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2 years ago

The number of 1 inch cubes that will fit into a box that is 7 inches wide blank inches long and 1 inch high is 154

1 answer:

8 0

All you need to find is : 7 × ? = 154

so you need to divide :
154 ÷ 7 = 22

so the length of the box is 22 inches

hope this helps : )

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A population of bacteria is initially 6000. After three hours the population is 3000. If this rate of decay continues, find the

serious [3.7K]

Answer:

The equation is $A=6000e^{-0.23t}$ at a rate of -23%.

Step-by-step explanation:

Decay can be represented by the equation $A=A_0e^{rt}$ . We can find the rate at which it decays by using t=3 hours and A=3000. This means $A_0=6000$ in this context.

$A=A_0e^{rt}\\3000=6000e^{r(3)}$

$0.5=e^{(24.5)r}$

After substituting, we divided by 6000 to each side to get 0.5 on the left. Now to solve for r, we will take the natural log of both sides and use log rules to isolate r.

$ln 0.5=ln e^{(3)r}\\ln 0.5=3r (ln e)\\\frac{ln0.5}{3} =r$

We know $lne=1$ so we were able to cancel it out and divide both sides by 3.

We solve with a calculator $\frac{ln0.5}{3} =r\\-0.23=r$

We change -0.23 into a percent by multiplying by 100 to get -23% as the rate.

The equation is $A=6000e^{-0.23t}$

5 0

3 years ago

A pencil holder shaped like a triangular prism is shown in the picture. The height of the pencil holder is 12 cm, and the volume

algol13

Answer:

18cm

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

The dwarves of the Grey Mountains wish to conduct a survey of their pick-axes in order to construct a 99% confidence interval ab

Dmitry_Shevchenko [17]

Answer:

The minimum sample size needed is 125.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

$\pi = 0.25$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 25 percent of the pick-axes are in need of repair?

This minimum sample size is n.

n is found when $M = 0.1$