the standard deviation of the scores on a skill evaluation test is 421 points with a mean of 1728 points. if 309 tests are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 36 points? round your answer to four decimal places.

A right rectangular prism is:

The Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

To investigate whether the span of a person's dominant hand is greater than that of their non-dominant hand, the most appropriate statistical technique would be the Paired samples t-test.

The Paired samples t-test is used when comparing the means of two related groups or conditions. In this case, the dominant and non-dominant hands are related because they belong to the same individuals in the study. By comparing the means of the dominant and non-dominant hand spans, we can determine if there is a significant difference between the two.

The other options listed, ANOVA (Analysis of Variance), Independent samples t-test, Wilcoxon's matched-pairs signed rank test, and Mann-Whitney U test, are not suitable for this scenario because they are designed for different types of comparisons:

- ANOVA is used when comparing the means of three or more independent groups, which is not the case here.

- Independent samples t-test is used when comparing the means of two independent groups, which is not the case here as the measurements are paired.

- Wilcoxon's matched-pairs signed rank test and Mann-Whitney U test are non-parametric tests that are used when the data do not meet the assumptions of parametric tests. However, in this case, we have paired measurements, and the paired samples t-test is the appropriate parametric test.

Therefore, the Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

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We know that the measures of dispersion tend to see how numbers are scattered around the mean. In this case, we are asked to find three of the measures of dispersion which are; range, variance and standard deviation.

We first have to arrange the data in the proper order as follows;

20.1, 21.7, 23.2, 24.0, 30.9, 33.5, 58.4, 60.0, 74.8, 110.8

It is now easier for us to find the range of the data set as the difference between the largest and the smallest value; 110.8 – 20.1 = 90.7

The mean of the dataset is = 20.1 +  21.7+  23.2 + 24.0 + 30.9 + 33.5 + 58.4 + 60.0 + 74.8 + 110.8/10

= 45.74

Now;

Variance = (20.1 - 45.74)^2 + (21.7 - 45.74)^2 + (23.2 - 45.74)^2 + (24.0 - 45.74)^2 + (30.9 - 45.74)^2 + (33.5 - 45.74)^2 + (58.4 - 45.74)^2 + (60.0 - 45.74)^2 + (74.8 - 45.74)^2 + (110.8 - 45.74)^2/10

= 657.4 + 577.9 + 508.1 + 472.6 + 220.2 +149.8 + 160.3 + 203.3 + 844.5 + 4233/10

= 802.71

Standard deviation = √variance = √802.71

= 8.96

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The proceeds received by Oliver when settling the 90-day interest-bearing note in 60 days at a discounted rate of 6% p.a.  to $247,500  by the formula. discounted rate of 6% p.a. amount to $247,500.

Proceeds = Face Value * (1 - Discount Rate * Time/360)

In this case, the face value of the note is $250,000, the discount rate is 6% p.a., and the time is 60 days. Plugging these values into the formula, we can calculate Oliver's proceeds.

Proceeds = $250,000 * (1 - 0.06 * 60/360)

Simplifying the expression, we have:

Proceeds = $250,000 * (1 - 0.01)

Proceeds = $250,000 * 0.99

Proceeds = $247,500

Therefore, Oliver's proceeds when settling the note in 60 days at a discounted rate of 6% p.a. amount to $247,500.

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Answer:

hi

Step-by-step explanation:

2(3x+4)=2×3x +2×4= 6x+8

hope it helps

Answer:

6x+8

Step-by-step explanation:

2(3x+4)

Distribute

2*3x + 2(4)

6x+8

Answer:

option 4

Step-by-step explanation:

-3.4x + 4.7 - (3 + 2.9x) = -3.4x + 4.7 - 3  - 2.9x  (combine like terms)

                                   = -3.4x - 2.9x + 4.7 - 3

                                  = - 6.3x + 1.7

If two number have same sign, add and put the common sign for the answer.

