Answer:
a. 〈4,3〉
b. 〈-2,7〉
c. 〈11,4〉
Step-by-step explanation:
a. u + v
〈1,5〉 + 〈3, −2〉
〈1+3,5-2〉
〈4,3〉
b. u - v
〈1,5〉 - 〈3, -2〉
〈1-3,5-(-2)〉
〈-2,7〉
c. 2u + 3v
2*〈1,5〉 + 3*〈3,-2〉
〈2*1,2*5〉 + 〈3*3,3*(-2)〉
〈2,10〉 + 〈9,-6〉
〈2+9,10-6〉
〈11,4〉
To draw the vectors, let's put them on the origin (0,0), so let's draw the line until the point of its component form, with an arrow. The vectors are shown below.
(x+3)(x+4)
x^2+4x+3x+12
x^2+7x+12
A fraction is numerator over denominator, most of the time whole numbers
I love equations! Ok this is what you do...
Combine like terms.
8d - 4d - 6d - 8 = 2d
4d - 6d - 8 = 2d
-2d - 8 = 2d
Now you need to isolate the variable. (Add 2d to both sides.)
-8 = 4d
Divide 4 from 4d and -8.
-2 = d
Lets check our work.
8(-2) - 4(-2) - 6(-2) - 8 = 2(-2)
-16 + 8 + 12 - 8 = -4
-8 + 12 - 8 = -4
4 - 8 = -4
-4 = -4
The solution is correct.
I hope this helps love! :)
Answer:
99.7%
Step-by-step explanation:
The empirical rule formula states that:
68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ
Step 1
We have to find the number of standard deviations from the mean
μ = Mean = 1800 hours
σ = Standard deviation = 25 hours
For 1725 hours
μ - xσ =
1800 - 25x = 1725
25x = 1800 - 1725
25x = 75
x = 75/25
x = 3
For 1875 hours
1800 + 25x = 1875
25x = 1875 - 180
25x = 75
x = 75/25
x = 3
Step 2
From the above calculation, the bum of standard deviations from the mean is 3
Hence, the percentage of light bulbs last between 1725 hours and 1875 hours is 99.7%
