(a) Bernoulli process: ~ bin(8,p) (r) for p = 0.25, i. Draw the probability distributions (pdf) for X p=0.5, p = 0.75, in each their separate diagram. ii. Which effect does a higher value of p have on the graph, compared to a lower value? iii. You are going to flip a coin 8 times. You win if it gives you precisely 4 or precisely 5 heads, but lose otherwise. You have three coins, with Pn= P(heads) equal to respectively p₁ = 0.25, p2 = 0.5, and p3 = 0.75. Which coin gives you the highest chance of winning?

The correlation value would remain the same regardless of the units used for measuring heights and weights.

The correlation between two variables measures the strength and direction of their linear relationship. It is a dimensionless value that ranges from -1 to 1, where 1 represents a perfect positive correlation, -1 represents a perfect negative correlation, and 0 represents no correlation. The correlation value is unaffected by the choice of units used for measurements.

In this scenario, if the heights were recorded in inches and weights in pounds instead of meters and kilograms, the correlation between the two variables would not change. The correlation is determined by the pattern and strength of the relationship between the data points, not the units of measurement. The mathematical formula for calculating correlation does not involve any conversion of units. Therefore, whether the data is measured in meters and kilograms or inches and pounds, the correlation value would remain the same.

In conclusion, the correlation between heights and weights would be the same regardless of whether the measurements were made in meters and kilograms or inches and pounds. The choice of units does not alter the underlying relationship between the variables and, therefore, has no impact on the correlation value.

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Answer: ok what is it

Step-by-step explanation:

The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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To determine the distance between the buildings, we can use trigonometry and the given information. Let's consider the triangle formed by Sari, building A, and building B. The side opposite the 40° angle is the distance between the buildings that we want to find.

Using the tangent function, we can set up the following equation: tan(40°) = opposite/adjacent. tan(40°) = distance between the buildings/20 meters. To find the distance between the buildings, we rearrange the equation: distance between the buildings = 20 meters * tan(40°). Using a calculator, we can evaluate the expression: distance between the buildings ≈ 20 meters * 0.8391 ≈ 16.782 meters. Therefore, the buildings are approximately 16.782 meters apart. To determine the distance between the buildings, we can use trigonometry and the given information. Let's consider the triangle formed by Sari, building A, and building B. The side opposite the 40° angle is the distance between the buildings that we want to find.

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Answer:

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

Step-by-step explanation:

Let the equation of the given exponential function is,

y = a(b)ˣ

Graph of the given exponential function passes through (0, 2) and (-1, 6)

For a point (0, 2),

2 = a(b)⁰

a = 2

For another point (-1, 6),

6 = 2(b)⁻¹

3 = b⁻¹

b = \(\frac{1}{3}\)

Therefore, equation of the exponential function will be,

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

Answer:

x=40

Step-by-step explanation:

120=3x due to vertical angles theorem

120/3

40

x=40

Therefore , using  pigeonhole principle we get 101 students must be present to guarantee that at least three students.

According to the pigeonhole principle, which is used in discrete mathematics, some pigeonholes must contain two or more pigeons if we must fit expression N + 1 or more pigeons into N Pigeon Holes. An illustration would be if there were Kn+ 1 pigeons dispersed across n holes, where K is a positive variable, and at least K + 1 pigeons were present in each hole.

Here,

You must do the math first. Add one to the result after (n-1)/m.

Now, if you compare this question, you will see that students (pigeons) and states are holes, and given that at least three students must originate from the same state, the answer is three. Divide (n-1)/m and add 1 to the result if you looked at the previous example.

Now, if you go through the process backwards, you must first subtract 1 from the results

(it is 3-1 = 2), multiply by 50 (m = 50), which becomes

(m*2 = 100), and then add 1 again (n-1 makes 1 go to the right side, making it Plus)...

N = 101 is the result.

Therefore , the 101 students must be present to guarantee that at least three students.

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Answer:

\(2\frac{5}{8} cups = 1\frac{1}{2}\ batches\)

Step-by-step explanation:

Given

\(1\frac{3}{4} cups = 1\ batch\)

Required

Number of cups for \(1\frac{1}{2}\) batches

\(1\frac{3}{4} cups = 1\ batch\)

Multiply both sides by \(1\frac{1}{2}\)

\(1\frac{1}{2} * 1\frac{3}{4} cups = 1\ batch * 1\frac{1}{2}\)

\(1\frac{1}{2} * 1\frac{3}{4} cups = 1\frac{1}{2}\ batches\)

Express fractions as improper fractions

\(\frac{3}{2} * \frac{7}{4} cups = 1\frac{1}{2}\ batches\)

\(\frac{21}{8} cups = 1\frac{1}{2}\ batches\)

Express fraction as improper fraction

\(2\frac{5}{8} cups = 1\frac{1}{2}\ batches\)

ANSWER

EXPLANATION

We want to find the union of the two sets given:

The union of the two sets is the combined set of all numbers that are in the two sets.

Therefore, we have that:

That is the answer.

Step-by-step explanation:

1)  Total rectangle area =  W x H = 12 x 8 = 96 cm^2

 area of triangle (shaded portion) = 1/2 base * height = 1/2 * 7 x 8 = 28 cm^2

              Nonshaded portion = 96 - 28 cm^2 = 68 cm^2

          ratio shaded:nonshaded is then   28 : 68 = 7:17

2)   Look at the two middle triangles :  Height of each = 8 cm

       then reading across the diagram  height + base + height = 21 cm

            so base = 5 cm

   area of ONE triangle = 1/2 * base * height = 1/2 * 5 * 8 = 20 cm^2

        total area for FOUR of them  = 80 cm^2

Answer:

x = 62

Step-by-step explanation:

the angle between a tangent and the radius at the point of contact = 90°

then Δ PTO is right

the sum of the 3 angles in the triangle = 180° , so

x = 180 - 90 - 28 = 180 - 118 = 62

Answer:

Step-by-step explanation:

TP is a tangent to the circle at centre O

means

TP is perpendicular to TO

Then

m∠OTP = 90°

Then

OTP is a right triangle

Then

x = 90 - 28

  = 62

Answer:

i cant help u w this

Step-by-step explanation:

idk

Based on the given data, the professors' grading procedures have different variances. To determine if the difference is statistically significant at the 2% level of significance, we can use a two-sample F-test. The F-statistic is calculated by dividing the larger variance by the smaller variance. In this case, the F-statistic is 2.97. Using a critical value of 5.05, we can reject the null hypothesis that the variances are equal. Thus, the decision is that there is a statistically significant difference in the variance of the professors' grading procedures.

In statistics, variance is a measure of the spread of a distribution. When comparing two variances, we can use a two-sample F-test to determine if they are statistically different. The F-statistic is calculated by dividing the larger variance by the smaller variance. If the calculated F-value is greater than the critical value, we reject the null hypothesis that the variances are equal.

In this case, the professors' grading procedures have different variances, with Professor 1 having a larger variance than Professor 2. Using a two-sample F-test, we determined that the difference in variances is statistically significant at the 2% level of significance. This means that there is strong evidence to suggest that the professors' grading procedures differ in their spread of grades.

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There is not one particular frequency distribution that is correct, but there are frequency distributions that are less desirable than others. This statement is TRUE.

If interpreted linguistically, frequency distribution is the process of distributing frequencies. In statistics, frequency is the number of times a variable is represented by numbers or numbers. Conditions that are carried out repeatedly in the number series, frequency is also defined as frequency, frequent to rare.

Frequency distribution is a condition that describes the presence of frequency starting from symptoms that appear in the form of numbers, then distributed, divided to radiated. Presentation of numbers in this frequency designation can be in the form of tables, graphs and pictures. Until then the most frequently mentioned term appeared, namely the frequency distribution table.

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The percentage who work nights are working weekends is 82.5%

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

Nighr and weekend = 52%

Night = 63%

Using the above as a guide, we have the following:

Night wokers on weekend = 52%/63%

Evaluate

Night wokers on weekend = 82.5%

Hence, the percentage who work nights are working weekends is 82.5%

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If Station 1 (at 74, 41) is 44 km away and Station 2( at 0,43 ) is 38 km away. The required approximate location of the GPS receiver is (42, 10).

The location of the GPS receiver can be determined with the help of trilateration. Trilateration is a process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres, or triangles. If three stations (or more) are in known locations, with a known distance from the point of interest, we can determine the position of the GPS receiver with the help of trilateration.

