1.### What are the next three numbers in this sequence? 12, 9, 6, 3...

Answer:
0, -3, -6

Explanation:

The sequence is decreasing by 3 each time. So, the next three numbers would be obtained by subtracting 3 from the previous number. Therefore, the next three numbers in the sequence are 0, -3, -6.

2.### A rectangular yard measures 8m x 6m. What happens to the area if each dimension is doubled?

Answer:
It becomes four times greater.

Explanation:

If the dimensions of a rectangle are doubled, the area will increase by a factor of 4.

The original area of the rectangular yard is calculated by multiplying its length and width:

Area = Length × Width = 8m × 6m = 48 square meters.

When both dimensions are doubled (8m × 2 = 16m and 6m × 2 = 12m), the new area will be:

New Area = New Length × New Width = 16m × 12m = 192 square meters.

Comparing the new area to the original area:

192 square meters (new area) / 48 square meters (original area) = 4.

So, when each dimension is doubled, the area becomes 4 times the original area.

The original area of the rectangular yard is calculated by multiplying its length and width:

Area = Length × Width = 8m × 6m = 48 square meters.

When both dimensions are doubled (8m × 2 = 16m and 6m × 2 = 12m), the new area will be:

New Area = New Length × New Width = 16m × 12m = 192 square meters.

Comparing the new area to the original area:

192 square meters (new area) / 48 square meters (original area) = 4.

So, when each dimension is doubled, the area becomes 4 times the original area.

3.### Evaluate:
a). 2/5 + [-(3/7)]
b). -(2/9) + 1/6
c). -(2/3) x 1/4
d). 7/12 ÷ [-(1 3/4)]

Answer:
A) -(1/35) b) -(1/18) c) -(1/6) d) -(1/3)

Explanation:

Let's solve each of these step-by-step:

a). (2/5 + [- (3/7)])

This is equivalent to (2/5 - 3/7).

To add or subtract fractions, you need a common denominator. In this case, it is 35.

(2/5) can be represented as (14/35) and (3/7) can be represented as (15/35).

(14/35 - 15/35 = -1/35)

So, a). (2/5 + [- (3/7)] = -1/35)

b). (- (2/9) + 1/6)

To add or subtract these fractions, you need a common denominator. The least common multiple of 9 and 6 is 18.

(- (2/9)) can be represented as (-4/18) and (1/6) can be represented as (3/18).

(-4/18 + 3/18 = -1/18)

So, b). (- (2/9) + 1/6 = -1/18)

c). (- (2/3) x 1/4)

To multiply these fractions, multiply the numerators together and then multiply the denominators together.

(-2 x 1 = -2)

(3 x 4 = 12)

So, c). (- (2/3) x 1/4 = -2/12)

But, (-2/12) can be simplified to (-1/6).

d). (7/12 ÷ [- (1 3/4)])

First, convert (- (1 3/4)) to an improper fraction:

(- (1 3/4) = - (4 + 3)/4 = -7/4)

Now, to divide by a fraction, you multiply by its reciprocal:

(7/12 ÷ [- (1 3/4)] = 7/12 x -4/7)

(7 x -4 = -28)

(12 x 7 = 84)

So, d). (7/12 ÷ [- (1 3/4)] = -28/84)

But, (-28/84) can be simplified to (-1/3).

In summary:

a) -1/35

b) -1/18

c) -1/6

d) -1/3

a). (2/5 + [- (3/7)])

This is equivalent to (2/5 - 3/7).

To add or subtract fractions, you need a common denominator. In this case, it is 35.

(2/5) can be represented as (14/35) and (3/7) can be represented as (15/35).

(14/35 - 15/35 = -1/35)

So, a). (2/5 + [- (3/7)] = -1/35)

b). (- (2/9) + 1/6)

To add or subtract these fractions, you need a common denominator. The least common multiple of 9 and 6 is 18.

(- (2/9)) can be represented as (-4/18) and (1/6) can be represented as (3/18).

(-4/18 + 3/18 = -1/18)

So, b). (- (2/9) + 1/6 = -1/18)

c). (- (2/3) x 1/4)

To multiply these fractions, multiply the numerators together and then multiply the denominators together.

(-2 x 1 = -2)

(3 x 4 = 12)

So, c). (- (2/3) x 1/4 = -2/12)

But, (-2/12) can be simplified to (-1/6).

d). (7/12 ÷ [- (1 3/4)])

First, convert (- (1 3/4)) to an improper fraction:

(- (1 3/4) = - (4 + 3)/4 = -7/4)

Now, to divide by a fraction, you multiply by its reciprocal:

(7/12 ÷ [- (1 3/4)] = 7/12 x -4/7)

(7 x -4 = -28)

(12 x 7 = 84)

So, d). (7/12 ÷ [- (1 3/4)] = -28/84)

But, (-28/84) can be simplified to (-1/3).

In summary:

a) -1/35

b) -1/18

c) -1/6

d) -1/3

4.### What is the value of Pi?

Answer:
3.14

Explanation:

The value of Pi is commonly represented as 3.14, which is an approximation of the mathematical constant π. It is often used in mathematical calculations involving circles and is widely recognized as the standard value for Pi.

5.### If 5 men make a car in 5 days, then how many days will 10 men take to make 2 cars?

Answer:
5 days

Explanation:

First, let's find out how many man-days it takes to make one car:

5 men × 5 days = 25 man-days (to make 1 car)

Now, if 10 men are working, they can complete those 25 man-days of work in:

25 man-days ÷ 10 men = 2.5 days (to make 1 car)

For 2 cars, it will take:

2 cars × 2.5 days/car = 5 days

So, 10 men will take 5 days to make 2 cars.

5 men × 5 days = 25 man-days (to make 1 car)

Now, if 10 men are working, they can complete those 25 man-days of work in:

25 man-days ÷ 10 men = 2.5 days (to make 1 car)

For 2 cars, it will take:

2 cars × 2.5 days/car = 5 days

So, 10 men will take 5 days to make 2 cars.

6.### Continue each pattern for 3 more terms. 7, 14, 28...

Answer:
56, 112, 224

Explanation:

The pattern in the given sequence is that each term is double the previous term. Starting with 7, the next term is obtained by multiplying 7 by 2, resulting in 14. Continuing this pattern, the next term is 28. To find the next three terms, we continue doubling the previous term: 28 * 2 = 56, 56 * 2 = 112, and 112 * 2 = 224. Therefore, the next three terms in the sequence are 56, 112, and 224.

7.### A bracelet is to be made from 2 red and 5 blue beads. How many different bracelets can be made?

Answer:
5040

Explanation:

In this scenario, you have a total of 2+5=7 beads, and you want to arrange them in a circular order (since it's a bracelet). So, the number of different bracelets can be calculated as P(7,7):

P(7,7)=7!/(7−7)!=7!/0!=7!

7!=7×6×5×4×3×2×1=5040

Therefore, there are 5040 different bracelets that can be made using 2 red and 5 blue beads.

P(7,7)=7!/(7−7)!=7!/0!=7!

7!=7×6×5×4×3×2×1=5040

Therefore, there are 5040 different bracelets that can be made using 2 red and 5 blue beads.

8.### All the angles of a triangle add up to equal:

Answer:
180 degrees

Explanation:

The sum of all angles in a triangle is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry. Regardless of the size or shape of the triangle, the sum of its angles will always be equal to 180 degrees. Therefore, the correct answer is 180 degrees.

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