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3 years ago

IS 3.

Mathematics

1 answer:

coldgirl [10]3 years ago

6 0

Answer:

1. a. 2,000

2. b. 10 years

3. a. 6.72937

4. d. 9%

Step-by-step explanation:

1. If 58% are boys, the percentage of girls is:

= 100 - 58

= 42%

That means 840 is 42% of the students in class. The students in class are therefore:

= 840 / 42%

= 2,000 students

2. If Birr 300 is invested at 6% per year, the amount in interest it earns per year is:

= 300 * 6%

= Birr 18

To get to Birr 180, it would take:

= 180/18

= 10 years

3. When a number is in percentage that means that it is a fraction with the denominator being 100. The number is decimal will therefore be it divided by 100:

= 672.937/100

= 6.72937

4. The investment accrued Birr 12 out of Birr 400 in 4 months. This means that it increased by:

= 12/400

= 3%

A year can be divided into three by 4 months. This means that the yearly rate is therefore:

= 3% * 3

= 9%

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Find the number a for which x=5 is a solution of the given equation.

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Step-by-step explanation:

x + 8a = 25 + ax - 7a

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5 + 8a = 25 + 5a - 7a

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5 + 10a = 25

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Answer: With 11 pipes, you need 31.82 minutes to fill the tank.

Step-by-step explanation:

Let's define R as the rate at which one single pipe can fill a tank.

We know that 7 of them can fill a tank in 50 minutes, then we have the equation:

7*R*50min = 1 tank

Whit this equation, we can find the value of R:

R = 1 tank/(7*50min) = (1/350) tank/min.

Now that we know the value of R, we can do the same calculation but now with 11 pipes.

Then the time needed to fill the tank, T, is such that:

11*(1/350 tank/min)*T = 1 tank

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3 years ago

The bisector of a straight angle forms two acute angles. True False

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4 years ago

The perimeter of a rectangle is equal to 40. If the length is halved and the width is divided by 3, the new perimeter is decreas

Tanzania [10]

Answer:

Step-by-step explanation:

M = Original perimeter = 40

M = 2 w + 2 l = 2 ( w + l )

40 = 2 ( w + l )

Divide both sides by 2 (simplify)

20 = w + l

w + l = 20

Subtract w from both sides

w + l - w = 20 - w

l = 20 - w

If the length is halved and the width is divided by 3 mean:

New length l1 = l / 2 = ( 20 - w ) / 2 = 10 - w / 2

New width w1 = w / 3

The new perimeter is decreased by 24 mean:

P1 = New perimeter = 40 - 24 = 16

P1 = 2 w1 + 2 l1 = 2 ( w1 + l1 )

16 = 2 ( w1 + l1 )

Divide both sides by 2

8 = w1 + l1

w1 + l1 = 8

w / 3 + 10 - w / 2 = 8

Subtract 10 to both sides

w / 3 + 10 - w / 2 - 10 = 8 - 10

w / 3 - w / 2 = - 2

2 w / 6 - 3 w / 6 = - 2

- w / 6 = - 2

Multiply both sides by - 6

( - 6 ) ∙ ( - w / 6 ) = ( - 2 ) ∙ ( - 6 )

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P = 2 w + 2 l = 2 ( w + l ) = 2 ∙ ( 12 + 8 ) = 2 ∙ 20 = 40

New length:

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New width:

w1 = w / 3 = 12 / 3 = 4

New rectangle will be the square. ( the square is a special case of the rectangle )

New perimeter:

P1 = 2 w1 + 2 l1 = 2 ( 4 + 4 ) = 2 ∙ 8 = 16

The length of the original rectangle:

l = 8

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