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.

Malice

I recently finished a part graphic novel, part comic book called Malice, by Chris Wooding. So basically, this book is a part of a series, so I won't be able to say a whole lot. Malice takes place in England, and there is a comic book of the same name. What's very weird is that it is possible to end up in the comic, if you take certain objects (six items as I recall), and say the words, "Tall Jake take me away" six times, then a tall, dark guy (who is Tall Jake) will then appear when you're alone, and then take you to the world, Malice. Malice is a realm that lots of kids in the real world have heard about, but very, very few survive their first night (what I have read about in Malice shows that this world is much, much more different than our world. For starters, there are two tickets, black and white. Black tickets can take you anywhere throughout parts of Malice (yes, when it comes to "parts of Malice", you may think of that movie Zootopia), and white tickets are able to take you throughout parts of Malice, AND back home. But there are the consequences. Perhaps you may be wondering, all those kids who found white tickets and could get home, why can't they just tell someone about what had happened? As it turns out, the survivors lose memory of everything that had previously occurred. Malice also has its hazards, such as monsters called "Chitters", mechanical fiends that can "drink" time out of you. So by that, I mean make you a whole lot older). Seth and Kady, the main characters of the story think this whole thing is a really stupid myth, but after their friend Luke disappears and suddenly appears in the newest issue of Malice, things don't seem so silly after all. However, after they both wind up in Malice themselves, the two realize they are not alone. There are groups opposing Tall Jake, one of which is called Havoc. Will Seth and Kady be able to survive in Malice? Read to find out.

Anger

I have my ways to express anger. Sometimes, I say the things I don't mean to say, just to let you know.

A Dog's Life

Recently, I have finished a novel called A Dog's Life, by author Ann M. Martin. This story is told from a stray dog's point of view in life. At first, she has a family which are a mother, and her brother, named Bone. The main character's name is Squirrel, which is a pretty weird name. Her life is perfect, until she is separated from the rest of her family. The story is something like Zhang Leping's comic book, Sanmao, which is about a boy who lives on his own. Only difference is, after their mother disappears, Squirrel is with Bone for a brief time, while in Sanmao, he is all alone. However, Squirrel and Bone eventually part ways after a human takes him for a pet, while leaving Squirrel behind. Then, Squirrel must face the dangers of strays' lives. Changing seasons, very busy highways, and other humans. Along the story, Squirrel has all sorts of adventures. One of them is meeting another stray, which looks like Bone, named Moon. For a big part of the book, they explore the rest of the world together, finding new towns, until a fateful day when a truck accidentally hits both dogs, and kills Moon. After being taken from the truck driver's family to the vet, Squirrel lives with them for the whole summer, until they move back to the city leaving her behind. Lonely again, Squirrel ages time to time, until she is too old to hunt. Her life is hard, until she meets a friend who will change the rest of her life forever. What's crazy, is that this book was actually inspired by the author's dog.

Choremonster

Finished your laundry? Taken out the trash? Want a reward? Lately, for our "points system", we have been using, instead of Google Docs, a new app called "ChoreMonster". Which is something similar. There, we come up with a bunch of random chores, and then, when we have completed one, we can click on whatever chore we have completed, and then be given a certain amount of "points" and some tickets, both can be used for something. For the tickets, they can be used to spin the spinner, or to spend on new monsters. The monsters each have their own description of what chores they are supposed to help you with, I think the monsters are just for fun. Also, we can use the tickets to buy a "monster short" which is a short and funny video about some monsters. Now, the points, they can be spent for something somewhat similar. It is a rewards section, where the points can be spent so you can get some cool rewards, like ice cream, or video games. Now, keep in mind that these rewards and videos cost a certain amount too. So save up, do your chores, and you'll probably get to see that one movie you always wanted to watch.

Taiwan Trip List

== toiletry ==
0.5gallon ziplock bags
baby wiper
tissue
toothbrush
toothpaste
mouth wash
floss
contact lens
soap
shampoo
lotion
q-tips
comb

antibiotics ointment
AllerClear
nosespray
Cortesoine
bug bite / itchy ointment
eye drops

== clothing ==

swimsuit
t-shirt x 6
shorts x 6
underwear t-shirt x 6
underpants x 6
socks x 6
light jacket x 1
jeans x 1

flip flops
sneakers
small bath towel
small blanket

== travel pack ==

water bottle

small fan

bug repellent
sunscreen x 2
lip balm with sunblock
hand sanitizer
bandit
chewing gum

UMBRELLA WITH UV PROTECTION

BACKPACK

WALLET
Money

plane PILLOW
sunglasses x 2

survival stuff in a can
hat

ponchos
bag

== stationary ==

pencil
pencil eraser
pencil case
pen
journal book
paper

== electronics ==
camera (case, charger, battery, memory card)
iPhone / charger
kindle / charger

The Lost Hero

Recently, I have read, and finished a book called The Lost Hero, by Rick Riordan, also the author of the Percy Jackson books. The Lost Hero is the first book of a new series, which takes place after the final book in the Percy Jackson Series. There are three main characters, Jason, Piper, and Leo. Each is experiencing something very strange. Jason has lost his memory, so he can't remember anything. Not even his own friends. So after a freak storm hits the wilderness school they were going to, things start to get even weirder. Apparently, their teacher, coach Hedge was actually a saytr half goat, half human, and was protecting them. Saytrs are from Greek mythology, and now Jason is seeing one face to face! Jason also has a sister, but he doesn't remember her either. Now, Piper has a famous actor for a father, however he has been missing for three days. She doesn't understand why her boyfriend (Jason) has suddenly forgot who she is. After the freak storm takes their "protector" (coach Hedge) they are whisked away to a place known as Camp Half-Blood, they are supposedly safe. From what? Now, for the last character, Leo, he is really good with tools, so after meeting a bunch of kids who have the same interests, he feels like he's in heaven. But eventually, something weird happens; he is immune to fire! And if that wasn't weird enough, Leo and his friends are supposed to have gods for parents! What is going on? Where is Percy Jackson (who wasn't present at all in the whole book), and who are their parents? Read the book yourself to find out.