use the unique factorization of integers theorem to prove the following statement. if n is any positive integer that is not a perfect square, then n is irrational. the following is a proposed proof by contradiction of the statement with at least one incorrect step. suppose not. suppose there exists an integer n such that n is not a perfect square and n is rational. by definition of rational number, there exist integers a and b such that n

Answer: p = - 6y - 2x + 8

Step-by-step explanation:

p = 2l + 2w

p = 2(4+5y-3x) + 2(2x - 8y​)

p = 8 + 10y - 6x + 4x- 16y

p = - 6y - 2x + 8

Answer:

P=-2x-6y+8 i believe

Step-by-step explanation:

P= 2(4+5y-3x) + 2(2x-8y)

P= 8+10y-6x +4x-16y

=8+10y+−6x+4x+−16y

=(−6x+4x)+(10y+−16y)+(8)

=−2x−6y+8

Answer:

Graph B represents an increasing function

Step-by-step explanation:

If you look at the other graphs, they are either stagnant on one line or going downwards.

Graph B, on the other hand, is growing on both the x and y axis.

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The probability of at least one appearance in a 21-alternate period is 0.969803

(a) The appearance  rate is 10 passengers nanosecond , so the anticipated number of advents  in nanosecond is also 10. The probability of no advents  in one minute is given by the Poisson distribution with parameter lambda = 10:

P(X = 0) = \(e^{(-lambda)}\) \(lambda^{0}\) / 0! =  \(e^{(-10)}\)* \(10^{0}\) / 1! = 0.000045 (rounded to 6 decimal places)

Therefore, the probability of no arrivals in one-minute period is 0.000045.

(b) To compute the probability that three or fewer passengers arrive in one-minute period, we can use the cumulative distribution function (CDF) of the Poisson distribution:

P(X <= 3) = sum from i=0 to 3 of P(X = i)

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= \(e^{-10}\) *\(10^{0}\) / 0! + \(e^{(-10)}\) * \(10^{1}\)/ 1! + \(e^{(-10)}\) * \(10^{2}\) / 2! + \(e^{(-10) }\)* \(10^{3}\)/ 3!

= 0.010336 (rounded to 6 decimal places)

Therefore, the probability that three or fewer passengers arrive in one-minute period is 0.010336.

(c) The arrival rate is 10 passengers per minute, which is equivalent to 10/60 = 1/6 passengers per second. Therefore, the expected number of arrivals in a 21-second period is (1/6) * 21 = 3.5 passengers. The probability of no arrivals in a 21-second period is given by the Poisson distribution with parameter lambda = 3.5:

P(X = 0) = \(e^{(-lambda)}\) * l\(lambda^{0}\) / 0! = \(e^{(-3.5)}\) * \(3.5^{0}\)/ 1! = 0.030197 (rounded to 6 decimal places)

Therefore, the probability of no arrivals in a 21-second period is 0.030197.

(d) The probability of at least one arrival in a 21-second period is equal to 1 minus the probability of no arrivals:

P(at least one arrival) = 1 - P(no arrivals)

= 1 - 0.030197

= 0.969803 (rounded to 6 decimal places)

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Answer:

x=3.25

Step-by-step explanation:

To solve this you would have to distribute the 3 to both numbers in the parenthesis and then you'd combine like terms. Once you combine like terms it'll be a bit easier to solve. When I distributed and combined like terms I got 3x-12-10=4-11x and then I solved and got x=3.25

Not sure if this is how your supposed to solve this problem for your assignment but for us it's usually like this...if it happens to be wrong then I'm sorry.

Using logical reasoning, we can conclude that the costumes of 6 friends are:

So, We know:

So, the conclusions can be:

Therefore, using logical reasoning, we can conclude the costumes of 6 friends are:

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not the correct answer

Step-by-step explanation:

325:5 et 195:5

65 et 39

maybe xd ad something else please

The evergreen tree grew 2.4 feet taller the next year.

