All categories

3 years ago

2. (i) Express 2016 as the product of its prime factors.

Mathematics

1 answer:

oksian1 [2.3K]3 years ago

4 0

Answer:

N=14

Step-by-step explanation:

The first thing you want to do is write 2016 as its prime factorization: 2016 = 25*32*7. The 32 is already a square. We need too multiply one more factor of 2 to make 26, which has 23 = 8 as its square root. We also need to multiply by 7 to give 72. Therefore, to make a perfect square out of 2016, we need to multiply by 2*7 = 14. So, N =14.

I don't know if this really helps but i hope it helps!

You might be interested in

What is the smallest positive integer that Anastasia could have thought of?

Dima020 [189]

Answer:

Step-by-step explanation:

an integer is a natural counting number, such as 1...2...3...4... and so on....

zero is not considered an integer because it is a neutral number.

therefore, the smallest possible positive integer would have to be 1!

i hope this helped you!

stay safe!

3 0

3 years ago

We measure the diameters for a random sample of 25 oak trees in a neighbourhood. Diameters of oak trees in the neighbourhood fol

jarptica [38.1K]

Answer:

The required confidence inteval = 94.9%.

Step-by-step explanation:

Confidence interval: Mean ± Margin of error

Given: A confidence interval for the true mean diameter of all oak trees in the neighbourhood is calculated to be (36.191, 42.969).

i.e. Mean + Margin of error = 42.969 (i)

Mean - Margin of error = 36.191 (ii)

Adding (i) and (ii), we get

$2Mean =79.16\\\\\Rightarrow\ Mean= 39.58$

Margin of error = 42.969-39.58 [from (i)]

= 3.389

Margin of error = $t^* \dfrac{\sigma}{\sqrt{n}}$

here n= 25 $, \ \sigma=8.25$

i.e.

$3.389=t^*\dfrac{8.25}{5}\\\\\Rightarrow\ t^* = \dfrac{3.389}{1.65}\\\\\Rightarrow\ t^* =2.0539 \$

Using excel function 1-TDIST.2T(2.054,24)

The required confidence inteval = 94.9%.

7 0

3 years ago

What is the height of the prism if the surface area is 460 mm2?

8_murik_8 [283]

The answer of this question is B

5 0

3 years ago

Read 2 more answers

If 32 teams participate in a standard single elimination tournament, how many games must be played to decide a champion?

SCORPION-xisa [38]

<h3>Answer: 31 games</h3>

======================================================

Explanation:

32/2 = 16 games will happen in round 1. Afterward, 16 teams are left.
16/2 = 8 games will happen in round 2. Afterward, 8 teams are left.
8/2 = 4 games happen in round 3.
4/2 = 2 games in round 4.
2/2 = 1 game as the final championship.

Count the number of times you divide by two and we have five occurrences of this. So there five rounds overall.

To get the total number of games played, we add up the quotients

16+8+4+2+1 = 31

----------------

Or as a shortcut we can simply subtract off 1 since 1+2+4+...+2^n = 2^(n+1)-1

We can write that rule as

$\displaystyle \sum_{k=1}^{n}2^k = 2^{n+1}-1$

which is equivalent to

$\displaystyle \sum_{k=1}^{n}2^{k-1} = 2^n-1$

3 0

4 years ago

The area of a rectangle is expressed as x4 - 9y2. What are the possible dimensions of the rectangle?

AnnyKZ [126]

This is a stupid question. The teacher who asked this needs to go back to school.

A = x⁴ - 9y²

That's going to be a number. As long as it's positive we can choose any length for our rectangle L and we can compute the width by W=A/L. So the correct answer is the dimensions are L by (x⁴ - 9y²)/L.

They don't want the correct answer. They want you to factor this expression. We'll do it, but don't believe for a second this factoring somehow constrains the possible dimensions of some rectangle.

We use the difference of two squares, a²-b² = (a+b)(a-b)

A = x⁴ - 9y² = (x²)² - (3y)² = (x²+3y)(x²-3y)

Answer: x²+3y by x²-3y

5 0

3 years ago