There are 130 people in a sports centre. 65 people use the gym 51 people use the swimming pool, 44 people use the track 15 people use the gym and the pool 14 people use the pool and the track 10 people use the gym and the track 1 person uses all 3 facilities A person is selected at random, what is the probability that this person doesn't use any facilities?

The false principle of Agile Development is D - Complexity is essential to development processes.

What is Agile Development?

Teams use the iterative agile development methodology for software development. Cross-functional, self-organized teams frequently adapt projects by analyzing the environment and user requirements.

The principle of Agile Development that is NOT correct is - "Complexity is essential to development processes".

In fact, Agile Development principles emphasize simplicity and minimizing complexity wherever possible.

This is because complexity can lead to a slower development process, difficulty in making changes, and increased risk of errors or bugs.

The other three principles listed are accurate principles of Agile Development.

Therefore, the incorrect option is D.

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Answer:

\(\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}\)

Step-by-step explanation:

Given

\(\cos(\theta) = -\frac{2}{3}\)

\(\theta \to\) Quadrant III

Required

Determine \(\tan(\theta) \cdot \cot(\theta) + \csc(\theta)\)

We have:

\(\cos(\theta) = -\frac{2}{3}\)

We know that:

\(\sin^2(\theta) + \cos^2(\theta) = 1\)

This gives:

\(\sin^2(\theta) + (-\frac{2}{3})^2 = 1\)

\(\sin^2(\theta) + (\frac{4}{9}) = 1\)

Collect like terms

\(\sin^2(\theta) = 1 - \frac{4}{9}\)

Take LCM and solve

\(\sin^2(\theta) = \frac{9 -4}{9}\)

\(\sin^2(\theta) = \frac{5}{9}\)

Take the square roots of both sides

\(\sin(\theta) = \±\frac{\sqrt 5}{3}\)

Sin is negative in quadrant III. So:

\(\sin(\theta) = -\frac{\sqrt 5}{3}\)

Calculate \(\csc(\theta)\)

\(\csc(\theta) = \frac{1}{\sin(\theta)}\)

We have: \(\sin(\theta) = -\frac{\sqrt 5}{3}\)

So:

\(\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}\)

\(\csc(\theta) = \frac{-3}{\sqrt 5}\)

Rationalize

\(\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}\)

\(\csc(\theta) = \frac{-3\sqrt 5}{5}\)

So, we have:

\(\tan(\theta) \cdot \cot(\theta) + \csc(\theta)\)

\(\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \tan(\theta) \cdot \frac{1}{\tan(\theta)} + \csc(\theta)\)

\(\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 + \csc(\theta)\)

Substitute: \(\csc(\theta) = \frac{-3\sqrt 5}{5}\)

\(\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 -\frac{3\sqrt 5}{5}\)

Take LCM

\(\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}\)

Answer:

Step-by-step explanation:

Answer:

1: is in the million

6: is in the hundred thousand

7: is in the ten thousand

5: is in the thousand

8: is in the hundred

9: is in the ten

2:is in the one

Answer:

\(\huge\boxed{\sf 11.74\ in.\²}\)

Step-by-step explanation:

Area of Rectangle:

Length = 11.8 in.

Width = 3.6 in.

Area = Length * Width

Area = 11.8 * 3.6

Area = 42.48 in.²

Area of 3 circles:

Diameter = 3.6 in.

Radius = D/2 = 3.6/2 = 1.8 in.

\(\sf Area = \pi r^2\\\\Area = (3.14)(1.8)^2\\\\Area = (3.14)(3.24)\\\\Area = 10.18\ in.^2\)

Area of 3 circles = 3(10.18) = 30.5 in.²

Area of the figure when the 3 circles are cut:

= Area of the rectangle - Area of 3 circles

= 42.28 - 30.5

= 11.74 in.²

\(\rule[225]{225}{2}\)

Hope this helped!

Solution of the equation x² -11x -5 =0 using quadratic formula is equal to x = (11 ±√141)/ 2 .

