Find a 3 digit postive interger,the sum of the digits is 14, the tens digit is two more than the ones digit, and if the digits are reversed, the number is unchanged

We can identify a polynomial identity by applying algebraic identities of polynomials and principles, it is possible to prove polynomial identities by simplifying identity.

In particular, an expression must not contain any square roots of variables, any fractional or negative powers on the variables, and any variables in any fractions' denominators in order to qualify as a polynomial term. A sizable subset of algebraic expressions are polynomials. Polynomials are any expressions where the powers of the variables are all whole numbers. They frequently have a wide range of applications since they encompass such a sizable portion of all algebraic expressions.

Given,

We can identify a polynomial identity by,

Whatever the values given to the variables, the equation for the polynomial identity is always true. By applying algebraic identities of polynomials and principles, it is possible to prove polynomial identities by simplifying identity. When factorizing or extending a polynomial, we can employ polynomial identities to our advantage.

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Answer:

2

Step-by-step explanation:

he must multiply the bracket by -

If it takes 6 minutes to set up an experiment using barium-122, then  12.5g of  barium-122 will be left when the experiment begins

Half life of barium-122 = 2 min

Mass of sample = 100 g

Mass of barium remain after 6 min = ?

Number of half lives = Time elapsed / half life

Number of half lives = 6 min/ 2 min

Number of half lives = 3

At time zero = 100 g

At 1st half life = 100 g/2 = 50 g

At 2nd half life = 50 g/2 = 25 g

At 3rd half life = 25 g/2 = 12.5 g

Therefore, If it takes 6 minutes to set up an experiment using barium-122, then  12.5g of  barium-122 will be left when the experiment begins.

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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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Chi-square test for independence to determine if gender and major are independent.

Hence, Chi-square test for independence to determine if gender and major are independent.

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The parametric representation for torus is x = bcos ∅ + a cos acos ∅

y = b sin ∅ + a cos a sin ∅

z = a sin a where , 0 ≤ a ≤ 2π , 0 ≤ ∅ ≤ 2π

Parametric equation are the set of equations that express a set of quantities as explicit function of the numbers of independent variables known as parameter

Parametric representation are generally non unique so that the quantities may be expressed by the number of different parameterizations

According to the question,

The torus obtained by rotating about the z-axis the circle in the xz-plane with center (b, 0, 0) and radius a < b.

z = a sin a

y = |PQ| and x = |OP|

but , |OQ| = |OR| + |RQ| = b + a cos a

sin ∅ = |PQ| / |OQ|

So that , y = |OQ| sin ∅ = (b + a cos a ) sin ∅

Similarly ,

cos ∅ = |OP| / |OQ|

so that x =  (b + a cos a ) cos ∅

Hence , a parametric representation for a torus is

x = bcos ∅ + a cos acos ∅

y = b sin ∅ + a cos a sin ∅

z = a sin a

where , 0 ≤ a ≤ 2π , 0 ≤ ∅ ≤ 2π

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Answer: x=1

Step-by-step explanation:

Total investment in the sinking fund compounded monthly will be $277.97

What is sinking fund?

A sinking fund may be a fund that an organization could place the money into from currently on to form their debt repayments easier. the foremost common example may be a bond fund employed by corporations to manage their debt.

Main body:

total money to accumulate = $46000

time = 9 years

rate = 9%

formula for sinking fund:

Contribution = Money to accumulate * (interest / ((interest + 1)compound frequency * period - 1))

investment = 46000((9/10) ^(12*8) - )

investment to be made = $277.97

Hence contribution every month is $277.97

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A 25-meter-long towing vessel is pulling barges forward. The ship is required to display a minimum of two white masthead lights at night.

A commercial vessel that is pulling, pushing, hauling aboard, or any mixture of pulling, pressing, or hauling alongside, is referred to as a towing vessel.

Thus, a 25-meter-long towing vessel is pulling barges forward. The ship is required to display a minimum of two white masthead lights at night.

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100% humidity is very common in many coastal zones, near rivers or   lakes or in your bathroom when you take a shower, and possibly in  Alaska as well as UAE.

Relative humidity:

                             Relative humidity is the ratio of the current absolute humidity to the highest possible absolute humidity (which depends on the current air temperature). A reading of 100 % relative humidity means that the air is totally saturated with water vapor and cannot hold any more, creating the possibility of rain. This doesn't mean that the relative humidity must be 100 percent in order for it to rain — it must be 100 percent where the clouds are forming, but the relative humidity near the ground could be much less.

0% humidity means there is an absence of water vapor in the air.

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The question is from social studies

The correct statement is;-

Option d; Disability benefits for the worker and the worker's dependents are provided by the Federal Insurance

Given,

Federal Insurance;-

Federal government insurance is a type of insurance that covers all state personnel working in offices and legally authorized divisions. Taxes for social security are typically used to pay for the coverage it offers.

Contrary to many private sector health benefit plans, the Federal Employees Health Benefits (FEHB) program offers coverage without a physical examination, does not impose age or physical condition restrictions, offers a variety of health insurance plans to choose from, and cannot be terminated by the plan you enroll in.

