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4 years ago

5

The volume of a rectangular box is 330 cubic inches. The length on one side of the top is 11 inches, and the height of the box i

s 3 inches. What is the area of the top of the box.

1 answer:

Fiesta28 [93]4 years ago

5 0

Answer: 110 square inches.

Step-by-step explanation:

The volume of a rectangular box would be:

$V=length*width*height$

In this case, we know the volume, the length and the height, and we don't know the width, so we're going to isolate it:

$width=\frac{V}{length*height}$

Substituting the data:

$width=\frac{330}{11*3} =10in$

This width is also the width of the top of the box, so the area of the top would be:

$A=length*width\\A=11*10\\A=110in^{2}$

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3 years ago

Tim wants to buy a new sound system for $145. He has already saved $65. He gets $20 for each lawn that he mows.

forsale [732]

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Step-by-step explanation:

Tim need to mow four lawns.

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3 years ago

A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of

yan [13]

Answer:

"The probability that the mean battery life would be greater than 948.8 minutes" is 0.1446.

Step-by-step explanation:

In this case, the quality control expert takes a <em>sample</em> of batteries. From these batteries, we want to find "the probability that the mean battery life would be greater than 948.8 minutes".

Different concepts needed to take into account to solve this question

Sampling Distribution of the Means

For doing this, we need to use the sampling distribution of the means, which results from taking the mean for each possible sample coming from a random variable $\\ x$ . Roughly speaking, each sample will have a different mean, $\\ \overline{x}$ , and the probability distribution for any of these means is called the <em>sampling distribution of the means</em>.

The sampling distribution of the means has a mean that equals the population's mean for the random variable $\\ x$ , i.e., $\\ \mu$ , and its standard deviation is $\\ \frac{\sigma}{\sqrt{n}}$ . We can express this mathematically as:

$\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$ [1]

Standardized Values for $\\ \overline{x}$

We can standardized the values for $\\ \overline{x}$ using <em>z-scores</em>:

$\\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [2]

This random variable $\\ Z$ follows a <em>standard normal distribution</em>, that is, $\\ Z \sim N(0,1)$ , and it is easier to find probabilities since the values for them are tabulated in the <em>standard normal table</em> (available in any Statistics book or on the Internet.)

What type of distribution follows the sampling distribution of the means?

A general rule of thumb is that this distribution (the sampling distribution of the means) follows a <em>normal distribution</em> if the sample size, $\\ n$ , is bigger than or equal to 30 observations, or $\\ n \geq 30$ . In this case, $\\ n = 109$ batteries. This is a result from the Central Limit Theorem, fundamental in Statistical Inference.

Standard Deviation

We have to remember that the standard deviation is the square root of the variance $\\ \sigma^2$ , or $\\ \sqrt{\sigma^2}$ .

$\\ \sigma^{2} =5929$
$\\ \sigma = \sqrt{5929} = 77$

Therefore, the standard deviation in this case is $\\ \sigma = 77$ minutes.

In sum, we have the following information to answer this question:

$\\ \sigma = 77$ minutes.
$\\ \mu = 941$ minutes.
$\\ n = 109$ batteries (the sample size is <em>large enough</em> to assume that the sampling distribution of the means follows a <em>normal distribution</em>).
$\\ \overline{x} = 948.8$ minutes.

What is the probability that the mean battery life would be greater than 948.8 minutes?

Well, having all the previous information, we can use [2] to solve this question (without using units):

$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ z = \frac{948.8 - 941}{\frac{77}{\sqrt{109}}}$

$\\ z = \frac{7.8}{\frac{77}{\sqrt{109}}}$

$\\ z = \frac{7.8}{7.37526}$

$\\ z = 1.05758 \approx 1.06$

This result is the <em>standardized value</em> or <em>z-score</em> for $\\ \overline{x}$ , considering $\\ \mu = 941$ and $\\ \sigma = 77$ .

We round <em>z</em> to two decimals digits since <em>standard normal table</em> only uses it as an entry to find probabilities.

With $\\ z = 1.06$ , we can consult the <em>cumulative standard normal table. </em>First, we need to find with $\\ z = 1.0$ in the first column in the table. Then, in its first raw, we need to find +0.06. The intersection for these two values determines the cumulative probability for $\\ P(z$ .

It is important to recall that $\\ P(z$ because $\\ z = 1.06$ is the standardized value for $\\ \overline{x} = 948.8$ minutes.

Then, $\\ P(z$

However, the question is about $\\ P(\overline{x} > 948.8) = P(z>1.06)$

And

$\\ P(\overline{x} > 948.8) + P(\overline{x} < 948.8) = 1$

Or

$\\ P(z>1.06) + P(z$

Then

$\\ P(z>1.06) = 1 - P(z$

$\\ P(z>1.06) = 1 - 0.8554$

$\\ P(z>1.06) = 0.1446$

Therefore, "the probability that the mean battery life would be greater than 948.8 minutes" is 0.1446.

6 0

4 years ago

What is the area of a rectangle with a width of x^2+x+1 and a length of 3x^2-2x-1?

Nostrana [21]

Answer: width= 2x-1 and length= 3x+2

Step-by-step explanation: SOLUTION: Choose a possible dimensions of a rectangle with a width= 2x-1 and length= 3x+2 so that its area is greater than 153cm² a. W= 13 L= 15 b. W= 11 L= 20

6 0

2 years ago

Express 8 1/5% as a mixed number or a fraction

Alexxandr [17]

Answer:

41/5

Step-by-step explanation:

First we change the 8 and 1/5% to 8.2%

Write the fraction down as a number over one = 8.2/1

Multiply both top and bottom by 10 for every number after the decimal point:

As we have 1 numbers after the decimal point, we multiply both numerator and denominator by 10. So,

8.2/1 = (8.2 × 10)

(1 × 10) = 82/10

Reduce the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD (82,10) = 2. So, (82÷2)/(10÷2) = 41/5 when reduced to the simplest form.

As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 82/10 is also equal to 81/5 when expressed as a mixed number.

7 0

3 years ago