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3 years ago

8

Betra is planning a party for her friends.The room rental cost is $50 plus an additional five dollars per person to cover food c

osts. Veteran has saved up $100. What is the maximum number of people that can attend her party?

1 answer:

liraira [26]3 years ago

4 0

She can have 10 people attend.

The room costs $50 dollars, so she has $50 left to spend on food costs.

$50/5 = 10 people

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Viefleur [7K]

Answer:

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Paladinen [302]

The solid shape is a cone and a half sphere. So the equation would be (cone volume) + (1/2 sphere volume):
$cone = \frac{1}{3} \pi {r}^{2} h \\ sphere = \frac{4}{3} \pi {r}^{3} \\ object = ( \frac{1}{3} \pi {r}^{2} h) + \frac{1}{2} ( \frac{4}{3} \pi {r}^{3} )$
If the volume of the cone is 270pi and the height of the cone is 10, then:
$270\pi = \frac{1}{3} \pi {r}^{2} (10) \\ 27 = \frac{1}{3} {r}^{2} \\ 80 = {r}^{2} \\ r = 9$
The radius of the object is 9 cm. Therefore, we can plug into the formula for the total volume:
$object = 270\pi + \frac{1}{2} ( \frac{4}{3} \pi {(9)}^{3} ) \\ = 270\pi + \frac{2}{3} (729\pi) \\ = 270\pi \: + 243\pi \\ = 513\pi$
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3 years ago

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3 years ago

The director of the library calculates that 29% of the library's collection is checked out. If the director is right, what is th

marusya05 [52]

Answer:

The probability that the proportion of books checked out in a sample of 412 books would differ from the population proportion by less than 4% is P=0.9255.

Step-by-step explanation:

The population's proportion is $\pi=0.29$

If we take a sample of 412 books (n=412), we have a standard deviation of the sampling distribution of:

$\sigma_M=\sqrt{\frac{\pi(1-\pi)}{n}}=\sqrt{\frac{0.29*0.71}{412}}=\sqrt{0.0005} =0.0224$

We have to calculate the probabilty that the sample proportion will be between 0.25 and 0.33.

$z_1=(0.25-0.29)/0.0224=-0.04/0.0224=-1.7857\\\\z_2=1.7857\\\\\\P(0.25$

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