The table shown below provides statistical data on the bowling scores for David and Elise.


David claims that his scores were more consistent than Elise’s scores. Which statement is MOST likely true about David’s claim?

David’s claim is correct because his mean score is greater than Elise’s mean score.

David’s claim is correct because the interquartile range for his scores is greater than the interquartile range for Elise’s scores.

check
David’s claim is incorrect because his mean score is greater than Elise’s mean score.

David’s claim is incorrect because the interquartile range for his scores is greater than the interquartile range for Elise’s scores.

The amount of grain can the container hold is 953.78 inch³ as it in the form of cylinder

Diameter of cylinder = 9 in

Radius of cylinder = 9 / 2 in

Radius of cylinder = 4.5 in

Height of cylinder = 15 inch

Volume of cylinder = Amount of grain can this container hold

Volume = πr²h

Substitute the values of radius and height

Volume = (3.14)(4.5)²(15)

Amount of grain can this container hold = 953.78 inch³

Hence, the amount of grain can the container hold is 953.78 inch³

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The indefinite integral of 5x /(5 − x^2) ^3 is (5 − x^2) ^−2 + C, where C is the constant of integration. The indefinite integral of 5x / (5 − x^2) ^3 can be found by using the substitution u = 5 − x^2. We have:

∫ 5x / (5 − x^2) ^3 dx

Let u = 5 − x^2, then du/dx = −2x and dx = −(1/2x) du. Making the substitution, we get:

∫ 5x /(5 − x^2) ^3 dx = ∫ (−1/2) (−2x) u^−3 du

= u^−2 + C, where C is the constant of integration.

Substituting back, we get:

∫ 5x / (5 − x^2) ^3 dx = (5 − x^2) ^−2 + C

To check the result by differentiation, we take the derivative of (5 − x^2) ^−2 + C with respect to x:

d/dx [(5 − x^2) ^−2 + C] = −2(5 − x^2) ^−3 (−2x) = 4x / (5 − x^2) ^3

Which is the original function. Hence, our result is correct.

In conclusion, the indefinite integral of 5x / (5 − x^2) ^3 is (5 − x^2) ^−2 + C, where C is the constant of integration. This can be checked by taking the derivative of the result and verifying that it gives us the original function.

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For a two-tailed hypothesis test with a sample size of 37 and a 0.10 level of significance, the critical values of the test statistic t are approximately ±1.691. These values determine whether we reject or fail to reject the null hypothesis based on the calculated t-value.

To find the critical values of the test statistic t for a two-tailed hypothesis test, we need to use the t-distribution table or statistical software. The critical values of t depend on the level of significance and the degrees of freedom (df), which are calculated as n-1, where n is the sample size.

For a two-tailed test with a level of significance of 0.10 and 37 degrees of freedom, we need to find the t-value that cuts off 0.05 of the area in each tail of the t-distribution. Using a t-distribution table or software, we find that the critical values of t are approximately ±1.691.

This means that if the calculated t-value falls outside the range of ±1.691, we reject the null hypothesis at the 0.10 level of significance, and conclude that there is significant evidence to support the alternative hypothesis. If the calculated t-value falls within the range of ±1.691, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the alternative hypothesis.

It is important to note that the critical values of t depend on the sample size and the level of significance. As the sample size increases, the degrees of freedom increase and the t-distribution approaches the normal distribution. Also, as the level of significance decreases, the critical values of t become more extreme, making it harder to reject the null hypothesis.

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A descriptive statistic is a number that summarizes and describes certain characteristics or properties of a batch of numbers.

These statistics provide insight into the central tendency, variability, and distribution of a set of data. Examples of descriptive statistics include measures of central tendency such as the mean, median, and mode, as well as measures of variability such as the range, standard deviation, and variance. These statistics are important for interpreting and understanding data, as they provide a quantitative summary of the data that can be used to make comparisons and draw conclusions. Descriptive statistics are used in a variety of fields, including economics, psychology, sociology, and biology, to name a few. They are an essential tool for researchers and analysts who need to make sense of large amounts of data.

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Answer:

The answer to your question is B) d≥ 5 because the best inequality that represents the number of days Amaya practices the guitar is "greater than or equal to 5". This is because Amaya practices the guitar at least 5 days a week, so the inequality that represents this would be d≥ 5.

Answer:

B

Step-by-step explanation:

Based on the given number line, we can see that the number of days Amaya practices the guitar falls on and to the right of the number 5. Since the number line is inclusive of 5, it means that Amaya practices for 5 days or more in a week.

