JD opened a savings account with $400. The simple interest rate is 3% per year.

You are creating identical candy bags using 18 chocolate bars and 30 peanut butter cups. What is the greatest number of bags you

xxMikexx [17]

If you can't split up the peanut butter cups, the identical bags would each have 1 chocolate bar and 1 peanut butter cup because 30 cannot be devided between 18 bags as whole numbers more than once.

6 0

2 years ago

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Which of the following represents the polynomial 5x + 3x^4 + 15 − 7x3 in standard form, the degree of the polynomial, and the nu

kkurt [141]

A polynomial is written correctly when the exponents are listed in order from highest to lowest. The highest exponent then dictates the degree of the whole polynomial. The first choice above is written in standard form from highest degree to lowest. Doesn't matter that we might skip the x-squared term or any other x-term, as long as they're in order from highest to lowest. The degree on that first polynomial, the one you're after, is 4 because that's the highest exponent, and there are 4 terms there. Terms are "bunches" of numbers and variables stuck together by multiplication and separated by + or - signs.

6 0

2 years ago

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The time for a visitor to read health instructions on a Web site is approximately normally distributed with a mean of 10 minutes

klio [65]

Answer:

a) The mean is 10 and the variance is 0.0625.

b) 0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.

c) 10.58 minutes.

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 establishes 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.

Normally distributed with a mean of 10 minutes and a standard deviation of 2 minutes.

This means that $\mu = 10, \sigma = 2$

Suppose 64 visitors independently view the site.

This means that $n = 64, = \frac{2}{\sqrt{64}} = 0.25$

a. The expected value and the variance of the mean time of the visitors.

Using the Central Limit Theorem, mean of 10 and variance of (0.25)^2 = 0.0625.

b. The probability that the mean time of the visitors is within 15 seconds of 10 minutes.

15 seconds = 15/60 = 0.25 minutes, so between 9.75 and 10.25 seconds, which is the p-value of Z when X = 10.25 subtracted by the p-value of Z when X = 9.75.

X = 10.25

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

By the Central Limit Theorem

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