All categories

4 years ago

Simplify leaving your answer with positive exponents.

Mathematics

1 answer:

vaieri [72.5K]4 years ago

4 0

$\bf \left( \cfrac{5m^{\frac{4}{3}}}{n^{\frac{2}{3}}} \right)^{-\frac{2}{3}}\left(\cfrac{m^4}{8n^5} \right)^{-\frac{4}{3}}\implies 
\left( \cfrac{n^{\frac{2}{3}}}{5m^{\frac{4}{3}}} \right)^{\frac{2}{3}}\left(\cfrac{8n^5}{m^4} \right)^{\frac{4}{3}}\impliedby 
\begin{array}{llll}
\textit{and now we}\\
\textit{distribute}\\
\textit{the exponent}
\end{array}$

$\bf \left( \cfrac{n^{\frac{2}{3}\cdot \frac{2}{3}}}{5^{\frac{2}{3}}m^{\frac{4}{3}\cdot \frac{2}{3}}} \right)\left( \cfrac{8^{\frac{4}{3}}n^{5\cdot \frac{4}{3}}}{m^{4\cdot \frac{4}{3}}} \right)\implies \cfrac{n^{\frac{4}{9}}}{5^{\frac{2}{3}}m^{\frac{8}{9}}}\cdot \cfrac{8^{\frac{4}{3}}n^{\frac{20}{3}}}{m^{\frac{16}{3}}}\implies \cfrac{8^{\frac{4}{3}}n^{\frac{4}{9}+\frac{20}{3}}}{5^{\frac{2}{3}}m^{\frac{8}{9}+\frac{16}{3}}}$

$\bf \cfrac{8^{\frac{4}{3}}n^{\frac{4+60}{9}}}{5^{\frac{2}{3}}m^{\frac{8+48}{9}}}\implies \cfrac{8^{\frac{4}{3}}n^{\frac{64}{9}}}{5^{\frac{2}{3}}m^{\frac{56}{9}}}$

You might be interested in

Help pleaseeeeeeeeeee

sesenic [268]

4/10 and 3/10 are the answers

7 0

4 years ago

While conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modem

Kitty [74]

Answer:

We conclude that this is an unusually high number of faulty modems.

Step-by-step explanation:

We are given that while conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems.

The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013.

Let p = population proportion.

So, Null Hypothesis, $H_0$ : p = 0.013 {means that this is an unusually 0.013 proportion of faulty modems}

Alternate Hypothesis, $H_A$ : p > 0.013 {means that this is an unusually high number of faulty modems}

The test statistics that would be used here One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion faulty modems= $\frac{10}{367}$ = 0.027

n = sample of modems = 367

So, the test statistics = $\frac{0.027-0.013}{\sqrt{\frac{0.013(1-0.013)}{367} } }$

= 2.367

The value of z-test statistics is 2.367.

Since, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since our test statistics is more than the critical value of z as 2.367 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that this is an unusually high number of faulty modems.

6 0

4 years ago

Find the length of the arc and express your answer as a fraction times pie

Elina [12.6K]

Solution:

Given a circle of center, A with radius, r (AB) = 6 units

Where, the area, A, of the shaded sector, ABC, is 9π

To find the length of the arc, firstly we will find the measure of the angle subtended by the sector.

To find the area, A, of a sector, the formula is

$\begin{gathered} A=\frac{\theta}{360\degree}\times\pi r^2 \\ Where\text{ r}=AB=6\text{ units} \\ A=9\pi\text{ square units} \end{gathered}$

Substitute the values of the variables into the formula above to find the angle, θ, subtended by the sector.

$\begin{gathered} 9\pi=\frac{\theta}{360\degree}\times\pi\times6^2 \\ Crossmultiply \\ 9\pi\times360=36\pi\times\theta \\ 3240\pi=36\pi\theta \\ Divide\text{ both sides by 36}\pi \\ \frac{3240\pi}{36\pi}=\frac{36\pi\theta}{36\pi} \\ 90\degree=\theta \\ \theta=90\degree \end{gathered}$

To find the length of the arc, s, the formula is

$\begin{gathered} s=\frac{\theta}{360\degree}\times2\pi r \\ Where \\ \theta=90\degree \\ r=6\text{ units} \end{gathered}$

Substitute the variables into the formula to find the length of an arc, s above

$\begin{gathered} s=\frac{\theta}{360}\times2\pi r \\ s=\frac{90\degree}{360\degree}\times2\times\pi\times6 \\ s=\frac{12\pi}{4}=3\pi\text{ units} \\ s=3\pi\text{ units} \end{gathered}$

Hence, the length of the arc, s, is 3π units.

4 0

1 year ago

Jarvis works in a garage £6 an hour. If he works on Saturday, he is paid time and a quarter. If he works on Sunday, he is paid t

xxMikexx [17]

Answer: He is paid $90 last weekend.

Step-by-step explanation:

Since we have given that

Amount he earns per hour = $6

If he works on Saturday, he is paid time and a quarter .

Amount would be

$6\times 1.25=\$7.5$