multiply the maclaurin series for e z and 1 1 z to obtain the series expansion for e z 1 z up to z 5 . on what disk does it converge?

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 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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Answer:352

Step-by-step explanation:

Answer:

The answer is 80

Answer:

400meters

Step-by-step explanation:

Find the speed of the hippopotamus by dividing distance with time

6000 meters ÷15minutes =400meters/minutes

Step-by-step explanation:

those are the answers if I am wrong you can correct

Answer:

(-3,1)  & (3, -1)

Step-by-step explanation:

Solving quadratic equation and linear equation:

2x² + y² = 19 -----------------(I)

x + 3y = 0 -----------------(II)

         x = -3y --------------(III)

Substitute x = -3y in equation (I) and we can find the value of y.

2(-3y)² + y² = 19

2*9y² + y²  = 19

  18y² + y² = 19

Combine like terms,

          19y² = 19

             y² = 19 ÷ 19

              y² = 1

              y = √1

              y = ±1

Substitute y = ±1 in equation (III) and find the value of x.

When y = 1,

              x = -3*1

              x = -3

When y = -1,

               x = -3*(-1)

             x = 3

Solutions:  (-3, 1) ; (3, -1)                  

4. There is no enough information.

5. ΔPEF ≅ ΔREF are congruent by SAS.

6. ΔKMO ≅ ΔOLK are congruent by SSS.

7. No enough information.

8. ΔPAN ≅ ΔKLC are congruent by SSS.

9. ΔABC ≅ ΔDEF are congruent by SSS.

The SSS and SAS are theorems of triangle congruence that can be used to prove that two triangles are congruent. To prove that two triangles are congruent by SSS, both triangles must have three pairs of corresponding lengths that are congruent, while SAS is used when the two triangles have two pairs of congruent sides that are corresponding, and a pair of congruent included angles.

4. There is no enough information to prove triangles HNJ and RDF are congruent by neither SAS nor SSS.

5. Triangles PEF and REF are congruent by SAS.

6. Triangles KMO and OLK are congruent by SSS.

7. No enough information.

8. Triangles PAN and KLC are congruent by SSS.

9. Triangles ABC and DEF are congruent by SSS.

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The graph of the quadratic equation with axis of symmetry x = - 2 is shown in figure.

What is Quadratic equation?

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The function is,

⇒ f (x) = - 3 (x + 2)² + 1

Now,

We know that;

If the function is of the form y = a (x - h)² + k;

Then, The vertex = (h, k)

And, Axis of symmetry is, x = h

Here, The function is,

⇒ f (x) = - 3 (x + 2)² + 1

⇒ f (x) = - 3 (x - (- 2))² + 1

By comparing we get;

h = - 2 , k = 1

So, Vertex of the function = (- 2, 1)

And, Axis of symmetry is;

⇒ x = - 2

Thus, The graph of the quadratic equation with axis of symmetry x = - 2 is shown in figure.

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Answer:

someone answer please ive been waiting for 2 hours :skull:

Step-by-step explanation:  please answer yall

Answers: A, A, A

1)A rectangle has an area of 405 cm square and width of 15 cm. The length of the rectangle is: 27 cm

15cmx 27cm= 405 cm

2)The x- and y- intercepts of the graph of the line 5x - 3y - 15 = 0 are, respectively: 3 and 5

(I don't really know how to explain this.......)

3)The expression that simplifies to 11x + 2y is: 4x+3y+7x-y

 4x+7x=11x

  3y-y = 2y

Therefore, it will equal to 11x+2y.

I really hope this helps!

Please Mark Me Brainliest!!!

(I'm in 5th Grade Honors but I learn MS)

Answer:

All the answer are A

Step-by-step explanation:

Area = length times width

405 = x15  Divide both sides by 15

27 = x

For the x intercept  Let y = o and solve for x

5x - 3y -15 = 0

5x - 3(0) -15 = 0

5x -15 = 0  Add 15 to both sides of the equation

5x = 15  Divide both sides by 5

x = 3

The x intercept is (3,0)

For the y intercept Let x = 0 and sole for y

5x -3y -15 = 0

-3y -15 = 0  Add 15 to both sides of the equation

-3y = 15  Divide both sides by -3

y = -5

The y intercept is (0,-5)

4x + 3y + 7x - y  Combine the like terms

(4x + 7x) = (3y -y)

11x + 2y

The sales tax of his purchase if he lives in Florida where the sales tax rate is 6 percent is $67.92

The word "percent" comes from the Latin per centum, which means "hundred" or "by the hundredth." The symbol for "percent" emerged gradually from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and eventually vanished. The "cento" symbol was simplified to two circles divided by a horizontal line, from which the contemporary "%" symbol was formed.

The abbreviation "pct.", "pct," and sometimes "pc" are also used. A % is a dimensionless (pure) number with no unit of measurement.

Given,

Total purchase=$878

For two tables,

2×127=254

Total=878+254

=1132

6% of 1132 is,

(6/100)×1132

=$67.92

The sales tax of his purchase if he lives in Florida where the sales tax rate is 6 percent is $67.92

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The value of the given expression will be 4 / 3.

An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given logarithmic expression is log₂(∛16). The expression will be solved as below,

[tex]E = log_2\sqrt[3]{16}\\E = log_2(2^{\frac{4}{3})\\E = \dfrac{4}{3}log_22\\E = \dfrac{4}{3}[/tex]

Therefore, the solution of the expression will be equal to 4 / 3.

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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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In a binomial experiment, there are two possible results for each trial, which are referred to as "success" and "failure," respectively.

If the following criteria are satisfied, a statistical experimentation can be categorised as a binomial experiment:

Thus, in a binomial experiment, there are two possible results for each trial, which are referred to as "success" and "failure," respectively.

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The extrema of the quadratic equation is at the vertex, and it is a minimum at:

y = -1.75

Here we have the following quadratic equation:

y = 3x^2 - x - 2

We can see that the leading coefficient (the coefficient in the term with the largest exponent) is positive, this means that the parabola opens upwards.

This means that the vertex of the quadratic equation will be a minimum.

Remember that for a quadratic equation:

y = a*x^2 + b*x + c

The vertex is at:

x = -b/2a

So for our quadratic, the vertex is at:

x = -1/(2*3) = -1/6

Evaluating the quadratic equation there we get:

y = 3*(-1/6)^2 - (-1/6) - 2

y = -1.75

That is the minimum of the quadratic.

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The vertex of the curve is at (-2, -4) and the axis of symmetry is at -2

The curve opens downward.

from, the graph, the roots of the equation are -4 and 0

so if -4 is a root, (x + 4) is a factor and if 0 is a root, then x is a factor.

The equation of the curve is the product of the factors of the curve which is y = x(x + 4)

y = [tex]x^{2}[/tex] + 4x

the x coordinate of the vertex = -b/2a = axis of symmetry

where a is the coefficient of [tex]x^{2}[/tex] and b is the coefficient of x

so a = 1, b = 4

x coordinate of vertex = -4/2 = -2

substitute x = -2 into y =  [tex]x^{2}[/tex] + 4x to find the y-coordinate of the vertex

y = [tex](-2)^{2}[/tex] + 4(-2)

y = 4 -8

y = -4

vertex is (-2, -4)

The axis of symmetry is -b/2a which is -2

The curve opens downward as the vertex is at -4

In conclusion, the vertex of the parabola is (-2, -4) and the axis of symmetry is -2 and the parabola opens downward

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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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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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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 technological innovation could help solve an environmental issue that is likely to threaten Australia in the future is D. Using electric cars could help lessen droughts.

Streamflows decrease, water levels in lakes and reservoirs fall, and the depth to water in wells increases when rainfall is less than normal for a period of weeks to years. If the dry weather continues and water supply issues arise, the dry period may turn into a drought.

For the first time since 2017, Australia ended 2021 in an unusual climatic state, with no region in this famously vast, mostly brown land officially declared to be in drought. It should be noted that the country has drought challenges and electric cars could help reduce the water used.

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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:

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 = -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 value of 3 in 5.53 is 3 hundredths.

It is important to note that place values can be defined as the value that's represented by a digit based on the position that it takes. In mathematics, place value refers to the position or location of a digit in a number.

Each digit has a specific place in a number. The position of each digit will be expanded when we represent the number in general form. Those positions begin with a unit place, also known as one's position.

In this case, we want to know the value of 3 in 5.53. It should be noted that the first 5 is 5 ones, the second 5 is 5 tenths and the 3 is 3 hundredths.

Therefore, it's 3 hundredths.

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Complete question

What is the value of 3 in 5.53?

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]

Answer:

x=2

Step-by-step explanation:

add the x onto the other side so it is positive : 7=5+x

then subtract the 5 from both sides so you can isolate the x : 2=x

rewrite the equation: x=2

☆ Hello ☆

The value of x is 2.

[tex] \red{ \sf \underline {\underline{Explantation: }}}[/tex]

¿What are equations?

The equations represent an equality between two mathematical expressions that have at least one variable called unknown.

[tex] \sf \:Solution:[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\boldsymbol{\mathsf{7 - x = 5}}\\\boldsymbol{\mathsf{ - x = 5-7}}\\\boldsymbol{\mathsf{ - x = -2}}\ \\ {\mathsf{ x = 2}}\end{gathered}[/tex]

[tex] \bf \:Verification:[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\boldsymbol{\mathsf{7 - 2 = 5}}\\\boldsymbol{\mathsf{ 5=5}}\end{gathered}[/tex]

[tex]\green{ \sf \: The \: result \: is} \: \red{\longmapsto} \blue 5[/tex]

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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Check the picture below.