1. Perform Gauss-Jordan elimination on the augmented matrix shown.
O
-261
3
A. 0 1 -7
00 0
3
B. 0 -1 7
0
[102]
C.0 17
001
2370
[100]
D. 0 1 0
00

The number of points that are expected to lie inside the circle is 785.

A circle is a closed two-dimensional figure. In a circle, all points are equidistant from the centre.

As per the given question, the circle is inscribed in a square,

⇒ The area of the circle   =   π × r × r

                                           =   π × 1 × 1

∴ The area of the circle    =   π

⇒ The area of the square   =   s × s

                                             =   2 × 2

∴The area of the square    =    4  

The probability that a randomly selected point inside the square will lie inside the circle,

p   =   π / 4

The probability that a randomly selected point inside the square will lie outside the circle,

q   =  1 - p

q   =  1 - ( π / 4 )

⇒ Binomial trial with n   =   1000 and  p   =   π / 4,

Number of points expected to lie inside the circle(N)  =   n × p

                                                                                         =   1000 × ( π / 4 )

                                                                                         =   1000 × ( 3.14 / 4 )

                                                                                         =   1000 × ( 0.785 )

                                                                                  N    =   785  

Therefore, 785 expected points lie inside the circle.  

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The complete question is

Answer: 56 square

Step-by-step explanation:

The degree of the polynomial is 5, and the end behavior is:

as x → ∞, f(x) → -∞

as x → -∞, f(x) → ∞

For any given polynomial, we define the degree as the largest exponent on the polynomial.

On this case we have:

f(x) = 2x^3 - 3x^5 - x^2 + 1

We can see that the largest exponent is 5, so the degree is 5.

Now, for the ending behavior.

If we have an odd degree (like in this case) we will have opposite ending behaviors in both ends of the domain.

If the leading coefficient is negative (like in this case, it is -3) then the end behavior will be:

as x → ∞, f(x) → -∞

as x → -∞, f(x) → ∞

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There are no values within the interval that satisfies the condition stated by Rolle's theorem.

In accordance to Rolle's theorem, a function existing within an closed interval [a, b] has at a least a value c within that interval such that the first derivative f'(c) is equal to the slope of the secant line that passes through the two interval limits. That is to say, Rolle's theorem is defined by the following formula:

f'(c) = [f(b) - f(a)] / (b - a), where a < c < b

Where:

First, evaluate the function f(x) at x = - 4:

x = - 4

f(- 4) = (- 4)³ - 4 · (- 4)² - 16 · (- 4) + 8

f(- 4) = - 64 - 64 + 64 + 8

f(- 4) = - 56

Second, evaluate the function f(x) at x = 4:

x = 4

f(4) = 4³ - 4 · 4² - 16 · 4 + 8

f(4) = 64 - 64 - 64 + 8

f(4) = - 56

Third, determine the first derivative of the function f(x) and evaluate it at x = c:

f(x) = x³ - 4 · x² - 16 · x + 8

f'(x) = 3 · x² - 8 · x - 16

x = c:

f'(c) = 3 · c² - 8 · c + 16

Fourth, find the roots of the quadratic function found in the previous step.

3 · c² - 8 · c + 16 = 0

In accordance with the quadratic formula, the roots of the expression are 4 / 3 + i 4√2 / 3 and 4 / 3 - i 4√2 / 3, which are not real numbers.

Fifth, determine whether Rolle's theorem are applicable on the roots found in the previous step.

Since the roots of the polynomial 3 · c² - 8 · c + 16 are not real numbers, there are no number within the interval that satisfies Rolle's theorem.

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Answer:

140

Step-by-step explanation:

2x+5x+40=180

7x+40=180

7x=140

x=20

5x+40=BCD

5(20)+40

100+40

140

Answer:

x = 82°

Step-by-step explanation:

The three angles of the triangle add up to 180°

x + 40° + 58° = 180°

x + 98° = 180°

subtract 98°

x = 82°

Answer:

x = 82°

Step-by-step explanation:

The sum of the internal angles of a triangle = 180°

58° + 40° + x° = 180°

98° + x° = 180°

x° = 180° - 98°

x° = 82°

The required question based on number of posters is y = 109.95 + 65x.

The cost of additional posters = 65x, based on the mentioned information.The 100 posters make 1 set. Assuming the total number of posters be x. So, the additional sets will be calculated by the formula = (x - 100)/100.

Now, the equation will be the sum of the cost of first 100 posters and the cost of remaining posters.

y = 109.95 + 65x

Thus, the equation with the total cost (in dollars) as a function of the number (in hundreds) of posters ordered is y = 109.95 + 65x.

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Answer:

x = -72

Step-by-step explanation:

So first you need to get x on its own, so you you need to get rid of -16 by adding +16 which you get 0.

so now x=-88

whatever you do on one side you do on the other, so add 16 to the other side (-88) so you get -72.

x = -72

so the answer is -72

Thank you <3

The first statement is false and the second statement is true.

Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen. There are two types of random variables.

A random variable that takes a finite number of possible values can be defined as a Discrete random variable. A random variable that takes an infinite number of possible values can be defined as a Continuous random variable. A continuous random variable consists of only continuous values.

