Simplify the following expression.

Mathematics

1 answer:

Nitella [24]2 years ago

7 0

Answer:

Step-by-step explanation:

So to make it look simpler, rewrite it as this:

$\frac{4^{5} 7^{3} }{4^27^4}$

Now, you can cross out the 4^2 and 7^3

You're left with:

$\frac{4^3}{7}$

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The ratio of girls to boys in a class is 3:5 what fraction of the class are girls?

Wewaii [24]

Answer:

Hello!!

If the ratio of girls to boys in a class is 3:5, the fraction of the class that are girls is...

$\frac{3}{5}$

Hope this helps!!

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2 years ago

The owner of a small pet supply store wants to open a second store in another city, but he only wants to do so if more than one-

Andrei [34K]

Answer:

The answer is "The null hypothesis was rejected".

Step-by-step explanation:

Following are the right-tailed test:

Calculating the null and alternative hypothesis:

$H_0 : p = 0.3333\\\\H_a : p > 0.3333\\\\n = 150\\\\x = 64\\\\\hat{p} = \frac{x}{n} = \frac{64}{150} = 0.4267\\\\P_0 = 0.3333\\\\1 - P_0 = 1 - 0.3333 = 0.6667\\\\$

$z = \frac{\hat{p} - P_0}{[\sqrt{\frac{P_0 \times (1 - P_0 )}{n}}]}$

$= \frac{0.4267 - 0.3333}{[\sqrt{\frac{(0.3333 \times 0.6667)}{150}}]}\\\\= 2.426$

Calculating the right-tailed test:

$P(z > 2.426) = 1 - P(z < 2.426) = 1 - 0.9924 = 0.0076\\\\P-value = 0.0076\\\\\alpha = 0.05\\\\P-value < \alpha$

Therefore, we reject the null hypothesis.

This example shows that more than a third of the families own pets in this town.

5 0

2 years ago

Someone please help!!! Can’t find this one anywhere!!! please and thank you!!!!!!!

Tema [17]

$\dfrac{ 2+ 2i}{5+4i}\\\\\\=\dfrac{(2+2i)(5-4i)}{(5+4i)(5-4i)}\\\\\\=\dfrac{10-8i + 10i -8i^2}{5^2 -(4i)^2}\\\\\\=\dfrac{10+2i +8}{25+16}~~~~;[i^2 =-1]\\\\\\=\dfrac{18+2i}{41}\\\\\\=\dfrac{18}{41} + \dfrac{2}{41}i$