= 3(4a^2 + 4a - 3) - 4a^2 + 28
= 12a^2 + 12a - 9 - 4a^2 + 28
= 8a^2 + 12a + 19
= 4a(2a + 3) + 19
it would take Janis 14 minutes to complete a package alone
<h3>How to determine the value</h3>
From the information given,
Let's say that
Carol working time = x = 30 minutes
Janis working time = y
x + y = 16 minutes
Let's make 'y' the subject
30 - 16 = y
y= 14 minutes
Thus, it would take Janis 14 minutes to complete a package alone
Learn more about word problems here:
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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 equation indicates that the center of the window is 12 feet from the ground and the distance the window spans 6 feet.
<h3>What is the general equation of a circle?</h3>
The equation of a circle is given by the formula,
where (a,b) is the coordinate of the center of the circle, and r is the radius of the circle.
According to the given equation, if we compare this equation with the general equation of the circle.
On observing this equation we will get that the value of (a,b) is (4,12).
Thus, The equation indicates that the center of the window is 12 feet from the ground
window span = diameter of circle
window span = 2r
= 2 × 3 (radius = 3)
= 6
Hence, The equation indicates that the center of the window is 12 feet from the ground and the distance the window spans 6 feet.
To learn more about Equation of the circle from the given link
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Answer:
Step-by-step explanation:
21.4÷4.75
- First- you have to move the decimal placement two times to the right
- Second- you have to put the number 21.4 under the dividing box
- Third- put the number 4.75 out to the left of the decimal box
- Fourth- when that's all completed you have to multiply the 475. until you get clos to the number 2140.
- Fifth- once done you have to subtract the multiplied number that you get you then subtract it from 2140
- Sixth- you keep on doing the fifth step until you get a reasonable answer
- Seventh- you write the answer down
- Eighth- there is no eighth step so you can stop reading this answer
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