Solve And Fill In The Boxes

(a) Using the empirical rule, we know that about 68% of the data falls within one standard deviation of the mean. Since the standard deviation is 44 years, we can calculate the range of years by adding and subtracting 44 from the mean of 1244. So, the range of years centered about the mean in which about 68% of the data will be found is between 1200 and 1288 A.D.

(b) About 95% of the data falls within two standard deviations of the mean. So, we can calculate the range of years by adding and subtracting twice the standard deviation (2 x 44 = 88) from the mean of 1244. The range of years centered about the mean in which about 95% of the data will be found is between 1156 and 1332 A.D.

(c) Almost all of the data falls within three standard deviations of the mean. So, we can calculate the range of years by adding and subtracting three times the standard deviation (3 x 44 = 132) from the mean of 1244. The range of years centered about the mean in which almost all of the data will be found is between 1112 and 1376 A.D.
Hi! I'd be happy to help you with this question. We'll use the empirical rule, which states that for a mound-shaped and symmetric distribution:

(a) About 68% of the data will fall within 1 standard deviation from the mean. In this case, the mean is 1244 and the standard deviation is 44 years. So, the range will be between (1244 - 44) and (1244 + 44), or 1200 and 1288 A.D.

(b) About 95% of the data will fall within 2 standard deviations from the mean. The range will be between (1244 - 2 * 44) and (1244 + 2 * 44), or 1156 and 1332 A.D.

(c) Almost all the data (approximately 99.7%) will fall within 3 standard deviations from the mean. The range will be between (1244 - 3 * 44) and (1244 + 3 * 44), or 1112 and 1376 A.D.

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The number of repeating digits in the group is 1

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

Number = 2/9

When evaluated, we have

Number = 0.222.....

The above nummber has repeating digits

When approximated, we have

Number = 0.2

In the above number, the number of repeating digits is 1

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If we let a = 0, b = 1, and c = 1, then the polynomial

[tex]x(x-1)(x^2 +[/tex]

Since the polynomial has integer coefficients, if one of the roots is a complex number, then its conjugate must also be a root. Therefore, options A and E cannot be roots of the polynomial, since they have non-real conjugates.

We know that the polynomial has degree 4, so it has four roots in total (counting multiplicities). We also know that two of the roots are integers, so let's call them a and b. Then the polynomial can be written as:

[tex](x - a)(x - b)(cx^2 + dx + e)[/tex]

where c, d, and e are integers (because they are the coefficients of the quadratic factor). We know that the leading coefficient is 1, so c must be nonzero.

Since the polynomial has two real roots, its discriminant must be nonnegative:

[tex]d^2 - 4ce > = 0[/tex]

We can use this inequality to rule out some of the answer choices. For example, option C cannot be a root, because if we substitute x = 1/2 + i into the polynomial, we get:

([tex](1/2 + i) - a)((1/2 + i) - b)(c((1/2 + i)^2) + d(1/2 + i) + e)[/tex]

The real part of this expression is:

(1/4 - a + 1/4 - b)(c(1/4 - 1) + d/2 + e) = -(a + b - 1/2)(3c/4 + d/2 + e)

If we assume that a and b are integers, then this expression is an integer multiple of 3c/4 + d/2 + e. However, we can choose values of c, d, and e such that 3c/4 + d/2 + e is not an integer (for example, if c = 4, d = 1, and e = 0, then 3c/4 + d/2 + e = 4.5). Therefore, the real part of the expression cannot be zero, and option C cannot be a root.

We can also rule out option D using the same argument. If we substitute x = 1 + i/2, then the real part of the expression is:

((1 + i/2) - a)((1 + i/2) - b)(c((1 + i/2)^2) + d(1 + i/2) + e)

(1 - a + i/2)(1 - b + i/2)(c(5/4 + i) + d(3/2 + i/2) + e)

The real part of this expression is an integer multiple of c(5/4) + d(3/2) + e, which can be non-integer for some choices of c, d, and e.

