Ask question

Ask question

All categories

4 years ago

6

A rectangular prism has a volume of 729ft3. The length, width and height are all the same. What is the length of each side of th

e prism?

1 answer:

creativ13 [48]4 years ago

8 0

9

because 9 x 9 x 9 = 729

You might be interested in

kiruha [24]

Answer:

90

Step-by-step explanation:

You would get 36 dollars from 90 liters.

The answer is in the photo.

6 0

3 years ago

What is the smallest number greater than 100 that is :

krek1111 [17]

I'd start by listing out the multiplies of all three past 100, like this:
102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130
104, 108, 112, 116, 120, 124, 128, 132, 136
110, 120, 130, 140
Now it's just a matter of finding the number that is the same for all three of them, which is 120.

8 0

3 years ago

Read 2 more answers

3.30 Survey response rate. Pew Research reported in 2012 that the typical response rate to their surveys is only 9%. If for a pa

Artist 52 [7]

Answer:

0% probability that at least 1,500 will agree to respond

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 15000, p = 0.09$

So

$\mu = E(X) = np = 15000*0.09 = 1350$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15000*0.09*0.91} = 35.05$

What is the probability that at least 1,500 will agree to respond

This is 1 subtracted by the pvalue of Z when X = 1500-1 = 1499. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1499 - 1350}{35.05}$

$Z = 4.25$

$Z = 4.25$ has a pvalue of 1.

1 - 1 = 0

0% probability that at least 1,500 will agree to respond

6 0

4 years ago

In a lab experiment, 80 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to doub

Effectus [21]

Answer:

The hourly growth rate is of 4.43%.

The function showing the number of bacteria after t hours is $P(t) = 80(1.0443)^t$

Step-by-step explanation:

Equation of population growth:

The equation for the population after t hours is given by:

$P(t) = P(0)(1+r)^t$

In which P(0) is the initial population and r is the growth rate, as a decimal.

The conditions are such that the number of bacteria is able to double every 16 hours.

This means that $P(16) = 2P(0)$ . We use this to find r.

$P(t) = P(0)(1+r)^t$

$2P(0) = P(0)(1+r)^{16}$

$(1+r)^{16} = 2$

$\sqrt[16]{(1+r)^{16}} = \sqrt[16]{2}$

$1 + r = 2^{\frac{1}{16}}$

$1 + r = 1.0443$

$r = 1.0443 - 1$

$r = 0.0443$

The hourly growth rate is of 4.43%.

80 bacteria are placed in a petri dish.

This means that $P(0) = 80$ .

$P(t) = P(0)(1+r)^t$

$P(t) = 80(1+0.0443)^t$

$P(t) = 80(1.0443)^t$

The function showing the number of bacteria after t hours is $P(t) = 80(1.0443)^t$

6 0

3 years ago

The quotient of 14 and a number is 1/3

djverab [1.8K]

Answer:

14 / 1/3

Step-by-step explanation:

3 0

3 years ago