Decide whether the following statements are true or false. Provide counter examples for those that are false, and supply proofs for those that are true. a. An open set that contains every rational number must necessarily be all of R. b. The Nested Interval Property remains true if the term "closed interval" is replaced by "closed set." c. Every nonempty open set contains a rational number. d. Every bounded infinite closed set contains a rational number. e. The Cantor set is closed.

The correct sampling method described in the question is a stratified random sample among the simple random sample,  stratified random sample, cluster random sample and  Voluntary random sample

The sampling method described in the question is a stratified random sample.

In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.

In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.

Other sampling methods mentioned in the question are:

Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.

Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.

Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.

Therefore, the correct sampling method described in the question is a stratified random sample.

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Step-by-step explanation:

surface area of hemisphere=2πr²

Answer:

Rs 12,500

Step-by-step explanation:

the price before VAT = 100/10 × Rs 5000 =

Rs 50,000

the price before discount = 50,000 / 80%

= 50,000/0.8 = 62,500

so the discount amount = 62,500-50,000

= Rs 12,500

Probabilities assume outcomes of an experiment are equally likely  is a characteristic of the classical approach to probability.

Probability is simply how likely commodity is to be.

Whenever we ’re doubtful about the outgrowth of an event, we can talk about the chances of certain issues — how likely they are. The analysis of events governed by probability is called statistics.

What are the 3 types of probability?

There are three major types of chances

Theoretical Probability.

Experimental Probability.

self-evident Probability.

What are the 2 introductory laws of probability?

The addition rule and the addition rule are used for calculating the probability of A and B, as well as the probability of A or B for two given events A, B defined on the sample space.

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Answer:

B

Step-by-step explanation:

Both II and IV are correct

Answer:

B

Step-by-step explanation:

Answer: C) Draw segment TU and point R on segment TU.

The construction he set up so far is pretty much almost done. If he draws a ray through points T and U (with T as the endpoint), then ray TU combines with ray TS to get angle STU. This angle is congruent to angle BCD.

The point R is introduced so that we call this angle STR instead of angle STU, but it's the same basic idea. You could also replace "ray" with "line" or "line segment" to get the same basic construction of copying an angle.

The interger is closest to 20 is 19 or 21

Answer:

He'll need approximately 2 bags of fertilizer to cover the whole yard.

Step-by-step explanation:

In order to solve this problem, we can use a rule of three in a way that 3.8 lb of fertilizer is related to 1000 square feet in the same proportion as "x" lb of fertilizer is related to 1307.25 square feet. This is done below:

\(\frac{3.8}{x} \text{ } \frac{\text{lb}}{\text{lb}} = \frac{1000}{1307.25} \text{ } \frac{\text{ft}^2}{\text{ft}^2}\\\\1000*x = 3.8*1307.25\\1000*x = 4967.55\\x = 4.96755\)

Since each bag comes at a 3.8 lb package, then he'll need:

\(bags = \frac{4.97}{3.8} = 1.3\)

He'll need approximately 2 bags of fertilizer to cover the whole yard. Since he can't buy 0.3 bags, we rounded the number to next integer.

After solving, the probability that we select a gold marble is 2/31.

In the given question,

A bag contains 2 gold marbles, 8 silver marbles, and 21 black marbles.

So, Total marbles = 2+8+21

Total marbles = 31

As we know that, probability refers to the likelihood that an event will occur. If we don't know how such an event will end out, we can analyze the probability or likelihood of various outcomes. Statistic is the analysis of events that follow a probability distribution.

We have to randomly select one marble from the bag then we have to find the probability that we select a gold marble is

P(G) = Total number of gold marble/Total marbles

P(G) = 2/31

Hence, the probability that we select a gold marble is 2/31.

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(A) If Two independent events, A and B, are such that P(A) = 0. 2 P(A U B) = 0. 8, then probability P(B) =  5/8.

The possibility of the result of any random event is referred to as probability. This term refers to determining how likely an event is to occur. What are the chances of getting a head when we toss a coin in the air, for instance? The quantity of outcomes depends on the response to this question. Here, the outcome could be either head or tail. Thus, there is a 50% chance that the result will be a head.

The probability serves as a gauge for the likelihood that an event will occur. It gauges how likely an event is to occur. The probability equation is given by;

P(E) = Number of Favourable Outcomes/Number of total outcomes

We know that

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = P(A) + P(B) - P(A).P(B)

0.8 = 0.2 + P(B) - 0.2.P(B)

0.5 = P(B)  - 0.2.P(B)

0.5 = 0.8.P(B)

P(B) = 0.5/0.8

P(B) = 5/8

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30 L of 26% and 15L of 20% of each mixture should be added to make 45 l of a solution that is 24% alcohol.