It can be determined by the following method:

1: Plot the given stations on a coordinate plane. Stations are:

Station 1: (74, 41)

Station 2: (0, 43)

2: Calculate the distance of the GPS receiver from each station using the distance formula.

Distance Formula: The distance formula is used to find the distance between two points in the coordinate plane. The distance between points (x1,y1) and (x2,y2) is given by

d = √[(x2 - x1)² + (y2 - y1)²]

Station 1: Distance from station 1 = 44 kmSo, d1 = 44 km

Station 2: Distance from station 2 = 38 kmSo, d2 = 38 km

3: Plot the given distances as the circle on the coordinate plane.

Circle 1: Centred at (74, 41) with a radius of 44 km.

Circle 2: Centred at (0, 43) with a radius of 38 km.

4: The intersection of two circles. Circle 1 and Circle 2 intersect at point P (approx) (42, 10). So, the approximate location of the GPS receiver is (42, 10).

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Answer:

$7,507

Step-by-step explanation:

The speed of the airplane is the ratio of the distance to the time

The initial average speed of the airplane is approximately 110.8 mph

Reason:

Given parameters are;

The distance between Portland Oregon and Seattle Washington = 145 miles

The decrease in travel time when the speed is increase by 20 mph =  minutes

The initial speed of the airplane, v = Required;

Solution;

\(t = \dfrac{145}{v}\)

\(t - \dfrac{12}{60} = \dfrac{145}{v + 20}\)

Therefore;

\(\dfrac{145}{v} - \dfrac{12}{60} = \dfrac{145}{v + 20}\)

Which gives;

\(\dfrac{145}{v + 20} - \dfrac{145}{v} + \dfrac{12}{60} = 0\)

Therefore

0.2·v² + 4·v - 2,900 = 0

v ≈ ±110.8 mph

The initial average speed of the airplane, v≈ ± 110.8 mph

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Answer:

25

Step-by-step explanation:

i just know

Answer:

Step-by-step explanation:

standard form is:

Ax+By=C

for problem 2:

y= 1/2 x-8

y- 1/2 x - 8= 0

rearrange:

- 1/2x + y +8 = 0

2 (- 1/2x + y + 8) = 0

-x + 2y + 16= 0

-x + 2y = -16

leading coefficient can't be negative

so multiply everything by -1

x -2y = 16

Answer:

1 yes   no

Step-by-step explanation:

1 this is in standard form as it is  a linear form and the intercepts can be found  

2 This is not  in standard form as it is a linear equation and both the x and y intercepts cant  be found  so must be written in the form AX+BY=C

so

-x + 2y = -6

and leading coefficient cant be - so multiply by -1

so

x-2y=6

Answer:

1/32  lb per slice

Step-by-step explanation:

We want the pounds per slice, or lb/slice.

We have 0.25 lbs and 8 slices, so:  (0.25 lb/8 slices)

(0.25 lb/8 slices) = (1/8)(0.25)

(1/8)(0.25)(4/4) = 1/32 lb per slice

Check:

(8 slices)*(1/32 lb/slice) = 8/32 lb

8/32 = 1/4 lb total  YES

Answer:

3

Subtract the smaller number from the greater number.

You get -3, right?

Remeber the key rule- negative minus negative is positive.

The derivate of f(y) is -9y^6 - 33y^4 + 84y^2.

To differentiate the given function f(y), we will use the product rule and the chain rule of differentiation. Let's break down the function into two parts:

f(y) = (1 y^2 - 9 y^4) * (y + 3y^3)

Using the product rule, we can differentiate each part separately:

f'(y) = (1 y^2 - 9 y^4)' * (y + 3y^3) + (1 y^2 - 9 y^4) * (y + 3y^3)'

The derivative of the first part is:

(1 y^2 - 9 y^4)' = 2y - 36y^3

Now we need to differentiate the second part using the chain rule. Let's call the inner function u:

u = y + 3y^3

Using the power rule, the derivative of u with respect to y is:

u' = 1 + 9y^2

Now we can substitute these values back into our original equation:

f'(y) = (2y - 36y^3) * (y + 3y^3) + (1 y^2 - 9 y^4) * (1 + 9y^2)

Simplifying further:

f'(y) = 2y^2 + 6y^4 - 36y^4 - 108y^6 + y^2 + 9y^4 - 9y^6 + 81y^2

Combining like terms:

f'(y) = -9y^6 - 33y^4 + 84y^2

Therefore, the derivative of f(y) is -9y^6 - 33y^4 + 84y^2.