Percentage can be derived by dividing the given value by the total value, and then multiplying the result by 100.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

It is given by:

Percentage = (given value / total value) * 100%

From the question, the tree has a base height of 20m, if it grew 20% taller then;

tree height = 12 x (20/100)

tree height = 12 x 0.2

tree height = 2.4

Therefore, the tree grew 2.4 feet taller the next year.

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Using proportions, it is found that the measure of the inscribed angle B is of 30º.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In a circle, the inscribed angle is half the measure of the outside angle. Hence, in this problem, the measure of angle B is of 50% of 60º, hence:

m<B = 0.5 x 60º = 30º.

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Answer:

Using proportions, it is found that the measure of the inscribed angle B is of 30º.

Step-by-step explanation:

When using the `foreach` function, the signs of the first and second derivatives of the function appear to be negative over the given interval. What is the `foreach` function?The `foreach` function in PHP is utilized for iterating over arrays or objects. The `foreach` function works by stepping through each value of an array, and one iteration can be done for each of the array's elements, which can include key-value pairs. It is mainly utilized to execute a block of code for each element of an array.What is a derivative?A derivative is a calculus concept that refers to the slope of a function at a certain point. It is usually the rate at which a function's value changes as its input variable changes. Derivatives are widely utilized in many fields, including physics, engineering, and economics.How to determine the signs of the first and second derivative?We can determine the signs of the first and second derivative by finding the derivative of the given function f(x). Once we find the derivative of the function, we can put the values in a table like the following:X    1   1.1   1.2   1.3   1.4   1.5f(x) 7.1 6.1 5.0 3.8 2.5 1.1 We can calculate the first derivative of f(x) by the following formula:f'(x) = f(x + 1) - f(x)We can calculate the second derivative of f(x) by the following formula:f"(x) = f'(x + 1) - f'(x)Based on the table above, we can determine that the signs of the first and second derivatives of the function are negative over the given interval.

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The signs of the first derivative of the function F(x) over the given interval are not consistent, so it is difficult to determine whether it appears to be positive or negative.

The first derivative of a function represents the rate of change of the function at a given point, while the second derivative represents the curvature or concavity of the function at that point.

To determine the signs of the first derivative of F(x) over the given interval, we need to find the slope of the tangent line at each point. We can do this by calculating the difference between consecutive y-values and dividing by the corresponding difference in x-values.

For example, the slope between (1, 7.1) and (1.1, 6.1) is (6.1 - 7.1)/(1.1 - 1) = -1, which indicates a negative slope. However, the slope between (1.2, 5.0) and (1.3, 3.8) is (3.8 - 5.0)/(1.3 - 1.2) = -12, which indicates a much steeper negative slope.

We can repeat this process for each pair of consecutive points to find the sign of the first derivative at each point. However, since the signs of the slopes are not consistent over the given interval, we cannot determine whether the first derivative appears to be positive or negative.

In other words, the function may be increasing or decreasing at different rates over different portions of the interval, which makes it difficult to make a general statement about the sign of the first derivative.

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Answer:

Uhm i think its ABD weeweee

Step-by-step explanation:

Because monkeys wooowooo not weewee so the commentary would be weeeweee

Jeff needs to start watering at 8:57 a.m. to be ready to leave for swim practice at 9:50 a.m.

Let's start by calculating the total watering time as follows -

5 locations * 25 minutes each = 125 minutes of watering time

4 locations * 2 minutes each for changing the sprinkler = 8 minutes for changing the sprinkler.

Hence, total time = 125 minutes + 8 minutes = 133 minutes

So, Jeff needs 133 minutes for watering the garden. The latest time he should start is 9:50 a.m. - 133 minutes = 9:50 a.m. - 2 hrs 13 minutes = 8:57 a.m.

Therefore, Jeff needs to start watering around 8:57 a.m. to be ready to leave for swim practice at 9:50 a.m.

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The sequence \(an=6ne^{(-5n)}\) is decreasing and bounded.

To determine whether the sequence \(an=6ne^{(-5n)}\)  is increasing, decreasing, or not monotonic and whether it is bounded or not, follow these steps:

1. Analyze the sequence's formula:
[tex]an=6ne^{(-5n)}\) can be rewritten as \(an=6n \frac{1}{e^{(5n)} }\)

2. Examine the factors in the formula:
The first factor, 6n, is increasing as n increases. The second factor, \(\frac{1}{e^{5n} }\), is decreasing as n increases since the exponent in the denominator is increasing, causing the overall value to decrease.

