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valkas [14]
3 years ago
11

Ruben bought 6 new books for his collection. This increased his collection by 12%. How many books did he have before his purchas

es?
Mathematics
1 answer:
Norma-Jean [14]3 years ago
4 0

Answer:  The required number of books that Ruben had before purchases is 50.

Step-by-step explanation:  Given that Ruben bought 6 new books for his collection that increased his collection by 12%.

We are to find the number of books that Ruben had before purchases.

Let x denotes the number of books that Ruben had before purchases.

Then, according to the given information, we have

x+6=x+12\%\times x\\\\\\\Rightarrow 6=\dfrac{12}{100}x\\\\\\\Rightarrow 6=\dfrac{3x}{25}\\\\\\\Rightarrow 3x=150\\\\\Rightarrow x=\dfrac{150}{3}\\\\\Rightarrow x=50.

Thus, the required number of books that Ruben had before purchases is 50.

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The average score of all golfers for a particular course has a mean of 75 and a standard deviation of 4. Suppose 64 golfers play
Vilka [71]

Answer:

0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.

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 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 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.

In this problem, we have that:

\mu = 75, \sigma = 4, n = 64, s = \frac{4}{\sqrt{64}} = 0.5

Find the probability that the average score of the 64 golfers exceeded 76.

This is 1 subtracted by the pvalue of Z when X = 64.

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

By the Central Limit Theorem

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

Z = \frac{76 - 75}{0.5}

Z = 2

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.

6 0
3 years ago
What is equivalent to 3^4/3^7
Misha Larkins [42]

i believe your answer will be 0.04 or 4/100

OR if you need an equivalent expression, that would be 81/2187

5 0
3 years ago
If 433 = 100% then what percent does 383 equal
Goryan [66]

Answer:

88.46%

Step-by-step explanation:

433 - 383 = 50

50 ÷ 433 = 0.1154

0.1154 x 100 = 11.54%

100% - 11.54% = 88.46%

<u>Check work:</u>

433 x 88.46% = 383

5 0
3 years ago
What is the measure of angle X?
Alinara [238K]
Using one of the above equations, you can find the value of x.
tan x = 84/13 => x = tan-¹(84/13)
x = 81.20°

Hope that helps

4 0
3 years ago
Read 2 more answers
A box of national brand cornflakes is $2.09 for 12 ounces. A box of store label cornflakes is $3.09 for 20 ounces.
grin007 [14]

Answer:

A)

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B) The larger box is cheaper per ounce.


C) 2.09 – .30 = 1.79 for 12 ounces. So than $1.79/12= .15/oz.

They  would both be the same so there would be no better deal.


4 0
3 years ago
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