How is the margin of error affected by sample size by confidence level?

The horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

To determine the horizontal asymptote of a function, we need to examine the behavior of the function as x approaches positive or negative infinity. In this case, as x becomes very large or very small, the terms involving x-2 and x-3 become insignificant compared to the higher power of (x-3) squared in the denominator.

As x approaches positive or negative infinity, the (x - 2) term in the numerator does not affect the overall behavior of the function. However, the (x - 3)^2 term in the denominator becomes dominant.

Since (x - 3)^2 will always be positive, the function is always positive or zero. Therefore, as x approaches positive or negative infinity, the function approaches zero or a positive value but never crosses the horizontal line y = 0. Hence, the horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

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Answer:

\(3x\cdot \:2-5x-2=0\)

\(6x-5x-2=0\)

\(6x-5x=x\)

\(x-2=0\)

\(x-2+2=0+2\)

\(x=2\)

\(-----------\)

Hope it helps..

Have a great day!!

Answer:

2, -1/3

Step-by-step explanation:

3x^2 - 5x - 2 = 0

Find the factors of 3*-2 that are the same as the addends for -5:

3*-2 = -6

Factors of -6: -6*1

Addends: -6 + 1

3x^2 - 6x + x - 2 = 0

(3x^2 - 6x) + (x - 2) = 0

(factor in each parantheses)

3x(x - 2) + 1(x - 2) = 0

(3x + 1)(x - 2) = 0

(set each of the terms to 0 and solve)

3x + 1 = 0

3x = -1

x = -1/3

x - 2 = 0

x = 2

Hope it helps (●'◡'●)

Answer:

12

Step-by-step explanation:

the angle is defined by equation ((n-2)*180)/n,where n is number of sides of a regular polygon

so here 180n-360=150n

30n=360

n=12

To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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The segment FG is reflected by the rule (x, y) → (-x, y). Hence, option C is the correct answer.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century. In geometry, object transformations constitute the foundation for the majority of proofs. Transformations allow us to change any image in a coordinate plane. The rules of transformations can be utilised to better understand the images used in video games.

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation.

FG has points at F(-6, -3) and G(-3, 6), and F'(6, -3) and G'(3, 6).

It is reflected by the rule (x, y) → (-x, y).

Hence, option C is the correct answer.

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The value of f(3/4) is 5/4.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given is a function.

f(x) = 2x - 1/4

We have to find the value of the function when the input value x = 3/4.

For that, substitute 3/4 in place of x.

f(3/4) = (2 × 3/4) - 1/4

         = 6/4 - 1/4

         = 5/4

Hence the value of the function is 5/4.

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Answer:

A. day 12

Step-by-step explanation:

because that is when both lines meet

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A 5-gallon container of water weighs approximately 41.7 pounds (18.9 kilograms). This is because water has a density of 1 kilogram per liter or 8.34 pounds per gallon. Therefore, a 5-gallon container holds 18.9 liters of water, which weighs 18.9 kilograms or 41.7 pounds.

A gallon of water is equivalent to 8.34 pounds of water. So 5-gallon of water is equivalent to

= 5 * 8.34

= 41.70

A gallon of water is equivalent to 3.78 litres of water. So 5-gallon of water is equivalent to

= 5 * 3.78

= 18.90

A litre of water is equivalent to 1 kilogram of water. So 18.90 litres of water is equivalent to

= 18.90 * 1

= 18.90

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First, we need to define rational numbers

Rational numbers are numbers that can be express as a quotient or fraction

From the question given, The square root of 16 is 4, this can be express as 4/1

Hence, it is a rational number

Therefore the correct option is A

Answer:

5... 36, 49

6.... 3, 0

The volume of the cylinder is 164.85 ft³.

We have the dimension of cylinder

Radius = 15/2 =7 .5 ft

Height = 7 ft

Now, the formula for Volume of Cylinder is

= 2πrh

Plugging the value of height and radius we get

Volume of Cylinder is

= 2πrh

= 2 x 3.14 x 7.5/2 x 7

=  3.14 x 7.5 x 7

= 164.85 ft³

Thus, the volume of the cylinder is 164.85 ft³.

