Write 14 is 7 times a number c as an equation

Given the piecewise function shown below, select all of the statments that are true.

timurjin [86]

The given the piecewise function is :

$f(x) = \[ \begin{cases} 
 2x & x \ \textless \ 1 \\
 5 & x=1 \\
 x^2 & x\ \textgreater \ 1 
 \end{cases}
\]$

To find f(5) ⇒ substitute with x = 5 in the function → x²
∴ f(5) = 5² = 25

To find f(2) ⇒ substitute with x = 5 in the function → x²
∴ f(2) = 2² = 4

To find f(-2) ⇒ substitute with x = 5 in the function → 2x
∴ f(-2) = 2 * (-2) = -4

To find f(1) ⇒ substitute with x = 1 in the function → 5
∴ f(1) = 5
================================
So, the statements which are true:
$\framebox {B. f(2) = 4} \ \framebox {D. f(1) = 5}$

8 0

3 years ago

Which number is the best approximation for π/3 : 1, 1.03, 1.05, or 1.07?

Evgen [1.6K]

Answer:

1,05

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

The distribution of SAT II Math scores is approximately normal with mean 660 and standard deviation 90. The probability that 100

gayaneshka [121]

Using the normal distribution and the central limit theorem, it is found that there is a 0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

In this problem:

The mean is of 660, hence $\mu = 660$ .

The standard deviation is of 90, hence $\sigma = 90$ .

A sample of 100 is taken, hence $n = 100, s = \frac{90}{\sqrt{100}} = 9$ .

The probability that 100 randomly selected students will have a mean SAT II Math score greater than 670 is 1 subtracted by the p-value of Z when X = 670, hence:

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

By the Central Limit Theorem

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