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3 years ago

A hiker discovers a skull that contains 41% of its original amount of C-14. Find the age of the skull to the nearest year

1 answer:

3 0

We need the half-life of C-14 which is 5,730 years.
Now, we will need a half-life equation:
elapsed time = half-life * log (bgng amt / ending amt) / log 2
We'll say beginning amount = 100 and ending amount = 41
elapsed time = 5,730 * log (100/41) / log 2
elapsed time = 5,730 * log ( 2.4390243902 ) / 0.30102999566
elapsed time = 5,730 * 0.38721614327 / 0.30102999566
elapsed time = 5,730 * 1.2863041851 
elapsed time = 7,370.523 years

Source:
http://www.1728.org/halflife.htm

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In an auditorium, a charity show is conducted in order to raise at least $3,750. The auditorium can accommodate up to 180 specta

Maksim231197 [3]

Answer:

See explanation

Step-by-step explanation:

Let $x,\ x\ge 0$ be the number of students and $y,\ y\ge 0$ be the number of adults on the show.

1. Tickets cost $15 for students, so x student tickets cost $15x.

Tickets cost $25 for adults, so y adult tickets cost $25y.

Total cost of all tickets is $(15x + 25y).

The charity show is conducted in order to raise at least $3,750, thus

$15x+25y\ge 3,750$

2. The auditorium can accommodate up to 180 spectators, hence

$x+y\le 180$

3. We get the system of inequalities:

$\left\{\begin{array}{l}x\ge 0\\y\ge 0\\x+y\le 180\\15x+25y\ge 3,750\end{array}\right.$

Plot all solutions sets to each inequality and the common region is the solution set to the system of inequalities. This region is not empty, so the charity will reach its goal. For example, if they sell 50 students tickets and 125 adult tickets, they will raise $\$(15\cdot 50+25\cdot 125)=\$3,875$

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3 years ago

Finding the perimeter of each rectangle 96ft width 124ft length

dezoksy [38]

Answer:

440 ft

Step-by-step explanation:

Perimeter(p) of a rectangle is 2l + 2w

Where 'l' is the length and 'w' is the width.

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Step-by-step explanation:

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3 years ago

An investigator wants to assess whether the mean m = the weight of passengers flying on small planes exceeds the FAA guideline o

stira [4]

Answer:

$H_{0}: \mu= 185$ and $H_{a}: \mu > 185$

Step-by-step explanation:

The null hypothesis $H_{0}$ states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. We can write the null hypothesis in the form $H_{0}: parameter = value$

In this context, the investigator's null hypothesis should be that the average total weight is no different than the reported value by the FAA. We can write it in this form $H_{0}: \mu= 185$ .

The alternative hypothesis $H_{a}$ states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. We can write the alternative hypothesis in one of three forms

$H_{a}: parameter > value\\H_{a}: parameter < value\\H_{a}: parameter \neq value$

The investigator wants to know if the average weight of passengers flying on small planes exceeds the FAA guideline of the average total weight of 185 pounds. He should use $H_{a}: \mu > 185$ as his alternative hypothesis.

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3 years ago