Therefore, the inequality that BEST represents the number of days, d, she practices is:

B) d ≥ 5

This inequality indicates that the number of days Amaya practices (d) is greater than or equal to 5.

The probability of a penny falling out is,

⇒ 3 / 11

We have to given that;

A cup has some coins in it.

And, The cup tips over and 1 coin falls out.

Here, By given table;

Total number of coins are,

⇒ 3 + 5 + 2 + 1

And, Number of penny coins are,

⇒ 3

Hence, The probability of a penny falling out is,

⇒ P = number of penny / total number of coins

⇒ P = 3 / 11

So, The probability of a penny falling out is,

⇒ 3 / 11

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Therefore, the distribution of B(s) + B(t) is a normal distribution with mean 0 and variance 2(t - s).

The distribution of the sum of two independent Brownian motions, B(s) and B(t), where s ≤ t, is itself a normal distribution.

If we consider B(s) and B(t) as two random variables, each following a normal distribution with mean 0 and variance t - s, then their sum B(s) + B(t) will also follow a normal distribution. The mean of the sum will be 0 + 0 = 0, and the variance of the sum will be (t - s) + (t - s) = 2(t - s).

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Answer:

Step-by-step explanation:

65 degrees since opposite side also has 65

If the assumption for using the chi-square statistic that specifies the number of frequencies in each category is violated, the researcher can take a couple of steps to address the issue.

First, they can obtain a larger sample, which may help to achieve a better distribution of frequencies across the categories. This can improve the reliability and validity of the chi-square test.
Additionally, the researcher can collapse some categories to ensure that each one has a sufficient number of observations. By combining similar categories, the chi-square test's assumptions may be better satisfied, leading to more accurate conclusions.
If obtaining a larger sample or collapsing categories does not resolve the issue, the researcher might consider choosing a different statistical test that is more appropriate for their data and research question. This alternative test should be carefully selected based on the study's design, the type of data being analyzed, and the specific research objectives.
In summary, when the assumptions for using the chi-square statistic are violated, researchers can take several steps to address the issue: obtain a larger sample, collapse some categories, or choose a different statistical test. Each approach has its merits, and researchers should carefully evaluate their options to ensure the most accurate and meaningful conclusions are drawn from their data.

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The term that best describes the disorder that Ahmed has is given as follows:

c. major depression.

What differs depression from the other disorders cited in this problem is the length of the duration of the symptoms.

Ahmed has been feeling the symptoms for the past three weeks, which is a large time, as the other disorders such as anxiety and panic attacks have an alternance of time where the person feel the symptoms with times where the people is feeling good, without the symptoms.

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The value of z in the equation 1/4z= -7/8 + 1/8z is -7.

The value of the unknown z in the equation is determined by solving for the unknown from the equation.

The given equation is as follows:

1/4z= -7/8 + 1/8z

To find the value of z in the equation, we simplify the equation.

Multiply both sides by 8 to eliminate the denominators:

8 * (1/4)z = 8 * (-7/8) + 8 * (1/8)z

2z = -7 + z

Next, subtract z from both sides to isolate z:

2z - z = -7

z = -7

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A. X receives a net investment rate of 6% and Y receives a net investment rate of 4%.

B. X receives a final net investment rate of 5.8% and Y receives a final net investment rate of 3.8%.

C.  X: 5.8%, Y: 3.8%

A. Assuming X and Y split the gains from the swap in such a way that X gets 60% of the gains and Y gets 40% of the gains, the net investment rates that X and Y can get is as follows:

X: 5,000,000 x 0.06 = 300,000

Y: 5,000,000 x 0.04 = 200,000

Therefore, X receives a net investment rate of 6% and Y receives a net investment rate of 4%.

B. If a Financial Intermediary (FI) charges 0.2% a year (split equally between X and Y), the final rates that the two parties are receiving is as follows:

X: 5,000,000 x (0.06 - 0.002) = 298,000

Y: 5,000,000 x (0.04 - 0.002) = 198,000

Therefore, X receives a final net investment rate of 5.8% and Y receives a final net investment rate of 3.8%.

C. The swap between X and Y in the presence of a financial intermediary can be illustrated in the following diagram:

X: 5,000,000 x 0.06 = 300,000

Y: 5,000,000 x 0.04 = 200,000

FI: 0.2% (split equally between X and Y)

X: 5,000,000 x (0.06 - 0.002) = 298,000

Y: 5,000,000 x (0.04 - 0.002) = 198,000

X: 5.8%

Y: 3.8%

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The Type I error in this case would be if we conclude that the mean number of years Americans work before retiring is not 34, when in reality it is 34 years.

