8 times ( 5 times 2+3) = 8 times (15+3) = 8 times 13 + 104
Answer:
C. 7
Step-by-step explanation:
We have been given graphs of two exponential functions, f and g.
We can see that our parent function f(x) is translated k units to get function g(x).
The rules for translation are mentioned below.
Horizontal shifting:
= Graph shifted to right by a units.
= Graph shifted to left by a units.
Vertical shifting:
= Graph shifted upwards by a units.
= Graph shifted downwards by a units.
Upon comparing our given graph with transformation rules we can see that our function f(x) is translated k units upward to get function g(x).
Now let us find the value of k from our given graph.
We can see that initial value (y-intercept) of f(x) is -4 and initial value of g(x) is 3. Difference between y-intercepts of both functions is 7.
Our parent function f(x) is shifted 7 units upwards to get new function g(x), therefore the value of k is 7 and option C is the correct choice.
Answer:
(-0.84, 0) and (-5.16, 0).
Step-by-step explanation:
Answer:
(a) 283 days
(b) 248 days
Step-by-step explanation:
The complete question is:
The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 268 days and a standard deviation of 12 days. (a) What is the minimum pregnancy length that can be in the top 11% of pregnancy lengths? (b) What is the maximum pregnancy length that can be in the bottom 5% of pregnancy lengths?
Solution:
The random variable <em>X</em> can be defined as the pregnancy length in days.
Then, from the provided information .
(a)
The minimum pregnancy length that can be in the top 11% of pregnancy lengths implies that:
P (X > x) = 0.11
⇒ P (Z > z) = 0.11
⇒ <em>z</em> = 1.23
Compute the value of <em>x</em> as follows:
Thus, the minimum pregnancy length that can be in the top 11% of pregnancy lengths is 283 days.
(b)
The maximum pregnancy length that can be in the bottom 5% of pregnancy lengths implies that:
P (X < x) = 0.05
⇒ P (Z < z) = 0.05
⇒ <em>z</em> = -1.645
Compute the value of <em>x</em> as follows:
Thus, the maximum pregnancy length that can be in the bottom 5% of pregnancy lengths is 248 days.