Therefore, the only possible answer choices are A and B. To determine whether they are roots of the polynomial, we can use the fact that the sum and product of the roots are given by:

a + b + (complex roots) = -d/c

ab(complex roots) = e/c

We know that a and b are integers, so if we can find a polynomial with integer coefficients that has roots a, b, and either A or B, then that root is also a root of the original polynomial.

For option A, we have:

1 + i√11/2 = 2(cos(75°) + i sin(75°))

Therefore, if we let a = 0, b = 1, and c = 1, then the polynomial

[tex]x(x-1)(x^2 +[/tex]

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An equation that best models the data is [tex]y = 380(1.04)^x[/tex]

In Mathematics and Geometry, an exponential function is typically represented by the following mathematical equation:

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

Where:

Based on the table, we would calculate the value of a and b as follows;

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

380 = a(b)⁰

a = 380

Next, we would determine value of b as follows;

395 = 380(b)¹

395 = 380b

b = 395/380

b = 1.04

Therefore, the required exponential function is given by;

[tex]f(x) = y = 380(1.04)^x[/tex]

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The 99% confidence interval for the average number of hours a student spends studying for a statistics exam is (2.059, 5.941) hours.

To find a 99% confidence interval for the average number of hours a student spends studying for a statistics exam, we can use the formula:

CI = x ± z*(o/sqrt(n))

where CI is the confidence interval, x is the sample mean, z is the z-score for the desired confidence level (in this case, 99%), o is the population standard deviation, and n is the sample size.

Plugging in the given values, we get: CI = 4 ± 2.576*(6.25/sqrt(50)) CI = 4 ± 1.941 CI = (2.059, 5.941)

Therefore, the 99% confidence interval for the average number of hours a student spends studying for a statistics exam is (2.059, 5.941) hours.

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Step 1: The sample mean is (24+6+21+8+16+10+18)/7 = 15.7 (rounded to one decimal place)

Step 2: The sample standard deviation is calculated using the formula:

s = sqrt[(Σ(x - mean of x)^2) / (n - 1)]

where Σ is the sum of the squared deviations from the mean, mean of x is the sample mean, and n is the sample size.

Using the given data, we get:

s = sqrt[((24-15.7)^2 + (6-15.7)^2 + (21-15.7)^2 + (8-15.7)^2 + (16-15.7)^2 + (10-15.7)^2 + (18-15.7)^2) / (7-1)]

s = 6.679 (rounded to one decimal place)

Step 3: To find the critical value, we use a t-distribution with n-1 degrees of freedom and a confidence level of 80%. From a t-distribution table or using a calculator, we find the critical value to be 1.397 (rounded to three decimal places).

Step 4: Using the formula for the confidence interval:

CI = mean of x ± t*(s / sqrt(n))

where mean of x is the sample mean, t is the critical value, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

CI = 15.7 ± 1.397*(6.679 / sqrt(7))

CI = (9.47, 21.93)

So the 80% confidence interval for the average net change in a student's score after completing the course is (9.47, 21.93).

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Answer:

£14.75.

Step-by-step explanation:

1. Find how much 1 tub of ice cream cost. We can find this by dividing the cost of the 2 tubs in half:

5.90 / 2 = 2.95 = 1 tub ice cream

2. Multiply the cost of 1 tub of ice cream (2.95) by 5 to know the price of the 5 tubs:

2.95 x 5 = 14.75

Hence, 5 tubs of ice cream cost £14.75.

There is no such vector-valued function r(t) that satisfies the given condition.

I. There is no such vector ū that satisfies u + ū = (1, 2) because if we add any vector to u, we change its direction and magnitude, but the vector ū should have the same magnitude and opposite direction to u.

II. Let v = (1, 3, -1). Then u + v = (2+1, 1+3, 3-1) = (3, 4, 2) and u x v = (-5, 7, -1). So u x v = u + v. Therefore, v satisfies the given condition.

