Totsakan bought one can of pineapple chunks for $2. How many cans can Stefan buy if he has $16?

(a). Consider the parabolic function f(x) = ax² +bx+c, where a ±0, b and care constants. For what values of a, band c is f

ki77a [65]

Information about concavity is contained in the second derivative of a function. Given f(x) = ax² + bx + c, we have

f'(x) = 2ax + b

and

f''(x) = 2a

Concavity changes at a function's inflection points, which can occur wherever the second derivative is zero or undefined. In this case, since a ≠ 0, the function's concavity is uniform over its entire domain.

(i) f is concave up when f'' > 0, which occurs when a > 0.

(ii) f is concave down when f'' < 0, and this is the case if a < 0.

In Mathematica, define f by entering

f[x_] := a*x^2 + b*x + c

Then solve for intervals over which the second derivative is positive or negative, respectively, using

Reduce[f''[x] > 0, x]

Reduce[f''[x] < 0, x]

5 0

2 years ago

According to the National Bridge Inspection Standard (NBIS), public bridges over 20 feet in length must be inspected and rated e

slamgirl [31]

Answer:

1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Step-by-step explanation:

For each bridge, there are only two possible outcomes. Either it has rating of 4 or below, or it does not. The probability of a bridge being rated 4 or below is independent from other bridges. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

For the year 2020, the engineers forecast that 9% of all major Denver bridges will have ratings of 4 or below.

This means that $p = 0.09$

Use the forecast to find the probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Either less than 4 have a rating of 4 or below, or at least 4 does. The sum of the probabilities of these events is 1.

So

$P(X < 4) + P(X \geq 4) = 1$