In statistical hypothesis testing, there are two different sorts of errors that might happen: type I and type II.

while the null hypothesis is wrongly rejected while it is true, this is referred to as a type I error, also referred to as a false positive.

The null hypothesis is mistakenly accepted when it is wrong, which is known as a type II error, or false negative.

This would mean that we have falsely rejected the null hypothesis (that the mean is 34 years) and made a mistake by assuming that the mean is different than it actually is. The Type II error would be if we conclude that the mean is 34 years, when in reality it is not 34 years. This would mean that we have falsely accepted the null hypothesis and made a mistake by assuming that the mean is the same as it actually is not.

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Let's assume that the number of adults in the cinema is x. Since there were 40 more children than adults, the number of children would be x + 40.

The total amount paid altogether was 41200 naria, which means that the amount paid by the adults would be 50x and the amount paid by the children would be 30(x+40).

To find the total number of people in the cinema, we need to solve for x. We can start by simplifying the equation:

50x + 30(x+40) = 41200

80x + 1200 = 41200

80x = 40000

x = 500

Therefore, there were 500 adults and 540 children in the cinema, making the total number of people in the cinema 1040.

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We can list all possible outcomes in a table and count the number of outcomes that meet the criteria. There are 9 such outcomes, which gives a probability of 9/36, or 1/4.

To calculate the probability of rolling a sum greater than 3 but not exceeding 6 with 2 fair dice, we first need to determine the total number of possible outcomes when rolling the dice. Since each die has 6 possible outcomes, there are a total of 6 x 6 = 36 possible outcomes when rolling 2 fair dice.

| Die 1 | Die 2 | Sum |
|-------|-------|-----|
| 1     | 3     | 4   |
| 1     | 4     | 5   |
| 1     | 5     | 6   |
| 2     | 2     | 4   |
| 2     | 3     | 5   |
| 3     | 1     | 4   |
| 3     | 2     | 5   |
| 4     | 1     | 5   |
| 5     | 1     | 6   |

There are a total of 9 outcomes where the sum is greater than 3 but not exceeding 6. Therefore, the probability of rolling a sum greater than 3 but not exceeding 6 with 2 fair dice is 9/36, which simplifies to 1/4.
The probability of rolling a sum greater than 3 but not exceeding 6 with 2 fair dice can be calculated by dividing the number of outcomes where the sum is greater than 3 but not exceeding 6 by the total number of possible outcomes.

There are a total of 36 possible outcomes when rolling 2 fair dice, as each die has 6 possible outcomes. To determine the number of outcomes where the sum is greater than 3 but not exceeding 6, we can list all possible outcomes in a table and count the number of outcomes that meet the criteria. There are 9 such outcomes, which gives a probability of 9/36, or 1/4.

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The probability of the sum of two dice being greater than 3 but not exceeding 6 is 1/3 as there are 12 successful outcomes out of a total 36.

This question is about the probability in rolling two dice.

Therefore, the probability of this event is 12/36 or 1/3.

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A= 0.5x² -69.9x + 3,263​ is the equation of the given graph.

This is a quadratic equation of the form y = ax² + bx + c.

The graph opens up, so we must have that a is greater than zero, so we can discard the first option.

Second, we can see that the vertex is located in x = 70.

The vertex of a quadratic equation is: x = -b/2a

so we have:

70 = -b/2a

-b/2a =69.9/2×0.5

= 69.9

This is the only one that fits, so this is the correct option.

Hence, A= 0.5x² -69.9x + 3,263​ is the equation of the given graph.

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Answer:

1.5.1 : constant difference is 8

1.5.2: When there are 10 chairs stacked, it's 127 cm tall.

Step-by-step explanation:

There is a linear relationship between the height of the stack and the number of chairs.

1 chair = 55 cm + 0 extra cm = 55cm

2 chairs = 55cm + 8cm = 63 cm

3 chairs = 55cm + 8(2)cm = 71 cm

4 chairs = 55cm + 8(3)cm = 79 cm

1.5.1 the constant difference between all the underlined numbers above is 8.

1.5.2 You could just keep calculating above until you get 127 cm. (Your teacher might not like that, but it's an option!)

You can find the equation & either solve for the number of chairs OR graph it.

