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meriva
3 years ago
15

John find 1/5 of the bar chocolate he bought was already eaten by his brother. He eat 3/4 of what was remaining. Find the portio

n of the chocolate that is left after john eats.
Mathematics
1 answer:
larisa86 [58]3 years ago
3 0

Answer:

1/5 is left.

Step-by-step explanation:

Portion remaining after the bar was eaten by his brother = 1 - 1/5 = 4/5.

Portion remaining after John ate 3/4 of this = 4/5 - 3/4* 4/5 = 4/5 - 3/5

=  1/5.

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Use mathematical induction to prove that for each integer n > 4,5" > 2^2n+1 + 100.
Flura [38]

Answer:

The inequality that you have is 5^{n}>2^{2n+1}+100,\,n>4. You can use mathematical induction as follows:

Step-by-step explanation:

For n=5 we have:

5^{5}=3125

2^{(2(5)+1)}+100=2148

Hence, we have that 5^{5}>2^{(2(5)+1)}+100.

Now suppose that the inequality holds for n=k and let's proof that the same holds for n=k+1. In fact,

5^{k+1}=5^{k}\cdot 5>(2^{2k+1}+100)\cdot 5.

Where the last inequality holds by the induction hypothesis.Then,

5^{k+1}>(2^{2k+1}+100)\cdot (4+1)

5^{k+1}>2^{2k+1}\cdot 4+100\cdot 4+2^{2k+1}+100

5^{k+1}>2^{2k+3}+100\cdot 4

5^{k+1}>2^{2(k+1)+1}+100

Then, the inequality is True whenever n>4.

3 0
3 years ago
What is the area of a piece of plywood measuring 2 feet 8 inches long by 2 feet 4 inches wide? Give your answer in square inches
Kruka [31]

Given

piece of plywood measuring 2 feet 8 inches long by 2 feet 4 inches wide.

What is the area of a piece of plywood .

To proof

Here plywood shape in the form of rectangle.

Formula

Area of rectangle = Length×Breadth

As given in the question

Length =2 feet 8 inches

Breadth = 2 feet 4 inches

First convert feet into inches

1 feet = 12 inches

2 feet 8 inches = 2×12 + 8

                       =  32 inches

Also

2 feet 4 inches  = 2×12 +4

                          = 28 inches

put is in the above formula

Area of plywood = 32 ×28

                            = 896 inches²

Therefore option (b) is correct

Hence proved


8 0
3 years ago
A relation that shows that one expression is equal to another expression
ratelena [41]

Answer:

yes of course it is sign but a fact no

7 0
3 years ago
What is 6(5−8v)+12=−54
zlopas [31]

Answer: v = 2

Step-by-step explanation:

30-48v+12 = -54

-48v = -54-30-12

\frac{-48v}{-48} = \frac{-96}{-48}

v = 2

7 0
4 years ago
Read 2 more answers
How to factor x^2+8x+12
Setler [38]
<span> x^2+8x+12 = </span>(x + 6)(x + 2)

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3 years ago
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