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2 years ago

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

1 answer:

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.

You might be interested in

Use an induction proof to prove this statement: 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

56% of 48 is 26.88.

6 0

3 years ago

Read 2 more answers