# The most difficult problems

- Possible combinations - word

How many ways can the letters F, A, I, R be arranged? - Two divided

Two divided by nine tenths. - Tenths digit

For 10.932, which digit is in the tenths place? - Two dogs

Izzy's dog is 10 1/2 years old. Paige's dog is 18 months old. How many years older is Izzy's dog? - Conical bottle

When a conical bottle rests on its flat base, the water in the bottle is 8 cm from it vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle? - Weigh in total

I put 3/5kg of grapes into a box which is 1/4kg in weight. How many kilograms do the grapes and the box weigh in total? - Two bodies

The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and seco - Two accounts

A banker divided $5000 between 2 accounts, one paying 10% annual interest and the second paying 8% annual interest. Express the amount invested in the 10% account in the terms of the amount invested in the 8% account. - The percent 2

The percent return rate of a growth fund, income fund, and money market are 10%, 7%, and 5% respectively. Suppose you have 3200 to invest and you want to put twice as much in the growth fund as in the money market to maximize your return. How should you i - Five harvests

In the seed company, they know that, out of 100 grains of a new variety, they get an average of 2000 grains after harvest. Approximately how many grains do they get out of 100 grains after five harvests? - Diagonal intersect

isosceles trapezoid ABCD with length bases | AB | = 6 cm, CD | = 4 cm is divided into 4 triangles by the diagonals intersecting at point S. How much of the area of the trapezoid are ABS and CDS triangles? - One third power

Which equation justifies why ten to the one-third power equals the cube root of ten? - College 2

College student is moving into a dormitory. The student rent a truck for $19.95 plus $0.99 per mile. Before returning the truck the student fills the tank with gasoline, which cost $65.32. Total cost $144.67. Using a linear equation, explain the process t - The Indian tent

The Indian tent is cone-shaped. Its height is 3.5 m. The diameter of the base is 2.5 m. How much canvas is needed to make a tire? - Parallel and orthogonal

I need math help in this problem: a=(-5, 5 3) b=(-2,-4,-5) (they are vectors) Decompose the vector b into b=v+w where v is parallel to a and w is orthogonal to a, find v and w - Bisectors

As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE. - Surface area of a cube

What is the surface area of a cube that has an edge of 3.5? - Regular hexagonal pyramid

Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture. - Octagonal pyramid

Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°. - Tetrahedral pyramid

Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.

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