Answer:
y=-5/3x+20
Step-by-step explanation:
Let the equation of the required line be represented as ![\[y=mx+c\]](https://tex.z-dn.net/?f=%5C%5By%3Dmx%2Bc%5C%5D)
This line is perpendicular to the line ![\[y=\frac{3}{5}x+10\]](https://tex.z-dn.net/?f=%5C%5By%3D%5Cfrac%7B3%7D%7B5%7Dx%2B10%5C%5D)
![\[=>m*\frac{3}{5}=-1\]](https://tex.z-dn.net/?f=%5C%5B%3D%3Em%2A%5Cfrac%7B3%7D%7B5%7D%3D-1%5C%5D)
![\[=>m=\frac{-5}{3}\]](https://tex.z-dn.net/?f=%5C%5B%3D%3Em%3D%5Cfrac%7B-5%7D%7B3%7D%5C%5D)
So the equation of the required line becomes ![\[y=\frac{-5}{3}x+c\]](https://tex.z-dn.net/?f=%5C%5By%3D%5Cfrac%7B-5%7D%7B3%7Dx%2Bc%5C%5D)
This line passes through the point (15.-5)
![\[-5=\frac{-5}{3}*15+c\]](https://tex.z-dn.net/?f=%5C%5B-5%3D%5Cfrac%7B-5%7D%7B3%7D%2A15%2Bc%5C%5D)
![\[=>c=20\]](https://tex.z-dn.net/?f=%5C%5B%3D%3Ec%3D20%5C%5D)
So the equation of the required line is ![\[y=\frac{-5}{3}x+20\]](https://tex.z-dn.net/?f=%5C%5By%3D%5Cfrac%7B-5%7D%7B3%7Dx%2B20%5C%5D)
Among the given options, option 4 is the correct one.
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.
Answer:
Step-by-step explanation:
If you call "5x-2x^2+1" an "equation," then you must equate 5x-2x^2+1 to 0:
5x-2x^2+1 = 0
This is a quadratic equation. Rearranging the terms in descending order by powers of x, we get:
-2x^2 + 5x + 1 = 0. Here the coefficients are a = -2, b = 5 and c = 1.
Use the quadratic formula to solve for x:
First find the discriminant, b^2 - 4ac: 25 - 4(-2)(1) = 25 + 8 = 33
Because the discriminant is positive, the roots of this quadratic are real and unequal.
-b ± √(discriminant)
Applying the quadratic formula x = --------------------------------
2a
we get:
-5 ± √33 -5 + √33
x = ----------------- = --------------------- and
2(-2) -4
-5 - √33
---------------
-4
Step-by-step explanation:
<u>Step 1: Let's simplify step-by-step.</u>
<u>Step 2: Combine Like Terms:</u>
Answer:
Hope this helps.
Answer:
r =5 in
Step-by-step explanation:
Area of a circle is given by
A = pi r^2
We know the area and pi
78.5 = 3.14 r^2
Divide by 3.14
78.5/3.14 = 3.14 /3.14 r^2
25 = r^2
Take the square root of each side
sqrt(25) = sqrt(r^2)
5=r
