Probability
Wedgely has to decide on an outfit for tomorrow’s banquet. She has a red, blue, yellow, purple dress. She also has different accessories, pearl earrings, diamond necklace, emerald bracelet, and sapphire hair clip. Lastly, she needs to decide what footwear she should wear, red heels, yellow heels, blue flats, brown slippers, and silver heels. What is the probability that she will pick out a purple dress and yellow heels?
韦奇利需要决定明天宴会的服装。她有一条红、蓝、黄、紫四色的连衣裙。她还有不同的配饰，珍珠耳环、钻石项链、祖母绿手镯和蓝宝石发夹。最后，她需要决定穿什么鞋：红色高跟鞋、黄色高跟鞋、蓝色平底鞋、棕色拖鞋和银色高跟鞋。她选择紫色连衣裙和黄色高跟鞋的概率是多少？
The probability of picking a purple dress and yellow heels is 1/20.
6x - 9y - 12 = 9
3x - y + 4 =18
x=? y=?
(5,1)
A triangle has side lengths of 9 cm, 12 cm, and 15 cm.
Is this triangle a right-angled triangle?
一个三角形的边长分别为 9 厘米、12 厘米和 15 厘米。
这个三角形是直角三角形吗？
Yes
9² + 12² = 15²
81 + 144 = 225
Therefore,
yes, this is a right-angled triangle.
The radius of a sphere is 7cm, find its volume?
(Hint: V = 4/3 π r³)
一个球体的半径是7厘米，求它的体积？
（提示：V = 4/3 π r³）
V= 4/3 n 7³
Therefore,
Its volume is 1436.03cm³.
Jack, Hopsy, Jig and Rover went out for dinner together, they spent $6968.80. They decided to split the bill. How much money do they each have to pay if they have to add a 21% tip after tax?
杰克、霍普西、吉格和罗孚一起出去吃饭，花了6968.80美元。他们决定分摊账单。如果加上税后21%的小费，他们每人要付多少钱？
6968.80 / 4 = 1742.2
1742.2 x 1.13 x 1.21 = 2382.11
Therefore,
They each have to pay $2382.11.
There are 3 identical spinners with 6 equal sections, if 2 of the sections are red, what is the possibility of getting at least 1 red after spinning all the spinners?
有 3 个相同的转盘，每个转盘有 6 个相等的部分，如果其中 2 个部分是红色，那么旋转所有转盘后，至少出现 1 个红色的可能性有多大？
4/6 sections are not red
(2/3)³ = 8/27
1 - 8/27 = 19/27
Therefore,
The probability of spinning at least 1 red is 19/27.
A right-angled triangle has the side lengths of Xcm and Ycm . X equals to 25 - Y and Y = X - 7. What is the length of the hypotenuse? (Leave it as a square root)
一个直角三角形的边长为 Xcm 和 Ycm。X 等于 25 - Y，Y = X - 7。斜边的长度是多少？（取平方根）
X = 16cm Y = 9cm
Hypotenuse = √337
Ms Grouchstick is building a rectangular house with dimensions of 45 cm by 23 cm. She wants to make a profit of $8000 so she charges $43,190. What's the cost of building per square centimetre?
格罗奇斯蒂克女士正在建造一栋长方形房屋，尺寸为45厘米 x 23厘米。她希望赚取8000澳元的利润，因此她收取的费用为43190澳元。每平方厘米的建筑成本是多少？
43190 - 8000 = 35190
45 x 23 = 1035
35190/1035 =34
Therefore,
It costs $34 per square centimetre
The Toy School pays $15/hr and The Wizard of Oz pays $13/hr but includes a $120 bonus/month. Which play pays better after one month if you work 40 hours per week and by how much?
《玩具学校》的时薪为15美元，《绿野仙踪》的时薪为13美元，但包含每月120美元的奖金。如果你每周工作40小时，一个月后哪部剧的片酬更高？高多少？
Toy School = 15(40)(4) = 2400
Wizard of Oz = 13(40)(4)+120 = 2200
Therefore,
The Toy School pays better by $200 per month.
Edgely has a bag containing 5 blue, 3 white and 6 pink marbles. She selects 2 marbles from the bag, what is the probability that she will pick out a blue marble, followed by a pink marble.
Edgely 的袋子里装有 5 颗蓝色弹珠、3 颗白色弹珠和 6 颗粉色弹珠。她从袋子里选了 2 颗弹珠，请问她先选出一颗蓝色弹珠，然后又选出一颗粉色弹珠的概率是多少？
5/14 x 6/13 = 15/91
Therefore,
The probability of picking out a blue marble followed by a pink marble is 15/91.
Ted E Bear has a ladder that’s 3.26m long. She puts the ladder 1.93m away from the wall with the top of the ladder touching the wall. What’s the distance between the floor and the top of the ladder? (Round to the nearest 100th)
泰德·E·熊有一架3.26米长的梯子。她把梯子放在离墙1.93米的地方，梯子的顶端贴着墙。梯子顶端到地板的距离是多少？（四舍五入到最接近的百分位）
a² + b² = c²
1.93² + b² = 3.26²
3.72 + b² = 10.63
10.63 - 3.72 = b²
6.91 = b²
b = 2.63
Therefore,
The distance between the floor and the top of the ladder is 2.63m.
The surface area of a cube is 864cm², what's its volume?
一个立方体的表面积是864cm²，它的体积是多少？
864/6 = 144
√144 = 12
side length = 12
12³ = 1728
Therefore,
The volume is 1728cm³.
Saw earns $6,730 each month. She spends 51% of her income on necessities, 15% on taxes, and 11% on wants. The remaining amount is deposited into a savings account that earns 1.24% simple interest bimonthly. How much money will Saw have in her savings account after 1.5 years?
Saw 每月收入 6,730 美元。她将收入的 51% 用于生活必需品，15% 用于纳税，11% 用于生活必需品。剩余金额存入储蓄账户，每两个月可获得 1.24% 的单利。一年半后，Saw 的储蓄账户里会有多少钱？
100% - 51% - 15% - 11% = 23%
0.23 x 6730 x 18 months = 27,862.20
Bimonthly = 2 months = 18/2 = 9
Interest= 27,862.20 × 0.0124 × 9= 3,105.46
27,862.20 + 3,105.46 = 30,967.66
Therefore,
Saw will have $30.967.66 in her savings account after 1.5 years.
There are 24 balls labelled 1-24 in a box. Ann wants to pick out a ball 3 times without replacing it. What is the probability that all 3 balls she picks out are labelled an even number?
盒子里有24个标有1-24的球。Ann想把一个球取出3次，不放回原处。她取出的3个球都是偶数的概率是多少？
12/24 x 11/23 x 10/22 = 5/46
Therefore,
The probability that all 3 balls she picks out are labeled an even number is 5/46.
A right triangle has the side length of 11(√3) and 4(√8). What is the length of the hypotenuse?
(Leave it as a square root)
一个直角三角形的边长为 11（√3）和 4（√8）。斜边的长度是多少？（保留平方根）
a² + b² = c²
[11(√3)]²+ [4(√8)]² = c²
121(3) + 16(8) = c²
363 + 128 = c²
491 = c²
Therefore,
The length of the hypotenuse is √491.
Principal Matthews has a $5000 debt with a 3.78% biweekly simple interest rate. If she pays back $183 every week, how many weeks would it take for her to repay her debt?
校长马修斯有一笔 5000 美元的债务，每两周的单利为 3.78%。如果她每周偿还 183 美元，那么她需要多少周才能还清债务？
It would take her 38 weeks to repay her debt, including interest.
There is a spinner with 4 sections, yellow, red, green, and blue. If the probability of spinning a red is 1/4 less than spinning a yellow and the probability of spinning a green is 1/7 more than spinning a red. If the chance of spinning a blue is 1/8 then what is the probability of spinning a yellow?
一个旋转器有四个色块，分别是黄、红、绿、蓝。如果旋转出红色的概率比旋转出黄色的概率小1/4，旋转出绿色的概率比旋转出红色的概率大1/7。如果旋转出蓝色的概率是1/8，那么旋转出黄色的概率是多少？
Yellow = Y
Red = Y - 1/4
Green = Y - 1/4 + 1/7
Blue = 1/8
Y + (Y - 1/4) + (Y - 1/4 + 1/7) + 1/8 = 1
3Y -13/56 = 1
23/56 =Y
Therefore,
The probability of spinning yellow is 23/56.