If two numbers have different sign, subtract and the answer will have the sign of the bigger number

Answer:

A. The system could have no solution or infinitely many solutions.

Step-by-step explanation:

Parallel lines have the same slope, meaning that they cannot intersect. So, the system can either have no solution (no intersection), or infinite possible solutions (the same line).

Answer:

A. {(5, –4), (–4, 5), (–5, 4), (4, –5)}

Step-by-step explanation:

Since there is one value of  

y

for every value of  

x

in  

(

5

,

−

4

)

,

(

−

4

,

5

)

,

(

−

5

,

4

)

,

(

4

,

−

5

)

, this relation is a function.

The relation is a function.

Answer:

.

Step-by-step explanation:

The Poisson distribution is applied to events where the probability of occurrence of a certain number of events in a fixed interval of time, space, or distance is small but not necessarily "very small". False.

The Poisson distribution is used to model events that occur randomly and independently over a continuous or discrete interval of time, space, or distance, such as the number of phone calls received at a call center in an hour, the number of cars passing through a toll booth in a given time period, or the number of emails received per day. The Poisson distribution is characterized by a discrete probability mass function that describes the probability of a certain number of events occurring in a given interval, and it is widely used in probability theory and statistics for modeling events with low to moderate occurrence rates.

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The poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is very small.

Given statement is False.

Because, The Poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is not necessarily very small, but rather where the events occur randomly and independently at a constant average rate.

The Poisson distribution models the number of events that occur in a fixed time interval or within a certain area or volume of space, assuming that the events occur independently of each other and at a constant average rate. It is used in many fields, such as biology, physics, economics, and engineering, to model the occurrence of rare or common events.

The Poisson distribution has several important properties, including:

Its mean is equal to λ, and its variance is also equal to λ.

It is a discrete distribution, meaning that it models only whole numbers of events.

It is often used to model rare or unusual events, but can also be used for events that occur frequently, as long as they occur independently at a constant average rate.

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Answer:

x = 23

Step-by-step explanation:

if line j is parallel to line k then

5x + 9 + 33 + x = 180 add like terms

6x + 42 = 180 subtract 42 from both sides

6x = 138 divide both sides by 6

x = 23

The statement "The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is 1/(a-b)" is False.

In a uniform distribution, the probability density function (PDF) is constant within the interval [a, b]. The height of the PDF represents the density of the probability distribution at any given point within the interval. Since the PDF is constant, the height remains the same throughout the interval.

To determine the height of the PDF, we need to consider the interval length. In a uniform distribution defined on the interval [a, b], the height of the PDF is 1/(b - a) for the PDF to integrate to 1 over the entire interval. This means that the total area under the PDF curve is equal to 1, representing the total probability within the interval [a, b].

Therefore, the correct statement is that the height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is not 1/(a - b), but rather it is a constant value necessary for the PDF to integrate to 1 over the interval, i.e., 1/(b - a).

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Answer:

3

Step-by-step explanation:

5(2x + 1) = 35

10x + 5 = 35

10x = 30

x = 3

Check the picture below.

\(\cfrac{1^2}{2^2}=\cfrac{110}{A}\implies \cfrac{1}{4}=\cfrac{110}{A}\implies A=440~in^2\)

A store has initiated a contest talk that involves guessing the number of peanuts in a mask. The contest requires more than 100 words to elaborate on how it is carried out. Here's how the contest talk goes:Contest TalkThe store has a jar filled with peanuts, and it is covered by a mask.

The customers are requested to guess the number of peanuts in the jar and win a prize. The jar is only visible from the outside, and the customers are not allowed to touch or remove the cover from the jar.The customers will provide their guess by filling a form provided by the store. The form will include their name, contact information, and their guess. The customers will be asked to submit their guesses in a box provided by the store.The contest will run for a week, and the winner will be announced the next day after the contest ends. In the case of a tie, the winner will be selected through a lucky draw. The winner will receive a gift hamper worth $50, and the second runner up will receive a gift card worth $25.The customers are encouraged to participate and increase their chances of winning. The store management believes that this contest talk will attract more customers and enhance their brand awareness among their target audience.

