PLEASE HELP!!!! The problem is in the photo below.

Fill in the blanks to show the steps in solving the inequality -2x + 12<-4

professor190 [17]

-2x + 12 < - 4......subtract 12 from both sides
-2x + 12 - 12 < -4 - 12....simplify
-2x < -16...divide both sides by -2, changing the inequality sign
(-2/-2)x > -16/-2....simplify
x > 8

8 0

3 years ago

What are the domain and range of the function f(x) = 3x + 5? domain: (negative infinity, infinity); range: (0, infinity) domain:

AlekseyPX

Answer:

Domain : (-∞,∞) Range : (-∞,∞)

Step-by-step explanation:

Given:

f(x) = 3x+5

To find: Domain and Range of f(x)

Domain is the set of values that x can take.

Range is the set of values of y corresponding to the values of x in the domain.

Here x can take any value and the domain is the set of real numbers i.e (-∞,∞).

f(x) = 3x + 5

The graph of f(x) is a straight line that extends from -∞ to +∞ and hence the range is (-∞,∞).

3 0

3 years ago

Read 2 more answers

The ideal size of a first-year class at a particular college is 150 students. The college, knowing from past experiences that on

katen-ka-za [31]

Answer:

6.18% probability that more than 150 first-year students attend this college.

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

For each item selected, there are only two possible outcomes. Either it is defective, or it is not. This means that we use concepts of the binomial probability distribution to solve this problem.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .