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Answer: The sum of rational and irrational number is always irrational...

Answer:

When both rational and irrational numbers are written in decimal form, rational numbers can be written as finite decimals and infinite recurring decimals, such as 4=4.0, 4/5=0.8, 1/3=0.33333... and irrational numbers can only be written as infinite non-recurring decimals, such as √ 2=1.414213562…………According to this point, people define irrational numbers as infinite non-recurring decimals. 2. All rational numbers can be written as the ratio of two integers; irrational numbers cannot.

(Rational number): A number that can be accurately expressed as the ratio of two integers. 　　 Such as 3, -98.11, 5.72727272..., 7/22 are all rational numbers. 　　 Integers and fractions are all rational numbers. Rational numbers can also be divided into positive rational numbers, 0 and negative rational numbers. 　　 Irrational numbers refer to infinite and non-recurring decimals such as: π 　　·The difference between irrational and rational numbers: 　　 1. When both rational and irrational numbers are written in decimal form, rational numbers can be written as finite decimals and infinite cyclic decimals. 　　 For example, 4=4.0, 4/5=0.8, 1/3=0.33333... and irrational numbers can only be written as infinite and non-cyclic decimals. 　　 For example, √2=1.414213562…………According to this point, people define irrational numbers as infinite and non-cyclic decimals. 　　2, all rational numbers can be written as the ratio of two integers; irrational numbers cannot. Based on this, some people suggested that irrational numbers should be removed from the "irrational" hat, and rational numbers should be called "comparative numbers" and irrational numbers should be called "irrational numbers". Originally, irrational numbers are not unreasonable, but people don't know much about it at first. 　　Using the main difference between rational and irrational numbers, we can prove that √2 is irrational. 　　Proof: Assume that √2 is not an irrational number, but a rational number.Since √2 is a rational number, it must be written as the ratio of two integers: √2 = p / q Since p and q do not have a common factor to be reduced, p / q can be considered to be the reduced fraction, the simplest form of fraction. Put √2 = p / q squared on both sides Get 2 = (p ^ 2)/(q ^ 2) Is 2 (q ^ 2) = p ^ 2 Since 2q ^ 2 is an even number, p must be an even number, so set p = 2m From 2 (q ^ 2) = 4 (m ^ 2) Get q ^ 2 = 2m ^ 2 Similarly, q must be an even number, let q = 2n Since p and q are both even numbers, they must have a common factor of 2, which contradicts the previous assumption that p/q is a reduced fraction. This contradiction is caused by the assumption that √2 is a rational number. Therefore √2 is an irrational number.

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Answer:

only 5

Step-by-step explanation:

The height of the building is approximately 227 feet.

In the given question, a man wants to measure the height of a nearby building. He places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building.

The total length of the building's shadow is 162 ft, and the pole casts a shadow that is 5.5 ft long. We have to determine the height of the building.The given situation can be explained with the help of a diagram.

As shown in the figure above, let AB be the building and CD be the 7 ft pole. The height of the building is represented by the line segment AE, which is to be determined. Let the length of the shadow of the pole be CD and that of the building be BD.

Therefore, the length of the total shadow will be BC or CD + BD.According to the question, the shadow of the pole is exactly covered by the shadow of the building. This implies that the two triangles AEF and CDF are similar. Hence, the corresponding sides are proportional. Therefore, we have:AE/EF = CD/DF

On substituting the values from the given data, we get:

AE/(EF + 5.5) = 7/5.5.... (1)

Similarly, we can write from the given data:

BD/DF = 162/5.5.... (2)

From equations (1) and (2), we can write:

AE/(EF + 5.5) = BD/DF => AE/(EF + 5.5) = 162/5.5.... (3)

On solving the above equation for AE, we get:

AE = (7/5.5) × (162/5.5 - 5.5)≈ 226.6 ft

Therefore, the height of the building is approximately 227 feet.

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Answer:

Step-by-step explanation:

step 1

100%/the total number = percent for one probability

100/5 = 20%

2 and 4 is even.

total even number * percent for one probability = total percent for even number

20% * 2 = 40%

therefore total even number is 40%

The probability is:

Step-by-step explanation:

Remember the formula for probability:

\(\boxed{\!\!\boxed{\bold{Probability=\frac{Favourable~outcome}{total~outcomes}\quad}}\!\!}\)

In this case, the favourable outcome (an even number) is 2, because there are only 2 even numbers in the set.

As for the total outcomes, there are 5 of them, because we have 5 numbers total.

So the probability of choosing an even number is 2/5.

Answer:

45%

Step-by-step explanation:

9/20

The formula is given by:

Where

In this case,

Therefore, the investment will be worth $584.88 after 3 years.

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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A rough estimate of the actual probability is \(0.43\), or \(43\)%.

When compared to a collection of possible occurrences that do not occur, probability may be thought of as a numerical indicator of how likely it is that an event will occur. All potential outcomes must be known as a set.

Information about the possibility that a certain thing will happen is provided by probability. For instance, meteorologists utilise weather patterns to forecast the likelihood of rain. Probability theory is utilised in epidemiology to comprehend the connection between exposures as well as the risk of health outcomes.

In three of the seven experiments, the volcano erupted once or twice throughout the course of the next half century (trial 1, 3, and 7).

Trial 1: 1 eruption

Trial 2: 0 eruptions

Trial 3: 1 eruption

Trial 4: 0 eruptions

Trial 5: 0 eruptions

Trial 6: 0 eruptions

Trial 7: 2 eruptions

Therefore, the experimental probability that the volcano will erupt in \(1\) or \(2\) of the next \(5\) decades is:

experimental probability \(=\) number of successful trials / total number of trials

experimental probability \(= 3 / 7\)

experimental probability \(= 0.4286\)

So the experimental probability is approximately \(0.43\) or \(43\)%.

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Answer:

6

Step-by-step explanation:

h=3(12/6)

Answer:

Step-by-step explanation:

?

Answer:

0.708

Step-by-step explanation:

The calculation of linear correlation coefficient r is shown below:-

Cost        Number

9                 85

2                 52

3                  55

4                  68

2                  67

5                  86

9                  83

10                 73

linear correlation coefficient r = 0.70772136

or

= 0.708

For better understanding find the spreadsheet at attached and follow some steps to reach the answer

Step 1 Put the values of cost and number

Step 2

Step 2 Go to data, select data analysis now click on Correlation and click ok

Step 3 Select the range from A2 to B9

Step 4 Then click OK to get the result

The value of the linear correlation coefficient, r, as calculated using Microsoft excel is: 0.708.

(See image attached below)

Therefore, the value of the linear correlation coefficient, r, as calculated using Microsoft excel is: 0.708.

(See image attached below)

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For finding a 95% confidence interval:

a) The sample mean is x = 16.13.

The sample standard deviation is s = 6.948.

The degrees of freedom are df = 10.

The critical value of t for a 95% confidence interval is t = 2.228.

The margin of error is ME = t × s/√n = 2.228(6.948)/√11 = 4.263.

The 95% confidence interval is x ± ME = 16.13 ± 4.263 = (11.867, 20.393).

b) The 95% confidence interval is (11.867, 20.393).

This means that we are 95% confident that the true population mean number of visits per physical therapy patient is between 11.867 and 20.393 visits.

c) This is because the confidence interval is a range of values that is likely to contain the true population mean. If many samples of the same size are taken from the same population, then about 95% of the confidence intervals from these samples will contain the true population mean.

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Answer: We have 7 quarters and 5 dimes.

Explanation

Given

• Jeff has 12 coins

• Total value: $2.25.

• He has only quarters and dimes.

Procedure

We have to build two equations in order to find the quantity of each. Considering that q represents the quarters and d the dimes, and we have 12 coins, then we can build our first equation:

Additionally, considering that we have a total value of $2.25, a dime is 0.1 dollars and a quarter is 0.25 dollars, we can build our second equation:

If we isolate the q variable in the first equation we get:

Then, we can replace that expression of q in the second equation and simplify:

Finally, we replace this value in the isolated expression of q:

Answer: 1/9 and -5

Step-by-step explanation:

To find the slope of a line that passes through two points, we can use the formula:slope = (y2 - y1) / (x2 - x1)where (x1, y1) and (x2, y2) are the two points.Using the points (5,4) and (-4,3), we have:slope = (3 - 4) / (-4 - 5)slope = -1 / -9slope = 1/9The slope of the line that passes through the points (5,4) and (-4,3) is 1/9.

The slope of a line can be found by using the formula:m = (y2 - y1) / (x2 - x1)Where (x1, y1) and (x2, y2) are the coordinates of the two points.Using the points (10,8) and (9,13), we can plug in the values and get:m = (13 - 8) / (9 - 10)m = 5 / -1m = -5So, the slope of the line that passes through the points (10,8) and (9,13) is -5.

The slope between the first two points is -1/9. This can be calculated by finding the change in y (4-3) divided by the change in x (5-(-4)), which is -1/9. The slope between the second two points is 5. This can be calculated by finding the change in y (13-8) divided by the change in x (9-10), which is 5. Therefore, the slope that passes through the given points is -1/9.

Answer:

U = 17 1/7

T = 51 3/7

S = 61 3/7

Step-by-step explanation:

Given

T+S+U=130\

T=3(U)

S= T+10 we have to find value of u

First step:

find S and T in terms of U

T is given

T = 3U

S = T +10 , using T = 3U

S = 3U+10

Using the above value in T+S+U=130

3U + 3U+10 + U = 130

=> 7U = 130-10 = 120

=> U = 120/7 = 17 1/7

T = 3U = 3*120/7 = 360/7 = 51 3/7

S = T+10 = 360/7 + 10 = (360+70)/7 = 430/7 = 61 3/7

Thus,

U = 17 1/7

T = 51 3/7

S = 61 3/7

The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.

To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.

Add the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (2/2)² = 319 + (2/2)²

x² + 2x + 1 = 320

The left-hand side of the equation can now be factored as a perfect square:

(x+1)² = 320

This is the equation in the form (x+a)²=b, where a=1 and b=320.

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The complete question is as follows:

What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?

x² + 2x = 319

Answer:

50 m²

Step-by-step explanation:

2 cm for length = 5 m. 4 cm for width = 10 m. Area = width • length. 10•5=50

Answer:

Step-by-step explanation: To find the mean of the dot plot, you will need to add all of the dots together.

For example: Above 2, there are 3 dots , so you would need to multiply 2 by three to get 6 dots above the number 2.

Do that for all of the numbers on the dot graph from 1 - 6, and you will have this equation:

1 + 6 + 18 + 20 + 15 + 12

Next, you will need to add all those numbers together and you will get 72.

Lastly, divide by how many numbers there are, and there are 6 numbers.

So, that will be 72/6 which is 12.

Your answer will be 12.

Answer:

2/3 c please give me brainliest

Step-by-step explanation:

The simplified equation is (π2 / 2) * ∫[0, ∞] (x(2x-1) * e(-x) / (Γ(x) * Γ(1 - x)) DX

a. To prove B(x+1, y) = x * B(x, y), proceed as follows.

Start with B(x+1, y) = [(x+1)! * y!] / ((x+y+2)!) (using the definition of B(x, y)).

Rewrite 1 / (x+1) to (x+y+2 - (y+1)) / (x+y+2) .

Using the formula above, express B(x+1, y) as (x+y+2) / (x+y+2) * [(x+1)! to rewrite. * y!] / ((x+y+2)!) - (y+1) / (x+y+2) * [(x+1)! * y!] / ((x+y+2) !).

Simplify the formula to (x+y+2) / (x+y+2) * B(x, y) - (y+1) / (x+y+2) * B(x, y) increase.

Simplify further to B(x, y) - (y+1) / (x+y+2) * B(x, y).

Note that B(x, y) can be expressed as (x / (x+y+1)) * B(x, y) .

Substitute this formula in the previous step to get,

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y).

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y)

= x * B(x, y)

You have now proved B(x+1, y) = x * B(x, y).

b. We wish to prove the identity Γ(2x) = ((2sin(πx))) * Γ(x) * Γ(x + 1/2).

Integrate ∫[0, ∞] (x(2x-1) * Start with dx.

Evaluating this integral using the permutation u = du is obtained.

Simplify the integral to (1/2) * Γ(x + 1/2).

Express sin(πx) as π / (Γ(x) * Γ(1 - x)).

Let the original integral be π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) * e(-x) * (1/sin( πx) Rewrite.)) DX.

Substituting the equations,

The integral, π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) *

We get * (π / (Γ(x) * Γ(1 - x)))) dx.

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The solution is, x = 0 , y = 4, solutions that this linear system of equation  have.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

Solve the following system:

{y = 4 - 3 x | (equation 1)

x + 2 y = 8 | (equation 2)

Express the system in standard form:

{3 x + y = 4 | (equation 1)

x + 2 y = 8 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x + y = 4 | (equation 1)

0 x+(5 y)/3 = 20/3 | (equation 2)

Multiply equation 2 by 3/5:

{3 x + y = 4 | (equation 1)

0 x+y = 4 | (equation 2)

Subtract equation 2 from equation 1:

{3 x+0 y = 0 | (equation 1)

0 x+y = 4 | (equation 2)

Divide equation 1 by 3:

{x+0 y = 0 | (equation 1)

0 x+y = 4 | (equation 2)

Collect results:

Answer: {x = 0 , y = 4

Hence, The solution is, x = 0 , y = 4, solutions that this linear system of equation  have.

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Complete question:

How many solutions does this linear system have?

y=-3x+4

x + 2y = 8

O

O

O

O

one solution: (8,0)

one solution: (0,8)

no solution

infinite number of solutions

Answer:

270cm

Step-by-step explanation:

20*6 + 10+20/2*10= 150+ 120 =270

Answer:

300litres

Step-by-step explanation:

capacity of water tank=1000litres

7/10 parts of tank is emptied,

so, to know the litres of water left in the tank has to be equal to 1000litres-emptied tank

let X to represent water left in the tank

X=1000litres-(7/10*1000litres)

X=1000litres-700litres

X=300litres

hence, litres of water left in the tank =300litres

since, full tank is 10/10 and you know the emptied tank has 7/10. meaning the remaining part of water is

10/10-7/10

3/10 of the tank with water

therefore, 3/10*1000litres

300litres.

We will have the following:

First, the smallest 5-digit integer with nonzero digits, none of which is repeated is:

Second, the greatest 5-digit integer with nonzero digits, none of which is repeated is:

Finally, we would have:

So, the solution is 86 420. [Option C]

According to the given statement, let's imagine that the teacher has x students.

He says that if as many students as he has now join his school, it means you add x.

Then a half as many he has, which means you add 1/2x.

Then a quarter as many he has, you add 1/4x.

Finally, if the boy also joins the school, it means you add 1 and obtain a total of 100 students.

Write this in an equation and solve for x:

The teacher has 36 students.

The critical value for a confidence level of 98% with a sample size of 32 is given as follows:

t = 2.4528.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 32 - 1 = 31 df, is t = 2.4528.

(df is one less than the sample size).

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Answer:

It is 3031.49 Inches.

Step-by-step explanation:

77 times 39.37

= 3031.49

#1

Answers are

Only this rest are not possible

#2

#3