3. Determine the overall trend of the sequence:
The sequence an is a product of an increasing factor and a decreasing factor. To determine the overall trend, we can examine the limit of the sequence as n approaches infinity.

4. Calculate the limit:
As n approaches infinity, the decreasing factor \(\frac{1}{e^{5n} }\) dominates the sequence, causing the limit of the sequence to approach 0. This indicates that the sequence is decreasing.

5. Determine if the sequence is bounded:
Since the sequence is decreasing and approaches 0 as n approaches infinity, it has a lower bound of 0. Additionally, the sequence is positive for all values of n, so it is also upper-bounded. Therefore, the sequence is bounded.

The sequence \(an=6ne^{(-5n)}\) is decreasing and bounded.

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Answer:

81 and 9 is the answer I got hope it helps

The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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Answer:

  (c)  20

Step-by-step explanation:

You want to find x, given that the external angle adjacent to a base angle of an isosceles triangle is (5x +12)°, and the other base angle is marked (3x +8)°.

The base angles of an isosceles triangle are congruent, so the other base angle is congruent to the marked base angle.

The external angle and the adjacent base angle are a linear pair, hence supplementary.

  (5x +12)° +(3x +8)° = 180°

  8x +20 = 180 . . . . . . . divide by °, collect terms

  8x = 160 . . . . . . subtract 20

  x = 20 . . . . . divide by 8

At 2:27pm, between 2 pm to 3 pm is the first right angle formed by hands of the clock.

Total degree in a click which is shaped like a circle: 360°

The number of degrees a minute hand will cover- 360 / 60 = 6°

The minutes the hands cover when right angle 90/ 6 = 15

This means when the hands are at a ninety-degree angle they are  15 minutes apart.

The number of degrees covered by the hour hand in an hour:

= 360 / 12

= 30°

The number of degrees covered by the hour hand in a minute:

= 360 / 12 × 60

= 0.5°

We have to start at 2:00, the time when the minute hand is at 0 degrees and the hour hand is at (360)*2/12 = 60 degrees.

We must find the time T it takes for the hour hand of the clock to move to an angle A(hour) at the same time that the minute hand is at an angle of

A(hour) + 90.

The minute hand rotates at 360 degree per hour

= (360 degree)/60 minutes

= 6 degree/minute

=0.1 s

The hour hand moves at 1/12th the speed of the second hand, so its rotational rate is

= 0.5 degrees/minute.

= 0.0083 degree/second)

So the angle A(minute) of the minute hand at any time t [ sec] will be A(m)

= 0.1 t.

The angle of the hour hand will be A(hour) = 60 + 0.0083 t.

60 degrees is added as the hour hand has a “head start” of 60 degrees at 2:00.

Now the task is to find the time t at which

A(m) = A(h) + 90

0.1 t = 60 + 0.0083 t + 90

This solves to give us the answer

= 1635.8 s  

=27.26 m

= 27 min 15.6 sec

So the hour and minute hands will form a right angle at 2:27 pm

(2 hours 27 minutes 15.6 seconds)

Therefore the correct answer is 2:27 pm.

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The Ruler Postulate (Axiom M-2) states that for any line l and any two distinct points o and P on l, there exists a bijection c l R such that c(o) = 0 and c(P) ≠ 0. This means that we can assign a unique real number to each point on the line, with point o corresponding to 0 and point P corresponding to some other non-zero real number.

Furthermore, the postulate requires that the distance between any two points A and B on the line is equal to the absolute value of the difference between their assigned real numbers, i.e. d(A,B) = |c(A) - c(B)|. This ensures that the distance function on the line behaves consistently with the usual notion of distance in real numbers.

Overall, the Ruler Postulate provides a way to measure distances and assign coordinates to points on a line in a way that is consistent with the real numbers. The use of a bijection ensures that each point on the line corresponds to a unique real number, which is necessary for the distance function to be well-defined.

