the decimal representation of , where and are relatively prime positive integers and , contains the digits 2, 5, and 1 consecutively, and in that order. find the smallest value of for which this is possible.

The next number in sequence is 185.

What is arithmetic progression?

A sequence within which each term is made by adding or subtracting an explicit variety to the preceding variety is an arithmetic sequence.

Main body:

Step 1:

Find the pattern and write the recursive formula: [tex]\left \{ {{a_{n+1} =a_{n} +12} \atop {a_{n+1} =a_{n} +13}} \right.[/tex]

as the sequence is 123,135,148,160,173..

so 1st term 12 is added in 2nd term 13 is added

so after 173 , 12 will be added ,

173+12 = 185

hence, the next number in sequence is 185.

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Answer:

15,000

Step-by-step explanation:

The population of a city has increased by 26% since it was last measured. If the current population is 18,900 , what was the previous population?

increase of 26% means the current population is 126% of the previous.

126% = 1.26

18,900 = 1.26x

divide both sides by 1.26:

18,900/1.26 = 1.26x/1.26

x = 15,000

previous population was 15,000

The answer is outlier. a value in a set of data that "lies outside" (is much smaller or greater than) the majority of the other values.

Any figure derived from your sample data is referred to as a sample statistic (or simply a statistic). The sample mean, median, sample SD, and percentiles are a few examples. A statistic is a random variable since it is based on information gained by random sampling, which is a random experiment.

A sample is a statistical term for a population that has been analytically subset. As a result of the usage of samples, investigations may be completed faster and with more manageable data.

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The dimensions of the rectangle must be l =b = 10 units.

A rectangle is a closed flat shape, having four sides, and all angles equal to 90 degrees. The opposite sides of the rectangle are equal and parallel. diagonals are equal and bisect each other.

Perimeter of a rectangle, P = 2 ( l + b) units.

where,

“l” is the length of the rectangle

“b” is the breadth of the rectangle

area of rectangle = l×b square units.

Given:

ramay wants to fence which means the perimeter of a rectangle is 40 feet.

therefore rectangle's perimeter = 40

2(l+b)=40,

l+b=20.

When the rectangle is square, the area is the greatest. When its length equals its width.

As per the question for getting the largest area, l = b= 10,

and the area will be

10×10=100 square units.

therefore, the dimensions of the rectangle must be l =b = 10 units

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Four  electrons are required for the reduction of one molecule of oxygen to water in the mitochondria

Reduction means that a reaction in which electrons are added to a compound or molecule; the compound or molecule that gains electrons is said to be reduced

Water has 2 hydrogen and each hydrogen needs only one electron. Hence, four electrons along with four hydrogen atoms are required to reduce one molecule of oxygen (O₂) to two molecules of water (H₂0) in the mitochondria

Therefore, four electrons along with four hydrogen atoms are required to reduce one molecule of oxygen (O₂) to two molecules of water (H₂0) in the mitochondria

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Answer:

Dolly Parton

Step-by-step explanation:

hopes this helps please mark brainliest

The correct answer will be c. computing the average distance between every pair of observations between two clusters

What is Cluster Analysis?

Grouping "things" into "similar" groups is one of the most fundamental, straightforward, and frequently overlooked techniques (or processes) of comprehending and learning, on which cluster analysis is based. To create clusters of a particular type, this process uses a variety of different algorithms and techniques. It is also a component of data management in statistical analysis.

A multivariate data mining technique called cluster analysis aims to group things (such goods, responders, or other entities) based on a set of user-selected features or characteristics. Data compression, machine learning, pattern recognition, information retrieval, and other areas all use this essential and crucial phase of data mining, which is also a widely used method for statistical data analysis.

Here as per the given question, there are two clusters given.

Hence, computing the average distance between every pair of observations between two clusters.

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The linear system of equation y = x+2 and 6x = 4y+10 has only one solution.

