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Answer:

A and E, The first and the last

Given collinear points A, B, and M, with M dividing AB internally in the ratio of 7:5, and a point P not on the line AB, it can be shown that PM is equal to the sum of PA and PB.

Let's consider the line segment AB, where M is a point that divides it internally in the ratio of 7:5. This means that the ratio of AM to MB is 7:5.

Now, let's consider the triangle PAB, where P is a point not on the line AB. We want to show that PM is equal to the sum of PA and PB.

Since M divides AB internally in the ratio of 7:5, we can express AM and MB in terms of their lengths. Let's assume the length of AM is 7x and the length of MB is 5x.

Using this information, we can express the lengths of PA and PB in terms of x as well. Let's denote the length of PA as y and the length of PB as z.

Since M divides AB internally in the ratio of 7:5, we can write:

AM/MB = 7x/5x = 7/5

Similarly, we can express the ratios of PM to PA and PM to PB:

PM/PA = 7x/y

PM/PB = 5x/z

We need to show that PM is equal to PA + PB:

PM = PA + PB

Substituting the ratios we derived earlier:

(7x/y) = (5x/z) + 1

To simplify the equation, we can multiply both sides by yz:

7xz = 5xy + yz

Next, we can factor out the common factor of y:

7xz = y(5x + z)

Now, we can divide both sides by (5x + z):

PM = y

Therefore, we have shown that PM is equal to PA + PB.

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Answer:

1. The set of whole numbers contains the set of rational numbers.  FALSE.

The set of integers contains the set of rational numbers

2. Every terminating decimal is a rational number.       TRUE

3. Every square root is a rational number.       FALSE

Many square roots are irrational numbers, meaning there is no rational number equivalent.

4. The integers are closed under addition.      TRUE

Answer:

(Disclaimer: all digits in the answers are in the measuring unit degrees)

1) 15

2) 16

3) 46

4) 59.

Step-by-step explanation:

The first one is said to add up to 89, so you have to do 89 subtract 44 and 30 as they are told. That = 15

The second one is a right angle, meaning it adds up to 90. You do 90 - 74 as that is the value told. That = 16

Angles on a straight line = 180 so you have to do 180 - 134 as that is the value told. This = 46

This is 54 as opposing angles on two lines are =. That means this = 59 too.

(a) The parity check matrix H is:

1 1 1 0 1

0 1 0 1 1

0 1 1 0 0

To find the parity check matrix H, we can use the fact that H is the transpose of the generator matrix G with an identity matrix on the right side.

Given the generator matrix G:

1 0 0 1

1 1 1 0

1 0 1 1

0 1 0 0

1 1 0 1

We can rewrite G as:

1 0 0 1 1 1 0 0

1 1 1 0 0 1 1 0

1 0 1 1 1 0 1 1

0 1 0 0 1 1 0 0

1 1 0 1 0 1 1 1

Now, we can obtain the parity check matrix H by taking the transpose of G and removing the rightmost identity matrix:

H = Transpose(G without the rightmost identity matrix)

H =

1 1 1 0 1

0 1 0 1 1

0 1 1 0 0

Therefore, the matrix H is:

1 1 1 0 1

0 1 0 1 1

0 1 1 0 0

(b) The minimum distance of a linear block code is the smallest number of bit positions in which any two codewords differ. It determines the error detection and correction capability of the code.

To find the minimum distance of the code, we can examine the columns of the parity check matrix H. The number of non-zero entries in the smallest column gives us the minimum distance.

Looking at the parity check matrix H, we see that the smallest column has two non-zero entries in positions 1 and 2. Therefore, the minimum distance of the code is 2.

In conclusion, the minimum distance of the code is 2.

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Correction in the Question:

A wooded area is in the shape of a a trapezoid whose bases measure 128 m and 92 m and its height is 40 m. A 4 m wide walkway is constructed which runs perpendicular from the two bases. Calculate the area of the wooded area after the addition of the walkway.

Answer:

The wooded area after the addition of the walkway is 4240 [tex]m^2[/tex].

Step-by-step explanation:

we are given

length of the two bases = 128m and 92m

height of the trapezoid = 40m

the approximate figure of the given trapezoid is given as:

             __ __ __ 92 __ __ _

          /  |               |  |                 \

       /     | 40         |4|                    \

    /__ _| __ __     |  |__ __ __ __ \

                           128

Area of a trapezoid = [(a + b)/2] * height, where a and b are representing the bases of the given trapezoid.

Area = [(92 + 128)/2] * 40

        = [220/2] * 40  

        = 110 * 40

        = 4400 [tex]m^2[/tex]

Now there is a 4m wide walkway is to be constructed in that trapezoid. The pathway will be a rectangle as it has 4m width and 40m height as it is perpendicular to both the bases.  