The quantity of a substance, like salt, that is present in a specific volume of tissue or liquid, like blood, according to science. When there is less water present, the substance becomes more concentrated. You can determine how much solute has been dissolved in the solvent by looking at the concentration of the solution.

Here,

26x + 20(45-x) = 45(24) 

26x -20x = 45(24) -(20(45) 

6x = 4(45) = 180 x = 180/6 = 30 L of 26%

45-x = 45-30 = 15L of 20%

To make 45 l of a 24% alcohol solution, combine 30 l of 26% and 15 l of each mixture.

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For the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.

As given in the question,

Height of the right circular cone = 2.5 units

And radius of right circular cone = 7.5 units

Let r be the radius of the cylinder and h be the height of the cylinder.

Volume of a cylinder 'V' = π r² h

Cylinder is inscribed in right circular cone

From origin edge cylinder is inscribed at x distance in right circular cone.

r = 7.5 - x

h = (2.5 /7.5) x

  = x/3

V  = π ( 7.5 - x )² ( x / 3)

⇒ V = π ( x² -15x + 56.25 ) (x/3)

⇒ V = (π /3)( x³ - 15x² + 56.25x)

For maximum volume ,

dV/dx = 0

dV/dx = (π/3)( 3x² -30x + 56.25)

(π/3) ≠ 0

⇒ 3x² -30x + 56.25 = 0

⇒ 3 ( x² -10x + 18.75) = 0

3 ≠ 0

⇒ x² -10x + 18.75 = 0

x = [ - (-10) ± √ (-10)² -4(1)(18.75)]/2(1)

⇒ x = [ 10 ± √ 100 -75]/2

⇒ x=  ( 10 ± 5 ) / 2

⇒ x = 7.5 or 2.5

As r = 7.5 -x

Hence x ≠ 7.5

r = 7.5 -2.5

 = 5 units

h = x/3

  = 2.5/3

  = 0.8333 units

Therefore, for the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.

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Answer:

it must has equal sign or grater than and less than . so if you add that thing i can answer you ,ok

Slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that A cell phone company uses the equation C=$0.15t+$35.00

C is the total cost for a month of service.

t is the number of text messages.

We have to find the slope of the equation.

slope is 0.15 and 35.00 is the y intercept of the equation given.

Hence, slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

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Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

If the two number cubes are a standard six sided dice then the total of ways he can roll for the sum of 6 is 3

1+5 = 6

2+4 = 6

3+3 = 6

Hence the given statement  that there exists an s such that for any r > s there exists an m 2 n such that for all n m we have x n < r is proved.

What is non-decreasing sequence?

Non-decreasing sequences are a generalization of binary covering arrays, which has made research on non-decreasing sequences important in both math and computer science.

Proof:

For n 2 N, let s = sup x n.

Then, there exists a m 2 N such that x m r for any r > s.

Given that x n is a non-decreasing sequence, we get x n r for any n > m.

As a result, there is a m 2 N such that for any n > m, x n r for any r > s.

Hence proved.

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a. There are 7 different outcomes for the sequence of 6 coin tosses.

b. The probability, before the coin flips have begun, that f(6) = 0 is 5/16, f(6) = 1 is 15/64, and f(6) = 6 is 1/64.

c. The bar graph shows the frequencies of the different outcomes for this random walk, with bars representing the positions 0, 1, 2, 3, 4, 5, and 6.

a. The number of different outcomes for the sequence of 6 coin tosses can be calculated using the concept of combinations.

Since there are two possible outcomes (heads or tails) for each coin flip, the total number of different outcomes is\(2^6 = 64.\)

b. To calculate the probability of specific outcomes for f(6), we need to analyze the possible paths that Scott can take on the number line.

After 6 coin flips, Scott's position can be 0, 1, 2, 3, 4, 5, or 6.

To find the probability of f(6) = 0, Scott needs to have an equal number of heads and tails in his coin flips.

This corresponds to the number of ways to arrange 3 heads and 3 tails out of 6 flips, which is given by the binomial coefficient (6 choose 3).

So, the probability is \((6 choose 3) / 2^6 = 20 / 64 = 5 / 16.\)

To find the probability of f(6) = 1, Scott needs to have 4 heads and 2 tails or 2 heads and 4 tails.

The probability of getting 4 heads and 2 tails or vice versa is \((6 choose 2) / 2^6 = 15 / 64.\)

To find the probability of f(6) = 6, Scott needs to have all 6 heads in his coin flips, which has a probability of\((6 choose 6) / 2^6 = 1 / 64.\)

c. The bar graph representing the frequency of different outcomes for this random walk would have bars for the positions 0, 1, 2, 3, 4, 5, and 6. The height of each bar would correspond to the frequency or probability of that particular outcome.

d. Scott is most likely to land on the position 3 after the six coin flips

This is because the position 3 has the highest probability of occurrence, which is given by the binomial coefficient \((6 choose 3) / 2^6 = 20 / 64 = 5 / 16.\)

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Answer:

The answer is B!!