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Answer:

Step-by-step explanation:

when you divide fraction, turn the division into × and flip the other fraction

72/7÷8/7= 72/7×7/8=72/8 = 9

21÷7/3 = 21×3/7 =63/7=9

12/7÷2/7 = 12/7 × 7/2 = 12/2 = 6

9÷9/2=9×2/9=18/9= 2

4 2/3 ÷7/9 = 14/3 ×9/7=126/21 = 6

4 1/2 ÷1/2 = 9/2 × 2=18/2=9

The result of the expression 3x-(2x+10) for x = \(7\frac{5}{13}\) is -2.61

The expression is

3x-(2x+10)

The expression is the mathematical sentence with a minimum of two variables and at least one math operation.

The value of the x = \(7\frac{5}{13}\)

Convert the mixed fraction to the simple fraction

\(7\frac{5}{13}\) = 96/13

Convert the simple fraction to the decimal form

96/13 = 7.39

Substitute the value of x in the given expression 3x - (2x + 10)

= 3 × 7.39 - (2×7.39 + 10)

Multiply the terms first

= 22.17 - (14.78 + 10)

= 22.17 - (24.78)

= -2.61

Hence, the result of the expression 3x-(2x+10) for x = \(7\frac{5}{13}\) is -2.61

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Answer:

In 25 minutes, the monthly phone charges of both companies will be the same.

Step-by-step explanation:

If we allow m to represent the number of minutes, we can create two equations for C, the total cost of phone charges from both companies:

Phoenix equation:  C = 0.5m + 30

Nuphone equation: C - 0.10m + 40

Now, we can set the two equations equal to each other.  Solving for m will show us how many minutes must Abby use for the total cost at both companies to be the same:

0.5m + 30 = 0.10m + 40

Step 1:  Subtract 30 from both sides:

(0.5m + 30 = 0.10m + 40) - 30

0.5m = 0.10m + 10

Step 2:  Subtract 0.10m from both sides:

(0.5m = 0.10m + 10) - 0.10m

0.4m = 10

Step 3:  Divide both sides by 0.4 to solve for m (the number of minutes it takes for the total cost of both companies to be the same)

(0.4m = 10) / 0.4

m = 25

Thus, Abby would need to use 25 minutes for the total cost at both companies to be the same.

Optional Step 4: Check the validity of the answer by plugging in 25 for m in both equations and seeing if we get the same answer:

Checking m = 25 with Phoenix equation:

C = 0.5(25) + 30

C = 12.5 + 30

C = 42.5

Checking m = 25 with Nuphone equation:

C = 0.10(25) + 40

C = 2.5 + 40

C = 42.5

Thus, m = 25 is the correct answer.

Answer:

Step-by-step explanation:

80        40

___________

 100        50

Answer:

\(144 ft^2\)

Step-by-step explanation:

the area of the sidewalk is the area of the whole plot of land minus the area of the flower bed.

The area of the flower bed: length * width = Area; 10 * 8 = 80

The area of the whole plot:

  (3 + 10 + 3) * (3 + 8 + 3) = 16 * 14 = 224

224 - 80 = 144 ft squared

Assuming that each person recruited is counted only once and not repeatedly,

and that the scheme fails once there are no more people left to recruit, we can estimate the number of cycles it would take for the pyramid scheme to fail.

If each person recruited adds 8 more people, the number of people involved in the scheme will double with each cycle.

Starting with 8 people, after one cycle there would be 64 people involved, after two cycles there would be 512 people, after three cycles there would be 4,096 people, and so on.

Assuming that the entire population of North America (387,000,000 people) is available to be recruited, it would only take 9 cycles for the scheme to reach over 390,000,000 people, exceeding the entire population.

