Please help me on this, I'm really stuck. It would also be awesome if you elaborated on how you got the Lower Quartile (LQ) and Upper Quartile (UQ).

IQR - Inner Quartile Range

Answer:

Step-by-step explanation:

Rolling a number greater than 7 on a number cube with sides numbered 1 through 6: The probability of rolling a number greater than 7 on a number cube with sides numbered 1 through 6 is 0, as it is not possible to roll a number greater than 6 on a standard six-sided die.

Picking the 8 of Hearts from a standard deck of playing cards: The probability of picking the 8 of Hearts from a standard deck of playing cards is 0, as there is no 8 of Hearts in a standard deck of playing cards.

A spinner with 6 equal sections labeled 1 through 6 lands on a number less than 7: The probability of a spinner with 6 equal sections labeled 1 through 6 landing on a number less than 7 is 1, as all the sections are labeled with numbers less than 7.

Flipping a coin and having it land with the heads side facing up: The probability of flipping a coin and having it land with the heads side facing up is 0.5 or 50%, assuming the coin is fair and has two equally likely sides.

Rolling a sum of 14 with two number cubes with sides 1-6: The probability of rolling a sum of 14 with two number cubes with sides 1-6 is 0, as the highest possible sum that can be obtained by rolling two number cubes with sides 1-6 is 12 (6 + 6).

What is the probability of rolling an even number on a dice? The dice is numbered 1-6: The probability of rolling an even number on a dice numbered 1-6 is 0.5 or 50%, as there are three even numbers (2, 4, and 6) and three odd numbers (1, 3, and 5) on a standard six-sided die.

The following M & M colors are in the bowl: 4 yellow, 6 orange, 3 green, 5 blue, 2 brown. What is the probability of selecting a blue candy? The probability of selecting a blue candy from the bowl is 5/20 or 1/4, as there are 5 blue candies in the bowl out of a total of 20 candies.

A number cube is labeled 1 through 6. The probability of randomly rolling a 4 is 1 over 6. What is the probability of not rolling a 4? The probability of not rolling a 4 on a number cube labeled 1 through 6 is 5/6, as there are 5 possible outcomes that are not 4 (1, 2, 3, 5, and 6) out of a total of 6 possible outcomes.

Picking a purple ball from a bag containing 7 purple balls and 1 green ball: The probability of picking a purple ball from a bag containing 7 purple balls and 1 green ball is 7/8, as there are 7 purple balls out of a total of 8 balls in the bag.

im sorry I don't know how to delete this but i now realize that my awnser was completely wrong.

Check the picture below.

Teresa's expression, 8(4) - 8x, represents the area of the Quotations section. The expression is comprised of two parts: 8(4) and -8x.

8(4) represents the width of the Quotations section, as it is multiplied by the length of 4 units. This indicates that the Quotations section has a fixed width of 8 units.

-8x represents the variable length of the Quotations section. The term -8x indicates that the length of the section can vary based on the value of x, which is a variable. The negative sign indicates that the length decreases as the value of x increases, and vice versa.

Adnan's expression, 8(4 - x), also represents the area of the Quotations section. The expression is slightly different from Teresa's, as the subtraction operation (4 - x) is contained within the parentheses.

(4 - x) represents the variable width of the Quotations section. The expression indicates that the width of the section is determined by the value of x. As x changes, the width of the section changes accordingly.

8(4 - x) then multiplies the variable width by a fixed length of 8 units, indicating that the Quotations section has a fixed length of 8 units.

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Miss Austin is covering the topic of central tendency in statistics, specifically the mean. By giving her class 6 sets of data and asking them to identify which one can be most accurately summarized by the mean, she is testing their understanding of how the mean represents the average value of a set of data.

This also involves understanding how to calculate the mean and interpret its value in relation to the other values in the dataset. Therefore, Miss Austin is helping her class develop skills in data analysis and statistical reasoning. The use of the term "set" is not clear, but assuming it means "sets of data," it is relevant to the topic being covered.

Miss Austin is covering the topic of "Descriptive Statistics" in her class. Specifically, she is focusing on the concept of "mean" as a measure of central tendency to summarize data sets. By asking her students to identify which data set can most accurately be summarized by the mean, she is teaching them how to understand the appropriateness of using the mean for different sets of data.

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A congruence transformation that maps triangle RST to triangle UVW is a reflection along the line y = 1, followed by a translation 2 units right and down by 1 units.