Here,

The correct statement is;-

Option d; Disability benefits for the worker and the worker's dependents are provided by the Federal Insurance

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Answer:

a) 21.817

b) 29.93

Step-by-step explanation:

a)

solution:

By using Pythagoras theorem

AB = √(AC²-BC²)

= √(24²-10²)

= √476

= 21.817

b)

solution:

By using Pythagoras theorem

AB=√(AC²-BC²)

=√(36²-20²)

=√896

=29.93

The amount of pages the Jorge's printer can in 3/4 hours print is 72 pages.

A printer is a device that accepts text and graphic output from a computer and transfers the information to paper.

Note:

Therefore,

Make P₂ the subject of the equation

Where:

From the question,

Given:

Substitute these values into equation 2

Hence, the amount of pages it can print is 72 pages.

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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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The accident proportions differ between the two age groups is [tex]\frac{11}{100}[/tex].

We have given that,

number of clients under age of 18 = 500

number of accident = 180

Proportion of client under age of 18 =  [tex]\frac{180}{500}[/tex]  = [tex]\frac{18}{50}[/tex]

number of clients over age of 18 = 600

number of accidents = 150

number of clients over age of 18 = [tex]\frac{150}{600}[/tex] = [tex]\frac{15}{60}[/tex] = [tex]\frac{1}{4}[/tex]

Now we have to find proportion of difference between two age group,

[tex]\frac{18}{50}[/tex]  -  [tex]\frac{1}{4}[/tex] =  [tex]\frac{72 - 50}{200}[/tex]

          = [tex]\frac{22}{200}[/tex]

          =  [tex]\frac{11}{100}[/tex]

Therefore the difference between two age groups is  [tex]\frac{11}{100}[/tex] .

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The hourly pay before the increase for marta and khalid is 21 and 17.5.

Given:

the ratio of martas hourly pay to khalids hourly pay is 6:5 both marta and Khalid get an increase of 1.50 in their hourly pay The ratio of Martas hourly pay to Khalid hourly pay after this increase is 13:11

Let x and y be the hourly pay before increase

x/y = 6/5

x = 6/5*y

x + 1.50 / y + 1.50 = 13/11

11(x+1.50) = 13(y+1.50)

11x + 16.5 = 13y + 19.5

11(6/5*y) = 13y + 19.5 - 16.5

66y/5 = 13y + 3.5

66y - 13*5y / 5 = 3.5

66y - 65y = 17.5

y = 17.5

x = 6/5*17.5

= 105/5

x = 21

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The  inequality is Amount A= 15.5 x where x>6.

What is inequality?

An inequality compares two values ​​and indicates whether one is less than, greater than, or simply not equal to the other. In mathematics, the relationship between two expressions or values ​​that are not equal  is called an inequality.

Here ,Given , Cost of 1 gift basket = $15.50

Let the no. of gift basket be 'x'

=>  x > 6

Therefore, Amount of money She will spend

=> $15.50x where x > 6

=>A = 15.5x : x > 6

Therefore the inequality is Amount A= 15.5x where x>6.

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The sequence is convergent and the sum of the geometric series is 3/2=1.5.

The geometric series was significant in the early development of calculus, is utilized throughout mathematics, and can serve as an introduction to commonly used mathematical tools such as the Taylor series, complex Fourier series, and matrix exponential.

The name geometric series implies that each phrase is the geometric mean of its two nearby terms, in the same way that the word arithmetic series implies that each term.

Given the geometric series 1+1/3+1/9+1/27+...we must verify the value of its common ratio to determine whether the geometric series is convergent or divergent. The value of a geometric series common ratio is used to determine whether it is convergent or divergent.

If |r| <1, the series is convergent.

If |r| >1, the series is divergent.

The common ratio is r.

The common ratio r = (1/3)/1 = (1/9)/(1/3) = (1/27)/(1/9)=1/3 is derived from the given series.

Because r = 1/3, which is smaller than one, the series is convergent.

Because the geometric series tends to infinity, we will apply the formula for calculating a geometric series sum to infinity to get its sum.

The first term = 1

S = a/1-r

a is the first term = 1

r is the common ratio = 1/3

S = 1/1-(1/3)

S= 1/(2/3)

S= 3/2

S=1.5

The sum of the geometric series is 3/2=1.5

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The probability we use is empirical probability.

The given statement,

The relative frequency of an event is used to calculate what type of probability,

Here, we use empirical probability.

The relative frequency of an event is closely related to an empirical probability, also known as an experimental probability. Empirical probability bases its estimation of the likelihood that a specific result will recur on the number of instances of that outcome within a sample set. The chance of "event X" occurring will be determined by how many times it occurs out of 100 trials.

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By solving the given word problem, the number of multiple-choice questions is 29 and short answers is 7.

In mathematics, word problem refers to a question including mathematical information written in ordinary language and requires students to apply their math knowledge to a real-life scenario. For the given case,

Let M be the number of multiple choice questions and N be the number of short answers.