Area of a rectangle = length * width

Area = 40 * 4

        = 160

Since the walkway will reduce the area of the trapezoid as it is constructed upon it therefore the wooded area after the addition of the walkway is

4400 + (-160) = 4240 [tex]m^2[/tex].

The sample mean of the given data series is 33.7 and the population mean is 35.86. The difference between the two quantities, rounded to two decimal places, is -2.16.

Sample mean and population mean are important terms in statistics. The sample mean is the average of a set of data taken from a larger population, while the population mean is the average of an entire population.

To find the sample mean of the given data series, we add up all the values and divide by the total number of values. Therefore,

Sample mean = (15+26+25+23+26+28+20+20+31+45+32+41+54+23+45+24+90+19+16+75+29) / 21
Sample mean = 33.7

To find the population mean, we use the same formula but with all the values of the population included. Therefore,

Population mean = (15+26+25+23+26+28+20+20+31+45+32+41+54+23+45+24+90+19+100+75+29) / 21
Population mean = 35.86

Finally, to find the difference between the two quantities, we subtract the sample mean from the population mean. Therefore,

Difference = Population mean - Sample mean
Difference = 35.86 - 33.7
Difference = -2.16 (rounded to two decimal places)

Therefore, the difference between the sample mean and population mean is -2.16.

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Answer:

it 10000

Step-by-step explanation:

79ib dlndokveik dinfl. kwbfb

Answer:

14 mm

Step-by-step explanation:

Just write down the answer.

Answer:

28mm

Step-by-step explanation:

is the right answer

In the given word problem, the rate of change is the change in the cost of the ice cream concerning the change in the number of scoops.

That is, the rate of change is the ratio of the change in the cost of ice cream and the change in the number of scoops. Let's first calculate the initial rate of change or slope of the given deal: When we buy a waffle cone, the cost is $3, and we can buy one scoop of ice cream for $1.50.So, for one scoop of ice cream, the total cost would be 3 + 1.50 = $4.50.

We can represent the cost of one scoop of ice cream with the help of a linear equation: y = mx + b. Here, the slope or the rate of change, m = Change in cost of ice cream/ Change in the number of scoops= 1.5/1= 1.5Therefore, the rate of change of the ice cream with respect to the number of scoops is $1.50/scoop.

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Answer:

C.

Step-by-step explanation:

Answer A and D are definitely incorrect.  Hope this helps Zoey. #Zoeyiscute:)

Answer: 360

Step-by-step explanation: Sum of exterior angles of any convex polygon is always 360, think about it.

When the sides of the triangle are in the ratio 5:7:8 and the longest side is 36 cm longer than the shortest side, the perimeter is 240cm.

Let's assume the shortest side of the triangle has a length of x cm. According to the given ratio, the sides of the triangle are in the ratio 5:7:8. Therefore, the lengths of the sides can be expressed as:

Shortest side: 5x

Second side: 7x

Longest side: 8x

We are also given that the longest side is 36 cm longer than the shortest side. So we can set up the following equation:

8x = 5x + 36

Now, let's solve this equation to find the value of x:

8x - 5x = 36

3x = 36

x = 36 / 3

x = 12

Now we can substitute this value back into the expressions for the side lengths to find their actual lengths:

Shortest side: 5x = 5 * 12 = 60 cm

Second side: 7x = 7 * 12 = 84 cm

Longest side: 8x = 8 * 12 = 96 cm

Finally, we can calculate the perimeter of the triangle by adding the lengths of all three sides:

Perimeter = Shortest side + Second side + Longest side

= 60 cm + 84 cm + 96 cm

= 240 cm

Therefore, the perimeter of the triangle is 240 cm.

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Answer:

27,804

Step-by-step explanation:

28x993= 27,804

Answer:

27,29,38,39,42,52,53

Step-by-step explanation:

Answer:

Here's a calculator that should help

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/algebra/completing-the-square-calculator.php

The inverse of the given function is represented by Data Table B.

A function is a law that relates a dependent and an independent variable.

The Inverse of the function is determined by interchanging the values of a and y in an f(x,y) function and then express the equation of y in terms of x.

Th table of the function is

Miles to go             Miles Travelled

0                                       0

100                                  310

200                                  450

340                                   550

650                                   650

The inverse of this data table will be

 Miles Travelled             Miles to go

650                                        650

340                                        550  

200                                       450

100                                        310

0                                             0

This is represented by Data Table B.

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Answer:

[tex]L^{2} + W^{2} = d^{2}[/tex]

d = 31.6

Step-by-step explanation:

[tex]L^{2} + W^{2} = d^{2}[/tex]

[tex]30^{2} + 10^{2} = d^{2}[/tex]

[tex]d^{2}[/tex] = 900 + 100

   =  1000

d = [tex]\sqrt{100}[/tex] = 31.6

Answer:

try this link!

