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3 years ago

A six-sided number cube is labeled with the numbers 1-6, one number on each face. Each number is used exactly once.

Mathematics

1 answer:

I am Lyosha [343]3 years ago

8 0

Answer:

Step-by-step explanation:

This question can be solved using fundamental counting principle which means to say that if there are "m" ways of doing one thing and there are "n" ways of doing other thing then there are total "m*n" ways of doing other things.

For example: if there are 4 type of pens and 3 type of notebook then there are "4*3" ways to write on notebook using the pens.

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Using the above mentioned principle we have

six sided cube with number 1 to 6 written on it hence in first roll there are six possible outcome(1 or 2 or 3 or 4 or 5 or 6) similarly there are 6 possible outcome in other roll as well.

If the combination of outcome is to be deduced then there are 6*6 ways of outcome based on fundamental counting principle.

Hence there are 6*6 = 36 ways of possible outcomes.

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A police helicopter descends 128 feet to

rewona [7]

Answer:

h - d = 477 meters

Where: h = original height

d = amount the helicopter descended

The original height of the helicopter is given to be h

Step-by-step explanation:

5 0

3 years ago

In a particular triathlon the athletes cover 1/24 of the total distance by

pav-90 [236]

Answer:

15/8

Step-by-step explanation:

Let "d" be the total distance, that is, the distance for swimming (s), running (r) and going by bike (b).

d = s + r + b [1]

1/24 of the total distance is covered by swimming.

s = 1/24 d [2]

1/3 of the distance is covered by running.

r = 1/3 d [3]

If we replace [2] and [3] in [1], we get

d = 1/24 d + 1/3 d + b

b = d - 1/24 d - 1/3 d

b = 24/24 d - 1/24 d - 8/24 d

b = 15/24 d = 5/8 d

The ratio of the distance covered by bike to the distance covered by running is:

b/r = (5/8 d)/(1/3 d) = 15/8

5 0

3 years ago

When playing the roulette at a casino, you have exactly 1/35 chance of winning in each round if you play a single number. Your f

Vikentia [17]

Answer:

0.2275 = 22.75% probability that you actually won that round

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Fireworks going off

Event B: You won

Probability of fireworks going off.

100% of 1/35 = 0.0286(when you win)

10% of 34/35 = 0.9714(you lost). So

$P(A) = 0.0286 + 0.1*0.9714 = 0.12574$

Probability of you winning and fireworks going off:

100% of 1/35, so $P(A \cap B) = 0.0286$

If you failed to see the outcome of a round, but you see the fireworks going off, then what is the probability that you actually won that round?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0286}{0.12574} = 0.2275$

0.2275 = 22.75% probability that you actually won that round

8 0

3 years ago

Solve the 3 × 3 system shown below. Enter the values of x, y, and z. X + 2y – z = –3 (1) 2x – y + z = 5 (2) x – y + z = 4 (3)

Svet_ta [14]

<h2>Answer:</h2>

$\boxed{x=1, \y=-1, \ z=2}$

<h2>Step-by-step explanation:</h2>

We will use the Gaussian elimination method to solve this problem. To do so, let's follow the following steps:

Step 1: Let's multiply first equation by −2. Next, add the result to the second equation. So:

$\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\~~ x&-~~~~~ y&+~~~~ z&~=~4\end{array}$

Step 2: Let's multiply first equation by −1. Next, add the result to the third equation. Thus:

$\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&-~~~3~ y&+~~2~ z&~=~7\end{array}$

Step 3: Let's multiply second equation by −35, Next, add the result to the third equation. Therefore:

$\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&&+~~\frac{ 1 }{ 5 }~ z&~=~\frac{ 2 }{ 5 }\end{array}$

Step 4: solve for z, then for y, then for x:

$\frac{ 1 }{ 5 } ~ z & = \frac{ 2 }{ 5 } \\ \\ \boxed{z & = 2}$

$-5y+3z &= 11\\-5y+3\cdot 2 &= 11\\ \\ \boxed{y &= -1}$

By substituting $y=-1 \ and \ z=2$ into the first equation, we get the $x$ . So:

$x+2(-1)-2=-3 \\ \\ x-2-2=-3 \\ \\ \boxed{x=1}$

6 0

4 years ago

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100/9 write as a mixed number plz

stira [4]

Answer: 11 1/9

Step-by-step explanation:

7 0

3 years ago