$\left[3\cdot(-2)^3(5)^{-2}\right]^2=\left[3(-8)\cdot\dfrac{1}{5^2}\right]^2=\left(-24\cdot\dfrac{1}{25}\right)^2=\left(-\dfrac{24}{25}\right)^2\\\\=\dfrac{24^2}{25^2}=\dfrac{576}{625}$

explanation

$(-2)^3=(-2)(-2)(-2)=-8\\\\a^{-n}=\dfrac{1}{a^n}\to5^{-2}=\dfrac{1}{5^2}=\dfrac{1}{(5)(5)}=\dfrac{1}{25}\\\\a^2\geq0\ \text{for any real number}\to\left(-\dfrac{24}{25}\right)^2=\left(\dfrac{24}{25}\right)^2\\\\\left(\dfrac{a}{b}\right)^2=\dfrac{a^2}{b^2}\to\left(\dfrac{24}{25}\right)^2=\dfrac{24^2}{25^2}=\dfrac{(24)(24)}{(25)(25)}=\dfrac{576}{625}$

6 0

4 years ago

Rounding to the first decimal place, calculate the mean for the following distribution of homicide rates in the 12 metropolitan

Lelechka [254]

Solution :

Given :

X = homicide rate (homicides per 100,00 population)

n = 12 = metropolitan areas

Area X (homicides per 100,000 population)

Mesa, AZ 4.1

Seattle, WA 3.8

Portland, OR (tie) 3.4

New York, NY(tie) 3.4

Virginia beach, VA 3.3

San Jose, CA 3.1

EI, Paso, TX 2.6

Austin, TX 2.6

San Diago, CA 2.4

Suffolk County 2.2

Montgomery, MD 2.0

Fairfax, VA 1.7

Therefore, the mean of X = $\bar X = \frac{\sum X_i}{n}$

$=\frac{34.9}{12}$

= 2.9

Therefore, the mean of homicide rater in the 12 metropolitan areas is 2.9 homicide per 100,000 population.

7 0

3 years ago