So we are given a system:
Substitute x = 2 we get the system:
Multiply the first equation by -5 and the second by 2 we get the system:
Adding the two equations we get :
We find the value of y by using any of the other equations like this:
Final solution:
The sound intensity of the Pile Driver is 39.5
or nearly 40 times the sound intensity of the jackhammer.
Given with Loudness in dB for pile driver = 112 dB
We have to convert it in terms of sound intensity.
First,
112dB/10 = 11.2
Then we'll use this as exponent of 10
(10)^(11.2) = 1.5849 * 10 ^ 11
Then use the equation of Watts per square meter to find the intensity:
I / (10^-12 W/m^2) =1.5849 * 10 ^ 11
I = sound intensity = 0.158
Then compare:
Sound intensity of Pile Driver/ Sound intensity of Jackhammer
(0.158) / (0.004)
= 39.5
or nearly 40 times the jackhammer.
Their lines intersect at this point, which mean that they did the same thing, so it can't be A or D, and we dont know the total number of pages so we can't for sure say it's B.
So it's C, because we can see that the point is on 10 for the x-axis, which represents # of nights, and 150 for the y-axis, which represents # of pages read.
Angle ABC = 130
Angle ABC = Angle ADC = 130 (Opposite angles are equal)
Angle DAB = 180 - 130 = 50 (consecutive interior angles)
I HOPE IT IS HELPFUL:D
Answer:
Step-by-step explanation:
The mean of the gas mileages is 317÷16=19.8125
317 is the sum total of all the figures and 16 is the number of figures in the distribution
Standard deviation is the square root of the variance and the variance is the mean of all squared deviations
The 16 squared deviations are
7.9102(×2) + 3.2852(×2) + 0.6602(×3) + 0.0352(×4) + 1.4102(×3) + 10.1602 + 17.5352 = 56.4382
56.4382÷16 = 3.5274
This is the Variance. The standard deviation is herefore √3.5274 =1.878 ~ 1.88 (to 2 decimal places)
(B) Chebyshev's inequality predicts that 75% of the selection will fall within 2 standard deviations of the mean
2×1.88=3.76
19.8125-3.76 = 16.05
19.8125+3.76= 23.57
The gas mileages are between 16.05 and 23.57
(C) the actual % of SUV models of the sample that fall in the above range is (15/16 × 100) = 93.75%
(D) the empirical rule gives the more accurate prediction
