law's of exponents
e^(x-5)*e^(3x+8) = 19
e^(x-5+3x+8) = 19
e^(4x+3) = 19
take the natural log, which is base "e" of both sides.
ln[e^(4x+3)] = ln[19]
4x +3 = ln[19]
4x = ln[19] - 3
x = (ln[19] - 3) / 4
x = -0.0139
Find the mean of the following data. (a) 9, 7, 11, 13, 2, 4, 5, 5 (b) 16, 18, 19, 21, 23, 23, 27, 29, 29, 35 (c) 2.2, 10.2, 14.7
Rufina [12.5K]
Answer:
a) 7 b) 24 c) 8.5 d) 11.4 (i think)
Step-by-step explanation:
Answer:
Step-by-step explanation:
Parts of the question are missing.
y = a(x-h)² + k is a vertical parabola.
If a is positive, the parabola opens upwards.
If a is negative, the parabola opens downwards.
The vertex is at (h, k)
Decimal form is 3.96811878
Answer:
The probability is 0.97682
Step-by-step explanation:
We start by finding the z-values of the runner times given.
Mathematically;
z-score = (x-mean)/SD
From the question, mean = 13 seconds and SD = 0.3 seconds
So for 12.4 seconds, we have;
z = (12.4-13)/0.3 = -0.6/0.3 = -2
For 14 seconds, we have;
z = (14-13)/0.3= 1/0.3 = 3.33
So the probability we want to calculate is;
P(-2<z<3.33)
We can find this using the standard normal distribution table
Mathematically;
P(-2<z<3.33) = P(z<3.33) - P(z < -2)
Using the standard normal distribution table, the value of this is;
P(-2<z<3.33) = 0.97682