III. There is no such vector-valued function r(t) because if r(t) = (x(t), y(t)) satisfies the condition that r'(t) = 2r(t), then we have:

x'(t) = 2x(t) and y'(t) = 2y(t)

These are two separate first-order differential equations, which have general solutions of the form:

x(t) = c1e^(2t) and y(t) = c2e^(2t)

where c1 and c2 are constants determined by the initial conditions. However, the vector-valued function r(t) = (x(t), y(t)) cannot have a constant magnitude because its components are functions of t that grow exponentially with time. Therefore, there is no such vector-valued function r(t) that satisfies the given condition.

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The areas of the sectors for arc lengths of 4, 5, 10, and l units are approximately 3.14, 3.93, 9.42, and 0.84l units², respectively.

To find the area of a sector of a circle, we need to use the formula:

Area of sector = (angle of sector/360) x πr²

where r is the radius of the circle.

For each given arc length, we need to find the angle of the sector first. The formula for finding the angle of a sector is:

angle of sector = (arc length / radius) x 180/π

Using this formula, we get:

For 4 units arc length:
angle of sector = (4/6) x 180/π ≈ 38.2 degrees
Area of sector = (38.2/360) x π x 6² ≈ 3.14 units²

For 5 units arc length:
angle of sector = (5/6) x 180/π ≈ 47.7 degrees
Area of sector = (47.7/360) x π x 6² ≈ 3.93 units²

For 10 units arc length:
angle of sector = (10/6) x 180/π ≈ 95.5 degrees
Area of sector = (95.5/360) x π x 6² ≈ 9.42 units²

For l units arc length:
angle of sector = (l/6) x 180/π ≈ (30l/π) degrees
Area of sector = [(30l/π)/360] x π x 6² ≈ 0.84l units²

So, the areas of the sectors for arc lengths of 4, 5, 10, and l units are approximately 3.14, 3.93, 9.42, and 0.84l units², respectively.
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They may require more advanced techniques from dynamical systems theory to fully understand the behavior of the system.

If both eigenvalues of a critical point of a linear system of differential equations in two dimensions are real and equal, the critical point is a degenerate node.

The behavior of the solutions near a degenerate node depends on the higher-order terms in the Taylor series expansion of the vector field around the critical point. Specifically, the critical point is asymptotically stable if the higher-order terms in the Taylor series expansion satisfy certain conditions, and unstable otherwise.

If the higher-order terms in the Taylor series expansion satisfy the so-called "center manifold" conditions, then the critical point is a center, and the solutions near the critical point exhibit periodic behavior.

In general, the classification of a critical point with real and equal eigenvalues can be more complicated than the case where the eigenvalues have different signs, and may require more advanced techniques from dynamical systems theory to fully understand the behavior of the system.

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Based on the results obtained, the firm can analyze the data and determine if there is a significant correlation between the two variables. This information can be used to develop marketing strategies for wine and tennis-related products and services.

A marketing research firm is conducting a study to understand the relationship between wine consumption and an interest in watching professional tennis on television. They randomly select 100 people and gather data on their wine-drinking habits and whether they watch tennis or not.

To analyze the data, the marketing research firm can create a cross-tabulation, also known as a contingency table, with two rows representing the categories of wine consumption (wine drinkers and non-wine drinkers) and two columns representing the categories of watching tennis (tennis watchers and non-tennis watchers).

From the data collected, the firm can calculate the percentages of people in each category (e.g., percentage of wine drinkers who watch tennis, percentage of non-wine drinkers who watch tennis, etc.) to determine if there is a relationship between wine consumption and an interest in watching professional tennis on television.

The marketing research firm can then use statistical tests, such as the chi-square test, to assess if the observed relationship between wine consumption and tennis watching is statistically significant or if it could have occurred by chance.

