Find the inverse of P(x)=-15x^2+350x-2000 and state it’s domain.
1 answer:
Answer:
The function given is:
P(x) = 15x² + 350x - 2000
or
y = 15x² + 350x - 2000
Interchange x and y:
x = 15y² + 350y - 2000
x = (y√15)² + 2(y√15)(45.19) + (45.19)² - (45.19)² - 2000
x = ( y√15 + 45.19)² - 4042.14
( y√15 + 45.19)² = x + 4042.14
Take square root:
y√15 + 45.19 = (√(x + 4042.14))
y√15 = (√(x + 4042.14)) - 45.19
The minimum value of x, for which function is defined and real, is x= -4042.14
Hence, the range of inverse is x ≥ -4042.14
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Answer:
Probability that the diameter of a selected bearing is greater than 111 millimeters is 0.1056.
Step-by-step explanation:
We are given that the diameters of ball bearings are distributed normally. The mean diameter is 106 millimeters and the standard deviation is 4 millimeters.
<em>Firstly, Let X = diameters of ball bearings</em>
The z score probability distribution for is given by;
Z = ~ N(0,1)
where, = mean diameter = 106 millimeters
= standard deviation = 4 millimeter
Probability that the diameter of a selected bearing is greater than 111 millimeters is given by = P(X > 111 millimeters)
P(X > 111) = P( >
) = P(Z > 1.25) = 1 - P(Z
1.25)
= 1 - 0.89435 = 0.1056
Therefore, probability that the diameter of a selected bearing is greater than 111 millimeters is 0.1056.
Answer:
<em>The weight of the parcel is approximately 6 kilograms.</em>
Step-by-step explanation:
The weight of the parcel is 12 lbs and 8 oz.
1 lb = 16 oz
So, 8 oz = lb.
<u>That means, 12 lbs and 8 oz</u> = (12 + 0.5) lbs = 12.5 lbs
Now, 1 lb = 454 g
So, 12.5 lbs = (12.5 × 454) g = 5675 g
As, 1 kilogram = 1000 g
That means, 1 g = 0.001 kilogram
So, 5675 g kilograms. <em>(Rounded to the nearest whole kilogram)</em>
Thus, the weight of the parcel is approximately 6 kilograms.