Write each expression as a single power of 10.
A. 10-2. 10-4
B. 106 10-1
104
107
.
C.
D. (10-3)4
10-8
E.
106

Leo might therefore have 36 or 48 toy soldiers, which is a choice between the two numbers.

The attempt to demonstrate that your integer is larger than anyone else's integer has persisted through the ages, despite their being more numbers than there are atoms in the universe. The largest number that is frequently used is a googolplex (10googol), which equals 101¹⁰⁰.

We'll name Leo's collection of toy soldiers "x" the amount. We are aware of:

We can infer x to be one of the following figures from the first condition: 28, 32, 36, 40, 44, 48, or 52.

To find out which of these integers meets the other two requirements, we can try each one individually:

x + 6 = 34 and x + 3 = 31, neither of which is a multiple of five, if x = 28.

X + 6 = 38 and X + 3 = 35, none of which is a multiple of 5, follow if x = 32.

When x = 36, x + 6 = 42, a multiple of 7, and x + 3 = 39, a multiple of 5, follow. This might be the answer.

x + 6 = 46 and x + 3 = 43, neither of which is a multiple of five, if x = 40.

x + 6 = 50 and x + 3 = 47, neither of which is a multiple of five, if x = 44.

When x = 48, x + 6 = 54, a multiple of 7, and x + 3 = 51, a multiple of 5, follow.

x + 6 = 58 and x + 3 = 55, neither of which is a multiple of five, if x = 52.

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Yes, the data give convincing evidence to support Phoebe's hunch. As the result of the test is a p-value that is 0.1 of less than 0.05.

The p-value is the probability of obtaining a result as extreme or more extreme given that the null hypothesis is true. The p-value is calculated by comparing the test statistic to the probability distribution under the null hypothesis.

The ratio of seniors bringing a bag lunch= 78/104 or 0.75,

while the ratio of sophomores bringing a bag lunch= 52/80 or 0.65.

This indicates that the proportion of seniors bringing a bag lunch is higher than the proportion of sophomores bringing a bag lunch.

Further, the difference between the proportions is

0.75-0.65 = 0.1,

which is a large enough difference to be considered significant.

The result of the test is a p-value of less than 0.05, which is statistically significant and indicates that the difference in the proportions is due to the different ages, and not due to chance.

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The equation representing total fraction strip is  ³/₃ + ¹/₃ = ⁴/₃.

option B.

A fraction is a mathematical representation of a part of a whole or a ratio between two numbers. It consists of a numerator, which represents the number of parts being considered, and a denominator, which represents the total number of parts in the whole.

For this case, 1 is divided into, and 1 divide into 3.

To obtain the total fractions, we will add the individual fractions as shown below;

For this first fraction = ¹/₃ + ¹/₃ + ¹/₃

For the second fraction = ¹/₃

Total fraction = 3(¹/₃ + ¹/₃ + ¹/₃) + ¹/₃

Total fraction = ³/₃ + ¹/₃ = ⁴/₃

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Answer:

Step-by-step explanation:

To find the probability of choosing a random number that starts with 2, we need to find two things:

1. The total number of valid four-digit numbers that can be created from the digits 0-9 where the first and last digits are even and no digit can repeat.

2. The number of valid four-digit numbers that start with 2 and meet the other criteria.

Let's begin by calculating the total number of valid four-digit numbers.

There are 5 even digits (0, 2, 4, 6, 8) to choose from for the first and last digits. For the second digit, there are 9 digits to choose from (since 0 cannot be repeated), for the third digit there are 8 digits to choose from (since we used one digit already and neither the first nor last digit can be repeated), and for the last digit there are only 4 choices left (since we used 5 for the first digit, and one more can’t be repeated). Therefore, the total number of valid four-digit numbers is:

5 * 9 * 8 * 4 = 1,440

Now we need to calculate the number of valid four-digit numbers that start with 2.

We already determined that there are 5 even digits to choose from for the last digit, leaving 8 digits for the second and 7 for the third digit (since the first digit is fixed). So the number of valid four-digit numbers that start with 2 is:

5 * 8 * 7 * 1 = 280

Therefore, the probability of choosing a random number that starts with 2 is:

280 / 1,440 = 0.1944 rounded to 4 decimal places.

So the answer to the problem is 97/500, which simplifies to 0.1940 when rounded to 4 decimal places.

The largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9 has dimensions x = 1.5, y = 1, and z = 2.25, with a maximum volume of 3.375 cubic units.

To find the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9, we can use the method of Lagrange multipliers.

