A 9-foot piece of wood is cut into shelves. If each is 3/7 foot in length, how many shelves are there?

Mathematics

1 answer:

Aloiza [94]3 years ago

6 0

Hello!

To find how much shelves we cut, we need to divide 9 feet by 3/7 feet. When dividing by fractions, it is like multiplying its reciprocal.

This means that the reciprocal of 3/7 is 7/3.

$9 / \frac{3}{7} = \frac{9}{1} * \frac{7}{3} = \frac{63}{3} = 21$

Therefore, if each shelf is 3/7 feet in length, then there are 21 shelves.

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A company with a large fleet of cars wants to study the gasoline usage. They check the gasoline usage for 50 company trips chose

Nookie1986 [14]

Answer:

The 95% confidence interval is given by (25.71536 ;28.32464)

And if we need to round we can use the following excel code:

round(lower,2)

[1] 25.72

round(upper,2)

[1] 28.32

And the interval would be (25.72; 28.32)

Step-by-step explanation:

Notation and definitions

n=50 represent the sample size

$\bar X= 27.2$ represent the sample mean

$s=5.83$ represent the sample standard deviation

m represent the margin of error

Confidence =88% or 0.88

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Calculate the critical value tc

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 88% of confidence, our significance level would be given by $\alpha=1-0.88=0.12$ and $\alpha/2 =0.06$ . The degrees of freedom are given by: