5x - 4y = 19 x + 2y = 8
1 answer:
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Answer:
The instantaneous rate of change of with respect to
at the value
is 18.
Step-by-step explanation:
a) Geometrically speaking, the average rate of change of with respect to
over the interval by definition of secant line:
(1)
Where:
,
- Lower and upper bounds of the interval.
,
- Function exaluated at lower and upper bounds of the interval.
If we know that ,
and
, then the average rate of change of
with respect to
over the interval is:
The average rate of change of with respect to
over the interval
is 27.
b) The instantaneous rate of change can be determined by the following definition:
(2)
Where:
- Change rate.
,
- Function evaluated at
and
.
If we know that and
, then the instantaneous rate of change of
with respect to
is:
The instantaneous rate of change of with respect to
at the value
is 18.
Answer:
The probability that a jar contains more than 466 g is 0.119.
Step-by-step explanation:
We are given that a jar of peanut butter contains a mean of 454 g with a standard deviation of 10.2 g.
Let X = <u><em>Amount of peanut butter in a jar</em></u>
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = population mean = 454 g
= standard deviation = 10.2 g
So, X ~ Normal()
Now, the probability that a jar contains more than 466 g is given by = P(X > 466 g)
P(X > 466 g) = P( >
) = P(Z > 1.18) = 1 - P(Z
1.18)
= 1 - 0.881 = <u>0.119</u>
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.