ArithmeticBrains1234

Just note that in base 8, anything above 8 gets carried to the next place value. Eg., 4 + 5 = 11, as 4 + 5 is 9, and 8 out of that 9 is carried to the 10s place to become a 1.

Therefore,

4 base(8) + 7 base(8) = 13 base(8)

This is because 7 + 4 = 11, and taking away 8 we get 3. The 3 stays in the unit's place, and the 8 that we took away becomes the 1 in the tens place.

(13 base(8) is just 11 in base(10)) 

This is simply a system of equations and can be solved using substitution.

Let c represent the price of a child ticket.

Let a represent the price of an adult ticket.

We know:

5a +3c = 21

and

8a + 4c = 32

2a + c = 8

c = 8 - 2a

Now, using substitution:

5a +3c = 21

5a +3(8 - 2a) = 21

5a + 24 - 6a = 21

-a = -3

a = 3

c = 8 - 2a

c = 8 - 2(3)

c = 8 - 6

c = 2

Therefore the price of an adult ticket is $3 and the price of a child ticket is $2.

We can solve this with a system of equations.

Let l represent the rectangle's length.

Let w represent the rectangle's length.

We know that:

l = 3w - 9

and 

Perimeter = 222

Since the perimeter is simply 2(l+w);

2(l+w) = 222

l + w = 111

Now substitute in 3w +9 into l + w = 111:

l + w = 111

(3w - 9) + w = 111

4w - 9 = 111

4w = 120

w = 30

l = 3w - 9

l = 3(30) - 9

l = 90 - 9

l = 81

Therefore the length is 81 ft, and the width is 30 ft.

For the minute hand to 60 minutes is a full rotation of the clock, or 360°.

5:45 - 5:35 = 10 minutes.

10 minutes is 1/6 of 60 minutes, so 10 minutes is 1/6 of 360° = 60°.

Now we can calculate the arc using the angle of 60°.

Arc length = (60/360)(πr²)

                  = (1/6)(3.14)(6²)

                  = 18.84

Therefore, the length of the arc made by the hand is 18.84 inches.

First, find the area of the picture:

5*7 = 35 in²

The area of just the frame is:

80 - 35 = 45 in²

Now, note that the frame is nothing but 4 equal squares for the corners of the frame and 4 rectangles.

The corners have an area of x².

Two of the rectangles have an area of 5x, and the other 2 have an area of 7x.

Therefore the area of the frame is

4(x²) + 2(5x) + 2(7x) = 4x² + 24x

Which equals:

4x² + 24x = 45

Solving the quadratic, we get:

4x² + 24x = 45

4x² + 24x - 45 = 0

(2x-3)(2x+15) = 0

 2x - 3 = 0

2x = 3

x = 1.5

(The other solution for x would be negative)

Therefore, the width is 1.5 in².

Solved! :)

We can compare the areas of the shapes to the probability that points will get chosen inside them.

Area of the Triangle = bh/2

                                 = 7*4/2

                                 = 14 m²

Area of the Trapezoid = (ab/2)h

                                    = (8*13/2)*4

                                    = 52*4

                                    = 208 m²

Area of the Rectangle = bh

                                    = 17*25

                                    =  425 m²

Now, the final probability is =

\({14 + 208}\over{425}\)

= 222/425

A dozen is 12; thus 12 dozen is 12*12 = 144.

144/36 = 4

 Therefore Denis is making 4 times as many cookies; meaning he needs 4 times the ingredients.

(1 1/2) * 4 = 6 cups of flour

(2 3/4) * 4 = 11 cups of sugar

(1/8) * 4 = 1/2 cup of milk

Thus Denis needs 6 cups of flour, 11 cups of sugar, and 1/2 cup of milk to make 12 dozen cookies.

Both questions use the same triangle:

Note that an isosceles right triangle is a 1-1-sqrt(2) triangle;

meaning that we can find the legs by dividing the hypotenuse by sqrt(2).

\(14{\sqrt {2}}{\div }{\sqrt {2}}=14\)

1. The leg of the triangle is 14 units long.

 The area is simply bh/2, where b=14 and h=14.

\({\frac {bh} {2}}={\frac {14{\times }14} {2}}=98\)

2. The area of the triangle is 98 square units.

Note the triangle is isosceles.

Therefore angle ABC and angle ACB are equal, meaning angle ACB is also y degrees.

Since the sum of the angles in a triangle is 180, we can find that 2y + 24 = 180:

2y + 24 = 180

2y  = 156

y=78

Thus the value of y is 78 degrees.

Using one of the rectangular faces as a base for the next pyramid, there would be the addition of 1 vertex, 4 edges, and 4 faces.

Using one of the triangular faces as a base, there would be the addition of 1 vertex, 3 edges, and 3 faces.

Therefore for a minimal sum, one of the triangular faces must be the base of the pyramid.

The existing figure has 6 vertices, 9 edges, and 5 faces.

6+9+5 = 20

With the addition of the pyramid, there would be an extra 1 vertex, 3 edges, and 3 faces.

1+3+3 = 7

But note that the base of the pyramid would no longer be a face - so we subtract one from our total:

20+7-1= 26.

Thus, the minimal sum is 26.