A 99-inch candle burns down in 12 hours. At what rate does the candle burn, in inches per hour?
2 answers:
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The first step is to find the slope of the given line by putting its equation in the form y = mx + b.
9y = x - 18
Dividing both sides by 9, gives:
y = (x/9) - 2
The slope of the given line is therefore 1/9.
Let the slope of the perpendicular line be m.
The product of the two slopes must equal -1 for the lines to be perpendicular.
Therefore m = -9.
At this stage the equation of the required line is y = -9x + b.
Now we need to find the value of b.
Plugging the given values of a point on the line (6, -1) into the equation gives:
-1 = -54 + b; from which b = 53.
The required equation for the line is:
f(x) = -9x + 53.
9y = x - 18
Dividing both sides by 9, gives:
y = (x/9) - 2
The slope of the given line is therefore 1/9.
Let the slope of the perpendicular line be m.
The product of the two slopes must equal -1 for the lines to be perpendicular.
Therefore m = -9.
At this stage the equation of the required line is y = -9x + b.
Now we need to find the value of b.
Plugging the given values of a point on the line (6, -1) into the equation gives:
-1 = -54 + b; from which b = 53.
The required equation for the line is:
f(x) = -9x + 53.
Answer:
Step-by-step explanation:
From the given information:
There are 30 collections of gems, of which 8 are worthless;
Thus, the number of the genuine diamonds = 30 - 8 = 22.
Let X = random variable;
X consider the value as 0 (for 2 worthless stone selection),
X = 1200(1 worthless stone & 1 genuine stone)
X = 2400 (2 genuine stones selected)
However, the numbers of ways of selecting and chosen Gems can be estimated as:
Thus;
To find E(X):
E(X) = (0 × 0.0644) + (1200 × 0.4046) + (2400 × 0.5310)
E(X) = 0 + 485.52 + 1274.4
E(X) = 1759.92