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The critical value of z separates the rejection region from the nonrejection region while observed value of z is the value calculated for a sample statistic such as x.

A critical value of z is used when the sampling distribution is normal, or close to normal. The critical value of z refers to the point that cuts off area under graph for the standard normal distribution separating the rejection and nonrejection region of the data. The Critical value of z can indicate what probability any particular variable will have. These values are typically obtained from a table such as the standard normal distribution table. The observed value of z is a value determined for a sample statistic x. It is a test statistic for Z-tests that measures the difference between an observed statistic and its hypothesized population parameter in units of the standard deviation.

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The efficiency of slotted aloha by letting n approach infinity is 1/e and the maximum value of probability is 1/n.

Given that:

No. of nodes = (n)

The efficiency of slotted aloha by letting n approach infinity is E (p)= np(1-p)^(n-1).

By derivation,

E' (p) =  n(1-p)^(n-1) - np(n-1)(1-p)^(n-2)

E' (p) =  n(1-p)^(n-2) x [(1- p) - p(n-1)]

E' (p) =  n(1-p)^(n-2) x [1-np]

Let E'(p) =0

i.e. Either,  n(1-p)^(n-2) = 0

=> p = 1 (minima)

Or [1-np] = 0

=> p = 1/n (maxima)

So, for the value of p* = 1/n, we can maximize this expression.

When  p = 1/n, the efficiency of slotted aloha is

E(p*) = n.1/n (1-1/n)^(n-1)

E(p*) = (1-1/n)^(n-1)

E(p*) = (1-1/n)^n/(1-1/n)

Since, [tex]\lim_{n \to \infty} (1-1/n) = 1\\[/tex]

[tex]\lim_{n \to \infty} (1-1/n)^n = 1/e[/tex]

So, when n approaches infinite,

Efficiency =>  [tex]\lim_{n \to \infty} E(p*) = 1/e[/tex]

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Answer:

1. EF ≈ 22.00

2. m∠E ≈ 36.20°

3. m∠F ≈ 53.81°

Step-by-step explanation:

1. Use the trigonometric function sine.

sin(60°) = EF / 25.4

EF = 25.4 sin(60°)

EF ≈ 22.00

2. Use the inverse of the trigonometric function sine (denoted arcsin).

sin(m∠E) = 15/25.4

m∠E = arcsin(15/25.4)

m∠E ≈ 36.20°

3. Use the inverse of the trigonometric function cosine (denoted arccos).

cos(m∠F) = 15/25.4

m∠F = arccos(15/25.4)

m∠F ≈ 53.81°

Answer:

A

Step-by-step explanation:

The others involve more multiplication and addition/subtraction rather than division.

The mathematical domain of the function is 0<or = 5<or = -0.3

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

the type of behavior that is appropriate for a given person, object, or institution; the reason why something exists; a role. any formal event or gathering that is public or social. a variable connected to or reliant upon another variable: A price depends on both supply and demand.

According to the above statements:-

The mathematical domain of the functions are:-

0<or = 5<or = -0.3

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The number of movies on which Avery's songs were played is 2 times

From the question, we have the following parameters that can be used in our computation:

Songs played in commercial = $40

Songs played in movie = $140

Total earnings = $480

Number of times played on commercial = 7

The above parameters when represented as an equation is

Total earnings = Songs played in commercial * Number of times played on commercial + Songs played in movie * Number of times played in a movie

Substitute the known values in the above equation, so, we have the following representation

40 * 7 + 140 * Number of times played in a movie = 480

Evaluate the products

280 + 140 * Number of times played in a movie = 480

So, we have

Number of times played in a movie = 200/140

Evaluate

Number of times played in a movie = 2

Hence, the number of times is 2 times

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Answer:If Amy is not tardy, then she will not get a detention

Step-by-step explanation:

The graph which represents the equation f ( x ) = [ x + 1 ] is Option 4.

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = [ x + 1 ]

The function f ( x ) can be written as

y = [ x + 1 ] , where the equation f ( x ) = y

Substituting the value for x , we get

a)

when x = 0

The value of equation is

y = [ x + 1 ]

y = [ 0 + 1 ]

y = 1

So , the coordinates are ( 0 , 1 )

b)

when x = 1

The value of equation is

y = [ x + 1 ]

y = [ 1 + 1 ]

y = 2

So , the coordinates are ( 1 , 2 )

c)

when x = 2

The value of equation is

y = [ x + 1 ]

y = [ 2 + 1 ]

y = 3

So , the coordinates are ( 2 , 3 )

d)

when x = -1

The value of equation is

y = [ x + 1 ]

y = [ -1 + 1 ]

y = 0

So , the coordinates are ( -1 , 0 )

Hence ,

On plotting the points in the graph , we get the equation as y = x + 1

And the solution is Option D.