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Based on the given information, there is insufficient context to provide a clear answer.

The information provided states that there are 297 individuals living alone and mentions that the sample size is testing the hypothesis. However, crucial details, such as the original proportion (P0), the alternative hypothesis (Ha), and the observed proportion (p), are missing. These elements are necessary to conduct a hypothesis test and determine whether there is sufficient evidence to conclude a change in the proportion.

Additionally, the statement regarding "Because np0(1−P0)=10, the sample size is testing the hypothesis Satisfied" is unclear and requires further clarification.

To accurately assess whether there is sufficient evidence to conclude a change in the proportion, it is crucial to provide the missing information, such as the alternative hypothesis, observed proportion, and a clear statement of the hypothesis being tested. This will allow for a proper hypothesis test and interpretation of the results at the given significance level.

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Answer:     0

Step-by-step explanation:

Answer:

34352.0

Step-by-step explanation:

Answer:

4 < x < 36;  values that apply are 5, 16, 20, 35

Step-by-step explanation:

use triangle inequality theorem:

the sum of any two sides is greater than the third

16 + x > 20;   x > 4

16 + 20 > x;   x < 36  

The expression -4(3d - 1) + 2 (7d + 9) is simplified to 2(d + 10)

Algebraic expressions are described as expressions that are made up of terms, coefficients, variables, constants and factors.

These expressions are also composed of mathematical operations, such as;

We have the expression;

-4(3d - 1) + 2 (7d + 9)

expand the bracket

-12d + 4 + 14d + 18

collect the like terms

-12d + 14d + 4 + 18

add the like terms

2d + 20

2(d + 10)

Hence, the expression is 2(d + 10)

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Answer:

2d + 22

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The property we use,

→ Distributive property.

The expression is,

→ -4(3d - 1) + 2(7d + 9)

Let's simplify the expression,

→ -4(3d - 1) + 2(7d + 9)

→ -4(3d) -4(-1) + 2(7d) + 2(9)

→ -12d + 4 + 14d + 18

→ (-12d + 14d) + (4 + 18)

→ (2d) + (22)

→ 2d + 22

Hence, the answer is 2d + 22.

The probability that a card is a spade or a king, given that it is black is 3/26 or 0.1154 or 11.54%

In a standard deck of cards, we have the following readings

Black cards = 26

Black spade or king = 3

So, we have the probability formula to be

Probability = Black spade or king/Black cards

This gives

Probability = 3/26

Evaluate

Probability = 0.1154

Express as percentage

Probability = 11.54%

Hence, the probability that a card is a spade or a king, given that it is black is 3/26

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The length of the altitude is 10. 4 yards

The formula for the perimeter of an equilateral triangle is expressed as;

P = 3a

Where;

Substitute the values

36 = 3a

Divide the value by the coefficient  of a

a = 36/3

a = 12 yards

Using the Pythagorean theorem, we get;

12² = h² + 6²

Find the square values

144 = h² + 36

collect like terms

h² = 108

Find the square root

h = 10. 4 yards

Hence, the value is  10. 4 yards

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Answer:

m<9

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

6m−34<20

Step 2: Add 34 to both sides.

6m−34+34<20+34

6m<54

Step 3: Divide both sides by 6.

6m /6 < 54 /6

m<9

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A) The prime numbers are; 1, 3, 23

B) The two numbers divisible by 4 are; 8 and 28

C) The two odd composite numbers are; 15 and 33

D) A multiple of 9 is; 18

We are given the set of numbers as;

1,3, 8, 15, 18, 23, 28 and 33.

A) Prime numbers are numbers that are only divisible by themselves and 1. In this list they are;

1, 3, 23

B) Numbers that are divisible by 4 divide 4 without remainder. In this list they are; 8 and 28

C) Odd composite numbers are odd integers which are not prime numbers. In this list they are; 15 and 33

D) Multiple of 9 is number that is gotten by multiplying an integer with 9. The only one on the given list is 18.

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Answer:

Step-by-step explanation:

-x10−x+3=0

x≈−1.1530188,1.06806865