1
Select the correct answer.
What is the standard form of this complex number?
(2 + 2i)
(1 - 0)
OA. 0 + 21
OB. 1 - 1
Oc. o ?
OD. 1 + 1

The Pythagoras is the sum of the square of two sides is equal to the square of the longest side. Steve is 4 steps in the north.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Pedro found a treasure map that said to take 12 steps north, then 8 steps south.

Steve in relationship to where he started will be

By Pythagoras theorem

\(\rm H^2 = P^2+B^2\\\\H^2 = (0.0)^2 + (12-8)^2\\\\H^2 = 4^2\\\\H \ = 4\)

Steve is in 4 steps in the north.

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The null hypothesis can be rejected at α = 0.01 but not at α = 0.05 level of significance. Hence the correct option is option (c)Fail to reject H, at a=0.05 but reject at a =0.01.

A 95% confidence interval for the proportion of viewers of a certain reality television show who are over age 30 is (0.26, 0.35). The show's producers want to test the hypothesis H.: p=0.25 against H:p=0.25. The appropriate conclusion that the producers can draw is that they can fail to reject H, at a=0.05 but reject at a =0.01.

Hypothesis testing is a systematic procedure for selecting the best feasible hypothesis for a particular set of data. It is a decision-making method for statistical hypothesis testing of the validity of a statement regarding a population parameter.

The following are the hypothesis statements of the problem:

Hypothesis H0: p = 0.25 (Null Hypothesis)Hypothesis Ha: p ≠ 0.25 (Alternative Hypothesis)Hypothesis testing at α = 0.05 level of significance can be performed using the following formula:

Z= (p - Po) / [Po (1 - Po)/ n]Where, Po = 0.25p = (0.26+0.35)/2 = 0.305n = (Zα/2/ E)^2 = (1.96 / 0.04)^2 = 240.1Z = (0.305 - 0.25) / [0.25 (1 - 0.25)/ 240.1] = 3.18For a two-tailed test at α = 0.05, the Z critical values are Zα/2 = ±1.96.The Z value calculated (3.18) is greater than Z critical value (1.96).

Therefore, the null hypothesis can be rejected at α = 0.01 but not at α = 0.05 level of significance. Hence the correct option is option (c)Fail to reject H, at a=0.05 but reject at a =0.01.

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The number of units produced increases from 2 to 452 as the number of factory workers increases from 0 to 90, which gives;

Part A:

Part B:

Part C:

Part A:

The correlation is the relationship between variables based on statistical data.

From the given table, the difference between consecutive terms of the x and y-values are constant, therefore as the x-values increases, the corresponding y-value increases.

Change in x-values, ∆x = 10 - 0 = 20 - 10 = 30 - 20 = 10

Change in y-values, ∆y = 52 - 2 = 102 - 52 = 152 - 102 = 50

Therefore;

Part B:

Given that the rate of change of the x-values is constant, and the rate of change of the y-values is a constant, the function relating the x and y-values is a linear function, which can be found as follows;

Slope of the equation, m = ∆y/∆x

Which gives;

m = 50/10 = 5

y - 2 = 5•(x - 0)

The function that best fits the data is therefore;

Part C:

The slope of the function is the coefficient of the variable x in the equation, y = m•x + c

The y-intercept of the function is the value of the constant term, c, in the equation, y = m•x + c

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For a Poisson process with rate λ, the interarrival times between events are exponentially distributed with parameter μ = 1/λ. So, the time between the (n-1)-th and n-th event, denoted as Tn, follows an exponential distribution with parameter μ = 1/3 minutes.

Since Sn is the sum of the first n interarrival times, we have:

Sn = T1 + T2 + ... + Tn

The sum of n exponential random variables with parameter μ is a gamma random variable with shape parameter n and scale parameter μ. Therefore, Sn follows a gamma distribution with shape parameter n and scale parameter μ.

In this case, n = 10 and μ = 1/3. So, E[S10] can be calculated as:

E[S10] = n * μ = 10 * (1/3)

= 10/3 minutes.

Therefore, E[S10] = 10/3 minutes.

b. E[S4|N(1) = 3]:

Given that N(1) = 3, we know that there are 3 events in the first minute. Therefore, the time of the 4th event, S4, will be the sum of the first 3 interarrival times plus the time between the 3rd and 4th event.

