Which of the following is a rational number?

How are radicals and rational exponents related?

icang [17]

Answer:

Any radical in the form can be written using a fractional exponent in the form . The relationship between and works for rational exponents that have a numerator of 1 as well. For example, the radical can also be written as , since any number remains the same value if it is raised to the first power.

Step-by-step explanation:

8 0

3 years ago

Erin deposited $400 in a saving account earning 3% yearly compound interest. write an equation to represent how much money (y) E

bekas [8.4K]

$~~~~~~ \textit{Compound Interest Earned Amount \underline{in 15 years}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$400\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yeary, thus once} \end{array}\dotfill &1\\ t=years\dotfill &15 \end{cases}$

$A=400\left(1+\frac{0.03}{1}\right)^{1\cdot 15}\implies A=400(1.03)^{15}\implies A\approx 623.19 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=400(1.03)^x~\hfill$

4 0

2 years ago

A sample of 1000 college students at NC State University were randomly selected for a survey. Among the survey participants, 102

cupoosta [38]

Answer:

The upper endpoint of the 99% confidence interval for population proportion is 0.13.

Step-by-step explanation:

The confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

<u>Given:</u>

<em>n</em> = 1000

$\hat p$ = 0.102

$z_{\alpha /2}=z_{0.01/2}=z_{0.005}=2.58$

*Use the standard normal table for the critical value.

Compute the 99% confidence interval for population proportion as follows:

$CI=\hat p\pm z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.102\pm 2.58\times\sqrt{\frac{0.102(1-0.102)}{1000}}\\=0.102\pm0.0248\\=(0.0772, 0.1268)\\\approx (0.08, 0.13)$