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3 years ago

7

The average amount of time it takes Greg to mow x lawns can be defined by the expression 28x + 5. In this scenario, what does th

e number 28 percent represent?

1 answer:

inna [77]3 years ago

6 0

Answer:

the answer is 140 hope this helped

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A popular soft drink is sold in 2-liter (2000 milliliter) bottles. Because of variation in the filling process, bottles have a m

andrezito [222]

Answer:

a) 0.27% probability that the mean is less than 1995 milliliters.

b) 2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.

Step-by-step explanation:

To solve this problem, it is important to understand the normal probability distribution and the central limit theorem

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 2000, \sigma = 18$

A) If the manufacturer samples 100 bottles, what is the probability that the mean is less than 1995 milliliters?

So $n = 100, s = \frac{18}{\sqrt{100}} = 1.8$

This probability is the pvalue of Z when X = 1995. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{1995 - 2000}{1.8}$

$Z = -2.78$

$Z = -2.78$ has a pvalue of 0.0027

So 0.27% probability that the mean is less than 1995 milliliters.

B) What mean overfill or more will occur only 10% of the time for the sample of 100 bottles?

This is the value of X when Z has a pvalue of 1-0.1 = 0.9.

So it is X when $Z = 1.28$

$Z = \frac{X - \mu}{s}$

$1.28 = \frac{X - 2000}{1.8}$

$X - 2000 = 1.8*1.28$

$X = 2002.3$

2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.

3 0

3 years ago

Given that D(x) = 2x, select all of the following that are true statements.

GaryK [48]

It is D
You welcome

8 0

2 years ago

Number 8 only please

givi [52]

Answer:

Should be roughly 79.76% if I'm doing this right.

Step-by-step explanation:

Looking at the problem, you're given 3 things:

1) 6.8 million tonnes are recycled;

2) 6.8 million tonnes is 27% of the total household waste;

3) 20.1 million tonnes could be recycled.

Since they're asking for what percentage of <em>total</em> household waste could be recycled, you're looking at a multi-step cross multiplication problem.

It's not very difficult though, don't worry.

So I'm gonna start by telling you to just forget that the word "million" exists for the moment. You only need 6.8, 20.1, and 27%.

Setting up the first part of the problem requires you to convert 27% into a fraction. That's $\frac{27}{100}$ .

6.8 is 27% of some mysterious number that we need to figure out what percent of household waste could be recycled, so that'll be set up on the opposite side of the equal sign as the equivalent to 27.

So we're starting out with this: $\frac{6.8}{?} =\frac{27}{100}$

Since you're trying to initially find the total household waste, we're setting x as the variable to solve for.

$\frac{6.8}{x} =\frac{27}{100}$

Cross-multiplying** means you multiply the numerator of one side of the equal sign to the denominator of the other side of the equal sign, and vice versa (denominator of one side to numerator of other). So multiply 6.8 to 100, and 27 to x.

$680=27x$

Now that you have this, you have to isolate x. Divide both sides by 27 to do this.

$25.185185...=x$

I'm gonna round that for simplicity's sake, because 185 repeats.

$25.2=x$

So we have 25.2 million tonnes of total household waste. Great! Now we can find the <em>percentage </em>of household waste that could be recycled.

Since we have how much could be recycled and the total, we just need to solve for the percent this time. So this is what the set-up will look like:

$\frac{20.1}{25.2} =\frac{x}{100}$

x being the percent we're solving for.

Cross-multiply again:

$2010=25.2x$

Divide both sides by 25.2:

$79.761904761904...=x$

Then round for simplicity's sake:

$79.76=x$

And you get 79.76% of household waste could be recycled.

Hope this helped!

**Be careful with cross-multiplying when you get to higher level math though. Not every situation allows for cross-multiplying. In fact, you can only cross-multiply when there's an equal sign.

6 0

3 years ago

What’s the volume of one cylinder?

r-ruslan [8.4K]

Answer:

For the first one its: Volume = 402.12in³

For the second one its: Volume = 201.0619 in³

Step-by-step explanation:

For the first one work:

Volume = 3.1416 x 42 x 8

= 3.1416 x 16 x 8

For the second one work:

Volume = 3.1416 x 42 x 4

= 3.1416 x 16 x 4

5 0

3 years ago

Read 2 more answers

Scaling up a 4 inch by 6 inch image by 50% results in which of the following image size

Monica [59]

50% or 1/2 of 4 is 2 50% or 1/2 of 6 is 3 so then just add them to the respective number since its going up by 50% or 2 in by 3 in \[\frac{ 6 }{ 9}\]

6 0

3 years ago

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