Let the sides of the rectangular box be represented by the variables x, y, and z. We want to maximize the volume V = xyz subject to the constraint x + 3y + 4z = 9.

The Lagrangian function is then given by L = xyz + λ(x + 3y + 4z - 9).

Taking the partial derivatives of L with respect to x, y, z, and λ, and setting them equal to zero, we get:

yz + λ = 0

xz + 3λ = 0

x*y + 4λ = 0

x + 3y + 4z - 9 = 0

Solving these equations simultaneously, we get:

x = 1.5, y = 1, z = 2.25, and λ = -0.5625

Therefore, the maximum volume of the rectangular box is V = 1.512.25 = 3.375 cubic units.

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Therefore, the difference in the price of 300 cm of ribbon between shop A and shop B is £1.20.

In mathematics, an equation is a statement that two expressions are equal. It usually contains one or more variables, which are typically represented by letters, and may contain constants and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. An equation can be true or false depending on the values of the variables. Solving an equation means finding the values of the variables that make the equation true.

Here,

To find the difference in price between the two shops, we need to first calculate the cost per centimeter of ribbon for each shop:

Shop A: £1.68 / 140 cm = £0.012 per cm

Shop B: £1.72 / 215 cm = £0.008 per cm

Now, we can calculate the cost of 300 cm of ribbon at each shop:

Shop A: 300 cm x £0.012 per cm = £3.60

Shop B: 300 cm x £0.008 per cm = £2.40

The difference in price between the two shops for 300 cm of ribbon is:

£3.60 - £2.40 = £1.20

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The measure of the angle that it is complementary which is represented by 90-x is always true. Option A

An acute angle is simply defined as an angle that measures from 90° and 0°. This means that it is smaller than a right angle.

It is formed in the space between two intersecting lines or planes, or from the intersection of two shapes.

A complementary angle can be defined as a pair of angles whose sum is equal or equivalent to 90 degrees.

From the information given, we have that;

x is the acute angle

The complementary angle is 90 - x

We can see that the angle x must be complementary to be subtracted from 90 degrees.

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The complete question:

If the measure of an acute angle is represented by x, then the measure of its complement is represented by 90 – X.

always true

sometimes true

never true

Therefore , the solution of the given problem of unitary method comes out to be V has a value of -13/3.

By using preexisting variables, this common convenience, or all essential components from the initial Bishop malleable study that adhered to a specific methodology, the objective may be accomplished. If the term affirmation result does not occur, both essential components will event miss the statement; however, if it does, it then becomes possible to reach the entity once more.

Here,

TU = 4v and QR = 5v plus 17 allow us to write:

=> QR = TU + UP + PS + SR + RQ

Inputting the numbers provided yields:

=> 5v + 17 =  4v + UP + v + 26 + SR + 5v plus

When we simplify the solution, we obtain:

=> UP + SR + 6v + 26 = 0

Because UP and SR are opposite and equivalent, we can write:

=> UP = -SR

By replacing this in the preceding solution, we obtain:

=> UP - UP + 6v + 26 = 0

When we simplify the solution, we obtain:

=> 6v + 26 = 0

26 is subtracted from both parts to yield:

=> 6v = -26

When we multiply both parts by 6, we get:

=> v = -26/6

If we simplify, we get:

=> v = -13/3

V therefore has a value of -13/3.

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Answer:

Step-by-step explanation:

To find the perimeter of an equilateral triangle is equalled to 3s.

35 x 3

105

The waterproof jackets that last five years offer the biggest savings, as they have a lower cost per jacket per year.

The cost curve, which in economics expresses production costs as a function of output. The loss function is a function that has to be minimised in mathematical optimization. A cost function evaluates how inaccurate the model is in estimating the connection between X and y.

Given that, cost of waterproof jackets that last for 5 years = $150 for 50 jackets.

Thus, cost of one jacket = 150/50 = $3.

The jacket lasts 5 years thus for 1 year the equivalent cost is:

3/5 = $0.60.

Now, for the other jacket:

Cost per year is = (80/50) / 2 = $0.80 per jacket per year.

Hence, the waterproof jackets that last five years offer the biggest savings, as they have a lower cost per jacket per year.

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In response to the stated question, we may state that x + y < 380 (the variable corporation plans to sell at most 380 boards of wood) (the company expects to sell at most 380 boards of wood)

A variable is anything that may be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. The letters x, y, and z are often used as generic variables symbols.

To indicate the amount of boards of each type of wood sold, consider the following variables:

Let x be the number of mahogany boards sold.

Let y represent the number of black walnut boards sold.

The system of inequalities representing the restrictions of this issue scenario may therefore be represented as follows:

[tex]x < 260[/tex] (the corporation has 260 boards of mahogany) (the company has 260 boards of mahogany)

y ≤ 320 (the corporation has 320 boards of black walnut) (the company has 320 boards of black walnut)

x + y < 380 (the corporation plans to sell at most 380 boards of wood) (the company expects to sell at most 380 boards of wood)

Furthermore, we know that the profit on the sale of the wood is $20 per board for mahogany and $6 per board for black walnut. Let P represent the total profit from the sale of the wood. Then: P = 20x + 6y

We may display the three boundary lines x = 260, y = 320, and x + y = 380 to graph this system of inequalities, and shade the feasible region that meets all three inequalities. The triangle bordered by the x-axis, y-axis, and the line x + y = 380 will be the viable region. Here's a basic idea of how the graph may look:

      |

 380 - * - - - - - - - - - - - - - - - - - -

       |  /\                                  

       | /   \                              

       |/     \                            

 260 - *-------* - - - - - - - - - - - - - - -

       0       320

        Mahogany   Black Walnut

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B) Quick Sort is algorithms sorts data by recursively splitting the array into smaller sub-arrays, until eventually reaching single-element sections, and then joins the sub-arrays back together in sorted order

Merge Sort is an effective algorithm for sorting the data items of a list or an array. This algorithm's fundamental idea is to break the unsorted list into many sub-lists until every sub-list contains only one item.

The merging procedure then recombines all of the sublists, resulting in a sorted list. Divide-and-conquer is the name given to this merging process. Merge Sort divides the original list into N sublists, each of which contains one element.

The Merge Sort algorithm is faster than other sorting algorithms when it comes to time complexity. The time complexity of Merge Sort is O (n log n), which is better than Bubble Sort and Insertion Sort.

It is a more efficient sorting algorithm than other algorithms, such as bubble sort, which has a higher time complexity of O (n²).

Therefore, we can say that Merge Sort is the most efficient algorithm to sort an array in ascending or descending order.

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a) A greedy algorithm is an approach to problem-solving that makes the locally optimal choice at each step with the hope of finding a globally optimal solution.

This means that at each step, the algorithm chooses the best available option without considering the future consequences of that decision.

(b) An example of a greedy algorithm that produces an optimal solution is the activity selection problem.

Given a set of activities with their start and end times, the goal is to select the maximum number of non-overlapping activities. The greedy algorithm sorts the activities by their end times and selects the first non-overlapping activity.

It then repeats this process with the remaining non-overlapping activities until all activities have been selected. This algorithm produces an optimal solution because selecting the activity with the earliest end time leaves the maximum amount of time available for the remaining activities.

(c) An example of a greedy algorithm that does not always produce an optimal solution is the knapsack problem.

Given a set of items with their weights and values, the goal is to maximize the value of items that can be carried in a knapsack of a given weight capacity. The greedy algorithm selects items based on their value-to-weight ratio until the knapsack is full.

However, this algorithm can fail to produce an optimal solution if there are items with high value but large weight, which cannot fit in the knapsack after the algorithm selects several low-value items with small weight. In such cases, a more sophisticated algorithm is required to find the optimal solution.

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Answer:

Step-by-step explanation: To obtain the function g(x) that represents the indicated transformations of the graph of f(x) = 2, which are a translation 1 unit up followed by a horizontal stretch by a factor of 2, we can follow these steps:

To translate f(x) = 2 one unit up, we can add 1 to the function: f(x) + 1.

To horizontally stretch f(x) + 1 by a factor of 2, we can multiply the input (x) by 1/2: f(1/2 x) + 1.

Therefore, the function g(x) that represents the indicated transformations of f(x) is:

g(x) = f(1/2 x) + 1

g(x) = 2(1/2 x) + 1

g(x) = x + 1

The value we obtain from the table will be subtracted from 1 to obtain the probability that we are looking for.P(z < 1.75) = 0.9599 (from the standard normal distribution table)Therefore, P(z ≥ 1.75) = 1 - P(z < 1.75) = 1 - 0.9599 = 0.0401.The probability that a randomly selected individual with the degree will get a starting salary of at least $34,375 is 0.0401, or 4.01%.

We have been given that the starting salaries of individuals with a certain degree are normally distributed with a mean of $30,000 and a standard deviation of $2,500.We are required to determine the probability that a randomly selected individual with the degree will get a starting salary of at least $34,375.