As given in the question,

Given equation is equal to

x² -11x -5 =0

Solving the given equation using quadratic formula we get,

Standard quadratic equation is

ax² + bx + c =0

D = √b² -4ac

D >0 two distinct roots.

Roots given by:

x = ( -b ± √b² -4ac) /2a

Here a = 1 , b= -11, c= -5

D = √ (-11)² -4(1)(-5)

   = √121+20

   =√141 >0

Two distinct roots.

x = (-(-11) ± √141) /2(1)

  = (11 ±√141) /2

Therefore, Solution of the equation x² -11x -5 =0 using quadratic formula is equal to x = (11 ±√141)/ 2 .

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Using the Pigeonhole Principle, it can be shown that in a set of n positive integers, none exceeding 2n, there is at least one integer that divides another integer.

We can prove this statement by contradiction using the Pigeonhole Principle.

Suppose we have a set of n positive integers, none of which exceed 2n, and assume that no integer in the set divides another integer.

Consider the prime factorization of each integer in the set. Since each integer is at most 2n, the largest prime factor in the prime factorization of any integer is at most 2n.

Now, let's consider the possible prime factors of the integers in the set. There are only n possible prime factors, namely 2, 3, 5, ..., and 2n (the largest prime factor).

By the Pigeonhole Principle, if we have n+1 distinct integers, and we distribute them into n pigeonholes (corresponding to the n possible prime factors), at least two integers must share the same pigeonhole (prime factor).

This means that there exist two integers in the set with the same prime factor. Let's call these integers a and b, where a ≠ b. Since they have the same prime factor, one integer must divide the other.

This contradicts our initial assumption that no integer in the set divides another integer.

Therefore, our assumption must be false, and there must be at least one integer in the set that divides another integer.

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After finding the value of x, we need to substitute the value of x in either of the two equations to find the value of y. Finally, we get two solutions (10, 98) and (-3, 8).

Given the system of equations:y = x² - 3x - 2 ..............(1)

y = 4x + 28 ..............(2)

We need to solve this system of equations. Equate equation 1 and equation 2 so as to find the value of x.

x² - 3x - 2 = 4x + 28

Simplify and solve for x: x² - 7x - 30 = 0

(x - 10)(x + 3) = 0

x = 10

or x = -3

Substitute the value of x in either of the two equations to find the value of y. If x = 10:

y = x² - 3x - 2

= 10² - 3(10) - 2

= 98

Therefore, the solution is (10, 98). If x = -3:

y = x² - 3x - 2

= (-3)² - 3(-3) - 2

= 8

Therefore, the solution is (-3, 8).

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Answer:

54 degrees

Step-by-step explanation:

First, I need to find the value of t.

So, I create an equation. Angle BPK is a right angle, so I can just add the two inner angles and set it equal to 90.

(8t + 6) + (3t + 18) = 90

Now, just solve for t.

11t + 24 = 90

11t = 66

t = 6

Finally, substitute 6 in for t.

8(6) + 6

48 + 6

54

Answer:

3/5

7/13

10/7

Step-by-step explanation:

all of these are greater than 1/2

The measure of each angle formed by the three support beams for a bridge is 45 degrees.

The question states that three support beams for a bridge form a pair of complementary angles. Complementary angles are two angles that add up to 90 degrees.

Let's denote the angles as Angle A and Angle B. Since the angles are complementary, we can set up the following equation:

Angle A + Angle B = 90 degrees.

To find the measure of each angle, we need to divide 90 degrees by 2 since there are two angles.

Angle A = Angle B = 90 degrees / 2 = 45 degrees.

Therefore, each angle measures 45 degrees.

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The measure of each angle is 45 degrees.

To find the measure of each angle, we need to understand what complementary angles are. Complementary angles are two angles that add up to 90 degrees.

In this case, we have three support beams for a bridge that form a pair of complementary angles. Since the angles are complementary, their sum is 90 degrees.