Using the same reasoning as in part a, we know that the sum of the first 3 interarrival times follows a gamma distribution with shape parameter 3 and scale parameter 1/3. The time between the 3rd and 4th event, denoted as T4, follows an exponential distribution with parameter 1/3.

So, S4 = T1 + T2 + T3 + T4.

Since T1, T2, T3 are independent of T4, we can calculate E[S4|N(1) = 3] as:

E[S4|N(1) = 3] = E[T1 + T2 + T3 + T4]

= E[T1 + T2 + T3] + E[T4]

= (3/3) + (1/3)

= 4/3 minutes.

Therefore, E[S4|N(1) = 3] = 4/3 minutes.

c. Var(S10):

The variance of Sn, Var(Sn), for a Poisson process with rate λ, is given by:

Var(Sn) = n * σ^2,

where σ^2 is the variance of the interarrival times.

In this case, n = 10 and the interarrival times are exponentially distributed with parameter μ = 1/3. The variance of an exponential distribution is \(\mu^2\)So, \(\sigma^2 = \left(\frac{1}{3}\right)^2\)

= 1/9.

Substituting the values into the formula, we have:

Var(S10) = 10 * (1/9)

= 10/9.

Therefore, Var(S10) = 10/9.

d. E[N(4) − N(2)|N(1) = 3]:

Given that N(1) = 3, we know that there are 3 events in the first minute. Therefore, at time t = 2 minutes, there will be 3 - 1 = 2 events that have already occurred.

Now, we need to find the expected value of the difference in the number of events between time t = 4 minutes and t = 2 minutes, given that there were 3 events at t = 1 minute.

Since the number of events in a Poisson process follows a Poisson distribution with rate λt, where t is

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Answer:

0.79

Step-by-step explanation:

This value is the most opposite of the value above R, meaning that there is an association between the variables.

Answer:

.79

Step-by-step explanation:

Bc y not

The function The output is one more than twice the input x" is f(x) = 2x + 1.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

The given statement is "The output is one more than twice the input x"

Therefore, If 'x' is the input then the output is 2x + 1.

So, The function can be written as f(x) = 2x + 1.

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1) The wavelength of A is equal to 6.98 × \(10^{-8}\)meters

2) The wavelength of B is equal to 3.45 × \(10^{-11}\) meters

Since we know that the wavelength = speed of light / frequency

The speed of light is 3.00 × \(10^8\) meters per second.

For light sample A with a frequency of 4.30 × 10^15 Hz can be calculated as;

wavelength of A = (3.00 ×  \(10^8\)  m/s) / (4.30 × 10^15 Hz)

wavelength of A = 6.98 ×  \(10^{-8}\) meters

For light sample B with a frequency of 8.70 × \(10^18\) Hz can be calculated as;

wavelength of B = (3.00 ×  \(10^8\) m/s) / (8.70 ×\(10^18\) Hz)

wavelength of B = 3.45 ×  \(10^{-11}\)  meters

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```python

dot_product = sum(a[i] * b[i] for i in range(len(a)))```

In this program, the dot product is calculated using a generator expression inside the `sum` function.

Python program that calculates the dot product of two sequences of numbers:

```python

def dot_product(a, b):

   if len(a) != len(b):

       raise ValueError("Sequences must have the same length.")

   dot_product = 0

   for i in range(len(a)):

       dot_product += a[i] * b[i]

   return dot_product

# Example usage

a = [3.4, -5.2, 6]

b = [2.5, 1.6, -2.9]

result = dot_product(a, b)

print("Dot product:", result)

```

Output:

```

Dot product: -17.22

```

In this program, the `dot_product` function takes two sequences `a` and `b` as input. It first checks if the sequences have the same length. If they do, it initializes a variable `dot_product` to keep track of the running sum.

Then, it iterates over the indices of the sequences using a `for` loop and calculates the dot product by multiplying the corresponding elements from `a` and `b` and adding them to the `dot_product` variable.

Finally, the program demonstrates the usage of the `dot_product` function with the given example values and prints the result.

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The complete question is:

In mathematics, the dot product is the sum of the products of the corresponding entries of the two equal-length sequences of numbers. The formula to calculate dot product of two sequences of numbers a≡[a 0 ,a 1 ,a 2​ ,…,a n−1] and b=[b0,b 1,b 2,…,b n−1​] is defined as:  dot product =∑ (i=0 tp n-1)ai.bi

For example if a=[3.4,−5.2,6] and b=[2.5,1.6,−2.9] Dot product =3.4×2.5+(−5.2)×1.6+6×(−2.9)≡−17.22 Write a python program that calculates the dot product.

Answer:

No, he can only make 48 sliders with 7 pounds of ground beef.

He would need about 12 pounds to make 78 sliders

Step-by-step explanation:

A family taking a road trip vacation travels 126 miles in 3 hours.

We can calculate the constant of proportionality as:

Then, in 5 hours they would travel:

In 5 hours they would travel 210 miles.

Let's say we fit a batch of data to a least-squares regression line. Outliners are points with abnormally high residual values.

Finding the line that "fits" the scatter plot of the data points the best is the technique of linear regression. Given the value of the independent variable, this is typically used to forecast the value of the dependent variable.

Data points or observations that deviate greatly from the majority of the data due to their anomalous separation from the remainder are known as outliers. They must be taken into account since they have a significant impact on the regression line's slope.

As a result, the response is (c) Outliers can easily be detected by linear regression.

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Answer:

seventy seven( 77) hours

For the given distribution the mean is 20.74  , the variance is  1.652   and the standard deviation is 1.2853   .

In the question ,

probabilities are given ,

the mean is given by the formula,

mean = \(\sum\)x*p(x) ,

we get ,

mean = 19*0.21 + 20*0.23 + 21*0.30 + 22*0.13 + 23*0.13

= 3.99 + 4.6 + 6.3 + 2.86 + 2.99

= 20.74

For calculating the Variance we need to subtract the mean for every value x, then we square the result and multiply it by the respectively probability .

19 - 20.74 = -1.74 = (-1.74)²× 0.21 = 0.6357

20 - 20.74 = -0.74 = (-0.74)²× 0.23 = 0.1259

21 - 20.74 = 0.26 = (0.26)²× 0.30 = 0.0202

22 - 20.74 = 1.26 = (1.26)²× 0.13 = 0.2063

23 - 20.74 = 2.26 = (2.26)²× 0.13 = 0.6639

The variance = 0.6357 + 0.1259 + 0.0202 + 0.2063 + 0.6639

= 1.652

the standard deviation = √variance

= √1.652

= 1.2853

Therefore , the values are mean is 20.74  , the variance is 1.652  and standard deviation is 1.2853 .

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The range of lengths for the third piece is 3ft to 11ft.

We have to consider triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Possible range of lengths for the third piece of lumber can be calculated as follows.

The length would be:

= |4ft - 7ft|

= 3ft.

The longest length of the third piece would be the sum of the lengths of the two given pieces of lumber. So, the length would be:

= 4ft + 7ft

= 11ft.

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the general equation of the lines is

where m is the slope and b the y-intercept

• calculating the slope

where (x2,y2) is a right point from (x1,y1)

on this case (x2,y2) is (2,8) and (x1,y1) the other point

replacing

the slope is 3/2

• Calculating b

replace m and a point to solve b from the general equation. I will use the point (2,8)

• rewriting the equation

replace m and b on the general equation

Answer:

6,12,18,24,36,42,48,5,60,66,72,78,84,90,96

Step-by-step explanation:

got a friend help

Answer:

The slope is 3/2, and the y-intercept (b) is -1

Step-by-step explanation:

The slope-intercept form is y=mx+b. m is the slope and b is the y-intercept.

The given statement "The this pointer is not automatically passed to static member functions of a class." is false as static member functions can be called without creating an object of the class, and the "this" pointer is used to refer to the current instance of the class. Since no instance is required for static member functions, the "this" pointer is not applicable in this case.

In object-oriented programming, a class is a blueprint for creating objects, and member functions are functions defined within a class that can be called on objects of that class.

Static member functions, also known as class methods, are special member functions that are associated with the class itself rather than any specific object or instance of the class. They are declared using the "static" keyword.

Since static member functions do not operate on specific instances of the class, they do not have access to the "this" pointer. The "this" pointer is a hidden pointer that points to the current object instance, allowing non-static member functions to access the data members and other member functions of the object. However, static member functions do not have this pointer because they are not tied to any specific object.

Static member functions can only access static members of the class, which include static variables and other static member functions. They can be called using the class name itself, without creating an instance of the class. This is because they are not associated with any particular object but rather with the class as a whole.

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Angle A is 19 degrees.

Angle C is 90 degrees.

Side a is approximately 7.83.

Side c is approximately 34.50.

To solve the right triangle given that B = 71 degrees and b = 24, we can use the trigonometric ratios sine, cosine, and tangent.

Finding Angle A:

Angle A is the complementary angle to B in a right triangle, so we can calculate it using the equation:

A = 90 - B

Substituting the given value, we have:

A = 90 - 71

A = 19 degrees

Therefore, Angle A is 19 degrees.

Finding Angle C:

Since it is a right triangle, Angle C is always 90 degrees.

Therefore, Angle C is 90 degrees.

Finding Side a:

We can use the sine ratio to find the length of side a:

sin(A) = a / b

Rearranging the equation to solve for a, we have:

a = b * sin(A)

Substituting the given values, we have:

a = 24 * sin(19)

a ≈ 7.83

Therefore, the length of side a is approximately 7.83.

Finding Side c:

Using the Pythagorean theorem, we can find the length of side c:

c^2 = a^2 + b^2

Substituting the given values, we have:

c^2 = 7.83^2 + 24^2

c^2 ≈ 613.68 + 576

c^2 ≈ 1189.68

Taking the square root of both sides to solve for c, we have:

c ≈ √1189.68

c ≈ 34.50

Therefore, the length of side c is approximately 34.50.

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Given:-

Solution:-

\( \: \)

\( \: \)

\( \: \)

\( \: \)

Therefore , it will take her to read 1428 pages in 34 days.

\( \: \)

hope it helps! :)

Answer:

Given that the triangle with point C is the blue triangle and the triangle with the point C' is the red triangle, then to shift from the blue triangle to the red triangle, you must shift each point two units to the left and five units down, which is also T₍₋₃, ₋₅₎, by transformation notation

Step-by-step explanation:

The coordinates of the point C is (1, -1)

The coordinates of the point C' is (-2, -6)

Therefore, the translation required to shift the point C from to point C' is found as follows;

The difference between the x, and y-coordinates of the points C and C' are given as follows;

Δx, C to C' = (-2 - 1) = -3

Δy, C to C' = (-6 - (-1)) = (-6 + 1) = -5

Therefore, the the transformation from C to C' it T₍₋₃, ₋₅₎

Which can be presented as, given that the triangle with point C is the blue triangle and the triangle with the point C' is the red triangle, then to shift from the blue triangle to the red triangle, you must shift each point two units to the left and five units down.

Answer:

the answer is b

Step-by-step explanation:

Answer:

is really is B

:))))))))))))))))))))))))))))))))))))))))

The area of the given figure is 44 units.

Answer:

6x²5y²6 cm²

Step-by-step explanation:

(2xy3) x (4x5y6)

(2x) x (4x) = 6x²

(y) x (5y) =5y²

6x²5y²6 cm²

Answer:

£60

£150

£210

Step-by-step explanation:

2:5:7 = 14

420/14=30

Mrs Allen: 30*2=60

Mrs Broome: 30*5=150

Mr Collins: 30*7=210

Answer:

The measure of angle ∠PQS is 28.5°

Step-by-step explanation:

If a ray bisects an angle, then it divides it into two equal angles in measures and the measure of each one is half of the measure of this angle.

In our question

∵ Ray QS bisects ∠PQR  

→ That means it divides it into two angles PQS and SQR

∴ m∠PQS = m∠SQR = \(\frac{1}{2}\) m∠PQR

∵ m∠PQR = 57°

→ Multiply its measure by  \(\frac{1}{2}\) to find the measures its parts

∴ m∠PQS =  \(\frac{1}{2}\) × 57°

∴ m∠PQS = 28.5°

∴ The measure of angle ∠PQS = 28.5°