The linear equation is y = x+2 and 6x = 4y+10

Now we solve the equations by substitution:

Using the value of y from the first equation and substituting in the second equation we get:

6x = 4y + 10

6x = 4(x+2)+10

or, 6x-4x = 8 + 10

or, 2x = 18

or, x = 9

at x=9 , y =11

Hence solution is (9,11) which represents the point of intersection of the two lines.

The phrase "solution of a linear equation" refers to the set of variable values in a linear equation that results in all possible solutions. Linear equations use unknown quantities as one or more variables to simulate real-world problems.

The intersection or meeting points of the lines or planes used to represent the linear equations are referred to as the solutions. The solution set is the collection of values for each variable in a system of linear equations.

Disclaimer: the complete question is :

How many solutions does this linear system have y = x+2 and 6x = 4y+10 have?

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Saddle points are critical point that the function didn't in local maximum points nor in a local minimum position. Saddle pointly mostly happen in the multivariable functions. In simple, saddle point is everything on the function accept the local maxima and minimum maxima. The proof what is the saddle shown in the picture. As you can see, the curve besides local maxima and minimum maxima is create an area like a saddle, thats why its called saddle point.

Saddle point availability can be calculate by this logic: lets say we have r = f(q, w), then the point (q, w, r) is told to be a saddle point if each derivatives fq(q, w) and fw(q, w) subside,and f  is not in any local maximum or local minima value at (x, y).

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The Mizzi Corporation ha created a demand function for one of it wrench et. The expense function a a function in term of p is E=−2,254p+81,294.

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The numerical value of the probability is occur after 14 minutes is 0.75.

The probability that the reaction will occur after 14 minutes is 0.75 when a specific chemical's reaction time when exposed to heat always happens after 12 minutes but before 16 minutes.

Given that,

A specific chemical's reaction time when exposed to heat always happens after 12 minutes but before 16 minutes. A uniform distribution can be used to model the reaction times for this substance.

We have to calculate the probability that the reaction will occur after 14 minutes. Calculate the probability's numerical value and shade that area of the graph.

We know that,

In the uniform distribution,

The probability is given by the Area of the Rectangle.

Area = Base x Height.

Height = 1 / (16 - 12) = 1 / 4 = 0.25

Base = 17 - 14 = 3

We need to find the probability (X >14).

The required probability = 3 × 0.25 = 0.75

Therefore, The probability that the reaction will occur after 14 minutes is 0.75 when a specific chemical's reaction time when exposed to heat always happens after 12 minutes but before 16 minutes.

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The two positive numbers are 6 and 11

From the question, we understand that:

There are two positive numbers

Represent these numbers with x and y

So, we have the following equations

x = y - 5

6x - 3y = 3

Substitute x = y - 5 in 6x - 3y = 3

6(y - 5) - 3y = 3

Open the brackets

6y - 30 - 3y = 3

Evaluate the like terms

3y = 33

Divide by 3

y = 11

Substitute y = 11 in x = y - 5

x = 11 - 5

So, we have

x = 6

hence, the numbers are 6 and 11

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The average book owned by other people is 112 which is greater than Michael's.

What is average?

In standard language, a mean could be a single range taken as representative of a listing of numbers, typically the total of the numbers divided by what numbers are within the list.

Main Body:

Books owned by Michael = 97

Average book owned by people = sum of all books / total people

avg. book owned = (225+142+29+103+61)/5

avg book owned by people = 560/5

                                               = 112

Hence books owned by avg people is 112.

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The angle of elevation from the boat to the cliff top is approximately 31 degrees.

The  boat is 150 meters from the base of a cliff that is 90 meters high. The angle of elevation from the boat to the cliff top can be calculated as follows:

The situation form a right angle triangle. The angle of elevation can be found using trigonometric ratios.

tan ∅ = opposite / adjacent

where

∅ = angle of elevation

Hence,

tan ∅ = 90 / 150

∅ = tan ⁻¹ 0.6

∅ = 30.9637565321

∅ ≈ 31 degrees

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Palindromes are a string of digits/alphabets that are read the same way as they are from the right as from the left.

We can understand palindromes using the basic example of the number - 1234321. In this number, we can see that if we read the number from the right, it is going to be read as 1-2-3-4-3-2-1. And if we read this number from the left, it is going to be 1-2-3-4-3-2-1. This shows how the sequence of bits in a palindrome is going to be the same from both ends.

In the case of odd-length palindromes like the one above, there is going to be one middle that is going to be alone. In the case of even-length palindromes such as 1111, the numbers all have a pair.

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A treaty is defined as a peaceful accord closed between States written down and represented by worldwide regulation, whether typified in a solitary instrument or in at least two related instruments and whatever its specific assignment.

Treaty is an exceptionally misconstrued term, so we really want a meaning of deal that is exact and definitive. The definition that makes reference is the one tracked down in the Vienna Show on the Law of Deals of 1969.

Presently, there is likewise a Vienna Show of 1986 which manages understanding among States and worldwide associations, however for the essential definition manages arrangement between States. The necessities are:

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It is true that the last decade has seen a sharp decline in competing authoritarian regimes.

Competing authoritarian – dictators submit to meaningful multiparty elections but engage in serious democratic abuses – proliferated in the post-Cold War era. Africa, Asia, Latin America, post-communism Based on an in-depth study of 35 cases in Eurasia, this book examines the fate of competing authoritarian regimes from 1990 to 2008. , in places such as Eastern Europe and the United States, the external costs of abuses have led incumbents to relinquish power rather than crack down, leading to democratization. political pressure has been weaker and the country has democratized less frequently.

Competitive authoritarianism is a type of hybrid government, or political regime that combines elements of democracy and authoritarianism. Highly competitive dictatorships regularly hold intense multi-party elections. However, the “playing field” is not the same. Media control, abuse of state resources, coercion and/or limited fraud give incumbents an unfair advantage over the opposition. These governments are not democratic because elections are not free and fair. But they aren't entirely authoritarian either. Unfair, but not completely pointless. In competitive authoritarian regimes, there is real competition and some uncertainty about the outcome of elections.

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The tree's diameter is increased by 1.4/π inches and the increase in the tree's cross sectional area is 32.2 square inches.

According to the question,

We have the following information:

The diameter of a tree was 23 inches. During the following year, the circumference increased 2.8 inches.

Now, let's take the radius of the tree to be r inches.

Following formula is used to find the circumference of the circle = 2πr where r is the radius

Using differentiation, we have:

dC = 2πdr

dC = 2.8 inches

2πdr = 2.8

dr = 2.8/2π

dr = 1.4/π inches

Now, increase in the cross sectional area:

Area = [tex]\pi r^{2}[/tex]

Using differentiation:

dA = 2πrdr

Radius = diameter/2

Radius = 23/2 inches

Radius = 11.5 inches

dA = 2π*11.5*1.4/π

dA = 2*11.5*1.4

dA = 32.2 square inches

Hence, the tree's diameter is increased by 1.4/π inches and the increase in the tree's cross sectional area is 32.2 square inches.

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The point is [-13,-7] when the actual numbers are all at least two units away from 4.

Given that,

To specify the interval (or pair of intervals) on the real number line, use absolute value notation. (Utilize the x variable.) actual numbers are all at least two units away from 4.

We know that,

We get,

|-4-x| = 3

-3 = -4-x = 3

7 = -x = 13

-13 = x = -7

Therefore, The point is [-13,-7] when the actual numbers are all at least two units away from 4.

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Using Taxable income formula,

a) $22,200

b) Non- business loss = $12,200 ; business loss

= $10,000

c) $10,000

We have given that

Julie's taxpayer data as following

Net loss = $40,000

Income wage = $30,000

standard deduction = $12,200

a)Computation of taxable income of Julie for 2020

total taxable income is sum of wager , net loss and standard deduction

= - $40,000 + $30,000 - $12,200

= - $22,200

negative sign indicates loss

b) business wages = $30,000

net loss = $40,000

business loss = $30,000- $40,000

= -$10,000

Non- business loss = $12,200 = standard deduction.

c) Julie's 2019 NOL ( net operating loss) is just equal to business net loss

= $30,000- $40,000 = - $10,000

Hence, we get all required answers about Julie's loss.

