4) y =<br> Justify:<br> 63°<br> у

The diameter of holes for a cable harness is known to have a normal distribution with a standard deviation of 0. 01 inch. A rand

Sindrei [870]

For the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by ( 1.4983 , 1.5107 ) and ( 1.49635 , 1.51265 ) respectively.

As given in the question,

Confidence interval for population mean is given by:

$\bar{x}$ ± z × ( σ / √n)

Where,

σ = population standard deviation.

n= sample size

$\bar{x}$ = Sample mean

Given values from the random sample size are :

σ = 0.01 inches

n= 10

$\bar{x}$ = 1.5045

Critical value confidence interval (using x-value table)

z for 99% = 2.576 and Significance level = 0.01

z for 95% = 1.960 and Significance level = 0.05

99% two-sided confidence interval on the mean hole diameter is equal to :

$\bar{x}$ ± z × ( σ / √n)

= 1.5045 ± 2.576 × ( 0.01 / √10)

= 1.5045 ± 0.00815 (approximately)

= 1.5045 - 0.00815 , 1.5045 + 0.00815

= ( 1.49635 , 1.51265 )

95% two-sided confidence interval on the mean hole diameter is equal to :

$\bar{x}$ ± z × ( σ / √n)

= 1.5045 ± 1.960 × ( 0.01 / √10)

= 1.5045 ± 0.00620 (approximately)

= 1.5045 - 0.00620 , 1.5045 + 0.00620

= ( 1.4983 , 1.5107 )

Therefore, for the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by ( 1.4983 , 1.5107 ) and ( 1.49635 , 1.51265 ) respectively.

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4 0

1 year ago

What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 2x2 + x + 4

olga_2 [115]

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is

$(\sqrt{2},\sqrt{-2} )$ and $((7+\sqrt{2)} ,(7+\sqrt{-2}))$

We have given that,

f(x) = 2x^2 + x + 4

x g(x)

-2 1

-1 3

0 5

1 7

2 9

<h3>What is a polynomial function?</h3>

A polynomial function is a relation where a dependent variable is equal to a polynomial expression.

A polynomial expression is an expression including numbers and variables, where variables are raised to non-negative powers.

The general form of a polynomial expression is:

a₀ + a₁x + a₂x² + a₃x³ + ... + anxⁿ.

The highest power to a variable is the degree of the polynomial expression. When degree = 2, the function is a quadratic function.

When degree = 1, the function is a linear function.

<h3>How do we solve the given question?</h3>

The quadratic function is given to us:f(x) = 2x^2 + x + 4.

We need to determine the linear equation g(x).

Since it's a linear equation we use the two-point method to determine the equation.

<h3>What is the two-point?</h3>

y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)

We take the points g(-2) =1, g(-1) = 3

g(x) - g(1) = ((g(-2)-g(-1))/(-2+1))*(x-1)or,

g(x) - 1 = ((-2-(-1))/(-2+1))*(x-1)or, g(x) - 1 = -1(-x+1)or,

g(x) = x - 1 + 1 = x

∴ g(x) = x , is the linear function g(x)

We are asked to find the solution to the system of equations f(x) and g(x).To find the solution we need to check what is the common solution to both f(x) and g(x).

For that, we equate f(x) and g(x).2x^2 + x + 4 = x or, 2x² - x +x- 4 = 0or, 2x^2 - 4 = 02(x^2-2)=0x^2-2=0 $x^2-\sqrt{2}=0$ $(x-\sqrt{2}) (x+\sqrt{2})=0$ $(x-\sqrt{2})=0 \\x=\sqrt{2} or x=-\sqrt{2}$ g(-1) = 3(from the table) $g(\sqrt{2})=\sqrt{2} \ and \ g(\sqrt{-2}) =-\sqrt{2}$ $f(\sqrt{2}) = 2(\sqrt{2} )^2 + (\sqrt{2} ) + 3\\=2(2)+\sqrt{2} +3\\=7+\sqrt{2}$ $g(-\sqrt{2} )= 2(\sqrt{-2} )^2 + (\sqrt{-2} ) + 3\\=2(2)+\sqrt{-2} +3\\=7+\sqrt{-2}$

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is $(\sqrt{2},\sqrt{-2} )$ and $((7+\sqrt{2)} ,(7+\sqrt{-2}))$

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5 0

1 year ago

WORTH ALOT OF POINTS need help please

-BARSIC- [3]

Question 1- A circle is formed from the cross section of a plane and sphere
Question 2- A square is formed from the cross section of a plane and a cube
Question 3- A circle is formed from the cross section of a plane and cone
Question 4- A rectangle is formed from the cross section of a plane and rectangular pyramid.
Question 5- A circle is formed from the cross section of a plane and a cylinder

3 0

3 years ago

Read 2 more answers

Mariain buys a dress that costs 32 dollars she pays 10 percent sales tax

jeyben [28]

Answer:

the total cost would be $45.2

8 0

3 years ago

Is the square root of eight a rational or irrational number

shutvik [7]

$\bf \sqrt{8}\implies \sqrt{2\cdot 2\cdot 2}\implies \sqrt{2^2\cdot 2}\implies 2\sqrt{2}$

it just so happen that √2 is an irrational number, so any product with it as a factor, will yield an irrational number as well.

factoid: Ancient Greeks were scared of irrational numbers, and they steered clear from √2.

8 0

3 years ago

4) y = Justify: 63° у