All categories

2 years ago

Two number cubes are rolled to determine how a token moves on a game board. The sides of

Mathematics

1 answer:

ahrayia [7]2 years ago

8 0

Answer:

D. The mathematical expectation of Option A is 1. The mathematical expectation of Option B is 1.5. Option B offers a greater likelihood of advancing to the finish line.

Step-by-step explanation:

The result of a product is odd only when the two numbers are odds.

There are 6*6 = 36 possible outcomes when two dice are rolled. Only 9 of them are a combination of two odd numbers: {1, 1} {1, 3} {1, 5} {3, 1} {3, 3} {3, 5} {5, 1} {5, 3} {5, 5}. Then 36 - 9 = 27 outcomes are even.

P(even) = 27/36 = 0.75

Option A) Mathematical expectation: 0.75*4 + 0.25*(-8) = 1

Option B) Mathematical expectation: 0.75*5 + 0.25*(-9) = 1.5

You might be interested in

A local shop prints photos. The function f(x) = −x2 + 20x − 75 models the profit from one customer, where x is the number of pho

AnnZ [28]

Answer:

x = 5, x = 15; The zeros represent the number of photos printed to produce a maximum profit.

Step-by-step explanation:

F(x) = −x²+ 20x − 75

Let's f(x)= 0

0= -x²+20x-75

0= x²-20x+75

0=x²-5x-15x+75

0= x(x-5)-15(x-5)

0= (x-5)(x-15)

The zeros are

X= 5 or x = 15

And the xeros represent a number of photos printed to produce maximum profit

7 0

2 years ago

Which statements are true regarding triangle LMN? Check all that apply.

dimaraw [331]

Answer:

$NM = x$

$LM = x\sqrt{2}$

$tan (45) = 1$

Step-by-step explanation:

Step 1: Pythagoras Theorem

Pythagoras theorem relates the three sides of the triangle in such a way that the sum of the square of base and perpendicular is equal to hypotenuse, such as:

$LM^{2} =LN^{2} +NM^{2}$

Step 2: Trigonometric Functions

Only for a right angle triangle following three trigonometric relations are valid

$sin (\theta) = \frac{opposite}{hypotenuse}$

$cos (\theta) = \frac{adjacent}{hypotenuse}$

$tan (\theta)=\frac{sin (\theta)}{cos (\theta)} = \frac{opposite}{adjacent}$

Step 3: Verifying all the possible answers

A: Since, LN = x and using $tan (45) =1$

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{NM}{x} =1$

therefore, NM = x (true)

B: As NM = x therefore it can not be equal to $x\sqrt{2\\}$ .

C: Using Pythagoras Theorem

$LM^{2} =LN^{2} +NM^{2}$

$LM^{2} =x^{2} +x^{2}$

$LM^{2} =2x^{2}$

$LM = \sqrt{2x^{2}} = x\sqrt{2}$

It can also be proved using trigonometric relation

$cos (45) = \frac{x}{LM}$

$LM = \frac{x}{cos (45)}$

As, $\frac{1}{cos (45)}= \sqrt{2}$

Therefore

$LM = x\sqrt{2}$

D and E:

Using same approach similar to part A

Since, LN = x and NM = x

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{x}{x} =1$

Therefore, $tan (45) = 1$ and not equal to $\frac{\sqrt{2} }{2}$

3 0

2 years ago

Read 2 more answers

What did they call the bug that the astronauts brought back from the moon?

ludmilkaskok [199]

A lunatic (haha) .-.

7 0

2 years ago

Read 2 more answers

Hikers came across a part of a redwood stump. If the length of the chord is 8 feet, what was the diameter of the tree?

erastova [34]

So in the problem, the length of the chord there is the circumference of the tree. So in order to get the diameter of the tree, we must use the formula in getting the circumference of a circle that is stated as follows.

C = 2pi *Radius

so first we need the get the radius of the tree which represent by this formula:

Radius = C /2pi = 8/6.2832 = 1.2732 ft
Diameter = 2*radius = 2 * 1.27 32 = 2.5465 feet

In summary, the diameter of the tree is 2.565 feet.

7 0

2 years ago

Grace is 7 years older than Elena. Grace is also 15 years old.

Alex73 [517]

The 3rd one is the answer

4 0

2 years ago