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Answer:A

Step-by-step explanation:I took the test already trust me

Therefore, The Coordinates of the THIRD VERTEX is:  ( 5, -3 )

        Calculate the midpoint of the given vertices:

        MidPoint = ( -5 + 5/2,  3 + 3/2 )

        MidPoint = ( 0, 3 )

        Distance = √( -5 -5 )^2 + ( 3 - 3 )^2

        Distance = √( -10 )^2  +  (0)^2

        Distance = √100

        Distance =  10

        Side Length =  10/√3

        Side Length = 10/1.7

        Side Length = 5.88

        Height = √3/2  *  Side Length

        Height  = 1.7/2  *  5.88

        Height  =  5

Since the origin lies inside the triangle, The Third Vertex will have a Positive  X-Coordinate and a Negative Y-Coordinate.

       ( x, y )

        x  =  -5 + x/2

        y   =  3 + y/2

       x  =  5

       y  = -3

        Hence, The Coordinate  of the Third Vertex is:  ( 5, -3 )

I hope this helps!

Answer:

75.72

Step-by-step explanation:

Answer:

The third side is sqrt(77)

Step-by-step explanation:

Since this is a right triangle we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

2^2 + b^2 = 9^2

4+ b^2 = 81

Subtract 4 from each side

b^2 = 81-4

b^2=77

Take the square root of each side

sqrt(b^2) = sqrt(77)

b = sqrt(77)

The third side is sqrt(77)

The person who starts Priya does not always win, but rather the outcome depends on whether the total number of players is even or odd.

Let's record the game on paper for different numbers of players and see if the person who starts always wins.

Case 1: Two Players (Priya and Jada)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Priya is the winner. The person who starts (Priya) wins.

Case 2: Three Players (Priya, Jada, and Han)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Round 3: Han says SAFE.

Priya is the winner. The person who starts (Priya) wins.

Case 3: Four Players (Priya, Jada, Han, and Diego)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Round 3: Han says SAFE.

Round 4: Diego says OUT and leaves the circle.

Priya is the winner. The person who starts (Priya) wins.

From these examples, we can see that when the number of players is even, the person who starts always wins.

To find more numbers where the person who starts always wins, let's consider some additional cases:

Case 5: Six Players (Priya, Jada, Han, Diego, Alex, and Mia)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Round 3: Han says SAFE.

Round 4: Diego says OUT and leaves the circle.

Round 5: Alex says SAFE.

Round 6: Mia says OUT and leaves the circle.

Priya is the winner. The person who starts (Priya) wins.

Case 6: Eight Players (Priya, Jada, Han, Diego, Alex, Mia, Ethan, and Lily)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Round 3: Han says SAFE.

Round 4: Diego says OUT and leaves the circle.

Round 5: Alex says SAFE.

Round 6: Mia says OUT and leaves the circle.

Round 7: Ethan says SAFE.

Round 8: Lily says OUT and leaves the circle.

Priya is the winner. The person who starts (Priya) wins.

Based on these examples, we can observe that when the number of players is a multiple of 2, the person who starts always wins. There seems to be a pattern here: if the number of players is even, the starting person wins, while if the number of players is odd, the starting person loses.

Therefore, the person who starts does not always win, but rather the outcome depends on whether the total number of players is even or odd.

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The average score of all students, calculated by taking a weighted average based on the number of students in each group, is 38. The overall performance is slightly below the group averages.

The average score of students in the first, second, and third groups are 39, 32, and 43, respectively. There are 24 students in the first group, 26 students in the second group, and 27 students in the third group.

To find the average score of all students, we need to take a weighted average of the scores in each group, with the number of students in each group as the weights.

Here's how to do it: First, we calculate the total number of students:24 + 26 + 27 = 77. Then, we calculate the total score across all students: 39*24 + 32*26 + 43*27 = 936 + 832 + 1161 = 2929

Finally, we divide the total score by the total number of students to get the average score:2929/77 = 38. The average score of all students is 38.

This means that the overall performance of all the students is slightly below the average of the scores in each group.

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Answer:

I think the answer you're looking for is 86400

Step-by-step explanation: