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SashulF [63]
2 years ago
10

the amount of snowfall in jan was 2 3/4 feet. the amount of snowfall in february was 1 2/3 feet. how much snow fall was there in

january? (write answer in the simplest form)
Mathematics
1 answer:
Mkey [24]2 years ago
6 0

Answer this is an example 4 you

To do this problem, you need to change the way the fractions are displayed so that you can simplify them.

The first step is to change them to improper fractions: fractions like 4/3 that represent more than 100% (parts adding to more than one whole).

For example, to change the first fraction in this way, multiply the number in front (2) by the bottom number:

2 * 3 = 6

This means the 2 can also represent 6 / 3. Remember that 1 equals 3/3 so 2 equals 6/3. Now add this to the 1/3 you started with, and you end up with 7/3.

Do the same for the other fraction.

Now that you have both fractions written in this way, you can multiply each by the other's denominator to arrive at their LCD (least common denominator). It won't always be least, but you can always simplify further. In this case, the numbers are small enough that it likely won't matter.

You will end up with a fraction of halves: some number x, over 2, meaning x number of halves.

Your other fraction is 7/3. So the common denominator is the bottom numbers multiplied together: 2 * 3 = 6.

To change 7/3 to a fraction of sixths, you multiply the whole thing by two. This gets the bottom number to be six.

7 * 2 = 14

3 * 2 = 6

So this fraction can also be written as 14/6. Once again, do the same to the other fraction (but multiply by 3, to get the other fraction into sixths also, since it is currently halves).

Now you have two fractions that are both in parts of six. A ratio (x:y) is nothing more than a fraction itself. So if you had for example the ratio

2/5 : 10/5

This ratio could also be written as 1/5 : 5/5, or 1/5 to 1. Both numerators (the top number) are divisible by 2, so you can divide them both by 2 and end up with a simplified version of the same ratio.

Whatever ratio you end up with (14/6 : some other fraction), do the same thing to it. See if any of the numbers share a common factor, and simplify where possible. If it's not possible to simplify further, you're done.

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Evaluate the expression.<br> 23.6 - 2x3° divides by 2
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The height of a triangle is 7 ft more than its base. if the area of the triangle is 30 ft^ what is the lentgh of the base
Dmitriy789 [7]
Since the area of a triangle is in the form
area=0.5(base)(height)
height=base+7
let base=x
area=0.5(x)(7+x)
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6 0
3 years ago
of the 50 U.S states, 4 have names that start with the letter W. What percentage of U.S. states have names that start with the l
serious [3.7K]

Answer:

8% of of the Us states have the names that start with W.

Step-by-step explanation:

We are told that, of the 50 states, 4 have names that start with letter W, and to figure out what percentage of U.S. states have names that start with the letter W, we need to know what what 4 is what percent of 50.

We figure this out the following way:

Percent = \frac{4}{50} *100=0.08*100 =8

Percent = 8%

6 0
3 years ago
Andrew plans to retire in 32 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on pa
Debora [2.8K]

Answer:

a) 0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

b) 0.4129 = 41.29% probability that the mean return will be less than 8%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, 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 normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean 8.7% and standard deviation 20.2%.

This means that \mu = 8.7, \sigma = 20.2

40 years:

This means that n = 40, s = \frac{20.2}{\sqrt{40}}

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 13%?

This is 1 subtracted by the pvalue of Z when X = 13. So

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

By the Central Limit Theorem

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

Z = \frac{13 - 8.7}{\frac{20.2}{\sqrt{40}}}

Z = 1.35

Z = 1.35 has a pvalue of 0.9115

1 - 0.9115 = 0.0885

0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

(b) What is the probability that the mean return will be less than 8%?

This is the pvalue of Z when X = 8. So

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

Z = \frac{8 - 8.7}{\frac{20.2}{\sqrt{40}}}

Z = -0.22

Z = -0.22 has a pvalue of 0.4129

0.4129 = 41.29% probability that the mean return will be less than 8%

8 0
2 years ago
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