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Alex says that there is no numbers between 1/3 and 1/4 . Why might he think that and what would you tell him? Is there a number

Thepotemich [5.8K]

Answer:

Why might he think that and what would you tell him?

He thought perhaps that numbers were formed by rational numbers of the form $\frac{1}{x}$ , where $x\in \mathbb{N}$ . I would tell him that there are rational numbers $\frac{y}{z}$ , such that $\frac{1}{x}\le \frac{y}{z} \le \frac{1}{x+1}$ , where $x$ , $y$ , $z \in \mathbb{N}$ .

Is there a number that falls between these?

$\frac{7}{24}$ is a rational number between $\frac{1}{3}$ and $\frac{1}{4}$ .

Step-by-step explanation:

Why might he think that and what would you tell him?

He thought perhaps that numbers were formed by rational numbers of the form $\frac{1}{x}$ , where $x\in \mathbb{N}$ . I would tell him that there are rational numbers $\frac{y}{z}$ , such that $\frac{1}{x}\le \frac{y}{z} \le \frac{1}{x+1}$ , where $x$ , $y$ , $z \in \mathbb{N}$ .

Is there a number that falls between these?

Indeed, the average number of $\frac{1}{3}$ and $\frac{1}{4}$ , for instance. That is:

$\frac{y}{z} = \frac{\frac{1}{3}+\frac{1}{4} }{2}$

$\frac{y}{z} = \frac{\frac{7}{12} }{2}$

$\frac{y}{z} = \frac{7}{24}$

$\frac{7}{24}$ is a rational number between $\frac{1}{3}$ and $\frac{1}{4}$ .

8 0

2 years ago

Six more than the quotient of four and a number xxx.

Shalnov [3]

Answer:

$\large\boxed{\dfrac{4}{x}+6}$

Step-by-step explanation:

Six more than the quotient of four and a number x:

$\dfrac{4}{x}+6$

7 0

3 years ago

Read 2 more answers

Which value of "b" will make the trinomial 4x^2 + bx + 36 a perfect square trinomial? 0 24 O 6 O 12 O 4

Lena [83]

Answer:

48

Step-by-step explanation:

Reverse solve for a perfect Square

(b/2a)^2=36

(b/2(4))^2=36

(b/8)^2=36

b/8=6

b=48

48 makes the trinomial a perfect square trinomial.

4 0

2 years ago

What is 0.194 with only thhe 9 and 4 repeating as a fraction?

nirvana33 [79]

193/990 Would be the answer. If you want the steps to find it, just ask.

5 0

3 years ago

Constructing a brick staircase: A brick staircase has a total of 30 steps. The bottom step requires 100 bricks. Each successive

galben [10]

A) The first step needs 100 bricks, the second needs 98, the third needs 96, and so on. Therefore the number of bricks for the nth step is: a_n = a_1 + d(n-1), where a_1 = 100 (the first term), d = -2 (difference).
a_n = 100 - 2(n-1) = 102 - 2n, and for the 30th step, a_30 = 102 - 2*30 = 42. So the top step will need 42 bricks.

b) The total staircase will need: 100 + 98 + 96 + ... + 44 + 42, and there are n = 30 terms. Using the formula for the sum of an arithmetic sequence:
S = (a_1 + a_n)*n/2 = (100 + 42)*30/2 = 2130
Therefore, 2130 bricks are required to build the entire staircase.

7 0

3 years ago

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Nnh-jzpz-tyg. join today link fast guys please