.4 g/kg = 108.18 g of protein per day (rounded to 2 decimal places).

Therefore, Viola should consume approximately 108.18 grams of protein daily based on her weight and the recommended intake for collegiate volleyball players.

Answer:

False. Is the inverse process.

See explanation below.

Step-by-step explanation:

We need to remember two important concepts:

A parameter, is a quantity or value who describe a population desired, for example the population mean [tex]\mu[/tex] or the population standard deviation [tex]\sigma[/tex]

A statistic, is a quantity or value who represent the information of the sample data, for example the sample mean [tex] \bar X[/tex] or the sample deviation [tex] s[/tex]

Based on this we can analyze the statement:

"Inferential statistics involves using population data to make inferences about a sample"

False. Is the inverse process.

If we know the population data then we indeed have parameters and we don't need to do any type of inference in order to estimate these parameters with the statistics.

What we do generally is use the information from the sample in order to obtain statistics representative of the population with the aim to estimate the parameters unknown of the population

Answer:

564 of the cattle are female

Step-by-step explanation:

if 52% of them are male, then 48% are female.

.48*1175=564

Answer:

1227

Step-by-step explanation:

Step-by-step explanation:

Given  g(x) = x+2  and   f(x) = [tex]2^x+1[/tex]

If f(x) = g(x)

⇔[tex]2^x+1[/tex] = x+2

⇔[tex]2^x= x +1[/tex]

Only x= 1 and x=0 will be satisfy  the above equation.

If x= 1, it gives             and x=0 gives

[tex]2^1= 1+1[/tex]                       [tex]2^0=0+1[/tex]

⇔2=2                          ⇔1=1

Answer:

1 & 0

Step-by-step explanation:

Answer: n = 64

Step-by-step explanation:

Standard error (SE) of a statistical data is the standard deviation of its sampling distribution.

S.E = r/√n. .....1

Where,

SE = standard error

r = standard deviation

n = number of samples

Given:

r = 15

SE = 1.875

From equation 1, making n the subject of formula:

n = (r/SE)^2

n = (15/1.875)

n = 64

The expression in terms of [tex]x[/tex] that represents the number of feet Cody has walked toward Chelsea since they started walking is [tex]x_{Co} = x[/tex].

In this question we assume that both Cody and Chelsea have a uniform motion, in opposite sides and to their encounter. If both travel the same number of feet, the kinematic formulas for each walker are described below:

[tex]x_{Co} = x[/tex] (1)

[tex]x_{Ch} = 270 - x[/tex] (2)

[tex]x_{Co} = x_{Ch}[/tex] (3)

Where:

By (3), (2) and (1) we have the following equation:

[tex]x = 270 - x[/tex]

[tex]2\cdot x = 270[/tex]

[tex]x = 135\,ft[/tex]

The expression in terms of [tex]x[/tex] that represents the number of feet Cody has walked toward Chelsea since they started walking is [tex]x_{Co} = x[/tex]. [tex]\blacksquare[/tex]

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The expression to represent the number of feet Cody has walked toward Chelsea since they started walking is '270 - 2x'. Where 'x' represents the distance Cody has traveled and '2x' reflecting that Chelsea has traveled the same distance. The total is subtracted from 270, the initial distance, to find the remaining distance.

Given that Cody and Chelsea start walking towards each other from a distance of 270 feet and that they are walking at the same speed. If x represents the number of feet Cody has traveled since he started walking, given that Chelsea travels the same distance, the total distance they have both traveled together is represented by 2x. Since they started 270 feet apart, to find out how much more they still have to walk until they meet, you would subtract the total feet they've walked from the original distance. So this can be represented by the expression: 270 - 2x. This expression will give us the remaining distance after Cody has walked 'x' feet towards Chelsea.

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Answer:

d) 0.0132

Step-by-step explanation:

In a sample of size n, with proportion p, the standard error of the proportion is:

[tex]SE_{p} = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this problem, we have that:

[tex]p = 0.26, n = 1100[/tex]

So

[tex]SE_{p} = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.26*0.74}{1100}} = 0.0132[/tex]

So the correct answer is:

d) 0.0132

Final answer:

Explaining the calculation of the standard error for a proportion estimate based on a poll of truck drivers encountering aggressive dogs.

Explanation:

Question: In a recent poll of 1100 randomly selected home delivery truck drivers, 26% said they had encountered an aggressive dog on the job at least once. What is the standard error for the estimate of the proportion of all home delivery truck drivers who have encountered an aggressive dog on the job at least once?

Answer:

Calculate the standard error using the formula: SE = sqrt((p*(1-p))/n)

Substitute the values: p = 0.26 (proportion), n = 1100 (sample size)

SE = sqrt((0.26*(1-0.26))/1100) = sqrt((0.26*0.74)/1100) = sqrt(0.1924/1100) = sqrt(0.000175) ≈ 0.0132 (option d)

Answer:

A

Step-by-step explanation:

Answer:

a) 1

b) 1

Step-by-step explanation:

Data provided in the question:

X = The time in minutes between two successive arrivals

X has an exponential distribution with λ = 1

Now,

a) The expected time between two successive arrivals is minutes i.e

E(X) = [tex]\frac{1}{\lambda}[/tex]

or

E(X) = [tex]\frac{1}{1}[/tex]

or

E(X) = 1

b)  The standard deviation of the time between successive arrivals is minutes

i.e

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

or

σₓ = [tex]\sqrt{\frac{1}{1^2}}[/tex]

or

σₓ = 1

Answer:

The answer is cluster sampling

Step-by-step explanation:

Going back to the basic types of sampling and how they are acconplished, cluster sampling is accomplished by dividing the population into groups (usually geographical) which in the above question is referred to as the geographical area. These groups are called clusters or blocks. The clusters are randomly selected and each element in the selected clusters are used. Therefore the most realistic sampling method that represents the actual drillings, comparisons, and scientific examinations of several core samples within the same geographical area is cluster sampling.

Final answer:

Stratified sampling is the most realistic sampling method for geologists to represent the actual drillings, comparisons, and scientific examinations of several core samples within the same geographical area.

Explanation:

Stratified sampling is the most realistic sampling method for geologists to represent the actual drillings, comparisons, and scientific examinations of several core samples within the same geographical area. This method involves dividing the population into distinct subgroups based on certain characteristics and then randomly selecting samples from each subgroup.

For example, in geology, geologists may stratify the geographical area based on different rock types or layers to ensure a representative sample of the earth's structure. By using stratified sampling, geologists can account for the diverse composition and ages of various layers within the sampled area, leading to more accurate interpretations of the history and structure of the earth.

Stratified sampling allows geologists to focus their analyses on specific layers or formations within the earth's structure, providing a comprehensive understanding of the geological history of a particular area. This method enhances the reliability and validity of the findings obtained from multiple core samples taken within the same geographical region.

Solve for any of the variables; for instance, [tex]z[/tex]:

[tex]z=1-3x+2y[/tex]

[tex]z=-\dfrac{3-2x-y}3[/tex]

Then

[tex]1-3x+2y=-\dfrac{3-2x-y}3\implies11x-5y=6\implies\begin{cases}y=\frac{11x-6}5\\z=1-3x+\frac{22x-12}5\end{cases}[/tex]

Let [tex]x=t[/tex]; then the intersection is given by the vector-valued function

[tex]\vec r(t)=\left(t,\dfrac{11t-6}5,1-3t+\dfrac{22t-12}5\right)[/tex]

or

[tex]\vec r(t)=\left(t,\dfrac{11t-6}5,\dfrac{7t-7}5\right)[/tex]

Answer:

The probability that they are both aces is 0.00452.

Step-by-step explanation:

Consider the provided information.

Out of 52 playing card we need to select only 2.

Thus, the sample space is: [tex]^{52}C_2=1326[/tex]

Two cards are Ace.

The number of Ace in a pack of playing card are 4 and we need to select two of them.

This can be written as: [tex]^4C_2=6[/tex]

Thus, the probability that they are both aces is:

[tex]P(\text{Both are Ace})=\dfrac{6}{1326} \approx0.00452[/tex]

Hence, the probability that they are both aces is 0.00452.

Answer:

[tex]P(t) = 40e^{0.06931t}[/tex]

Step-by-step explanation:

The population exponential equation is as follows.

