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13 days ago

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As Evin is driving her car, she notices that after 1 hour her gas tank has 7.25 gallons left and after 4 hours of driving, it ha

s 3.5 gallons of gas left in it. What is the rate at which her car is using gas.

1 answer:

PIT_PIT [9.1K]13 days ago

5 0

7.25 gallons per hour

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The probability that a customer's order is not shipped on time is 0.06. A particular customer places three orders, and the order

AnnZ [9099]

Response:

a)

b) 0.044

Step-by-step breakdown:

Part a)

A Sonet consists of 14 lines. Raymond Queneau published a collection of 10 sonnets, each placed on separate pages. This implies that every page contains a 14-line poem. We are to determine how many unique sonnets can be created from the 10 published sonnets.

As the first line of a new sonnet can be chosen from any of the 10 published sonnets, it offers 10 options for the selection of the first line. Likewise, the second line of the new sonnet can also be from any of the 10 sonnets, leading to another 10 choices for the second line, and this applies identically for all 14 lines, resulting in 10 options for each line.

According to the fundamental principle of counting, the total number of possible sonnets would equal the product of the options available for all 14 lines.

Thus,

the number of sonnets created from those in the book = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 =

sonnets

Therefore,

can be formed from the 10 in the book.

Part b)

Next, we will ascertain how many sonnets can be generated that utilize none of the lines from the first and last page. Given that there are 10 pages total, the exclusion of the 1st and last leaves us with 8 pages (8 sonnets).

Consequently, the number of options for each line of such a sonnet will be restricted to 8 choices. Applying the fundamental principle of counting, the total sonnets with no lines from either the first or last sonnet is calculated as

$P = (0.94)^{3}$

This shows the number of favorable outcomes that ensure the selection of a sonnet does not result in lines from the first or last sonnet in the collection.

Thus,

The probability that no lines are selected from either the first or the last sonnet =

5 0

8 days ago

An electronic product contains 40 integrated circuits. The probability that any integrated circuit is defective is 0.01, and the

Zina [9171]

Answer:

The chance that there is one or more defective integrated circuits is 33.10%.

Detailed solution:

Each integrated circuit can be either defective or not, which provides only two possible outcomes. As a result, this scenario is well-suited to be analyzed using the binomial probability distribution.

About the binomial distribution

This distribution calculates the likelihood of exactly x successes in n repeated trials where each trial has two possible results.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

Here, $C_{n,x}$ represents the count of combinations of x items selected from n elements, described by the formula:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of the event X occurring.

Applying it to the problem

The product contains 40 integrated circuits, so $n = 40$ .

The probability that an individual integrated circuit is defective is 0.01, so $\pi = 0.01$ .

Finding the probability of at least one defective circuit

There are two cases: either at least one integrated circuit is defective (probability $P(X > 0)$ ) or none are defective (probability $P(X = 0)$ ). Since probabilities sum to 1, we want to determine $P(X>0)$ .

$P(X > 0) + P(X = 0) = 1$

$P(X > 0) = 1 - P(X = 0)$

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{40,0}.(0.01)^{0}.(0.99)^{40} = 0.6690$

$P(X > 0) = 1 - P(X = 0) = 1 - 0.6690 = 0.3310$

Hence, the probability of having one or more defective integrated circuits is 33.10%.

3 0

1 month ago

Read 2 more answers

Which construction might this image result from?

AnnZ [9099]

Option (C.) is the right choice!
It's about constructing the perpendicular bisector..!!!

5 0

19 days ago

Read 2 more answers

A tobacco company claims that the amount of nicotine in its cigarettes is a randomvariable with mean 2.2 mg and standard deviati

PIT_PIT [9117]

Response:

0.0000

Unusual

To explain step-by-step:

A tobacco company asserts that the nicotine content in its cigarettes behaves as a random variable with a mean of 2.2 mg and a standard deviation of.3 mg.

This means the population parameters are

$\mu =2.2 \\s = 0.3$

The likelihood that the sample average would equal or exceed 3.1

$=P(X\geq 3.1)\\=P(Z\geq \frac{3.1-2.2}{\frac{0.3}{\sqrt{100} } } )\\=P(Z\geq 30)\\$

equals 0.0000

8 0

8 days ago

What is the nearest ten thousand, the population of Vermont was estimated to be about 620,000 in 2008 . What might have been the

AnnZ [9099]

Answer:

The exact population of Vermont in 2008 could have been around 618,000

Step-by-step explanation:

* Here's how rounding to the nearest ten thousand works:

- Numbers ending with the last four digits between 0001 and 4999 are rounded down to the nearest lower multiple of ten thousand

- Example: 83,525 rounds down to 80,000.

- If the last four digits are 5000 or above, round up to the next higher ten thousand

- Example: 58,988 rounds up to 60,000

* Applying this rule to the problem given:

Since the rounded population is 620,000 to the nearest ten thousand, the actual population could be any value with the last four digits from 0001 to 4999 (like 618,000) or from 5000 upwards (like 624,000).

Therefore, 618,000 might represent the actual population of Vermont in 2008

6 0

1 month ago