So if we let C = the number of stacked chairs, our equation for H (height) would be:

H = 55 + 8(C-1)

If we substitute H = 127, solve for C.

127 = 55+ 8(c-1)

127 = 55+ 8c-8

127 = 47 + 8c

127 -47 = 8c

80 = 8c

10=c

When there are 10 chairs stacked, it's 127 cm tall.

Check that the answer works:

55 cm (1st chair) + 8*9 (8cm for each additional chair) = 55+ 72 = 127 cm

The value of the complementary angle of 54° is determined as  B = 36°.

Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

So if the measure of one angle is 54°, the value of its complementary angle is calculated as follows;

Mathematically, the formula for calculating the complementary angle of 54° is given as;

B + 54° = 90

B = 90 - 54°

B = 36°

Thus, the value of the complementary angle of 54° is determined as 36° since both angles will add up to 90 degrees.

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The complete question is below:

Use your knowledge of complementary and vertical angles to hit

this shot.

If angle A is 54° and angle B is its complementary angle. Angle B = ?

The solution set of the inequality is the one in option B;

x> 1 or x < -1

Remember that the absolute value inequality can be descomposed into two inequalities.

Here we have the simple inequality:

|x| > 1

Then we can decompose this into a compound inequality:

x > 1

x < -1

Then the solution is:

x > 1 or x < -1

The correct option is B.

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Answer:

Step-by-step explanation:

To find the average rate of change for an exponential function over an interval, we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where “a” and “b” are the endpoints of the interval, and “f” is the exponential function.

In this case, the interval is from x = 1 to x = 3, so a = 1 and b = 3. We are given the values of the function for these inputs:

f(1) = 7

f(2) = 9

f(3) = 13

Substituting these values into the formula, we get:

average rate of change = (f(3) - f(1)) / (3 - 1)

average rate of change = (13 - 7) / 2

average rate of change = 3

Therefore, the average rate of change for this function over the interval from x = 1 to x = 3 is 3.

The Lagrange form of the polynomial that fits the given data is L(x) = (1/4)*x^3 - (3/2)*x^2 + (17/4)*x - 3.

To find the Lagrange form of the polynomial that fits the given data, we can use the following formula:

Lagrange form:

L(x) = ∑ [y * l_i(x)], i=0 to n

where

l_i(x) = ∏ [(x - x_j)/(x_i - x_j)], j=0 to n, j ≠ i

In this formula, x and y are the given data points, n is the number of data points (n+1 is the degree of the polynomial), and L(x) is the polynomial that fits the data.

Using the given data x = {1, 2, 3, 5} and y = {0, 5, 26, 164}, we can compute the Lagrange form as follows:

l_0(x) = (x - 2)(x - 3)(x - 5)/(1 - 2)(1 - 3)(1 - 5) = -(x^3 - 10x^2 + 31x - 30)/4
l_1(x) = (x - 1)(x - 3)(x - 5)/(2 - 1)(2 - 3)(2 - 5) = (x^3 - 9x^2 + 23x - 15)/2
l_2(x) = (x - 1)(x - 2)(x - 5)/(3 - 1)(3 - 2)(3 - 5) = -(x^3 - 8x^2 + 13x - 6)/2
l_3(x) = (x - 1)(x - 2)(x - 3)/(5 - 1)(5 - 2)(5 - 3) = (x^3 - 6x^2 + 11x - 6)/4

L(x) = 0l_0(x) + 5l_1(x) + 26l_2(x) + 164l_3(x)
= (1/4)*x^3 - (3/2)*x^2 + (17/4)*x - 3

Therefore, the Lagrange form of the polynomial that fits the given data is L(x) = (1/4)*x^3 - (3/2)*x^2 + (17/4)*x - 3.

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We can calculate the number of individuals likely to fall within two standard deviations above the mean by finding 2.5% of 1000

individuals: 25.

What is mean?

In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.

If the IQ data for 1000 individuals are normally distributed, approximately 95% of the individuals will fall within two standard deviations above or below the mean. This is known as the empirical rule or the 68-95-99.7 rule.

So, to find out how many of the 1000 individuals are likely to fall within two standard deviations above the mean, we can use this rule. We know that 95% of the data fall within two standard deviations of the mean, which means that 2.5% of the data fall above two standard deviations above the mean.

Therefore, we can calculate the number of individuals likely to fall within two standard deviations above the mean by finding 2.5% of 1000 individuals:

2.5% of 1000 = (2.5/100) x 1000 = 25

So, approximately 25 of the 1000 individuals are likely to fall within two standard deviations above the mean.