A congruence transformation that maps triangle RST to triangle UVW is a rotation of 180°, followed by a translation 2 units left and down by 5 units.

In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;

In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.

By critically observing the geometric figures, we can reasonably infer and logically deduce that the pre-image underwent a sequence of congruence transformation to produce the image.

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More people that rode the roller coaster are between the ages of 11 and 30, than people that are between the ages of 41 and 60 is the best description of the data which is obtained by using the arithmetic operations.

What are arithmetic operations?

Any real number may be explained using the four basic operations, also referred to as "arithmetic operations." Operations like division, multiplication, addition, and subtraction come before operations like quotient, product, sum, and difference in mathematics.

We are given a chart. From the chart we get the following data:

Number of people aged 11 - 20 riding roller coaster = 20

Number of people aged 21 - 30 riding roller coaster = 15

Number of people aged 31 - 40 riding roller coaster = 10

Number of people aged 41 - 50 riding roller coaster = 5

Number of people aged 51 - 60 riding roller coaster = 0

Using addition operation, we get

Total people = 20 + 15 + 10 + 5 + 0

Total people = 40

Now,

Total riders between 11 - 30 = 20 + 15

Total riders between 11 - 30 = 35

Similarly,

Total riders between 41 - 60 = 5 + 0

Total riders between 41 - 60 = 5

Hence, the fourth option is the correct answer.

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Answer:

49th term = 225

Step-by-step explanation:

The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.

An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.

The general formula, for the nth term of an arithmetic progression, is thus:

Tn = a + (n - 1)d, where a = first term, and d = common difference.

In the sequence: -15, -10, -5, 0, 5...,

a = -15, and d = -10--15 = 5

T49 = -15 + (49 - 1)5 = 225

∴ 49th term = 225

Step-by-step explanation: Solve for y by simplifying both sides of the equation, then isolating the variable. y = 0

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The probability Milo will be assigned a writing homework is equal to 0,50.

Let us consider the event 'A' represents the assigned Math's homework.

And 'B' represents the assigned writing homework.

Probability of Milo assigned math homework = 0. 35

⇒P(A) = 0.35

Probability of Milo assigned math and writing homework = 0. 20

⇒P(A∩B ) = 0.20

Probability of Milo assigned either homework = 0. 65

⇒P(A∪B) = 0.65

Let the Probability of Milo assigned  writing homework = P(B)

Using the Formula of probability we get,

P(A∪B) = P(A) + P(B) - P(A∩B )

Substitute the value we have,

⇒ 0.65 = 0.35 + P(B) - 0.20

⇒P(B) = 0.65 - 0.15

⇒P(B) = 0.50

Therefore, the probability of writing homework being assigned to Mila is equal to 0.50.

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Answer:

To calculate the minimum sample size required for a given margin of error and confidence level, we can use the following formula:

n = (z^2 * p * (1-p)) / E^2

where:

Substituting the values, we get:

n = (2.576^2 * 0.5 * (1-0.5)) / 0.05^2

n = 664.3

Rounding up to the nearest whole number, the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 or less at a 99% confidence level is 665.

The Probability that a student will complete the exam 0.2676.

The probability of completing the exam in one hour or less is:

[tex]P (x < 60)[/tex]

= [tex]P (z < (60-83)/13)[/tex]

=[tex]P (z < -1.77)[/tex]

= 0.0384.

The probability that a student will complete the exam in more than 60 minutes, but less than 75 minutes is.

[tex]P (60 < x < 75)[/tex]

= [tex]P (x < 75)-P (x < 60)[/tex]

Now,

[tex]P (x < 75)[/tex]

=[tex]P (z < (75-83)/13)[/tex]

= [tex]P (z < -0.62)[/tex]

=0.2676.

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The scouts are using quantitative analysis.

there are 120 distinguishable outcomes when rolling five distinguishable dice where no number appears more than once.

When rolling five distinguishable dice where no number appears more than once, we are essentially looking for the number of permutations of a set of five distinct objects.

The formula for permutations of n distinct objects taken r at a time is given by:

n!/(n-r)!

In this case, we have n=5 and r=5, so the formula becomes:

5!/0! = 5! = 120

Therefore, there are 120 distinguishable outcomes when rolling five distinguishable dice where no number appears more than once.

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There are 720 distinguishable outcomes when rolling five distinguishable dice where no number appears more than once.

