Elsie bought a video game for $85.00. If the store charges 170% of its cost for the game, how much is the store's profit?

Mathematics

1 answer:

OLEGan [10]2 years ago

3 0

Answer:

$35

Step-by-step explanation:

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You are researching the penguin population in the Falkland Islands. There are 1000 penguins in the beginning of the first year:

kolbaska11 [484]

Answer:

The formula to determine the population of penguins at the end of the 7th year is:

$P_7=1.3^7\cdot P_0=6.275\cdot 1000=6275$

Step-by-step explanation:

With this information, we know that the initial population at end of year 0 is 1000 penguins.

The first year will born 500 chicks (50% of the population) and also 20% of the total population will die.

We can then model the population for the end of year 1 as:

$P_1=P_0+0.5P_0-0.2P_0=1.3P_0$

As this dynamic will continue with the years, we can generalize as:

$P_2=1.3P_1=1.3\cdot (1.3P_0)=1.3^2P_0\\\\P_n=1.3^nP_0$

Then, the value of the population at the end of the 7th year should be:

$P_7=1.3^7\cdot P_0=6.275\cdot 1000=6275$

8 0

2 years ago

Suppose a snow cone has a paper cone that is 8 centimeters deep and has a diameter of 5 centimeters. The flavored ice comes in a

Neko [114]

check the picture below.

so the cone itself has a height of 8, and a radius of 2.5, and the spherical scoop, ready to melt in it, has a radius of 2.5.

namely, will the volume of the sphere be larger than the cone? in which case the melted ice-cream will overflow.

$\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=2.5\\ h=8 \end{cases}\implies V=\cfrac{\pi (2.5)^2(8)}{3}\implies \implies \boxed{V=\cfrac{50\pi }{3}} \\\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad r=2.5\implies V=\cfrac{4(\pi )(2.5)^3}{3}\implies \boxed{V=\cfrac{125\pi }{6}} \\\\\\ \textit{the sphere's volume is larger, so yes, it will overflow}$