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Complete Question:

IQ data is collected for one thousand individuals. If the data are normally distributed, how many of these individuals are likely to fall within two standard deviations above the mean?

The total number of personal training sessions they would have received after 5 renewals is given as follows:

20 training sessions.

The total number of personal training sessions they would have received after 5 renewals is obtained applying the proportions in the context of the problem.

The person gets four free sessions after each renewal, hence after five renewals, the number of training sessions is given as follows:

5 x 4 = 20 training sessions.

(the proportion is applied as we get the number of sections for each renewal, hence for n renewals, we simply multiply the number n by the constant).

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The profit function of the company is P(x) = 448x - 7200

From the question, we have the following parameters that can be used in our computation:

Cost function. C(x) = 7200 + 52x

Revenue function. R(x) = 500x

the profit function of the company is calculated as

P(x) = R(x) - C(x)

substitute the known values in the above equation, so, we have the following representation

P(x) = 500x - 7200 - 52x

Evaluate

P(x) = 448x - 7200

Hence, the profit function of the company is P(x) = 448x - 7200

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The probability that there are three defective items in a sample of 100 items made by a factory with a 2% defect rate is 0.2197.

This problem involves the binomial distribution, which is used to model the number of successes in a fixed number of independent trials, where each trial has the same probability of success.

In this case, the trials correspond to the 100 items in the sample, and the probability of success is 2% or 0.02, which is the probability that an item is defective. T

he number of defective items in the sample is a random variable that follows a binomial distribution with parameters n = 100 and p = 0.02. The probability of getting exactly k defective items in the sample is given by the binomial probability mass function:

P(X = k) = (n choose k) * p^k * (1 - p)^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from n without regard to their order.

To find the probability of getting exactly three defective items in the sample, we plug in n = 100, p = 0.02, and k = 3 into the binomial probability mass function and evaluate:

P(X = 3) = (100 choose 3) * 0.02^3 * 0.98^97

= 0.2197

Therefore, the probability that there are three defective items in a sample of 100 items made by the factory is 0.2197 or about 22%.

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The probability of getting someone who tested positive, given that he or she had the disease is 0.17.

Given that, the individual actually had the disease

                 Yes       No

Positive      145      25

Negative      8        122

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

The probability of getting someone who tested positive, given that he or they did not have the disease, is computed as

P(Positive|No) = P(Positive ∩ No)/P(No)

P(Positive ∩ No)= 25/(145+25+8+122)

= 25/300

P(No)= (25+122)/(145+25+8+122)

= 147/300

P(Positive|No) = 25/300 ÷ 147/300

= 25/147

= 0.17

Therefore, the probability of getting someone who tested positive, given that he or she had the disease is 0.17.

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A sample size of at least 139 should be taken to ensure that the margin of error does not exceed 5, with a population variance of 144 and a 95% confidence level.

Margin of error = Z-score * (σ / √n)
where Z-score is the critical value for the level of confidence (in this case, 95%), σ is the population standard deviation (which is equal to the square root of the variance, so σ = 12), and n is the sample size.

We want the margin of error to be less than or equal to 5, so we can set up the following inequality:
5 ≥ Z-score * (σ / √n)

To find the value of the Z-score for 95% confidence, we can use a standard normal distribution table or calculator. The Z-score for 95% confidence is approximately 1.96.

Substituting the values we have into the inequality, we get:
5 ≥ 1.96 * (12 / √n)

Solving for n, we get:
n ≥ ((1.96 * 12) / 5)²
n ≥ 138.2976

Since we cannot have a fractional sample size, we need to round up to the nearest whole number:
n = 139

Therefore, a sample size of at least 139 should be taken to ensure that the margin of error does not exceed 5, with a population variance of 144 and a 95% confidence level.

In summary, the long answer to your question is that we used the formula for the margin of error, substituted the given values, solved for n, and rounded up to get a sample size of 139.

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Answer:

149,610 gallons

Step-by-step explanation:

To answer this question, we need to know the volume of Myron's swimming pool in cubic feet. Let's assume that the volume of Myron's swimming pool is 20,000 cubic feet.

Now we can use the given conversion factor to convert from cubic feet to gallons:

1 cubic foot = 7.48052 gallons

Therefore, the number of gallons of water needed to fill Myron's swimming pool is:

20,000 cubic feet x 7.48052 gallons/cubic foot = 149,610.4 gallons

So it will take approximately 149,610 gallons of water to fill Myron's swimming pool completely.