To determine how many distinguishable outcomes there are when rolling five distinguishable dice where no number

appears more than once, we can use the concept of permutations.

Since there are 6 sides on each die and no number can appear more than once, we need to find the number of ways

to arrange 5 unique numbers out of 6. This can be represented as a permutation, specifically 6P5.

To calculate 6P5, use the formula:

6P5 = 6! / (6-5)!

where "!" represents the factorial function.

Calculating the factorials:

6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

1! = 1

Now, divide the two factorials:

6P5 = 720 / 1 = 720

So, there are 720 distinguishable outcomes when rolling five distinguishable dice where no number appears more than once.

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The number of bacteria after 5 hours is approximately 1013.8.

We can use the formula for exponential growth to solve this problem. If a population grows at a rate proportional to its size, then we can writ

N(t) = N₀ × e^(rt),

where N(t) is the size of the population at time t, N₀ is the initial size of the population, r is the growth rate, and e is the mathematical constant approximately equal to 2.71828.

We know that the culture starts with 40 bacteria, so N₀ = 40. We also know that after 2 hours, the size of the population is 180. We can use this information to solve for r:

180 = 40 × e^(2r)

180/40 = e^(2r)

ln(180/40) = 2r

r = ln(180/40)/2

r ≈ 0.6931

Now we can use the formula to find the size of the population after 5 hours:

N(5) = 40 × e^(0.6931×5)

N(5) ≈ 1013.8

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If x is a non-negative real number, then the expression √ x is called the Principal square root. The answer is Principal Square Root.

What is Principal Square Root?

The positive square root of a non-negative real integer is the principal square root. It is the one and only non-negative real number that, when squared, yields the given non-negative real number. The principal square root of 9 is 3, for example, because 3 multiplied by itself equals 9.

The radical sign (√) is frequently used to represent the principal square root. The term √x denotes Principal square root of x. The sign can be used to indicate the negative square root of x in some settings, but this is less frequent.

The principal square root notion is significant in mathematics, including algebra, geometry, and calculus. It's used to solve equations, simplify expressions, and calculate lengths and distances. It's also used in a wide range of scientific and engineering applications.

Therefore, if x is a non-negative real number, then the expression √ x is called the Principal square root.

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If x is a nonnegative real number, then the expression √ x is called the square root of x. The square root of a nonnegative real number is a value that, when multiplied by itself, equals the original number.

If x is a nonnegative real number, then the expression √x is called the "principal square root" of x. The principal square root of a nonnegative real number x is the nonnegative real number that, when multiplied by itself, equals x. In other words, if y = √x, then y * y = x. This ensures that the result is also a nonnegative real number.

For example, the square root of 4 is 2 because 2 multiplied by 2 equals 4. The square root function is denoted by the symbol √ and is used to find the positive number that, when squared, gives the input value.

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We can see that they are similar because the ratio of the corresponding sides of the triangle are the same = 5/3.

A triangle is a polygon with three sides and three angles. It is one of the most basic shapes in geometry and is formed when three non-collinear points are connected by straight lines. The three sides of a triangle can have different lengths, and the three angles can have different measures. Triangles can be classified based on their sides and angles.

BC/DE = AD/AB

15/9 = AB/6

AB = (15 × 6)/9 = 90/9 = 10.

15/9 = 10/6 = 5/3.

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9. The volume of the triangular pyramid is given by:

V = (1/3)Bh

Here, B is the base area.

The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:

h = sqrt(26.7² - 11.7²) = 23.274 km

The area if the base is:

B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km

Now, the volume is:

V = (1/3)(136.89)(15) = 2053.35 cubic km

Hence, the volume of the triangular pyramid is 2053.35 cubic km.

9. The volume of the triangular pyramid is 2053.35 cubic km. 11. The area of the shaded portion is 348.19 cubic in 13. The slant height of the cone is 8.53 meters.

A fundamental conclusion in geometry relating to the lengths of a right triangle's sides is known as Pythagoras' theorem. According to the theorem, the square of the length of the hypotenuse, the side that faces the right angle, in any right triangle, equals the sum of the squares of the lengths of the other two sides, known as the legs.

9. The volume of the triangular pyramid is given by:

V = (1/3)Bh

Here, B is the base area.

The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:

h = √(26.7² - 11.7²) = 23.274 km

The area if the base is:

B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km

Now, the volume is:

V = (1/3)(136.89)(15) = 2053.35 cubic km

Hence, the volume of the triangular pyramid is 2053.35 cubic km.

11. The volume of a cone is given by:

V = (1/3)πr²h

The dimension of the bigger cone is radius is 9 in, and height 15 in:

V1 = (1/3)π(9 in)²(15 in) = 381.7 cubic in

The dimension of the smaller cone is radius is 4 in, and height 10 in:

V2 = (1/3)π(4 in)²(10 in) = 33.51 cubic in

Now, the area of the shaded portion is:

V1 - V2 = 381.7 - 33.51  = 348.19

13. The volume of a cone is given by:

V = (1/3)πr²h

Substituting the values we have:

542.87 = (1/3)π(6 m)²h

h = 542.87 / [(1/3)π(6 m)²] = 6.05 m

Now, using the Pythagoras Theorem for the slant height we have:

s² = r² + h²

s² = (6 m)² + (6.05 m)²

s² = 72.9

s = √(72.9) = 8.53 m

The slant height of the cone is 8.53 meters.

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Answer: To solve for c and v, we need to use the equation:

4c + 6v = 80

We have two variables and one equation, so we need another equation to solve for c and v. We can use the fact that the number of students transported by the drivers is 80. Since each car can seat 4 students and each van can seat 6 students, we can write:

4c + 6v = 80

c + v = number of drivers

Since we want to minimize the number of drivers, we want to minimize the value of c + v. We can use substitution to solve for c and v in terms of one variable. Solving for c in terms of v from the first equation, we get:

4c + 6v = 80

4c = 80 - 6v

c = (80 - 6v)/4

Substituting this expression for c into the second equation, we get:

c + v = number of drivers

(80 - 6v)/4 + v = number of drivers

Multiplying both sides by 4 to clear the fraction, we get:

80 - 6v + 4v = 4(number of drivers)

80 - 2v = 4(number of drivers)

20 - 0.5v = number of drivers

We want to minimize the value of c + v, so we want to minimize the value of v. Since v must be a whole number, we want to find the smallest integer value of v that satisfies the equation. We can plug in integer values of v and find the corresponding value of c, and check if the sum of c and v is less than or equal to the current minimum. Starting with v = 1, we get:

v = 1 -> c = 19.5 -> c + v = 20.5

v = 2 -> c = 18.0 -> c + v = 20.0

v = 3 -> c = 16.5 -> c + v = 19.5

v = 4 -> c = 15.0 -> c + v = 19.0

v = 5 -> c = 13.5 -> c + v = 18.5

v = 6 -> c = 12.0 -> c + v = 18.0

The smallest integer value of v that satisfies the equation is v = 6, which gives c = 12. Therefore, we need 12 cars and 6 vans to transport 80 students.

Step-by-step explanation:

Answer: 13

Step-by-step explanation:

Therefore, the 99% confidence interval for the population mean is 305 - 30 to 305 + 30, which is between 275 and 335 pages.

The correct interpretation of the 99% confidence interval is that we estimate with 99% confidence that the true population mean is between 275 and 335 pages. This is because the confidence interval is based on the sample mean and the standard deviation of the sample, and it provides a range of values within which we can be reasonably confident that the true population mean lies. The fact that the sample was randomly selected helps to ensure that the estimate is representative of the overall population of books in the library. The population standard deviation of 45 pages is used to calculate the standard error of the mean, which in turn is used to construct the confidence interval.
We estimate with 99% confidence that the true population mean is between 275 and 335 pages.

Explanation:
1. A random sample of 15 books is taken from the library.
2. The sample mean (305 pages) is calculated from the random sample.
3. The population standard deviation is given as 45 pages.
4. To construct a 99% confidence interval for the population mean, we need to use the standard deviation and the sample mean.
5. The formula for the margin of error in a confidence interval is: Margin of Error = Z-score * (Standard Deviation / [tex]\sqrt{SampleSize}[/tex])
6. For a 99% confidence interval, the Z-score is approximately 2.576.
7. Margin of Error = 2.576 * (45 / √15) ≈ 30
8. The confidence interval for the population mean is: (Sample Mean - Margin of Error) to (Sample Mean + Margin of Error)
9. Therefore, the 99% confidence interval for the population mean is 305 - 30 to 305 + 30, which is between 275 and 335 pages.

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the correct interpretation of the 99% confidence interval is:

"We estimate with 99% confidence that the true population mean is between 275.08 and 334.92 pages."

