At 0 hours: 24 boxes
After 1 hour: 24/2 = 12 boxes
After 2 hours: 12/2 = 6 boxes
After 3 hours: 6/2 = 3 boxes

She will have 3 boxes after 3 hours.

Hope this helps :)

5 0

2 years ago

We are standing on the top of a 320 foot tall building and launch a small object upward. The object's vertical altitude, measure

STALIN [3.7K]

Answer:

The highest altitude that the object reaches is 576 feet.

Step-by-step explanation:

The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be $h(t) = -16\cdot t^{2} + 128\cdot t + 320$ , the first and second derivatives are, respectively:

First Derivative

$h'(t) = -32\cdot t +128$

Second Derivative

$h''(t) = -32$

Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:

$-32\cdot t +128 = 0$

$t = \frac{128}{32}\,s$

$t = 4\,s$ (Critical value)

The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:

$h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320$

$h(4\,s) = 576\,ft$

The highest altitude that the object reaches is 576 feet.

6 0

3 years ago

The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean

kondor19780726 [428]

Answer:

68% of the incomes lie between $36,400 and $38,000.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $37,200

Standard Deviation, σ = $800

We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.

Empirical rule:

Almost all the data lies within three standard deviation of mean for a normally distributed data.
About 68% of data lies within one standard deviation of mean.
About 95% of data lies within two standard deviation of mean.
About 99.7% of data lies within three standard deviation of mean.

Thus, 68% of data lies within one standard deviation.

$\mu \pm \sigma\\=37200 \pm 800\\=(36400,38000)$

Thus, 68% of the incomes lie between $36,400 and $38,000.

5 0

2 years ago