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12345 [234]
2 years ago
11

5. A number cube has faces numbered 1 through 6, and a coin has two sides, heads and tails. The number cube will be rolled once,

and the coin will be flipped once.
Find the probabilities of the following events. (Express your answers as fractions in lowest terms.)
a. The number cube shows a 6.
b. The coin shows heads.
c. The number cube shows a 6, and the coin shows heads.
d. The number cube shows a 6, or the coin shows heads.
Mathematics
1 answer:
valkas [14]2 years ago
8 0

Answer your phone :

Step-by-step explanation:

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The distance of Rome is 15558 write the distance to Rome in scientific notation
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1.5558 * 10^4

Step-by-step explanation:

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A hotel installs smoke detectors with adjustable sensitivity in all public guest rooms. (a) State the null and alternative hypot
Lana71 [14]

Answer:

(a) <em>H₀</em>: There is no fire vs. <em>Hₐ</em>: There is a fire.

(b) A type I error occurs when we discard a true null hypothesis (<em>H₀</em>) and a type II error is made when we fail to discard a false null hypothesis (<em>H₀</em>).

(c) In this case, type II error has the more severe consequences.

Step-by-step explanation:

It is provided that a hotel installs smoke detectors with adjustable sensitivity in all public guest rooms.

(a)

The hypothesis can be defined as follows:

<em>H₀</em>: There is no fire.

<em>Hₐ</em>: There is a fire.

(b)

A type I error occurs when we discard a true null hypothesis (<em>H₀</em>) and a type II error is made when we fail to discard a false null hypothesis (<em>H₀</em>).

In this case a type I error will be committed if we conclude that there is a fire and the smoke detector sounds an alarm, when in fact there is no fire.

In this case a type II error will be committed if we conclude that there is no fire and the smoke detector does not sounds an alarm, when in fact there is a fire.

(c)

In this case, type II error has the more severe consequences.

Concluding that there is no fire as the smoke detector did not sound an alarm, when in fact there is a fire, will cause casualties and is harmful for the health of the guests.

Guests would not be alert about the fire as there was not any alarm, and many may loose their lives because of this.

7 0
2 years ago
One department head is chatting with another: "Today, our two budgets total $1.8 million. But that's only 3% of the company's wh
frez [133]

Answer: the company's whole budget is $60 000000

the budget of each of the two departments are $1200000 and $600000

Step-by-step explanation:

Let x represent the budget of one department.

Let y represent the budget of the other department.

The total budget is $1.8 million. It means that

x + y = 1800000 - - - - - - - - - -1

If you spend $2 for every $1 I do,it means that

x = 2y

Substituting x = 2y into equation 1, it becomes

2y + y = 1800000

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y = 1800000/3

y = $600000

x = 2y = 2 × 600000

x = $1200000

Let z represent the company's whole budget. If $1.8 million is only 3% of the company's whole budget, it means that

3/100 × z = 1800000

0.03z = 1800000

z = 1800000/0.03

z = $60000000

6 0
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