Pokemon Go

Perhaps you may remember the old Pokemon games you've played when you were a kid, going around, catching stuff, battling others, and possibly evolving the Pokemon you found, well the newest Pokemon game, which is called Pokemon Go, is something completely different. Where shall I start? Well, let's go back to the beginning. Pokemon Go was released on July 7th, 2016 by Niantic, its company. The way you play this game is very different from what you'd expect. Apparently, how you play it involves walking around your neighborhood/city/wherever you live, collecting Pokemon, and also retrieving loot from "Pokestops", random places which have all sorts of stuff like Pokeballs, and whatnot. I know, must sound pretty weird compared to what you probably played in the 1990s. This game is so popular, nowadays I see practically everyone looking on their phones. Some good things about Pokemon go is that it convinces people who've played games like Pokemon x and y to get out there and see a whole different world of where they live (Whenever I go outside to catch Pokemon, I kind of feel like I'm in their world, going a long way from home, even though we don't usually go that far, and in some cases, we go somewhere I am very familiar with), and also maybe becoming more social than previously, this can really help people who have social problems. Something else good about Pokemon Go is, personally for me, where I live. See, I live near a library which is known for having a lot of Pokestops. I don't know if this is something you like about Pokemon Go, but whatever. Going outside used to not really be my thing, but I've seen the world in a different way ever since I started playing Pokemon Go. However, there are also some problems with playing Pokemon Go like this, for example, safety. You may be walking along the crosswalk, and then bam! a car hits you before you can get out of the way. Then a second problem is people's personal property, there are most definitely those moments when you see a very, very rare Pokemon, or maybe a Pokestop on someone's lawn, he probably won't like it that you're trespassing just to catch a Dragonite, or say you go into a construction site, you'll be putting your own life in danger. Also, remembering your way back can be a big problem. Say you're hiking somewhere very unfamiliar, and then you notice a Pokestop you really need that's in a detour, and after a long time of walking just for something in a game, you can't remember your way back. One last problem (which I'm not really sure is that big of a deal) is where you live, some of you probably feel its unfair that Pokestops are closer to someone else's' house than yours. So yes, Pokemon Go may be very popular, but there are the hazards of playing it.    

How to do stuff in Math

Either enter an exact answer in terms of $\pi$pi or use $3\mathrm{.}14$3, point, 14 for $\pi$pi and enter your answer as a decimal.

16π

 units${}^2$start superscript, 2, end superscript

Hint #1

Getting started

We want to find the area of $\frac{1}{4}$start fraction, 1, divided by, 4, end fraction of a circle. Let's start by finding the area of the full circle.

Hint #2

Step 1: Find the area of the full circle

$\begin{array}{cc}& \pi r^2\\ \\ & \pi 8^2\\ \\ & 64\pi \\ \\ \end{array}$

Hint #3

Step 2: Find the area of $\frac{1}{4}$start fraction, 1, divided by, 4, end fraction of the circle

$\begin{array}{cc}\frac{1}{4}& \frac{1}{4}64\pi \\ \\ & \frac{64}{4}\pi \\ \\ & 16\pi \\ \\ \end{array}$

Hint #4

The answer

The area of the shape is $16\pi$16, pi units${}^2$start superscript, 2, end superscript.

(Note that we could also multiply $16$16 by $3\mathrm{.}14$3, point, 14 to get  $50\mathrm{.}24$50, point, 24 units${}^2$start superscript, 2, end superscript.)

Find the arc length of the semicircle.
Either enter an exact answer in terms of $\pi$pi or use $3\mathrm{.}14$3, point, 14 for $\pi$pi and enter your answer as a decimal.

 units

Hint #1

Getting started

We want to find the arc length of $\frac{1}{2}$start fraction, 1, divided by, 2, end fraction of a circle. Let's start by finding the circumference of the circle.

Hint #2

Step 1: Find the circumference of the circle

$\begin{array}{cc}& 2\pi r\\ \\ & 2\pi 11\\ \\ & 112\pi \\ \\ & 22\pi \\ \\ \end{array}$

Hint #3

Step 2: Find the arc length of $\frac{1}{2}$start fraction, 1, divided by, 2, end fraction of the circle

$\begin{array}{cc}\frac{1}{2}& \frac{1}{2}22\pi \\ \\ & \frac{22}{2}\pi \\ \\ & 11\pi \\ \\ \end{array}$

Hint #4

The answer

The arc length of the semicircle is $11\pi$11, pi units.

(Note that we could also multiply $11$11 by $3\mathrm{.}14$3, point, 14 to get $34\mathrm{.}54$34, point, 54 units.)

Justin lives in Saint Paul and goes to school in Minneapolis. In the morning, he has $3$3 transportation options (bus, cab, or train) to school, and in the evening he has the same $3$3 choices for his trip home.

If Justin randomly chooses his ride in the morning and in the evening, what is the probability that he'll use both the bus and the train?

Hint #11 / 4

$\text{Probability} = \dfrac{\text{Favorable combinations}}{\text{Total possible combinations}}$P, r, o, b, a, b, i, l, i, t, y, equals, start fraction, F, a, v, o, r, a, b, l, e, space, c, o, m, b, i, n, a, t, i, o, n, s, divided by, T, o, t, a, l, space, p, o, s, s, i, b, l, e, space, c, o, m, b, i, n, a, t, i, o, n, s, end fraction

Hint #22 / 4

There are $\blue3$start color blue, 3, end color blue possible choices for each trip, so there are $\blue3\times\blue3=9$start color blue, 3, end color blue, times, start color blue, 3, end color blue, equals, 9 total possible combinations. If Justin chooses randomly, all combinations are equally likely.

Hint #33 / 4

Each path through the tree represents one possible outcome. The green paths show the $\green2$start color green, 2, end color green favorable outcomes.

$\text{B}$$\text{C}$$\text{T}$$\text{Ride to school}$$\text{B}$$\text{C}$$\text{T}$$\text{B}$$\text{C}$$\text{T}$$\text{B}$$\text{C}$$\text{T}$$\text{Ride home}$

Hint #44 / 4

The probability that Justin will use both the bus and the train is $2$2 out of $9$9, or $\dfrac29$start fraction, 2, divided by, 9, end fraction .

If you flip three fair coins, what is the probability that you'll get heads on the first two flips and tails on the last flip?

Hint #11 / 4

$\text{Probability} = \dfrac{\text{Favorable outcomes}}{\text{Total possible outcomes}}$P, r, o, b, a, b, i, l, i, t, y, equals, start fraction, F, a, v, o, r, a, b, l, e, space, o, u, t, c, o, m, e, s, divided by, T, o, t, a, l, space, p, o, s, s, i, b, l, e, space, o, u, t, c, o, m, e, s, end fraction

Hint #22 / 4

If you flip three coins, there are $\blue2$start color blue, 2, end color blue possible outcomes for each individual flip, so there are $\blue2\times\blue2\times\blue2=8$start color blue, 2, end color blue, times, start color blue, 2, end color blue, times, start color blue, 2, end color blue, equals, 8 total possible outcomes. Since the coin is fair, each outcome is equally likely.

Hint #33 / 4

Each path through the tree represents one outcome. The green path shows the $\green1$start color green, 1, end color green favorable outcome.

$\text{H}$$\text{T}$$\text{First}$$\text{H}$$\text{T}$$\text{H}$$\text{T}$$\text{Second}$$\text{H}$$\text{T}$$\text{H}$$\text{T}$$\text{T}$$\text{H}$$\text{T}$$\text{H}$$\text{Third}$

Hint #44 / 4

The probability of getting heads on the first two flips and tails on the last flip is $\dfrac18$start fraction, 1, divided by, 8, end fraction .

Josh is hiking Glacier National Park. He has now hiked a total of $17 \text{ km}$17, space, k, m and is $2 \text{ km}$2, space, k, m short of being $\dfrac12$start fraction, 1, divided by, 2, end fraction of the way done with his hike.

Write an equation to determine the total length in kilometers $(h)$left parenthesis, h, right parenthesis of Josh's hike.

Find the total length of Josh's hike.

 $\text{km}$k, m

Hint #11 / 5

Let $h$h be the total length of Josh's hike.

Hint #22 / 5

$\dfrac12$start fraction, 1, divided by, 2, end fraction of Josh's hike is equal to $\dfrac12h \text{ km}$start fraction, 1, divided by, 2, end fraction, h, space, k, m. He is $2\text{ km}$2, space, k, m short of being done with $\dfrac12$start fraction, 1, divided by, 2, end fraction of his hike.

The distance Josh has hiked already is $\dfrac12h - 2$start fraction, 1, divided by, 2, end fraction, h, minus, 2.

Hint #33 / 5

Since the distance he has already hiked is $17 \text{ km}$17, space, k, m, let's set this equal to $17$17:

$\qquad \dfrac12h - 2=17$space, start fraction, 1, divided by, 2, end fraction, h, minus, 2, equals, 17

Now, let's solve the equation to find the total length of Josh's hike $(h)$left parenthesis, h, right parenthesis.

Hint #44 / 5

12h−212h−2+212h12h12h=17=17+2=19=1912=38add 2 to each sidedivide each side by 12

Hint #55 / 5

The equation is $\dfrac12h - 2=17$start fraction, 1, divided by, 2, end fraction, h, minus, 2, equals, 17.

The total length of Josh's hike is $38 \text{ km}$38, space, k, m.