Step-by-step explanation:

https://www.wylieisd.net/cms/lib09/TX01918453/Centricity/Domain/783/Math%20Connections%20Key.pdf

The confidence interval estimate of the population mean is (0.37, 0.75). The correct option is B No. Based on the confidence interval, it is not possible to say that the mean mercury level in tuna sushi is greater than 1 ppm.

The confidence interval includes 1 ppm, so the true mean could be 1 ppm or less. Additionally, at least one of the sample values is less than 1 ppm, so at least some of the fish are safe.

The sample standard deviation is calculated by finding the square root of the sum of the squared deviations from the mean for each value in the sample. The sample size is the number of values in the sample.

Confidence interval = sample mean ± 1.645 * (sample standard deviation / ✓(sample size))

Confidence interval = 0.51 ± 1.645 * (0.24 / ✓(7))

= (0.37, 0.75)

As you can see, the confidence interval includes 1 ppm, so the true mean could be 1 ppm or less.

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Answer:

4/5 hours

Step-by-step explanation:

Answer:

20/9 hours

Step-by-step explanation:

I got it right on the quiz

The probability that a randomly selected person will have a white blood cell count of between 2000 and 10,000 is 0.9223 approximately.

The given mean, standard deviation, and the range of values are as follows:

Mean = 7500

Standard deviation = 1750

Range of values = Between 2000 and 10000

We are required to calculate the probability of a random person having a white blood cell count between 2000 and 10000.

Let's find the Z values for 2000 and 10000.Z1 = (2000 - 7500) / 1750 = -3Z2 = (10000 - 7500) / 1750 = 1.43

The required probability is the sum of the probability of the given range of values.

The probability of the first value is:P(X < 2000) = P(Z < -3) = 0.00135

The probability of the second value is:P(X > 10000) = P(Z > 1.43) = 0.0764

To find the probability for the given range, we will subtract the probability of the second value from the probability of the first value.

P(2000 < X < 10000) = 1 - P(X < 2000) - P(X > 10000)P(2000 < X < 10000)

= 1 - 0.00135 - 0.0764P(2000 < X < 10000) = 0.9223

The probability that a randomly selected person will have a white blood cell count between 2000 and 10,000 is 0.9223, approximately.

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Answer:

3/2 I'm not sure I think it's that

Answer:

9.6

Step-by-step explanation:

Answer:

[tex]9.6[/tex]

Step-by-step explanation:

1) Simplify 3 × 0.2 to 0.6.

[tex]0.6 + 9[/tex]

2) Simplify.

[tex]9.6[/tex]

Hence, the answer is 9.6

The exact values of c in increasing order are: c = (10 - sqrt(7)) / 3, (10 + sqrt(7)) / 3

To verify that Rolle's Theorem can be applied to the function f(x) = x³ - 10x² + 31x - 30 on the interval [2, 5], we need to check if the following conditions are satisfied:

Let's check each condition:

f(x) = x³ - 10x² + 31x - 30 is a polynomial function and is continuous for all real values of x. So, it is continuous on [2, 5].

To check the differentiability, we need to find f'(x):

f'(x) = 3x² - 20x + 31.

The derivative f'(x) exists and is continuous for all real values of x. So, f(x) is differentiable on (2, 5).

Now, let's evaluate f(2) and f(5):

f(2) = (2)³ - 10(2)² + 31(2) - 30 = -10

f(5) = (5)³ - 10(5)² + 31(5) - 30 = 95

Since f(2) = -10 is not equal to f(5) = 95, we can conclude that Rolle's Theorem can be applied to the function f(x) = x³ - 10x² + 31x - 30 on the interval [2, 5] after differentiable.

To find the values of c in the interval (2, 5) such that f'(c) = 0, we need to solve the equation f'(c) = 3c² - 20c + 31 = 0.

Using quadratic formula:

c = (-(-20) ± sqrt((-20)² - 4(3)(31))) / (2(3))

c = (20 ± sqrt(400 - 372)) / 6

c = (20 ± sqrt(28)) / 6

c = (20 ± 2sqrt(7)) / 6

c = (10 ± sqrt(7)) / 3

The values of c in the interval (2, 5) such that f'(c) = 0 are:

c = (10 + sqrt(7)) / 3

c = (10 - sqrt(7)) / 3

Therefore, the exact values of c in increasing order are: c = (10 - sqrt(7)) / 3, (10 + sqrt(7)) / 3.

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Incomplete question:

Verify that Rolle's Theorem can be applied to the function f(x) = x³ - 10x² +31x-30 on the interval [2, 5]. Then find all values of c in the interval such that f' (c) = 0.

Enter the exact answers in increasing order.

To enter √a, type sqrt(a)

c = ?

1. The value of x is:

180° - 40° - 30° = 110°

2. The value of x is:

90°- 38° = 52°

Answer:

Step-by-step explanation:

180 = 40 + x + 30

110 = x

90 = 38 + x

52 = x