We know that the Z-score formula is given as:$$z=\frac{x-\mu}{\sigma}$$Where:x = Value for which we need to find the probability.μ = Mean of the distribution.σ = Standard deviation of the distribution.Using this formula, we can find the Z-score for the given data as follows:$$z=\frac{x-\mu}{\sigma}$$$$\frac{34,375-30,000}{2,500}=1.75$$Now, we can use the normal distribution table to find the probability of a Z-score being less than or equal to 1.75.

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The contrapositive of the zero product property is that if neither of the two real numbers is 0, then the product of the two numbers will not be 0. In plain language, this means that if neither of the two numbers are 0, then the product of the two numbers cannot be 0.

In an informal version, this can be stated as "if neither number is 0, then their product cannot be 0". This can be understood as "if neither number is 0, the result of multiplying them together cannot be 0". In other words, the product of two real numbers will not be 0 if neither of them is 0.

The explicit formula for the nth term of the sequence 16, 19, 22 is:

[tex]a_n = 16 + 3(n-1)[/tex]

What is an sequence ?

A sequence is an ordered list of numbers or other mathematical objects that follow a particular pattern. Each individual number or object in the sequence is called a term. The pattern that governs the sequence is usually defined by a rule or formula that determines how each term is related to the previous terms. Sequences can be finite or infinite, depending on whether there is a last term or not. They can also be arithmetic, geometric, or have more complicated patterns. The formula for the nth term of a sequence is typically derived from observing patterns or relationships among the given terms.

Finding the explicit formula for the given sequence :

To find the explicit formula for the given sequence 16, 19, 22, we can first observe that each term in the sequence is obtained by adding 3 to the previous term. That is, 19 = 16 + 3 and 22 = 19 + 3. This suggests that the sequence follows an arithmetic pattern, where each term is the sum of the first term and a multiple of a common difference d (in this case, d = 3) multiplied by the position of the term minus 1 (n-1).

Using this pattern, we can write the explicit formula as follows:

[tex]a_n = a_1 + d(n-1)[/tex], where [tex]a_1[/tex] is the first term and d is the common difference.

Plugging in the values for the first term and common difference in the given sequence, we get:

[tex]a_n = 16 + 3(n-1)[/tex]

Therefore, the explicit formula for the nth term of the sequence 16, 19, 22 is:

[tex]a_n = 16 + 3(n-1)[/tex]

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The target domain for a Poisson distribution is given the term (0, inf) which can be seen correct in option B.

A Poisson distribution's target domain is (0, inf). This means that the Poisson distribution can only be specified for non-negative integer values of the random variable it is modelling.

The Poisson distribution is a discrete probability function, which indicates that the variable may only take particular values from a finite list of integers. A Poisson distribution estimates how many times an event will occur in "x" amount of time. In other words, it is the probability distribution resulting from the Poisson experiment.

A Poisson experiment is a statistical experiment that categorises the experiment as either successful or unsuccessful. A limiting process of the binomial distribution is the Poisson distribution.

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Complete question:

What is the target domain for a Poisson distribution?

1) (-inf, inf)

2) (0, inf)

3) (-inf, 0]

4) [0, inf)

Answer:

NO.2- SSA is not the method to show the congruency of two triangles.

Answer:11

Step-by-step explanation:

The answer of the given question based on the finding the m∠QTS from a circle with the measure of minor arc the answer is the measure of angle ∠QTS is 60° degrees.

In geometry, arc is  portion of a curve or  circle. It is defined as the part of the curve that is contained between two points, called endpoints, on curve. The length of  arc is  fraction of the circumference of  circle, determined by the measure of  central angle that subtends it.

An arc is typically denoted by  two endpoints, with  small arc or arc symbol above the two letters. For example, an arc with endpoints A and B would be denoted as "⌒AB" or "AB".Arcs can be classified based on their measure or  position of their endpoints.

An arc with measure less than 180 degrees is called  minor arc, while an arc with measure greater than 180 degrees is called  major arc. An arc with measure equal to 180 degrees is called semicircle.

Since arc QS is a minor arc, we know that angle ∠QTS is half the measure of arc QS. Therefore, we have:

m∠QTS = (1/2) m arc QS

m∠QTS = (1/2) (120°) [Substituting the given value of m arc QS]

m∠QTS = 60°

Therefore, the measure of angle ∠QTS is 60° degrees.

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Answer:

We know that, the sum of interior angles of an n-sided polygon is (n−2)×180⁰

For a pentagon, n=5

so,

[tex] \implies \rm \: 6x + 6y = (n - 2)180[/tex]

[tex] \implies \rm \: 6(x + y) = (5 - 2)180[/tex]

[tex] \implies \rm \: 6(x + y )= 3 \times 180[/tex]

[tex] \implies \rm \: (x + y) = \dfrac{3 \times 180}{6} [/tex]

[tex] \implies \rm \: (x + y) = \dfrac{ 3 \times \cancel{180} \: \:30}{ \cancel6} [/tex]

[tex] \rm \implies \: x + y = 90[/tex]

[tex] \underline{\boxed{\implies \rm \: y= 90 - x}}[/tex]

There are many formulas related to a pentagon. A few basic ones are given below.

Option (A) x+1 is a positive odd integer.

Given that, x < y < z and all three are consecutive non-zero integers.Let the first number be x, then the other two consecutive non-zero integers will be (x+1) and (x+2).To find out the positive odd integer among these, let us take each of them and verify if they are positive odd integers.∴ x+1 is odd, x+2 is even∴ x+1 is the only positive odd integer out of the three.

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By answering the presented question, we may conclude that Therefore, the solution to the system of equations is: x = 36/31 and y = 57/31.

In mathematics, an equation is a statement stating the equivalence of two expressions. An equation generally made up of two sides delimited by a system of equations (=). For example, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The objective of equation solving is to identify the amount or amounts of the variables ( independent variables) that will allow this equation to really be true. Mathematics can be simple or complex, regular or quadratic, and contain one or more parts. In the equation "x2 + 2x - 3 = 0," for illustration, the variable x is elevated to the second power. Lines are employed in numerous different fields of mathematics, including arithmetic, calculus, and geometry.

From the given system of equations, we have:

[tex]8x + 7y = 17 ...(1)\\x - 3y = -5 ...(2)\\x = 3y - 5 ...(3)\\8(3y - 5) + 7y = 17\\24y - 40 + 7y = 17\\31y = 57\\y = 57/31\\x = 3(57/31) - 5\\x = 36/31[/tex]

Therefore, the solution to the system of equations is:

x = 36/31 and y = 57/31.

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The solution to the system of equations is: x = 36/31 and y = 57/31.

In mathematics, an equation is a statement stating the equivalence of two expressions. An equation generally made up of two sides delimited by a system of equations (=). For example, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The objective of equation solving is to identify the amount or amounts of the variables ( independent variables) that will allow this equation to really be true. Mathematics can be simple or complex, regular or quadratic, and contain one or more parts. In the equation [tex]"x^2 + 2x - 3 = 0,[/tex]" for illustration, the variable x is elevated to the second power. Lines are employed in numerous different fields of mathematics, including arithmetic, calculus, and geometry.

From the given system of equations, we have:

[tex]$\begin{aligned} & 8 x+7 y=17 \ldots(1) \\ & x-3 y=-5 \ldots(2) \\ & x=3 y-5 \ldots(3) \\ & 8(3 y-5)+7 y=17 \\ & 24 y-40+7 y=17 \\ & 31 y=57 \\ & y=57 / 31 \\ & x=3(57 / 31)-5 \\ & x=36 / 31\end{aligned}$[/tex]

Therefore, the solution to the system of equations is:

x = 36/31 and y = 57/31.

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Answer:3 1 /20

Step-by-step explanation:= 1+3/4+1+3/10

The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.

Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.

Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.

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The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.

Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.

Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.

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Complete Question:
A 95% confidence interval for a population mean was reported to be 152 to 160. If s 15, what sample size was used in this study?

The two options are as follows: a. 20, 24, 21, 19, 18.

This sample is a possible bootstrap sample.

A bootstrap sample is created by taking samples from the original sample with replacement. Therefore, we can include the original data multiple times.

Here, 20, 24, 19, 23, 18 is the original sample.

Sample a includes 20, 24, 19, 23, and 18 which are part of the original data, and 21 which is not part of the original data. Since we can include the original data multiple times in bootstrap samples, a is possible.b. 20, 20, 20, 20, 20This sample is not a possible bootstrap sample.

In the original sample, we have five unique data points: 20, 24, 19, 23, and 18. Sample b includes only one unique data point, 20, repeated five times. We cannot create a bootstrap sample with the same data point repeated multiple times. Hence A is correct.

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Answer:

54

Step-by-step explanation:

Add six each time -> 24 + 6 = 30 + 6 = 36 etc