Step-by-step explanation:

What do we know given from the statement above the photo? We are told <Q is congruent to <S, and QR is congruent to SR. So by given that, we have an angle (angle Q or angle S), a side (side QR or SR), and another angle (angle R), so we have ASA. I hope this helps!!

Answer:

b

Step-by-step explanation:

From the comment above the photo, what do we know? We are advised that <Q is <S, and that QR is SR-compatible. We've got a corner (angle Q or angle S), a line (side QR or SR), and a separate angle (angle R), so we have ASA. I hope that's good!!

the question is that a team of 8 people will take 6 days to paint a 4,800 square feet home.

We can use the formula T = k * A / N, where T is the time taken to paint the home, A is the area of the home, N is the number of people hired, and k is the constant of proportionality. We can find k by using the given information that a team of 6 painters do up a 2,400 square feet home in 8 days.

k = T * N / A = 8 * 6 / 2400 = 0.02

Now, we can use the formula to find the time taken by a team of 8 people to paint a 4,800 square feet home.

T = k * A / N = 0.02 * 4800 / 8 = 12 days

Therefore, the answer is that a team of 8 people will take 6 days to paint a 4,800 square feet home.

The time taken to paint a home varies directly with the area of the home and inversely with the number of people hired for the job. By using the formula T = k * A / N, we can find the time taken by a team of painters for different scenarios.

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Answer:

GL = square root of 2 = √2

Step-by-step explanation:

Given: GHJK is a square and its diagonals intersect at L

GJ and HK are its two diagonals.

We know that in a square diagonals bisect each other and if length of side is a, then length of its diagonal = √2 a.

Therefore, GJ=HK = √2×2

Since, diagonal intersect at L , L is mid point of GJ and HK

Therefore, GL = √2×2/2 = √2

Hence, GL = square root of 2

Answer:

Alternate interior angles theorem

Step-by-step explanation:

Hope it helps you in your learning process.

The given statement "The classical model of decision making assumes that managers have all of the information they need in order to make the optimum decision." is false because it is not necessary that they have all information.

The classical decision-making model assumes that managers have access to all the relevant information, but it does not necessarily assume that they have all the information they need to make the optimum decision.

The model also assumes that the decision-maker is rational and logical, able to identify and evaluate all alternatives and select the best one based on a careful analysis of the pros and cons of each option. However, in practice, managers may not have access to all the information they need, or they may be influenced by biases or external pressures that can lead to suboptimal decision-making.

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yes jxjfnsuspfjidheagdkhrsojieeidhj

Answer:

Step-by-step explanation:

Associative property says that the product will be the same regardless of the grouping of the operands.

Which of the four answer choices involves moving brackets to enclose differnent operands?

x*(y*z) = (x*y)*z is a big hint!

Answer:

$48

Step-by-step explanation:

Martin earns = $10 x \(\frac{24}{5}\) = $10 x 4.8 = $48

Answer:

The height of the prism is 2m

Step-by-step explanation:

Given;

The volume of pentagonal prism, V = 4.8 m^3

Area of the prism, A = 2.4 m^2

To determine the height of the prism, we consider the following;

Volume of any prism = Area of the prism x height of the prism

Height of the prism = volume of the prism / Area of the prism

Height of the prism = 4.8 / 2.4

Height of the prism = 2 m

Therefore, the height of the prism is 2m

The volume of the solid is 12sqrt(3).

To find the volume of the solid whose base is the region inside the circle x² + y² = 9, we need to integrate the area of each square cross-section perpendicular to the y-axis.

Let's consider a cross-section of the solid taken at y = k, where k is a value between -3 and 3 (the range of y-values for the circle x² + y² = 9). The width of the cross-section is the distance between the x-coordinates of the intersection points of the circle with the line y = k. These intersection points are (sqrt(9 - k²), k) and (-sqrt(9 - k²), k). Since the cross-section is a square, its area is equal to the square of the width, which is sqrt(9 - k²) - (-sqrt(9 - k²)) = 2sqrt(9 - k²).

Therefore, the volume of the solid is given by the integral of the area of each cross-section as follows:

V = ∫(-3 to 3) 2sqrt(9 - y²) dy

To evaluate this integral, we can use the substitution u = 9 - y², du = -2y dy:

\(V = \int (9 to 0) \sqrt{u} du/(-2)\\= -1/2 \times [2/3 \times u^{(3/2)}](9, 0)\\= 2/3 \times (27\sqrt{3} - 9\sqrt{9} )\\= 2/3 \times 18\sqrt{3} \\= 12\sqrt{3}\)

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Answer:

Answer B

Step-by-step explanation:

Answer:

B

Step-by-step explanation: