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?
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?
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)
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 before tax. 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?
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?
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.
Two movie tickets and three drinks cost $28.
Four movie tickets and one drink cost $34.
What is the cost of one movie ticket and one drink?
2m + 3d = 28
4m + 1d = 34
Movie Ticket = $7.40
Drink = $4.40
Therefore, the cost of one movie ticket and one drink is $11.80.
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)
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?
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?
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.
5/14 x 6/13 = 15/91
Therefore,
The probability of picking out a blue marble followed by a pink marble is 15/91.
17² - 8x + 2x - 7² = 9² + 11² - 7x - 9
X = -47
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)
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?
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?
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 labeled 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?
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.
3[8x + (4x-2x + 4) - 3(4x - 3) + 2] = 24
x=?
X = 3.5
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)
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.
A rectangular prism has a length of 24 cm and a width of 23 cm. If its surface area is 6,368 cm², then what’s its height?
2(24 x 23) + 2(24x) + 2(23x) = 6368
1104+ 94x = 6368
94x = 5264
x = 56
Therefore,
The height is 56 cm.
Principal Matthews has a $5000 debt with a 3.78% biweekly simple interest rate. If she takes 40 weeks to pay back her debt including interest, how much money does she need to pay each week?
5000 x 0.00378 = 189
Biweekly is twice a week
40/2 = 20
189 x 20 = 3780
3780 + 5000 = 8780
8780/40 = 219.50
Therefore,
Principal Matthews needs to pay $219.50 each week.
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?
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 - 28/56 + 8/56 + 7/56 = 1
3y - 13/56 = 1
3y = 69/56
y = 69/168 = 23/56
Therefore,
The probability of spinning yellow is 23/56.
3x+9y+3-6y = 90
4x+10y+5-5x = 20
x=? y=?
(25,4)
A car and a truck start at the same spot but the car drives North while the truck drives west. The car travels at a speed of 80km/h while the truck travels 65 km/h. After 7.25 hours, how far apart are they? (Round to the nearest 100th)
Car = 80(7.25)=580
Truck = 65(7.25)=471.25
a² + b² = c²
580² + 471.25² = c²
336400 + 222076.5625 = c²
558476.5625 = c²
747.31 = c
Therefore,
They are 747.31km apart.
A rectangular prism has a length of (2x+3) cm, a height of 4 cm, and a width of 6 cm. The total surface area of the prism is 208 cm². What is the volume?
2[(2x+3)(4)] + 2[(2x+3)(6)] + 2(4)6 = 208
x= 2.5
8 x 4 x 6 = 192
Therefore,
The volume is 192cm³.
Glow Toy just got her first part-time job and earns $480 per month. She budgets her paycheck like this: 35% for savings, 25% for personal expenses, 20% for helping with family groceries, 15% for transportation costs, and the remaining amount for emergency funds. However, Glow Toy realizes she needs an extra $25 per month for her phone bill, which she'll have to take from her savings category. After adjusting for the phone bill, what percentage of her income will Glow Toy actually be saving each month? (Round to the nearest tenth of a percent)
480 x 0.35 = 168
168 - 25 = 143
$143 ÷ $480 × 100% = 29.8%
Therefore,
Glow Toy will actually be saving 29.8% of her income each month after adjusting for the phone bill.