Continuous random variables are defined at intervals of values. Continuous random variables are represented by the area under a curve.

⇒  The number of cars that go through the drive-in window at a local bank each hour.

The number of cars can be counted and can be an integer like 10, 20,100 etc.

∵ The number of cars is countable it is not an example of a continuous random variable        

⇒ The high daily temperature in Anchorage.

High daily temperature can be an integer or function like 60°, 120° etc

∵ The high daily temperature is an example of a continuous random variable.

Therefore, The number of cars that go through the drive-in window at a local bank each hour is not an example of a continuous random variable and The high daily temperature in Anchorage is an example of a continuous random variable.

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The complete question is

The percent of the sophomores in the class of 28 sophomores and juniors is 42.86%.

According to the question,

We have the following information:

Total number in a class including sophomores and juniors = 28

Number of juniors in the class = 16

Now, we have the number of sophomores in this class:

Total number in the class- Number of juniors in the class

28-16

12

Now, we can easily find the percent of sophomores in the class by following the given steps:

Number of sophomores*100/Number of sophomores and juniors

1200/28

42.86%

Hence, the percent of the sophomores in the class of 28 sophomores and juniors is 42.86%.

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Answer:1/14

Step-by-step explanation:He divides 1/2 of the jar into sevenths, but if he had the whole jar it would be fourteen parts because 2x7=14, or 14÷2=7

The percentage of men who didn't expect to meet the height requirements be 96.29%

Given, that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches.

Find the percentage of men who meet the height requirements.

z(64) = (64-69)/2.8 = 1.7857

z(78) = (78-69)/2.8 = 3.2143

P(64 <= x <= 78) = P(1.78457<= z <=3.2143) = 0.0371 = 3.71%

So, the percentage of men who meet the height requirements be 3.71%

Now, the percentage men who didn't expect to meet the height requirements be

100 - 3.71 = 96.29%

Hence, the percentage of men who didn't expect to meet the height requirements be

96.29%

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The probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .

Given :

Population Proportion ( p ) = ( 44 % ) = 0.44

Sample proportion ( p hat ) = ( 40 % ) =  0.4

Size of sample ( n ) = 853

To find : P ( p hat < 0.4 )

Formula : ( p hat - p ) / [tex]\sqrt{ p * ( 1 - p ) / n }[/tex]

Substituting values in the above formula ,

z = ( 0.4 - 0.44 ) / [tex]\sqrt{ 0.44 * ( 1 - 0.44 ) / 853}[/tex]

z = - 2.3535

z - score = -2.3535

Finding the p - value :

p - value = 0.009299

Therefore , the probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .

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The probability that a carpet that is 7 ft × 12 ft contains no flaws is 0.732  

The Normal, Binomial, and Poisson Distributions are the three types of continuous and discrete data-based distributions used in probability and statistics. The distribution of unusual occurrences is another name for the Poisson distribution. This is mostly used to forecast the likelihood of future events based on how frequently the past events occurred. It offers the chance that a specific number of events might happen during a particular time frame.

The formula for Poisson distribution is given below:

       P(x) = (e^-x * m^x) / x!  

Here we have,

flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet  

Given the dimensions of carpet = 7 feet × 12 feet  

=> area of the carpet = 84 feet²

=> the expected mean of defects m = [1/270]*84 = 0.311

Now use the Poisson formula  

P[x] = e^-m × m^x / x!

=> P(x = 0) = e^-(0.31) × 0.31^(0) / 0!

= (0.732 × 1)/1 = 0.732

Therefore,

The probability that a carpet that is 7 ft × 12 ft contains no flaws is 0.732  

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The Central Limit Theorem gives the idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn .

Central Limit Theorem : In probability theory , the Central Limit Theorem establishes that , in many situations , when independent random variables are summed up , their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed .

The Central Limit Theorem gives the idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn .

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Answer:

b = 4A-a-c-d

Step-by-step explanation:

A = (a+b+c+d)/4 |*4

4A = a+b+c+d |-a-c-d

4A-a-c-d = b

The expression for the sum is (12 + n).

We are given two terms to add. The first number is 12, which is an integer. The second number is unknown. An integer is a number that has no decimal or fractional portion and can be negative or positive, including zero.

The second number is represented by a variable "n". A variable is a mathematical object's symbol and placeholder. A variable can, for example, represent an integer, a vector, or other data.

We need to write the expression for the sum of these two numbers. Let S represent the sum of these two numbers.

S = 12 + n

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[tex]{ \bold{ \sqrt[3]{V}}} [/tex]

Step-by-step explanation:

[tex]{ \green{ \sf{V = s³}}}[/tex]

Cube on both sides, then

[tex]{ \green{ \sf{s = \sqrt[3]{V}}}} [/tex]

The equation of the line, in slope-intercept form, that passes through

(4, 2) and (-2, -3) is y = 5/6 x - 4/3.

What is slope-intercept form?

The meaning of slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

Using two points and slope-intercept form we can find the equation of the line.

According to the given question:

The formula to find the slope of two points (x₁, y₁) and (x₂, y₂) is

m = (y₂ - y₁) / (x₂ - x₁)

The points given are (4, 2) and (-2, -3)

m = (-3 - 2) / (-2 - 4)

m = -5/ -6

m = 5/6

Now using the slope and the point (4, 2) the y intercept is

y = mx + b

2 = 5/6 (4) + b

2 = 10/3 + b

By further calculation,

b = 2 - 10/3

Taking LCM

b = (6 - 10)/3 = -4/3

By writing the equation in slope intercept form

y = mx + b

y = 5/6x - 4/3

Therefore, the equation of the line in slope intercept form is

y = 5/6 x - 4/3.

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Answer:

400meters

Step-by-step explanation:

Find the speed of the hippopotamus by dividing distance with time

6000 meters ÷15minutes =400meters/minutes

The amount of money the social worker can spend is $146.59 ≤ m ≤ $293.17

An equation shows the relationship between two or more numbers and variables.

Let m represent the amount of money the social worker can spend.

A social worker earns an average bi-weekly net pay of $1,465.87. Hence:

Monthly revenue = 2 * $1465.87 = $2931.74

For a debt of 5%:

m = 5% of $2931.74 = 0.05 * $2931.74 = $146.59

For a debt of 10%:

m = 10% of $2931.74 = 0.1 * $2931.74 = $293.17

$146.59 ≤ m ≤ $293.17

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Answer:

$158.80 ≤ m ≤ $317.61

Step-by-step explanation:

Hello,

So first step is we would use the bi-weekly net pay of $1465.87 then times it by 26 so it would look like this

1465.87 × 26 = 38112.62

Then we would divide 38112.62 by 12

38112.62 ÷ 12 = 3176.0516

Then, we would determine how much the social worker can spend if the monthly budget for debt is between 5% and 10%.

3176.0516 × 5% = 158.80

3176.0516 × 10% = 317.61

So, therefore the answer is $158.80 ≤ m ≤ $317.61.

Answer:352

Step-by-step explanation:

Answer:

y = 8x - 6

Step-by-step explanation:

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

We know that the y-intercept occurs when x = 0 so from the table, it's b = -6

We can use the slope formula to find the slope:

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\\ \frac{2-(-6)}{1-0} \\\frac{2+6}{1-0} \\8=m[/tex]

The recommended screen size for the television is 59.85 inches.

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, the expression for the size of the television is given as:

S = 0.228x² + 8.154x - 8.3

where x = 7 feet

S = 0.228x² + 8.154x - 8.3

S = 0.228(7)² + 8.154(7) - 8.3

S = 11.172 + 57.078 - 8.4

S = 59.85

The size is 59.85 inches.

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The likelihood that at least 150 people will collaborate and react in a fresh sample of 400 telephone numbers is 0.9953.

The probability informs us of the likelihood that an event will occur. It is necessary for the likelihood to fall between 0 and 1. The likelihood of success is 1, whereas the probability of failure is 0.

Given, that the market research  company has a history of having a 44% response rate for its telephone surveys.

Therefore, p=44%=0.44=μ

n=400

p=150/400

p=0.375

The standard deviation is then equal to,

σ=√(p(1-p))/n

σ=√(0.44(1-0.44))/400

σ=√(0.44×0.56)/400

σ=0.025

Using the z-table, the values are as follows:

z=(p-μ)/σ

z=(0.375-0.44)/0.025

z=-2.6

p(p>0.375)

=p(z>-2.6)

=1-p(z<-2.6)

=1-0.0047

=0.9953

=99.53%

Therefore, the likelihood that at least 150 people will participate and provide information in a new sample of 400 telephone numbers

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Answer:

Home Stores

4.85×5

= 24.25

Paint Supplies

£18

Pi written as 3.l4 and π in mathematics is the ratio for the diameter of a circle to the circumference of that circle. The value is unending

Pi, which is represented by the Greek letter p, or, is a shorthand for the ratio of a circle's diameter to its circumference. No matter how big the circle is, this ratio will always be equal to pi. The value of pi is about 3.14 in decimal notation.

We are to multiply Pi to any equation

let the equation be (20.5 + 3x)[tex]\pi[/tex]

pi is represented in numbers by 3.14

Hence we would have the equation to be of the form

(20.5 + 3x)3.14

multiply through the bracket

64.37 + 9.42x

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The equation of the line parallel to x - y = 3 and passes through pint (2,-4) is y = x - 6.

The equation of line is expressed as;

y = mx + b

The point-slope formula is expressed as;

y - y₁ = m( x - x₁ )

Where m is slope and b is the y-intercept.

Given the data in the question;

Point: (2,-4)

First, reorder the given equation in slope-intercept form and determine the slope.

x - y = 3

x = 3 + y

3 + y = x

y = x - 3

Hence,

The slope m = 1

To find the line parallel to the equation, the slope must be equal.

Find the line using point-slope formula.

y - y₁ = m( x - x₁ )

Plug in slope m = 1 and point: (2,-4)

y - ( -4 ) = (1)( x - 2 )

Simplify and convert to slope intercept form.

y + 4 = x - 2

y = x - 2 - 4

y = x - 6

Therefore, the equation of line is y = x - 6.

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