Answer:
Step-by-step explanation:
Equation of the function is,
f(x) = 2x² + 20x + 54
To convert the function in the form of f(x) = a(x - h)² + k
f(x) = 2(x² + 10x) + 54
= 2[x² + 2(5x) + 25 - 25] + 54
= 2[x² + 2(5x) + 5²] + 54 - 50
= 2(x + 5)² + 4
= 2[(x - (-5)]² + 4
Vertex of the quadratic equation (parabola) will be (-5, 4)
Therefore, f(x) has a minimum value at x = -5,
f(-5) = 4
"The function f(x) has a minimum value of 4, which occurs when x = 5"
Answer: 0.7471
Step-by-step explanation:
Given : The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of 
and a population standard deviation of 
.
Sample size = 50
Using formula 
, the z-value corresponding to x=98 will be:-
Z-value corresponding to x=103 will be:-
Using the standard normal distribution table for z-scores, we have
P-value = 
Hence, the probability we could select a sample of 50 adults and find that the mean of this sample is between 98 and 103 = 0.7471
This is a geometric sequence problem.
You have a sequence of;
2/3, 2, 6, 18, 54
Their common ratio is t1/t0 = 2/(2/3) = 3
Formula for G.P n terms is denoted by
ar^(n-1) = nth term
Where;
a - first term
r - common ratio
n - nth term in the sequence
So the exponential formula is basically that.
Example
To find the 3rd term which is 6
ar^(n-1) = (2/3)(3)^(3-1)
-> (2/3)(3)²
-> (2/3)(9)
-> (2)(3)
-> 6
There are one number is X, and another number is -9/10and sum is 2/3.
The answer is 95 of the unit rate