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Answer:

- 63

Step-by-step explanation:

Let's translate the sentences into expressions:

1. "product of negative 12 1/2 and 4.8" means:

      (-12 1/2)*(4.8)

    I'll simplify this by stating (-12.5)*(4.8)

2.   "three less than" means subtract 3, or

      -3

Now combine the two expressions:

   (-12.5)*(4.8) - 3

   (-60) - 3

= - 63

There are 36^10 ways  that contain only digits and lower-case letters and having the length is 10.

What is password?

A password, also known as a passcode, is private information that typically consists of a string of characters and is used to verify a user's identity.

We have to find the number of ways that contain only digits and lower-case letters and having the length is 10.

Since, there are total 10 digits from '0 to 9' and 26 lower case letters from

'a to z'.

The 10 slots in the password can be anything - digits as lower case letters.

that is,

10 + 26 = 36 options for each slot.

So, the total number of ways are, 36^10.

Hence, there are 36^10 ways  that contain only digits and lower-case letters and having the length is 10.

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Using law of sine and triangle rule, the value of n will be; 443 inches

The law of sines establishes the relationship between the sides and angles of an oblique triangle(non-right triangle). Law of sines and law of cosines in trigonometry are important rules used for "solving a triangle".

We can apply the sine rule to find the missing angle or side of any triangle using the requisite known data.

The formula is given as;

a / sin A = b / sin B = c / sin C

In this triangle NOP, we can find the value of angle P then;

∠N +  ∠O  +  ∠P = 180

57 + 55 +  ∠P = 180  :

since Sum of angles in a triangle is equal 180 degrees

∠P= 180 - 112

∠P = 68

Using law of sine;

p / sin P = n / sin N

490 / sin68 = n / sin57

n = [(490 x sin 57) / sin 68]

n = 443 inches

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Answer:

b = -3

Step-by-step explanation:

1. Rearrange Terms

-3(3 + 6b) = 36 - 3b

-3(6b + 3) = 36 - 3b

2. Distribute

-3(6b + 3) = 36 - 3b

-18b - 9  = 36 - 3b

3. Rearrange Terms

-18b - 9  = 36 - 3b

-18b - 9 = -3b + 36

4. Add 9 to both sides

-18b - 9 = -3b + 36

-18b - 9 + 9 = -3b + 36 + 9

5. Simplify

-18b - 9 + 9 = -3b + 36 + 9

-18b = -3b + 45

6. Add 3b to both sides

-18b = -3b + 45

-18b +3b = -3b + 45 + 3b

7. Simplify

-15b = 45

8. Divide both sides by the same factor

-15b = 45

[tex]\frac{-15b}{-15}[/tex] = [tex]\frac{45}{-15}[/tex]

9. Simplify

b = -3

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Answer:

WWWWWW

Step-by-step explanation:

Answer:48?

Step-by-step explanation:

I as of now am not completely sure of this is the correct answer.

Since, the average age of 33 fifth-graders is 11. the average age of 55 of their parents is 33. The average age of all of these parents and fifth graders is 24.75.

Average age of the population calculated as the arithmetic mean. Another parameter determining the average age of the population is the median age. High-level terms.

Given In the question:

Average age of 33 fifth graders is 11 years.

Average age of parents is 33 Years.

Therefore,

The sum of the ages of the fifth graders is 33 × 11,

and, the sum of the ages of the parents is 55 × 33.

Therefore, the total sum of all their ages must be 2178,

and given 33 + 55 = 88 people in total, their average age is

                                  = 2178/88

                                  = 99/4

                                  = 24.75    

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The probability that a randomly chosen death is a white person who died of diabetes is 0.024 determined using the law of total probability.

The law of total probability is a fundamental rule that connects marginal probabilities to conditional probabilities and expresses the total probability of an outcome via several distinct events. The rule states that if the probability of an event is unknown, it can be calculated using the known probabilities of several distinct events. It is given by P(A ∩ B) = P(A|B)P(B)

In order to determine the probability of an event (D) with not enough information to calculate it directly, a related event, say W can be taken and use that to calculate the probability for D.

Let the events that a person from a certain race die be denoted as:

P(W) = 0.86; P(B) = 0.12; P(A) = 0.02

Let the events that a person from a certain race dies of diabetes be denoted as:

P(D/W) = 0.0.028; P(D/B) = 0.044; P(D/A) = 0.035

Probability that a randomly chosen death is a white person who died of diabetes

P(W) x P (D/W) = 0.86 x 0.028 = 0.02408 ≈ 0.024

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Answer:

24

Step-by-step explanation:

The probability of a person guessing the right combination be

1/720.

Given, a small combination lock on a suitcase has ​wheels, each labeled with the 10 digits from 0 to 9.

we have to find the probability of a person guessing the right combination if there is no repeating of any digit.

as, we need three digit number to unlock the suitcase.

total combinations of the lock be,

10×9×8

= 720

only one combination can open the suitcase,

So, the probability of a person guessing the right combination be

1/720.

Hence, the probability of a person guessing the right combination be

1/720.

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The speed of the runner calculated by the properties of average speed is given by 33.45 feet and the upper limit is 43.45 feet in the last 3 seconds.

The first three seconds of a race saw a runner's speed rapidly grow.

The time is therefore 3 seconds.

The table provides her speed at half-second intervals.

We are aware,

Distance x Time = Speed

Similarly

Distance equals speed x time.

Δt equals 0.5 seconds

Then, the minimum distance travelled overall is equal to

0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4).

Terms are multiplied and added.

= 0.5 × 66.9

= 33.45 feet

The maximum distance travelled is equal to

0.5 (6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)

= 0.5 × 86.9

= 43.45 feet

As a result, her maximum distance in three seconds is 43.45 feet, and her maximum distance in three seconds is 33.45 feet.

Velocity is the rate at which an item's position changes as perceived from a certain point of view and as measured by a given unit of time (for example, 60 km/h northbound).

Velocity is also the direction at which an object is travelling. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that deals with the motion of bodies.

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Answer:

(65) (64)

Step-by-step explanation:

If the given point is p(x, y) and change the sign of its x coordinates and y coordinates, then the new location will be on third quadrant

The coordinates of the point p = (x, y)

In the graph, there are four quadrants.

In first quadrant the x axis value and y  axis value will be positive. In second quadrant the value of x will be negative and y will be positive. In the third quadrant the value of and y will be negative. In fourth quadrant the value of x will be positive and y will be negative

Here at first both x and y are positive and it will be on first quadrant. The the sign of the x coordinates and y coordinates will change sign. So both of them will be negative.

Therefore, the location of will be on third quadrant

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The correct answer is The standard deviation for Portfolio P is less than 25

This response is accurate because a portfolio made up of two stocks with a correlation of less than one will always have a standard deviation that is lower than the standard deviation of the stocks added in accordance with their weight in the portfolio. For example, in this scenario, both stocks have a weight of 50% and a standard deviation of 25%, so their sum will be.

The portfolio standard deviation will be smaller than 25% since (0.5*25%) + (0.5*25%) = 25%.

Therefore, the standard deviation for Portfolio P is less than 25

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Answer:

2 2/3

Step-by-step explanation:

If width i.e. x is 20 ft then the farmer will purchase the land.

Given,

width of land = x ft

length of land = ( x - 8 ) ft

Area of land =240 square feet

To determine x use formula,

Area of land =length * width

[tex]240=(x-8)*x\\\\240=x^2-8x\\\\x^2-8x-240=0\\\\x^2+12x-20x-240=0\\\\x(x+12)-20(x+12)=0\\\\(x+12)(x-20)=0\\\\x=-12\ or\ 20[/tex]

x cannot be negative.

x=20 ft

Thus, if width i.e. x is 20 ft then the farmer will purchase the land.

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Answer:

Step-by-step explanation:

$28.75

Answer:

D

Step-by-step explanation:

8 3/5 is a number greater than 8 but minor than 9

Answer:-9.9   -7 7.9 9.7

Step-by-step explanation:

Answer:

WE need to factorise (2x+4y)(2x−4y)

Given identity is (x+a)(x+b)=x

2

+(a+b)x+ab

Here x=2x,a=b=4y

Thus we have (2x+4y)(2x−4y)=(2x) 2

+(4y−4y)+(4y)(−4y)=4x2

−16y 2

Answer: 212.50

Step-by-step explanation: she has 60% or  127.5

Answer:b

Step-by-step explanation:

A+B+C=180

55+80+x=180

135+x=180

x=180-135

x=45