Answer:
Cov(X, Y) =0.029.
Step-by-step explanation:
Given that :
The noise in a particular voltage signal has a constant mean of 0.9 V. that is μ = 0.9V ............(1)
Also, the two noise instances sampled τ seconds apart have a bivariate normal distribution with covariance.
0.04e–jτj/10 ............(2)
Having X and Y denoting the noise at times 3 s and 8 s, respectively, the difference of time = 8-3 = 5seconds.
That is, they are 5 seconds apart,
τ = 5 seconds..............(3)
Thus,
Cov(X, Y), for τ = 5seconds = 0.04e-5/10
= 0.04e-0.5 = 0.04/√e
= 0.04/1.6487
= 0.0292
Thus, Cov(X, Y) =0.029.
Ounce of blue dye mixed with one gallon of white paint base = 3/4
Ounce of blue dye mixed with eight gallons of white paint base = 
= 3 × 2
=6
Ounce of pink dye mixed with one gallon of white paint base = 2/3
Ounce of pink dye mixed with eight gallons of white paint base = 
= 16/3
= 5.3
Hence, 6 ounce of blue dye and 5.3 ounce of pink dye are needed to mix with 8 gallons of paint.
=6
Answer: The scale factor is 4
Step-by-step explanation:
We know that the pyramids are similar. The volume of one of these pyramids is 13,824 cubic feet and the volume of the other one is 216 cubic feet. Then:
By Similar solids theorem, if two similar solids have a scale factor of 
, then corresponding volumes have a ratio of 
Then:
Knowing this, we can find the scale factor. This is:
![\frac{13,824}{216}=\frac{a^3}{b^3}\\\\\frac{13,824}{216}=(\frac{a}{b})^3\\\\\frac{a}{b}=\sqrt[3]{\frac{13,824}{216}}\\\\scale\ factor=\frac{a}{b}=4](https://tex.z-dn.net/?f=%5Cfrac%7B13%2C824%7D%7B216%7D%3D%5Cfrac%7Ba%5E3%7D%7Bb%5E3%7D%5C%5C%5C%5C%5Cfrac%7B13%2C824%7D%7B216%7D%3D%28%5Cfrac%7Ba%7D%7Bb%7D%29%5E3%5C%5C%5C%5C%5Cfrac%7Ba%7D%7Bb%7D%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B13%2C824%7D%7B216%7D%7D%5C%5C%5C%5Cscale%5C%20factor%3D%5Cfrac%7Ba%7D%7Bb%7D%3D4)
Step-by-step explanation:
A supplementary angle is an angle that is 180 degrees. We are given two angles that add up to 180, but we need to solve for x first.
The first step is to solve both angles. We know that both angles added together are supplementary, so they are equal to 180.
4x + 8 = unknown angle
6x + 3 = unknown angle
(4x + 8) + (6x + 3) = 180
Because we know a supplementary angle is 180 degrees, we can solve for x to find both angles.
Solve for x.
(4x + 8) + (6x + 3) = 180
10x + 11 = 180
10x = 169
x = 16.9
Now, we know the value of x, so we plug in x for both angles to determine which angle is smaller.
4x + 8
4(16.9) + 8
67.6 + 8 = 75.6 degrees
and the other angle
6x + 3
6(16.9) + 3
101.4 + 3 = 104.4 degrees
Now we know that the smaller angle is 75.6 degrees.
Also, to make sure the math is correct, when plugging in both numbers after finding x, they should add to 180.
75.6 + 104.4 = 180 so we know they are supplementary for sure.
Good luck!
Answer:
300 dollars
Step-by-step explanation:
60% of 500
(60/100) * 500 = 300
