The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with σ = 30 hours. A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038 hours.
If in the study of the lifetime of 60-watt light bulbs it was desired to have a margin of error no larger than 6 hours with 99% confidence, how many randomly selected 60-watt light bulbs should be tested to achieve this result?
Given Information:
standard deviation = σ = 30 hours
confidence level = 99%
Margin of error = 6 hours
Required Information:
sample size = n = ?
Answer:
sample size = n ≈ 165
Step-by-step explanation:
We know that margin of error is given by
Margin of error = z*(σ/√n)
Where z is the corresponding confidence level score, σ is the standard deviation and n is the sample size
√n = z*σ/Margin of error
squaring both sides
n = (z*σ/Margin of error)²
For 99% confidence level the z-score is 2.576
n = (2.576*30/6)²
n = 164.73
since number of bulbs cannot be in fraction so rounding off yields
n ≈ 165
Therefore, a sample size of 165 bulbs is needed to ensure a margin of error not greater than 6 hours.
The answer for angle b is: 25°
Answer:
Step-by-step explanation:
c
Answer:
g(p)h(p) = = p^4 + 2p^3 - 8p^2 -2p + 4
Step-by-step explanation:
Hello!
We will use the distributive property:
g(p) h(p) = ( p - 2 ) * ( p^3 + 4p^2 - 2 ) = ( p^3 + 4p^2 - 2 ) * ( p - 2 )
The distributive property allow us to multiply the first term <em>(p^3 + 4p^2 - 2) </em>by every member of the second member, that is <em>p </em>and <em>-2.</em>
g(p) h(p) = ( p^3 + 4p^2 - 2 ) * p + ( p^3 + 4p^2 - 2 ) * (-2)
Now we can do the same for the two resulting terms, that is, we can multiply every term in parenthesis<em> ( p^3 + 4p^2 - 2 ) </em>by the term on the rigth:
( p^3 + 4p^2 - 2 ) * p = (p^3)*p + (4p^2)*p - 2*p = p^4 + 4p^3 -2p
( p^3 + 4p^2 - 2 ) * (-2) = (p^3)*(-2) + (4p^2)*(-2)- 2*(-2) = -2p^3 - 8p^2 + 4
And now we can sum both terms and add monomials with the same exponent of t. Look at the underlined terms
g(p) h(p) = p^4 + <em><u>4p^3</u></em><em> </em>-2p - <u>2p^3 </u>- 8p^2 + 4 = p^4 +<em><u>2p^3</u></em> -2p - 8p^2 + 4
= p^4 + 2p^3 - 8p^2 -2p + 4
Answer:
f'(1) = 2
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
<u>Calculus</u>
The definition of a derivative is the slope of the tangent line.
Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = x²
Point (1, f(1))
<u>Step 2: Differentiate</u>
- Basic Power Rule: f'(x) = 2 · x²⁻¹
- Simplify: f'(x) = 2x
<u>Step 3: Find Slope</u>
<em>Use the point (1, f(1)) to find the instantaneous slope</em>
- Substitute in <em>x</em>: f'(1) = 2(1)
- Multiply: f'(1) = 2
This tells us that at point (1, f(1)), the slope of the tangent line is 2. We can write an equation using point slope form as well: y - f(1) = 2(x - 1)