Let's assume the measure of one angle is x degrees. The other angle will be (90 - x) degrees, as their sum is 90 degrees.

Since the three support beams form a pair of complementary angles, we can set up the equation:

x + (90 - x) = 90

By simplifying the equation, we have:

90 - x + x = 90

90 = 90

This equation is true for any value of x. Therefore, the measure of each angle can be any value, as long as their sum is 90 degrees.

So, the measure of each angle is not fixed, but it will always add up to 90 degrees.

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Answer:

Linda deposited $2500

Step-by-step explanation:

A, the measures of variation would all be 0. This is because variation measures the differences or spread of values within a dataset. If there is no mercury present in the tuna sushi, then all the values would be the same, resulting in no variation and all measures of variation would be 0.

that since there is no difference or spread in the data, it is not possible to calculate the range, variance, or standard deviation, which are the measures of variation. Therefore, the correct answer is option A.

In conclusion, if the tuna sushi contained no mercury, the measures of variation would all be 0, as there would be no variation in the data.

The measures of variation describe the dispersion or spread of a dataset. If the tuna sushi contained no mercury, that means there is no variation in mercury content. In this case, all data points would be the same (0 mercury), resulting in no dispersion or spread.

If tuna sushi had no mercury content, the measures of variation would be 0, indicating no dispersion in the data.

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Answer:

3

Step-by-step explanation:

The actual prime factors of 60 are 2, 3, and 5.

Answer:

3

Step-by-step explanation:

prime fatorizations are 2, 3, and 5

Answer: z > 14

Step-by-step explanation:

Move 3 to the right

Ebony’s bank balance is $400 was Day 8 and this can be explained below.

Jade cannot be true because for every transaction made during withdraws, a little amount of money is collected and as such the amount will never remain $400.

Note that the scenario for the above to occur is:

On day 4, her balance = $400

On day 5, her balance = $40

On day 6, her balance = $400

On day 7, her balance = $400

On day 8, her balance = $400

Another fact is that since she deposited 400 at first, on day 8, there will be a 0 increase so the amount will still be 400.

Therefore, if the above is the case, one can deduce the fact that her balance will still be $400.

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Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

Answer:

y=2/3x-3

Step-by-step explanation:

first, you have to isolate the y, so subtract 2x from both sides. -3y=-2x+9

Next, we must divide all sides by -3, so y=-2/-3x-3

Finally, simplify the equation to y=2/3x-3

Answer:

y=mx+b

y=2/3x + -3

2/3 is the slope  points are (0,-3)

Step-by-step explanation:

2x-3y =9

subtract 2x from each side leaving it -3y = -2x +9

now divide both sides by -3                 -3y/-3=-2x/-3 +9/-3

                                                                      y= 2/3+ -3

Considering the equation f(x, y) = y⁴/x, the directional derivative of f in the direction of u at the point p(1,3) is -183/39.

At the point p(1,3), the equation is calculated to determine the directional derivative in the direction of the vector u = 1 3 2i + 5j. Therefore, the directional derivative is given by:`Duf(p) = ∇f(p) · u`