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

In which P(t) is the population in t years from now, P(0) is the population in the current year and r(decimal) is the growth rate.e = 2.71 is the Euler number.

Find an exponential model for the population (in millions of people) at any time ????, in years after 1980.

There were 40 million people in 1980 (when ????=0).

This means tht P(0) = 40.

So

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

[tex]P(t) = 40e^{rt}[/tex]

80 million people in 1990.

1990 is 10 years after 1980. So P(10) = 80. We use this to find the value of r.

So

[tex]P(t) = 40e^{rt}[/tex]

[tex]80 = 40e^{10r}[/tex]

[tex]e^{10r} = 2[/tex]

Applying ln to both sides, since [tex]\ln{e^{a}} = a[/tex]

[tex]\ln{e^{10r}} = \ln{2}[/tex]

[tex]10r = 0.6931[/tex]

[tex]r = \frac{0.6931}{10}[/tex]

[tex]r = 0.06931[/tex]

So the exponential model for the population is:

[tex]P(t) = 40e^{0.06931t}[/tex]

The Cartesian coordinate point (-5,5) can be re-written in polar coordinates in two ways. The polar coordinates equivalent to (-5,5) in the range 0 <= theta < 2pi are (5sqrt(2), 7pi/4) and in the range -2pi <= theta < 0 are (5sqrt(2), -pi/4).

The Cartesian coordinate point (-5,5) can be expressed in polar coordinates using the polar coordinates formula: r = sqrt(x^2 + y^2) and theta = arctan(y/x).

For the first part of the question, we are asked to find the polar coordinates where the angle lies in the range 0 <= theta < 2pi. Using the two formulas above, we find r to be sqrt((-5)^2 + 5^2) = sqrt(50) or 5sqrt(2). The angle theta can be calculated using arctan(5/-5) = -pi/4. We add 2pi to this angle because theta should not be negative, and thus obtain a final result of (7pi/4). So, the polar coordinates equivalent to (-5,5) in the range 0 <= theta < 2pi are (5sqrt(2), 7pi/4).

For the second part of the question, we need the polar coordinates where the angle theta lies in the range -2pi <= theta < 0. In this case, the value for r remains the same as before. However, the angle is -pi/4, because it needs to be negative. Hence, the polar coordinates equivalent to (-5, 5) in the range -2pi <= theta < 0 are (5sqrt(2), -pi/4).

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Final answer:

The total number of possible birth orders with respect to gender in a family with five children is 32.

Explanation:

The appropriate counting technique to answer this question is A. permutations. Permutations are used when the selections come from a single group of items, no item can be selected more than once, and the order of the arrangement matters. In this case, the birth orders with respect to gender can be represented by arranging the genders of the children in different orders.

Since there are 5 children, there are 5 positions to fill. The first position can be filled with either a boy or a girl, so there are 2 options. The second position can also be filled with either a boy or a girl, so there are 2 options again. This goes on for all 5 positions.

Therefore, the total number of possible birth orders with respect to gender is 2 * 2 * 2 * 2 * 2 = 32.

The piano is 0.2 standard deviations below the average piano cost, while the guitar is 0.5 standard deviations above the average guitar cost. The drum set is 1 standard deviation below the average drum set cost. The drums have the lowest cost compared to other instruments of the same type, and the piano has the highest cost.

1.) To find how many standard deviations above or below the average piano cost is the piano, we need to calculate the z-score. The formula for calculating the z-score is

z = (x - mean) / standard deviation

Let's plug in the values for the piano:

z = ($4,000 - $4,500) / $2,500

z = -0.2

So, the piano is 0.2 standard deviations below the average piano cost.

2.) Following the same formula, let's calculate the z-score for the guitar:

z = ($600 - $500) / $200

z = 0.5

Thus, the guitar is 0.5 standard deviations above the average guitar cost.

3.) Using the formula for the z-score again, let's calculate the z-score for the drum set:

z = ($750 - $850) / $100
z = -1

The drum set is 1 standard deviation below the average drum set cost.

4.) The cost of the drums is the lowest when compared to other instruments of the same type.

5.) The cost of the piano is the highest when compared to other instruments of the same type.