All categories

2 years ago

Find log_{3} [27*\sqrt[4]{3} ] wihout using a calculator. Please show all work!

1 answer:

4 0

$\bf \textit{logarithm of factors}
\\\\
log_a(xy)\implies log_a(x)+log_a(y)\\\\
-------------------------------\\\\
log_3(27\sqrt[3]{3})\qquad 
\begin{cases}
27=3\cdot 3\cdot 3\\
\qquad 3^3\\
\sqrt[3]{3}=\sqrt[3]{3^1}\\
\qquad 3^{\frac{1}{3}}
\end{cases}\implies log_3\left( 3^3\cdot 3^{\frac{1}{3}} \right)
\\\\\\
log_3\left( 3^{3+\frac{1}{3}} \right)\implies log_3\left( 3^{\frac{4}{3}} \right)\implies \cfrac{4}{3}\cdot log_3(3)\implies \cfrac{4}{3}\cdot 1\implies \cfrac{4}{3}$

You might be interested in

MUSIC A song has 28 beats in 4 seconds. At this rate, how many beats are there in 30 seconds?

Deffense [45]

In 4 seconds, number of beats = 28
In 1 sec., it is = 28/4 = 7

Now, In 30 seconds, it would be: 30 * 7 = 210

In short, Your Answer would be: 210 beats

Hope this helps!

4 0

2 years ago

Read 2 more answers

Coronao Coronao Coronao now now

kari74 [83]

Need choices please ok

7 0

2 years ago

<img src="https://tex.z-dn.net/?f=6%5Cfrac%7B1%7D%7B5%7D%20%2B8%5Cfrac%7B4%7D%7B5%7D" id="TexFormula1" title="6\frac{1}{5} +8\fr

Allushta [10]

6 + 8 = 14

1/5 + 4/5 = 5/5 or 1

14 + 1 = 15

4 0

3 years ago

Read 2 more answers

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, So

tatyana61 [14]

Answer:

The probability that at least 13 flights arrive late is 2.5196 $\times 10^{-6}$ .

Step-by-step explanation:

We are given that Southwest Air had the best rate with 80 % of its flights arriving on time.

A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.

The above situation can be represented through binomial distribution;

$P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........$

where, n = number of trials (samples) taken = 18 Southwest flights

r = number of success = at least 13 flights arrive late

p = probability of success which in our question is probability that

flights arrive late, i.e. p = 1 - 0.80 = 20%

Let X = <u><em>Number of flights that arrive late</em></u>.

So, X ~ Binom(n = 18, p = 0.20)

Now, the probability that at least 13 flights arrive late is given by = P(X $\geq$ 13)

P(X $\geq$ 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18)

= $\binom{18}{13}\times 0.20^{13} \times (1-0.20)^{18-13}+ \binom{18}{14}\times 0.20^{14} \times (1-0.20)^{18-14}+ \binom{18}{15}\times 0.20^{15} \times (1-0.20)^{18-15}+ \binom{18}{16}\times 0.20^{16} \times (1-0.20)^{18-16}+ \binom{18}{17}\times 0.20^{17} \times (1-0.20)^{18-17}+ \binom{18}{18}\times 0.20^{18} \times (1-0.20)^{18-18}$

= $\binom{18}{13}\times 0.20^{13} \times 0.80^{5}+ \binom{18}{14}\times 0.20^{14} \times 0.80^{4}+ \binom{18}{15}\times 0.20^{15} \times 0.80^{3}+ \binom{18}{16}\times 0.20^{16} \times 0.80^{2}+ \binom{18}{17}\times 0.20^{17} \times 0.80^{1}+ \binom{18}{18}\times 0.20^{18} \times 0.80^{0}$

= 2.5196 $\times 10^{-6}$ .

7 0

3 years ago

Find the slope of the line that passes through (95, 2) and (-2, 95).

adoni [48]

Answer:

Slope is -93/97

Step-by-step explanation:

To find slope subtract the y's and put that answer in top of a fraction. Then subtract the x's and put that on the bottom of the fraction. If its a smaller number on top and bigger number on the bottom, that is a proper fraction. If the bigger number is on top then it is an improper fraction. If it divides evenly, then the answer will just be a whole number (what the questions calls an integer) All these answers can be positive or negative.

***BUT, you have to start the subtractions with the same point!!!

Let's start with (-2, 95) in front, for both subtractions. (But it could be either point, the answer comes out the same)

Subtract y's: 95-2 is 93.

Subtract x's: -2 - 95 is -97

The slope is 93/-97 it is a proper fraction.

We can put the negative sign in front instead of at the bottom, it looks better.(and is the same)

Slope is -93/97

5 0

2 years ago