However, in reality, the scheme would likely fail before then due to saturation, lack of new recruits, and legal action.

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a) The series (+1) + 22/ns is absolutely convergent, and

b)  The series (-1)n / ln(n) is also convergent.

(a) The given series is (+1) + 22/ns.

To determine if this series is absolutely convergent, conditionally convergent, or divergent, we need to examine the behavior of the absolute values of the terms. In this case, the series of absolute values is 1 + 22/ns.

When we take the limit as n approaches infinity, we can see that the term 22/ns approaches zero, and the term 1 remains constant. Therefore, the series of absolute values simplifies to 1, which is a convergent series.

Since the series of absolute values converges, the original series (+1) + 22/ns is absolutely convergent.

(b) The given series is (-1)n / ln(n), where n starts from 2.

Similarly, we need to analyze the behavior of the series of absolute values: |(-1)n / ln(n)|.

The absolute value of (-1)n is always 1, so we are left with |1 / ln(n)|. To determine the convergence or divergence of this series, we can use the limit comparison test.

Let's consider the series 1 / ln(n). Taking the limit as n approaches infinity, we have:

lim(n→∞) (1 / ln(n)) = 0.

Since the limit is zero, the series 1 / ln(n) converges. Now, we compare the original series |(-1)n / ln(n)| with 1 / ln(n).

Using the limit comparison test, we have:

lim(n→∞) (|(-1)n / ln(n)| / (1 / ln(n))) = lim(n→∞) |(-1)n| = 1.

Since the limit is a nonzero constant, the series |(-1)n / ln(n)| behaves in the same way as the series 1 / ln(n). Therefore, both series have the same convergence behavior.

Since the series 1 / ln(n) converges, the original series (-1)n / ln(n) is also convergent.

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Answer:

5.172

Step-by-step explanation:

Divide each digit of the dividend with the divisor starting from left to right. Bring down the next digit after each step

Divide 3 by 725. Write the remainder after subtracting the bottom number from the top number.

Bring down next digit 7. Divide 37 by 725. Write the remainder after subtracting the bottom number from the top number.

Bring down next digit 5. Divide 375 by 725. Write the remainder after subtracting the bottom number from the top number.

Bring down next digit 0. Divide 3750 by 725. Write the remainder after subtracting the bottom number from the top number.

Remember: A decimal number, say, 3 can be written as 3.0, 3.00 and so on. Bring down next digit 0. Divide 1250 by 725. Write the remainder after subtracting the bottom number from the top number.

Remember: A decimal number, say, 3 can be written as 3.0, 3.00 and so on. Bring down next digit 0. Divide 5250 by 725. Write the remainder after subtracting the bottom number from the top number.

Remember: A decimal number, say, 3 can be written as 3.0, 3.00 and so on. Bring down next digit 0. Divide 1750 by 725. Write the remainder after subtracting the bottom number from the top number.

End of long division (upto 3 decimal places).

37.5 ÷ 7.25 = 5.172

Variance and standard deviation are both measures of the dispersion or spread of a dataset, but they differ in terms of the unit of measurement.

Variance is the average of the squared differences between each data point and the mean of the dataset. It measures how far each data point is from the mean, squared, and then averages these squared differences. Variance is expressed in squared units, making it difficult to interpret in the original unit of measurement. For example, if we are measuring the heights of individuals in centimeters, the variance would be expressed in square centimeters.

Standard deviation, on the other hand, is the square root of the variance. It is a more commonly used measure because it is expressed in the same unit as the original data. Standard deviation represents the average distance of each data point from the mean. It provides a more intuitive understanding of the spread of the dataset. For example, if the standard deviation of a dataset of heights is 5 cm, it means that most heights in the dataset are within 5 cm of the mean height.

To illustrate the application of these measures, consider a dataset of test scores for two students: Student A and Student B.

If Student A has test scores of 80, 85, 90, and 95, and Student B has test scores of 70, 80, 90, and 100, we can calculate the variance and standard deviation for each student's scores.

The variance for Student A's scores might be 62.5, and the standard deviation would be approximately 7.91. For Student B, the variance might be 125 and the standard deviation would be approximately 11.18.

These measures help us understand how much the scores deviate from the mean, and how spread out the scores are within each dataset.

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Notice that the initial expression can be rewritten as shown below

The answer is 4 gallons per minute.

The mistake is that Jessie wrongly calculated (1/2)/(1/8) which should be solved using the next rule

She did

which is incorrect.

The intensity of sound from a concert speaker decreases with distance according to the inverse square law. This law states that the intensity is inversely proportional to the square of the distance.

So, if the intensity at a distance of 1 meter is I1, and the intensity at a distance of d meters is I2, the ratio of the intensities can be calculated using the formula:

(I1/I2) = (d2/d1)^2

Since we want to find the ratio of the intensities, we can substitute the given values:

(I1/I2) = (1/d)^2

Simplifying the equation, we get:

(I1/I2) = 1/d^2

Therefore, the intensity of sound from a concert speaker at a distance of 1 meter is (1/d^2) times greater than the intensity at a distance of d meters.

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The intensity of sound from a concert speaker at a distance of 1 meter is $\left(\frac{1}{x}\right)^2$ times greater than the intensity at a distance of $x$ meters.

The intensity of sound from a concert speaker decreases as the distance from the speaker increases. The relationship between intensity and distance is inversely proportional.

To determine how many times greater the intensity of sound is at a distance of 1 meter compared to the intensity at a distance of $x$ meters, we need to use the inverse square law formula:

$\frac{\text{Intensity1}}{\text{Intensity2}} = \left(\frac{\text{Distance2}}{\text{Distance1}}\right)^2$

Let's assume the intensity at a distance of $x$ meters is $I2$. Plugging in the values into the formula, we get:

$\frac{\text{Intensity1}}{I2} = \left(\frac{1 \text{ meter}}{x \text{ meters}}\right)^2$

Simplifying the equation, we have:

$\text{Intensity1} = I2 \times \left(\frac{1}{x}\right)^2$

This means that the intensity of sound at a distance of 1 meter is $\left(\frac{1}{x}\right)^2$ times greater than the intensity at a distance of $x$ meters.

For example, if $x$ is 3 meters, then the intensity of sound at a distance of 1 meter would be $\left(\frac{1}{3}\right)^2 = \frac{1}{9}$ times greater than the intensity at 3 meters.

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The coefficients of "x" and "y" are not multiples of each other. Therefore, there is no way to eliminate one variable and solve for the other. This indicates that the system has no solution.

The system of equations provided, 4x + 5y = 13 and -8x + 4y = 44, represents a set of linear equations with two variables, x and y. To determine if there is a solution, we can analyze the coefficients of x and y in each equation. By comparing the coefficients of y, we find that they are not proportional, meaning the lines represented by the equations are not parallel. However, when we compare the coefficients of x, we find that they are proportional with a ratio of -2. This implies that the lines are parallel and will never intersect. Therefore, the system has no common solution for x and y.

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It is unlikely for your height to be 70 inches exact because there are infinite number of possible ways.

Height is considered a continuous variable because it can take on any value within a certain range, including fractional values. Continuous variables are not limited to specific set of values, but can take on any value within a specified range. This is in contrast to discrete variables, which can only take on a specific, limited set of values. The continuous nature of height allows for precise measurement and calculation, as opposed to rounding to the nearest whole number.

When we talk about height, height is measure and hence it is a continuous variable. This means that it is possible for a person's height to be exactly 70 inches, but it is unlikely due to the vast number of possible values.

Hence, it is very unlikely for height to be specific.

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Answer: Im pretty sure the answers F.

Step-by-step explanation: Let me know if its correct!