In conclusion, the marketing research firm is using a systematic approach to study the relationship between wine consumption and an interest in watching professional tennis on television. This research can provide valuable insights for businesses in the wine and sports industries to better target their marketing efforts.

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Mr. Simon can serve 26 people with 20 containers of soup.

Given that: Mr.Simon has 20 containers of soup. 3 containers of soup feeds 4 people.

Frst, we need to know how many people can be fed by one container of soup.

We are given that 3 containers of soup can feed 4 people.

Hence, we can calculate how many people one container of soup can feed by dividing 4 people by 3 containers

One person ⇒  4/3

Next, we multiply the number of people per container by the total number of containers, which is 20 in this case.

This gives us:

= 20 × (4/3)

= 80/3

= 26.667

≈ 26

Mr. Simon can feed 80/3 people with 20 containers of soup. However, since we cannot serve a fractional part of a person, we should round the answer to a whole number. In this case, rounding down gives us 26.

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Answer:

D: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44

Step-by-step explanation:

Because the categories are unrelated to each other it would be unlikely that you would use a histogram in this situation. Histograms are often only used for change or continuous data about a particular group or sample.

D is correct becuase it makes use of a bar graph and the number of players per section are correctly allocated unlike answer choice C which switches some sports and the number of players they should have.

Answer: histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

An equilateral triangle has 3 congruent angles.

Each angle of an equilateral triangle measures 60°.

A square has 4 right angles.

Each angle of a square measures 90°.

The measures of the 2 angles of equilateral triangle and one right angle of the square have a total measure of

60° + 60° + 90° = 210°

A full circle has a degree measure of 360°.

x° = 360° - 210°

x = 150

You need approximately 5 terms (starting from n=4) to achieve an error less than 0.001.  To determine the number of terms required to approximate the sum of the series with an error of less than 0.001.

We can use the alternating series error bound formula:

Error ≤ |Rn| ≤ an+1

Where Rn is the remainder or error in the nth partial sum, and an+1 is the absolute value of the (n+1)th term in the series.

In this case, the alternating series is:

∑
[infinity]
n=4
(−1)n+1
n4

To find the absolute value of the (n+1)th term, we can plug in n+1 for n:

|an+1| = |(−1)n+2/(n+1)4|

Since we want the error to be less than 0.001, we can set up the inequality:

|an+1| ≤ 0.001

Plugging in the formula for |an+1| and solving for n, we get:

|(−1)n+2/(n+1)4| ≤ 0.001

(n+1)4 ≥ 1000

Taking the fourth root of both sides, we get:

n+1 ≥ 5.623

n ≥ 4.623

Therefore, we need at least 5 terms to approximate the sum of the series with an error of less than 0.001.

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Answer:

90

Step-by-step explanation:

The sum of the measures all the interior angles of a polygon having 14 sides is 2160°.

The formula we use for this is

Sum of interior angles of a polygon

= ( n-2)*180

Where “n” is the number of sides of the polygon.

Here n=14

So, sum = (14–2)*180 = 2160 degrees

Therefore, the sum of the measures all the interior angles of a polygon having 14 sides is 2160°.

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What will be the sum of the measures all the interior angles of a polygon having 14 sides?

Answer:

A: Chicken: 75 / Steak: 125 / Fish: 50

B: The wedding planner's claim is valid.

C: The wedding planner's claim is valid because if we follow the sample and use the ratio, the total amount of guests who might choose chicken and steak is about 200 people.

Apologies if this answer isn't thorough enough, I tried to do it as quickly as possible. Best of luck!

Answer:

(Excluding Xion) Each person will get 2 1/4 brownies

Step-by-step explanation:

9 brownies distributed equally to 4 friends.  If each person gets two brownies, there is one left over.  Divide 1 by 4 and you get 1/4.  1/4 in decimal form is 0.25.  2+0.25=2.25

Or you could just use a calculator to divide 9 by 4 and it would come up with 2.25

The median of the set of numbers after arranging them in order from least to greatest {0.6, 0.9, 1.7, 1.1, 2.5, 0.6} is 1.

To find the median of a set of numbers, we need to first arrange them in order from least to greatest.

The set of numbers given is 0.6, 0.9, 1.1, 1.7, 2.5, and 0.6.

Arranging them in order, we get 0.6, 0.6, 0.9, 1.1, 1.7, 2.5.

Since there are six numbers in this set, the median is the middle number when they are arranged in order. In this case, the middle numbers are 0.9 and 1.1. To find the median, we take the average of these two numbers:

Median = (0.9 + 1.1)/2 = 1.

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Step-by-step explanation:

0.6,0.6,0.9,1.1,1.7,2.5

The median is 0.9+1.1 / 2

2 /2 = 1

the median of the distribution is 1

The experimental probability it lands on yellow is 4/5

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

Number of times = 30

Results:  (R=7 Y=8 B=6 G=9)

The experimental probability it lands on yellow is

P(Yellow) = Y/Total

So, we have

P(Yellow) = 8/30

Simplify

P(Yellow) = 4/15

Hence, the probability is  4/15

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Null hypothesis: The percentage of stocks traded on the NYSE that went up on January 31, 2006, is not 30%.

Alternative hypothesis: The percentage of stocks traded on the NYSE that went up on January 31, 2006, is 30%.
To test the financial analyst's claim that 30% of the stocks traded on the NYSE went up on the same day, we can formulate the null and alternative hypotheses using the information about the DJIA stock market performance. Here are the hypotheses:
Null Hypothesis (H0): The proportion of stocks that increased in price on the NYSE is 30% (p = 0.30).
Alternative Hypothesis (H1): The proportion of stocks that increased in price on the NYSE is not 30% (p ≠ 0.30).
These hypotheses will help determine whether the analyst's claim about the overall stock market performance is accurate or not.

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The radius of the circle is 3 units and the center of the circle is (1, 0). Then the correct options are A, B, and E.

Given that:

Equation of circle, x² + y² - 2x - 8 = 0

Convert the equation into a standard form, then we have

x² + y² - 2x = 8

x² - 2x + 1 + y² = 9

(x - 1)² + y² = 3²

The radius of the circle is 3 units and the center of the circle is (1, 0). Then the correct options are A, B, and E.

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The complete question is given below.

Answer: the last one

Step-by-step explanation:

factor the quadratic expression, the greatest common factor is 3, 3(4x^2-12x+9) is a perfect trinomial square. There is only one root 3/2 but it is a double

Answer:

$80

Step-by-step explanation:

please mark brainliest answer

The Beta distribution is a continuous probability distribution with support on the interval [0,1], and is often used to model random variables that have limited range, such as probabilities or proportions.

The Beta [a, b] density has the form f(x) = {[(a+b)/([(a) r()) } Xa-1 (1 - X)B-1 +, where a and b are constants and 0 <= x <= 1. This density function describes the probability of observing a value x from a Beta [a, b] distribution.

The parameters a and b are often referred to as shape parameters, and they control the shape of the distribution. Specifically, the larger the values of a and b, the more peaked the distribution will be, while smaller values of a and b will lead to flatter distributions.

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Answer:

$63

Step-by-step explanation:

First find the cost of bananas per kilogram. To find that, divide $147 by 21

147/21=7

One kilogram of bananas costs $7

Now that you know the cost per kilogram, multiply $7 by the number of kilograms asked in the question, which in this case is 9

7*9=$63

9 kilograms of bananas costs $63

Answer: 63

Step-by-step explanation:

You can set up a proportion cost/weight=cost/weight

[tex]\frac{147}{21} = \frac{x}{9}[/tex]        Costs go on the top so x is cost for 9 kg

[tex]x=\frac{147*9}{21}[/tex]

x=63