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tekilochka [14]
2 years ago
5

An integer is chosen between 0 and 100. What is the probability that it is divisible by 7?

Mathematics
1 answer:
IgorC [24]2 years ago
8 0
Assuming 0 and 100 are included in the possible choices:

There are \left\lfloor\dfrac{101}7\right\rfloor=14 multiples of 7 between 0 and 100, so there is a \dfrac{14}{101}\approx0.1386 probability of choosing a multiple of 7.
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Use an induction proof to prove this statement:<br> For n≥1, 4^n+5 is divisible by 3.
Tpy6a [65]

Answer:

See below

Step-by-step explanation:

We shall prove that for all n\in\mathbb{N},3|(4^n+5). This tells us that 3 divides 4^n+5 with a remainder of zero.

If we let n=1, then we have 4^{1}+5=9, and evidently, 9|3.

Assume that 4^n+5 is divisible by 3 for n=k, k\in\mathbb{N}. Then, by this assumption, 3|(4^n+5)\Rightarrow4^k+5=3m,\: m\in\mathbb{Z}.

Now, let n=k+1. Then:

4^{k+1}+5=4^k\cdot4+5\\=4^k(3+1)+5\\=3\cdot4^k+4^k+5\\=3\cdot4^k+3m\\=3(4^k+m)

Since 3|(4^k+m), we may conclude, by the axiom of induction, that the property holds for all n\in\mathbb{N}.

3 0
2 years ago
Find the quotient and express in simplest form.
White raven [17]
-1/2 ÷9/5
=-1/2*5/9
=-5/18. answer.
-1*5 =5 numerator
2*9=18 denominator
4 0
3 years ago
need help ASAP plz
ruslelena [56]
First shape: no parallel nor perpendicular

Second shape: parallel sides

Third shape: parallel sides

Fourth shape: perpendicular sides

Fifth: perpendicular sides

Hope this helps!! Have a nice day!!
8 0
2 years ago
Using the equation x squared minus c equals 0 , what value of c has 9 and -9 as solutions.
Svetach [21]

9514 1404 393

Answer:

  c = 81

Step-by-step explanation:

The equation x² -c = 0 can be factored as ...

  (x -√c)(x +√c) = 0

which has roots ±√c.

The roots are given as ±9, so we have ...

  ±9 = ±√c

  c = (±9)² = 81

The value c = 81 makes the equation have ±9 as solutions.

3 0
2 years ago
What number is 56% of 48?
Digiron [165]
X = 56% * 48

x = 56/100 * 48

x = 28/50 * 48

x = 14/25 * 48

x = 672/25

x = 26.88



<span>56% of 48 is </span>26.88<span>.</span>
6 0
3 years ago
Read 2 more answers
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