What is the perimeter of triangle OJL

A jar contains 8 marbles numbered 1 through 8. an experiment consists of randomly selecting a marble from the jar, observing the

zepelin [54]

There are 8 possible outcomes for a marble being drawn and numbered.
{1,2,3,4,5,6,7,8}
There are 4 possible outcomes for a card being selected from a standard deck.
{ hearts, diamonds, clubs, spades}
So the number of outcomes in the sample space would be 8 x 4 = 32.

In the event "an even number is drawn", there are only 4 possible outcomes for a marble being drawn, {2,4,6,8}, whereas there are still 4 possible outcomes for a suit. So the number of outcomes in the event is 4 x 4 = 16.

In the event "a number more than 2 is drawn and a red card is drawn", there are 6 possible outcomes for the marble being drawn, {3,4,5,6,7,8}, whereas there are only two possible suits for a card being selected as red, {heart, diamond}. So the number of outcomes in this event is 6 x 2 = 12.

In the event "a number less than 3 is drawn or a club is not drawn", the number drawn could be 1 or 2 whereas a spade/heart/diamond could be selected. So the number of outcomes is 2 x 3 = 6.

3 0

3 years ago

12. For triangle MNP shown, find the value of x

amm1812

Answer:

$x=36\°\\\angle P=71 \°,\angle N=73 \°,\angle M=36 \°$

Step-by-step explanation:

Given:

The triangle is shown below.

We know that the sum of all interior angles of a triangle is equal to 180°.

Therefore,

$\angle M+\angle N+\angle P=180 \°\\\\x+2x+1+2x-1=180\°\\\\5x=180\°\\\\x=\frac{180}{5}\\\\x=36\°$

Now, plugging the value of 'x' in each angle measure and determining its values. We get:

$\angle M=x=36\°\\\angle P=2x-1=2(36)-1=72-1=71\°\\\angle N=2x+1=2(36)+1=72+1=73\°$

Therefore, the value of 'x' is 36° and the measure of the three angles are 36°, 71° and 73°.

8 0

4 years ago

In the Reflecting Ball Game a ball can be launched from points 1, 2, 3, 4, 5 or 6 in the direction shown. When a ball hits a sid

natulia [17]

Answer:

$24\sqrt{2}$

Step-by-step explanation:

We can measure the number of diagonals each path takes:

From point 1, the path travels 6 diagonals, ending up at point D.

From point 2, the path travels 12 diagonals, ending back at point A.*

From point 3, the path travels 3 diagonals, ending at point B.

From point 4, the path travels 9 diagonals, ending at point C.

From point 6, the path travels 10 diagonals, ending at point D.

Since your question mentions each are 2 cm by 2 cm, this is equivalent to $2\sqrt{2}$ .

We can easily conclude that the maximum is 12 diagonals. Thus, Solving our equation gives: 12 * $2\sqrt{2}$ = $24\sqrt{2}$ as our final answer.

*Note: This path will pass through point five, that is, following the diagram you described. If this is true, then there is no need to solve the longest possible path for point 5.

5 0

3 years ago

In any 15-minute period in a statistics class, the probability of observing at least one mistake made by professor Doe is 5%. Wh

777dan777 [17]

Hey there!

We can set this up a proportion to figure out the percent we need.

$\frac{mins}{percent} = \frac{15}{5} =\frac{60}{p}$