We first need to calculate the gradient of the function:`∇f(x, y) = <∂f/∂x, ∂f/∂y>`Differentiating f(x, y) partially with respect to x and y gives:```
∂f/∂x = -y⁴/x²
∂f/∂y = 4y³/x
```Therefore, the gradient of f is:`∇f(x, y) = <-y⁴/x², 4y³/x>`At the point p(1,3), the gradient of f is:`∇f(1,3) = <-81, 12>`

We need to normalize the vector u to get the unit vector in the direction of u.`||u|| = √(1² + 3² + 2² + 5²) = √39`

Therefore, the unit vector in the direction of u is:`u/||u|| = (1/√39) 3/√39 2i/√39 + 5/√39j`

Therefore, the directional derivative is:`Duf(p) = ∇f(p) · u = <-81, 12> · (1/√39) 3/√39 2i/√39 + 5/√39j`

Evaluating this expression gives:`Duf(p) = (-243 + 60)/39 = -183/39`

Therefore, the directional derivative of f in the direction of u at the point p(1,3) is -183/39.

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Answer:

a) 6x³ − 5x² − 39x + 35

b) no

Step-by-step explanation:

(2x^3 − 5) (3x² + 5x − 7)

Distribute:

3x² (2x − 5) + 5x (2x − 5) − 7 (2x − 5)

Distribute again:

6x³ − 15x² + 10x² − 25x − 14x + 35

Combine like terms:

6x³ − 5x² − 39x + 35

5x − 2 is the opposite of 2x − 5, so you would get the negative of the answer from part (a).

Answer: 1.28

Step-by-step explanation:

1. P(Z > 0.99) = 1 -Ф (0.99) = 1-0.8389 = 0.1611

2.P(Z <-0.99) = Ф(-0.99) = 0.161 (known that from [a] by symmetry)

3.P(Z <0.99) = Ф(0.99) = 0.8389

4. P(Z >0.99) = P(Z <-0.99) + P(Z > 0.99) = 2(0.1611) = 0.3222

The value z = 10.0 is out because it is too large. On comparing with the largest value, z = 3.99,

we get

5. P(Z < 10.0) > P(Z <3.99) = 1.0

6.P(Z > 10.0)<P(Z > 3.99) =10.0

7. On solving the equation

Ф(Z) = 0.9

for Z.

In Table A4, find the value of z corresponding to the probability 0.9. The  nearest value is Ф(1.28) = 0.8997. Therefore, z ≈ 1.28

The confidence interval (149.2, 206.4) can be written as ¯x ± me, where ¯x = 177.8 and me = 28.6. The sample mean (¯x) is the midpoint of the confidence interval

To express the confidence interval (149.2, 206.4) in the form of ¯x ± me, we need to calculate the sample mean (¯x) and the margin of error (me).

The sample mean (¯x) is the midpoint of the confidence interval and can be calculated by taking the average of the upper and lower bounds of the interval:

¯x = (149.2 + 206.4) / 2 = 177.8

Next, we calculate the margin of error (me) by finding the half-width of the confidence interval:

me = (206.4 - 149.2) / 2 = 28.6

Therefore, the confidence interval (149.2, 206.4) can be expressed in the form of ¯x ± me as:

¯x ± me = 177.8 ± 28.6

Hence, the confidence interval (149.2, 206.4) can be written as ¯x ± me, where ¯x = 177.8 and me = 28.6.

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The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.

In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.

The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.

Regarding the other statements:

In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.

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The product is 225.

Augmentation is an activity that addresses the fundamental thought of rehashed expansion of a similar number. The numbers that are multiplied are referred to as the factors, and the result that is produced when two or more numbers are multiplied together is referred to as the product of those numbers. Repeated addition of the same number can be made easier by using multiplication.

Given 15 x 15

the product can be done in many ways,

like add 15times 15 we get the answer,

or 15 is written as 10 + 5

so (10 + 5) x 15

10 x 15 + 5 x 15

150 + 75 = 225

Therefore, 15 x 15 is  225

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Answer:

There are 5 vowels in the English alphabet: A, E, I, O, and U. Since repetition is allowed, each letter can be any one of the 5 vowels.

The probability of the first letter being a vowel is 5/26, since there are 5 vowels out of 26 letters in total. The probability of the second letter being a vowel is also 5/26, and so on for the third and fourth letters.

Since the events of each letter being a vowel are independent, we can use the multiplication rule to find the probability of all four letters being vowels:

P(all 4 vowels) = (5/26) x (5/26) x (5/26) x (5/26) = (5/26)^4

Using a calculator, we get:

P(all 4 vowels) ≈ 0.0023

To express the answer as a percent, we multiply by 100:

P(all 4 vowels) ≈ 0.23%

Therefore, the probability that all 4 letters typed will be vowels, with repetition allowed, is approximately 0.23%.

Step-by-step explanation:

The length of the curve x = 1/3 √y (y − 3)  is 64/3.

The distance between two point along a segment of a curve is known as the arc length.

The equation of the curve is given by:

x = 1/3 √y (y − 3), 16 ≤ y ≤ 25

Length of the curve y = f(x) between point  x =a to x = b is given by:  

\(\int\limits^b_a {\sqrt{1+[f'(x)]^2} } \, dx\)

 √1 + [f′(x)]2 dx.

x = 1/3 √y (y − 3)

x = 1/3 * \(y^\frac{3}{2}\) - \(y^\frac{1}{2}\)

Let's find the first derivative of x.

dx/dy = 1/3. 3/2.  \(y^\frac{1}{2}\)- 1/2 .  \(y^\frac{1}{2}\)

dx/ dy = 1/2 ( \(y^\frac{1}{2}\) - \(y^\frac{-1}{2}\))

(dx/dy)^2= 1/4 (  \(y^\frac{1}{2}\) - \(y^\frac{-1}{2}\))^2

= 1/4(y + \(y^-^1\)-2)

1 + {f′(x)}2 = 1 + 1/4(y +\(y^-^1\)-2)

= 1/4 y + 1/4\(y^-^1\)+ 1/2

1 + {f′(x)}2= 1/4 (y + \(y^-^1\) + 2)

√[1 + {f′(x)}2] = 1/2 (  \(y^\frac{1}{2}\) +  \(y^\frac{-1}{2}\))

Length of curve  is given by:  

25

∫   \(\frac{\sqrt{y} }{2} +\frac{1}{2\sqrt{y} }\) dy

16

= \(\left \{ {{y=25} \atop {x=16}} \right.\) [\(y^\frac{3}{2}\)/3 + √y]

= [(25)3/2 /3 + √25] - [(16)3/2 /3 + √16]

= [125/3 + 5] - [64/3 + 4]

= 140/3 - 76/3

= (140 - 76)/3

= 64/3

So the length of the curve is 64/3

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The height of the tallest building is 1314 ft.

Given, Point K is the center of the river.

The tallest building is represented by WB and GR represent the other building the distance between the buildings is 625 ft the distance from point K is 1875 ft.

The architect designed the building represented by GR to be 876 ft.

Let WB be x,

Now, In triangle KRG and KBW,

KR/KB = GR/BW

(1875 - 625)/1875 = 876/x

1250/1875 = 876/x

x = 876×1875/1250

x = 1314

Hence, the height of the tallest building is 1314 ft

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\(\dfrac{9x^2}{y^2} -3x = 5 w\\\\\implies 9x^2 - 3x y^2 = 5wy^2 ~~~;[\text{Multiply both sides by}~ y^2]\\\\\implies 5wy^2 + 3xy^2 = 9x^2\\\\\implies y^2(5w +3x) = 9x^2\\\\\implies y^2 = \dfrac{9x^2}{5w +3x}\\\\\\\implies y = \pm \sqrt{\dfrac{9x^2}{5w +3x}} = \pm\dfrac{3x}{\sqrt{5w +3x}}\)

Answer:

4 packages

Step-by-step explanation:

We have to do 980/250.

So after you get that, you would get 3.92. It would not make sense to get 3.92 packages since that isn't possible on Amazon using common sense. Therefore we must round 3.92 to 4 packages.

Answer:

Ms.Dangerfeild should order 4 bags

Step-by-step explanation:

250 times 4 is 1000 so Ms.Dangerfeild will have 20 extra erasers.

Answer:

x = 46°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:

⇒ 180° - 130° = 50°

The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:

⇒ 180° - 96° = 84°

The interior angles of a triangle sum to 180°. Therefore:

⇒ 50° + 84° + x = 180°

⇒ 134° + x = 180°

⇒ 134° + x - 134° = 180° - 134°

⇒ x = 46°

Therefore, the size of angle x is 46°.