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2 years ago

What is f(5) if f(1) = 3. 2 and f(x 1) = Five-halves(f(x))?

2 answers:

8 0

Function assign value from one set to another. The value of f(5), if f(1) = 3.2 and f(x+1) = Five-halves(f(x)) is 125.

<h3>What is Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

As it is given the value of the function f(1) is 3.2, while the value of f(x+1) is $f(x+1) = \dfrac{5}{2}[f(x)]$ , therefore, in order to find the value of f(5), we need to calculate the value of f(4).

f(2)

$f(x+1) = \dfrac{5}{2}[f(x)]\\\\f(2)=f(1+1) = \dfrac{5}{2}[f(1)]\\\\f(2) = 2.5 \times 3.2\\\\f(2) = 8$

f(3)

$f(x+1) = \dfrac{5}{2}[f(x)]\\\\f(3)=f(2+1) = \dfrac{5}{2}[f(2)]\\\\f(3) = 2.5 \times 8\\\\f(3) = 20$

f(4)

$f(x+1) = \dfrac{5}{2}[f(x)]\\\\f(4)=f(3+1) = \dfrac{5}{2}[f(3)]\\\\f(4) = 2.5 \times 20\\\\f(4) = 50$

f(5)

$f(x+1) = \dfrac{5}{2}[f(x)]\\\\f(5)=f(4+1) = \dfrac{5}{2}[f(4)]\\\\f(5) = 2.5 \times 50\\\\f(5) = 125$

Hence, the value of f(5), if f(1) = 3. 2 and f(x+1) = Five-halves(f(x)) is 125.

Learn more about Function:

brainly.com/question/5245372

Zepler [3.9K]2 years ago

6 0

Answer:

Its 125

Step-by-step explanation:

got it right on ed

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Step-by-step explanation:

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Denominator. This is the number below the fraction line. For 16/8, the denominator is 8.

Improper fraction. This is a fraction where the numerator is greater than the denominator.

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Now let's go through the steps needed to convert 16/8 to a mixed number.

Step 1: Find the whole number

We first want to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.

16/8 = 2

Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.

Step 2: Get the new numerator

To work this out we'll use the whole number we calculated in step one (2) and multiply it by the original denominator (8). The result of that multiplication is then subtracted from the original numerator:

16 - (8 x 2) = 0

Step 3: Our mixed fraction

We've now simplified 16/8 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:

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You maybe have noticed here that our new numerator is actually 0. Since there is no remainder, we can remove the entire fraction part of this mixed number, leaving us with a final answer.

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a) 33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.

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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.

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The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 18.6, \sigma = 5.9$

a) What is the probability that a single student randomly chosen from all those taking the test scores 21 or higher?

This is 1 subtracted by the pvalue of Z when X = 21. So

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

$Z = \frac{21 - 18.6}{5.4}$

$Z = 0.44$

$Z = 0.44$ has a pvalue of 0.67

1 - 0.67 = 0.33

33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.

b) The average score of the 76 students at Northside High who took the test was x =20.4. What is the probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher?

Now we have $n = 76, s = \frac{5.9}{\sqrt{76}} = 0.6768$