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The greatest common divisor(GCD) of 15 and 45 is 15.

The greatest common divisor (GCD) of two or more integers, where at least one of them is not zero, is the largest positive integer that is a divisor of both numbers. For example, the GCD of 8 and 12 equals 4.

In the divisibility preorder relation, the GCD of a and b is their greatest positive common divisor. This signifies that a and b's common divisors are the same as their GCD divisors. The Euclidean algorithm or Euclid's lemma are widely used to establish this. This is the definition of "greatest" in the context of GCD generalizations.

Foe calculating the GCD of 15 and 45, we have to find the factors of 15 and 45.

Factors of 15:

1, 3, 5, 15

Factors of 45:

1, 3, 5, 9, 15, 45

From all these factors we have to choose the greatest factor that is exactly divisible by both 15 and 45,

So, the greatest factor is 15

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The length of the RS is 25 units, using SAS Congruence.

What is SAS Congruence?

Congruent refers to figures that are equal in all respects, particularly in terms of size and shape. Congruence is a mathematical concept that describes the relationship between two congruent figures. The relationship between two congruent figures is referred to as congruence. Let's now talk about the triangle SAS congruence. The phrase SAS congruence often referred to as Side Angle Side congruence, is used to define the relationship between two congruent figures. To fully grasp the significance of SAS, let's talk in-depth about the triangle SAS congruence.

We have specified that TQ is 18 units in length.

TQ = RT as a result,

and 2x + 10 = 18

2x = 18 - 10

2x = 8x2 = 4 units.

Now that both triangles satisfy the Right Angled Hypotenuse Side criteria or SAS concurrency criteria,

RS = QS.

= 9x - 11

= 9(4) - 11

= 25 units.

Hence, the length of the RS is 25 units, using SAS Congruence.

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After 34 hours, there are approximately 29 bacteria(to the nearest hundred) in the culture.

Combining two or more bacterium streptococcus to create a new number is the mathematical action known as multiplication. It is frequently represented by the letter "x" or an asterisk (*), and is also referred to as the "times" operation. Since multiplication may be regarded of as a shortcut for repeatedly adding a number to itself, it is closely connected to addition. For instance, multiplying two by three is identical to adding two plus two plus two, which equals six. Division and multiplication are connected because dividing one number by another is equivalent to multiplying the first number by the reciprocal of the second number. For example, 3 x 1/2 is equivalent to dividing 3 by 2, which equals 1.5.

How to solve?

N(t) = N0 * 2^(t/tau)

N(34) = 9 * 2^(34/1.6) = 9 * 2^(21.25)

To round this number to the nearest whole number, we can first calculate 2^(21.25) and then multiply it by 9. Since 2^(21.25) is approximately 3.2, the final answer is approximately 29. This means that after 34 hours, there are approximately 29 bacteria in the culture.

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Using compound interest formula [tex]A = p(1 +\frac{r}{n} )^{nt}[/tex], the amount Erica owed is $8,551.56.

The amount Erica owes for 6 years if 5300 dollars is loaned to her at the rate of 8% compounded monthly can be computed as follow:

Therefore, it is compounded 12 times.

[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]

where

Therefore,

p = 5300 dollars

t = 6 years

n = 12

r = 8%

Therefore,

[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]

[tex]A = 5300(1+ \frac{0.08}{12} )^{(12)(6)}[/tex]

A = 5,300(1 + 0.0066666666666667)⁷²

Therefore,

A = $8,551.56

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The answer of the equation 8(x-3) +7=2x(4-17) is x=1/2.

An equation is a statement that says that the value of two mathematical expressions is equal i.e., it is a mathematical sentence that has two equal sides separated by an equal sign.

We have the equation : 8(x-3) +7=2x(4-17)

Here we are not given Lin's solution so we can not find the error in her solution but we will solve this equation and find the value of x.