Based on the given information, we can calculate the 99% confidence interval for the true population mean of pages per book in the library.

Here are the steps to calculate the confidence interval:
Identify the given information:

population standard deviation [tex](\sigma) = 45[/tex] pages, sample size [tex](n) = 15[/tex] books, and sample mean [tex](\bar x) = 305[/tex] pages.
Calculate the standard error (SE) of the sample mean:

[tex]SE = \sigma / \sqrt n = 45 / \sqrt 15 \approx 11.62.[/tex]
The critical value (z) for a 99% confidence level:

[tex]z \approx 2.576[/tex] (from a standard normal distribution table or using a calculator).
Calculate the margin of error (ME):

[tex]ME = z \times SE \approx 2.576 \times 11.62 \approx 29.92.[/tex]
Determine the confidence interval:

[tex](\bar x - ME, \bar x + ME) = (305 - 29.92, 305 + 29.92) \approx (275.08, 334.92).[/tex]

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The most appropriate response to the claim would be: "At the 95% confidence level, the mean exercise time of all students might not be 10 hours per week based on the sample data."

Based on the given data, we can see that the sample mean exercise time is 7.8133 hours per week. The standard deviation of the exercise time is 5.8032, indicating that there is some variability in the data.

To determine whether the claim that the mean exercise time of all students is 10 hours per week is reasonable, we can conduct a hypothesis test.

Our null hypothesis would be that the mean exercise time of all students is equal to 10 hours per week, and the alternative hypothesis would be that the mean exercise time is different from 10 hours per week.

We can then calculate a test statistic and compare it to a critical value based on a t-distribution with n-1 degrees of freedom, where n is the sample size.

Alternatively, we can use the confidence interval provided in the table to make a statement about the claim.

We can see that the 95% confidence interval for the mean exercise time is [7.0769, 8.5497]. Since 10 is outside of this interval, we can say that at the 95% confidence level, the claim that the mean exercise time of all students is 10 hours per week is not supported by the data.

Therefore, the most appropriate response to the claim would be: "At the 95% confidence level, the mean exercise time of all students might not be 10 hours per week based on the sample data."

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Answer:47

7•7

Step-by-step explanation:

Answer:

The ramp makes a 33.06° or 33° angle with the ground.

Step-by-step explanation:

Given: h = 5.5 ft

o = 3 ft

Let's call the angle as angle A

The ramp forms a right triangle. We can then use the concept of pythagorean theorem.

Since the angle of elevation is opposite the height of 3ft and hypotenuse is given as 5.5 ft then we can use sinA = opposite/hypotenuse

Solve:

sin A = 3ft/5.5ft

sin A = 0.5454

A = Arcsin 0.5454

A = 33.06°

Step-by-step explanation:

4^-3   =   1/4^3   =   1/64

Answer:

Step-by-step explanation:

For the volume, it would be length times width times height, and it is a cube, so they are all the same, meaning it would be 6*6*6. That is equal to 216 cm3, which is the answer for the first one. The total area, meaning surface area, would be found by finding the area of one side, which is 6*6, which is 36, and then multiplying by the number of sides, because it is a square, cube. The surface area is also 216 cm2.

1) 216 cm3 (cm^3)

2) 216 cm2 (cm^2)

The better estimate is 10 gallons and 2 quarts.

10 gallons is a better estimate than 10 quarts because a gallon is larger than a quart. In fact, there are 4 quarts in a gallon. Therefore, 10 gallons is equivalent to 40 quarts, which is clearly larger than 10 quarts.

2 quarts is a better estimate than 2 cups because a quart is larger than a cup. In fact, there are 4 cups in a quart. Therefore, 2 quarts is equivalent to 8 cups, which is clearly larger than 2 cups.

Thus, the better estimates are 10 gallons and 2 quarts.

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It depends on the context in which the estimates are being used.

Gallons are a unit of measurement for volume commonly used in the United States and other countries. It is often used to measure the volume of liquids, such as gasoline, water, or milk.

Define Quarts?

It is a British unit of liquid or dry capacity equal to ¹/₄ gallon or 69.355 cubic inches or 1.136 liters.

If the estimates are for measuring liquid volume, then 10 gallons would be a better estimate than 10 quarts as it is a larger unit of measurement.

Similarly, if the estimates are for measuring liquid volume, then 2 quarts would be a better estimate than 2 cups as it is a larger unit of measurement.

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