As multiple-choice questions are worth 2 points each and the short answers are worth 6 points each and there is a total of 100 points:

2M + 6N = 100

The total number of questions on the test are 36:

M + N = 36

M = 36 – N

Substituting this into the first equation:

2(36 – N) + 6N = 100

72 – 2N + 6N = 100

4N = 100 – 72

4N = 28

N = 7

Substituting N in M = 36 – N

M = 36 – 7 = 29

Note: The question is incomplete. The complete question probably is: has a math test tomorrow with both multiple choice and short answer questions the multiple choice questions are worth 2 points apiece and the short answers are worth 6 points apiece. There is a total of 100 points in a test and 36 questions. How many questions of each type are on the test?

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The meaning to translate a triangle type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Lets take an example:

ΔXYZ with coordinates,

X(-9,6) , Y(2,3) AND Z(-2,-8).

Translation:

X - 3 units in x direction

Y - 3 units in x direction

Z - 3 units in x direction

After translation:

New coordinates are represented in yellow dots in the figure uploaded.

X(-9,6)→X(-9+3,6)→X(-6,6)

Y(2,3)→Y(2+3,3)→Y(5,3)

Z(-2,-8)→Z(-2+3,-8)→Z(1,-8)

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The marginal product of the 13th worker is 10 units of output.

Given, L represent the number of workers hired by a firm, and Q represent that firm's quantity of output.

Two points on the firm's production function are

(L = 12, Q = 122) and (L = 13, Q = 132).

we have to find the marginal product of the 13th worker,

As, to find the marginal product we find the slope,

so, Marginal Product of 13th Worker = (132 - 122)/(13 - 12)

Marginal Product = 10/1

Marginal Product = 10

So, the marginal product of the 13th worker is 10 units of output.

Hence, the marginal product of the 13th worker is 10 units of output.

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The height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

Given,

In the question:

Its angle of elevation (to the peak) is 3.5 degrees.

After you drove 13 miles closer, the angle of elevation is 9 degrees.

To find the approximate height of the mountain.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.

Now, According to the question:

It is given that:

In traveling across flat land you notice a mountain directly in front of you.

Applying tan ratio:

tan3.5 = h/(15+x)

Here h is the height of the mountain and x is the distance between the base of the mountain and to the second position of the car.

h = (15 + x) tan3.5

h = x tan9

(15 + x) tan3.5 = x tan9

x = 9.44

h = 9.44 tan9

h = 1.49 miles

Hence, the height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

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The percent decrease in capacity for a 12-Volt battery which had a capacity of 30 ampere-hour aging and has dropped to a capacity of 24 ampere-hours is 20%.

It is a product of the current that is drawn from the battery while the battery is able to supply the load until its voltage is dropped to lower than a certain value for each cell.

How to calculate the percent decrease of the battery capacity?
Original capacity = 30 ampere-hour

dropped capacity = 24 ampere-hour

% decrease = (original capacity - dropped capacity) / original capacity

= (30-24) / 30

= 0.2 * 100

= 20% decrease capacity.

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If confidence level is 99%, more error would be included in null hypothesis area.

There is no difference between groups or correlation between variables, according to the null hypothesis in statistics. In a hypothesis test, it is one of two competing hypotheses regarding a population. You can reject the null hypothesis and determine that the effect is statistically significant when your sample contains enough evidence to support it.

If confidence level is 99%, is the result more reliable than confidence level 95%?

If c level is 99%, more error would be included in null hypothesis area, than level 95%. if c level is 99%, it means '99% of deviation would be regarded as in the null area anyway.

So actually, c level 99% means it's less precise than 95%, right? Rather, if confidence level is very small like 5%, so the 'c' value goes closer to μ0, it would mean that we will regard more values to be error. So it must be more precise.

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Answer:

Shirley is 28.

Step-by-step explanation:

Well, to quickly find it:

We'd have to find two numbers that fit this description.

We already know it is going to be within the late 20's and early 30's at the start.

So we start with:

28 + 3 = 31

Then to verify we add these two numbers:

31 + 28 = 59

Now applying to the descriptions,

Shirley would be three years younger Susan.

So Susan would be 31. Shirley is 28.

The standard deviation of the sampling distribution is 177

From the question, the given parameters are

Population standard deviation = 5 cm

Toy cars = 1250

Mean = 10.5

These can be represented as

σ = 5

n = 1250

μ = 10.5

The sampling standard deviation is calculated as

σₓ = σ√n

So, we have

σₓ = 5 * √1250

Evaluate

σₓ = 177

Hence, the sampling standard deviation is 177

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Answer: ?

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

If you receive 400 points when you register on the game website. For every hour you play, you gain 50 extra points. You must play for 30 hours to reach 1,000 points.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, if you sign up with the game site, you get 400 points. You earn 50 more points for each hour that you play.

We have to find the hours you have to pay to get to 1,000 points,

The point remains after signing up,

=1,000 - 400

=600

If the earning is 50 more points for each hour that you play. The number of hours required,

=600 / 50

=30

Thus, you receive 400 points when you register on the game website. For every hour you play, you gain 50 extra points. You must play for 30 hours to reach 1,000 points.

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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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