            8(x-3) +7= 2x (4-17)    

      ⇒  8x - 24 +7 = 2x(-13)

      ⇒  8x -17= -26x

      ⇒  34x = 17

      ⇒  x= 17/34

      ⇒ x =1/2.

The solution of the above equation is x= 1/2.

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Each base angle 72 degrees  is the measure of the vertex angle of an isosceles triangle if the measure of the base angle is 36

For any triangle, the three angles always add to 180 degrees.

In an isosceles triangle, the base angles are the same measure. For now we don't know what they are, so let's call them x. The vertex angle is 36.

Adding the three angles (x, x, and 36) and setting that equal to 180 will help us find the value of x.

x+x+36 = 180

2x+36 = 180

2x+36-36 = 180-36 .... subtract 36 from both sides

2x = 144

2x/2 = 144/2 .... divide both sides by 2

x = 72

This triangle has two base angles of 72 each and the vertex angle of 36. As a check, the three angles should add up to 180

72+72+36 = 144+36 = 180

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Answer:

68 degrees

Step-by-step explanation:

We are given measurements of JFG and GFL already! Because of this, angle JFL will just be the sum of those two

36 + 32 =

68 degrees

So, JFL has a measure of 68 degrees

Answer: 68degrees

Step-by-step explanation:

Add both of the other angle measures to get angle JFL

To simplify the process of expanding a binomial of the type (a+b) n (a + b) n, use Pascal's triangle. The same numbered row in Pascal's triangle will match the power of n that the binomial is being raised to.

A triangular array of binomial coefficients known as Pascal's triangle can be found in algebra, combinatorics, and probability theory. Even though other mathematicians studied it centuries before him in India, Persia, China, Germany, and Italy, it is called after the French mathematician Blaise Pascal in a large portion of the Western world. Traditionally, the rows of Pascal's triangle are listed from row =0 at the top (the 0th row). Each row's entries are numbered starting at k=0 on the left and are often staggered in relation to the numbers in the next rows. The triangle could be created in the manner shown below: The top row of the table, row 0, contains one unique nonzero entry.

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(i) The lower end of the confidence interval is

22.8 - 0.80 = 22

and, The upper end of the confidence interval is

22.8 + 0.80 = 23.6

ii) Error bound is the same as the margin of error

Error bound = 0.8

This is incomplete question:

Complete question is :

Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. it randomly surveys 175 people. the sample mean is 23.1 hours. there is a known population standard deviation of 6.0 hours. the population distribution is assumed to be normal. note: if you are using a student's t-distribution, you may assume that the underlying population is normally distributed. (in general, you must first prove that assumption, though.)

Construct a 90% confidence interval for the population mean time to complete the tax forms.

i. State the confidence interval. (Round your answers to two decimal places.)

ii. Calculate the error bound. (Round your answer to two decimal places.

Now, According to the question:

Considering the central limit theorem, the distribution is normal since the number of samples is large. Also, the population standard

deviation is known. We would determine the z score.

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.90 = 0.1

α/2 = 0.1/2 = 0.05

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.05 = 0.95

The z score corresponding to the area on the z table is 2.05. Thus, confidence level of 90% is 1.645

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Confidence interval = mean ± z × σ/√n

Where

σ = population standard Deviation

Confidence interval = x ± z × σ/√n

x = 22.8 hours

σ = 6.4 hours

n = 175

i) Confidence interval = 22.8 ± 1.645 × 6.4/√175

= 22.8 ± 0.80

The lower end of the confidence interval is

22.8 - 0.80 = 22

The upper end of the confidence interval is

22.8 + 0.80 = 23.6

ii) Error bound is the same as the margin of error

Error bound = 0.8

Hence,(i) The lower end of the confidence interval is

22.8 - 0.80 = 22

and, The upper end of the confidence interval is

22.8 + 0.80 = 23.6

ii) Error bound is the same as the margin of error

Error bound = 0.8

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Answer: ?

Step-by-step explanation: Is that the whole question? I don't really understand the question.