What is a rational number between 6.2 and 6.3

Caroline bought 20 shares of stock at 10 ½, and after 10 months the value of the stocks was 11 ¼. If Caroline were to sell all h

OleMash [197]

20 shares at 10 1/2 (or 10.5) = 20 * 10.5 = 210
20 shares at 11 1/4 (or 11.25) = 20 * 11.25 = 225

so the profit made would be : 225 - 210 = $ 15 <==

4 0

1 year ago

For a polygon to be convex means that all of its interior angles are less than 180 degrees. Prove that for all integers n ≥ 3, t

Alexeev081 [22]

Answer: check explanation

Step-by-step explanation:

Let K(n) be the sum of the interior angles in any n-sided convex polygon which is exactly 180(n −2)

degrees.

CASE: n = 3. A 3-sided polygon is a triangle, whose interior angles were shown always to sum to be 180 degree

INDUCTION HYPOTHESIS: Suppose that K(b) holds for some b ≥ 3. Which means that the interior angles in any b-sided convex

polygon is exactly 180(n −2) degrees.

INDUCTION STEP: We need to show that K(n is greater than or equals to 3) . That is, the interior angles of any b+1-sided convex polygon

is exactly 180(b−2) = 180(b −1) degrees,

Let X be any (b+1)-vertex convex polygon, say with successive vertices x1, x2,..., xb+

Now Y is also a convex polygon , so by the induction hypothesis K(b), the sum of the interior

angles of Y is 180(k −2).

Now let T be the triangle with vertices xk , xb+1, x1. The sum of the interior angles in X is the sum of those

in Y plus the sum of those in T .

So the sum of the interior angles in X is

180(b −2)+180 = 180((b +1)−2) = 180(b −1).

Since X was arbitrary, we conclude that the sum of the interior angles of any (b +1)-sided convex polygon

is 180((b−2)+1) = 180(b−1). That is, P(b +1) holds.

And which means that n is greater or equals to 3

8 0

2 years ago

The student to faculty ratio at a small college is 17:3 the total number of students and faculty is 740. How many faculty member

larisa86 [58]

Answer:

111

Step-by-step explanation:

It is given that the student to faculty ratio at a small college is 17:3.

Let number of students and faculty members are 17x and 3x respectively.

It is given that total number of students and faculty is 740.

$17x+3x=740$

$20x=740$

Divide both sides by 20.

$x=37$

Number of student $=17\times 37=629$

Number of faculty members $=3\times 37=111$

Therefore, there are 111 faculty members at the college.

3 0

2 years ago

For an outdoor track meet to be cancelled, the temperature, t, outside must be colder than 35 degrees. Complete the following in

qwelly [4]

Answer: I'm pretty sure it would be -7º Celcius for it to be cancelled. Hope it helped!

7 0

2 years ago

Read 2 more answers

Here are seven tiles: 1,1,3,3,3,5,5. Tom takes a tile at random. He does not replace the tile. Tom then takes a second tile. A)

zzz [600]

Answer:

a) 2/42

b)16/42

Step-by-step explanation:

a) 2/7 x 1/6 = 2/42

b) (1,2) (1,3) (2,3)

P(1,2) = 2/7 x 3/6 = 6/42

P(1,3) = 2/7 x 2/6 = 4/42

P(2,3) = 3/7 x 2/6 = 6/42

Add all = 6/42 + 4/42 + 6/42 = 16/42

4 0

2 years ago