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Answer:

the answer is 40

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Answer:

Use the quotient property of logarithms, logb(x)−logb(y)=logb(xy) log b ( x ) - log b ( y ) = log b ( x y ) . log3(4010) log 3 ( 40 10 ). Step 2.

The total cost for 10 hours of work would be 25 + 50(10) = 525.

Cost is the monitorial associated with the purchase of production of food or service if can include the prices of material of which is over it and other expenses that are related to the production of the code of service cost is a major fraction of when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.
The marginal cost of producing 5 items can be calculated using the equation C(x)=1300+4x/10. The marginal cost is the cost associated with producing one additional item. To calculate the marginal cost, we can plug in x=5 into the equation.

The equation in slope-intercept form for cost, c, after h hours of service is c = 25 + 50h.

The total cost for 8 hours of work would be 25 + 50(8) = 425.

The total cost for 10 hours of work would be 25 + 50(10) = 525.

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The observed allele frequencies for the T102C locus are as follows: T allele frequency = 0.388 and C allele frequency = 0.612.


To calculate the observed allele frequencies, we divide the number of occurrences of each allele by the total number of alleles observed.

In this case, the T allele is observed in 108 TT genotypes and 194 TC genotypes, giving a total of 108 + 194 = 302 T alleles. Similarly, the C allele is observed in 194 TC genotypes and 48 CC genotypes, giving a total of 194 + 48 = 242 C alleles.

To calculate the T allele frequency, we divide the number of T alleles by the total number of alleles: 302 T alleles / (302 T alleles + 242 C alleles) = 0.388 (or approximately 0.39).

Similarly, the C allele frequency is calculated as: 242 C alleles / (302 T alleles + 242 C alleles) = 0.612 (or approximately 0.61).

Therefore, the observed allele frequencies for the T102C locus are T allele frequency = 0.388 and C allele frequency = 0.612.

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Answer:

SA : 253.5

Step-by-step explanation:

2(6.5)(6.5) + 2(6.5)(6.5) + 2(6.5)(6.5)

84.5 + 84.5 + 84.5 = 253.5

The magnitude of the correlation coefficient, regardless of the sign, provides information about the strength of the linear relationship between variables.

The sample correlation coefficient, r, ranges between -1 and 1. A value of 1 or -1 indicates a perfect linear relationship, where all data points lie precisely on a straight line. On the other hand, a value close to 0 indicates a weak or no linear relationship.

In the given scenario, r = .40 indicates a moderate positive linear relationship. Although the correlation is not perfect (not equal to 1), it still suggests a moderate degree of association between the variables. The positive sign indicates that as one variable increases, the other tends to increase as well, but not necessarily in a strictly linear fashion.

On the other hand, r = -.60 indicates a stronger linear relationship, albeit in the negative direction. The negative sign signifies an inverse relationship, meaning that as one variable increases, the other tends to decrease, but again, not necessarily in a perfectly linear manner. The magnitude, which is the absolute value of the correlation coefficient, indicates a stronger relationship compared to r = .40.

Therefore, it is important to consider both the magnitude and the sign of the correlation coefficient to assess the strength and direction of the linear relationship between variables.

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The requirements for a hypothesis test are satisfied.

To test the claim that the rate of polio is less for children given the Salk vaccine, we need to check if the requirements for a hypothesis test about two population proportions are met. The requirements are:

1. The samples are simple random samples and independent.
2. For each of the two groups, the sample size is at least 1000.

In this case, the study involved 401,974 children who were randomly assigned to two groups: the treatment group with 201,229 children and the placebo group with 200,745 children. This satisfies the first requirement, as the samples are simple random samples and independent. The sample size for both groups is also larger than 1000, meeting the second requirement.

Therefore, the requirements for a hypothesis test are satisfied, and we can proceed with testing the claim that the rate of polio is less for children given the Salk vaccine.

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The perimeter and area of a parallelogram can be determined if the length and width are known.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

Without additional information, it is not possible to determine the exact perimeter and area of each cookie. Assuming the length and width are given, we can use the formula for the perimeter of a parallelogram (2 times the sum of the length and width) and the formula for the area of a parallelogram (length times width) to find the desired quantities.

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Given:

The inequality is:

\(y>5x+3\)

To find:

The y-intercept, slope and type of line (solid or dotted).

Solution:

The slope intercept form of a line is:

\(y=mx+b\)            ...(i)

Where, m is the slope and b is the y-intercept.

We have,

\(y>5x+3\)

The relation equation is:

\(y=5x+3\)             ...(ii)

On comparing (i) and (ii), we get

\(m=5\)

\(b=3\)

It means the slope is 5 and the y-intercept is 3.

The sign of the inequality in the given inequality is ">". It means the boundary line is not included in the solution set. So, the boundary line is a dotted line.

Therefore, the slope is 5, the y-intercept is 3 and the line is a dotted line.

The drama club must sell at least 74 student tickets in order to meet the show's expenses.

Let's denote the number of student tickets sold as "S".

We know that each student ticket sells for $7.50, so the total revenue from student ticket sales is 7.50S dollars.

We are also given that each adult ticket sells for $10, and 37 adult tickets were sold. Therefore, the revenue from adult ticket sales is 10 * 37 dollars.

The total revenue from ticket sales must be at least $920 to cover the show's costs. Therefore, we can set up the equation:

7.50S + 10 * 37 ≥ 920

Now, we can solve this equation to find the range of possible values for S:

7.50S + 370 ≥ 920

7.50S ≥ 920 - 370

7.50S ≥ 550

S ≥ 550 / 7.50

S ≥ 73.33

Since the number of student tickets must be a whole number, the smallest possible value for S is 74. Therefore, the drama club must sell at least 74 student tickets in order to meet the show's expenses.

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The entire interval over which the function f(x) is negative could be (-8, 0).

In the given table, we can observe that as x increases from -8 to 0, the corresponding values of f(x) decrease from -16 to 0. This indicates that the function f(x) is negative in this interval.

Looking at the other intervals, we can see that as x decreases from -8 to -2, the values of f(x) also decrease, but they are positive. Similarly, for x values greater than 0, the values of f(x) are positive.

Therefore, the only interval where all the values of f(x) are negative is (-8, 0). Within this interval, the function f(x) takes on negative values for each x value

It's worth noting that we can't determine if the function is negative for values less than -8 or after 0, as the table does not provide data for those intervals. However, based on the given data, the interval (-8, 0) is the only interval where f(x) is negative.

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Answer:

18m + 30

Step-by-step explanation:

times everything in the bracket by 6

ANSWER:

5 positive integers

STEP-BY-STEP EXPLANATION:

We have the following inequality:

Solving for x:

Being only positive numbers, it would then remain:

Being only integers, it would then remain:

Which means that 5 positive integers satisfy the inequality (10, 11, 12, 13, 14)

Answer: the answe is not at all close to the actual Nobel rate.

Step-by-step explanation:

Answer:

the box will move to the left with a force of 6 N

Step-by-step explanation:

Given that:

Force exerted on the box to the left (F1) = 16N

Force exerted on box towards the right (F2) = 10N

Since the forces are a ting in opposite Direction :

Net force :

F1 - F2

16N - 10N = 6N

The net force will be the direction of the greater applied force :

Hence, the box will move to the left with a force of 6 N

Answer:a

Step-by-step explanation:

The race result will not be disqualified due to an illegal wind.

In order to determine whether the wind velocity during the race was legal, we need to compare the wind velocity w to the legal wind speed limit of 5 km/hr. In this case, the wind velocity is given as 5ij km/h, which is purely vertical wind. The direction of the wind is not relevant in this case, since the race is run in the direction of the vector v, which is a purely horizontal direction. Since the wind velocity w is purely vertical and the race is run in a purely horizontal direction, the wind velocity w has no effect on the race result. Therefore, the race result will not be disqualified due to an illegal wind.

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