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sasho [114]
3 years ago
11

student in two fifth grade classes were given the same english test. one class of 24 studmets had a mean 86, and the second clas

s of 23 students had a mean of 85. what is the mean for the total number of students in both classes to the nearest 0.1
Mathematics
1 answer:
Arada [10]3 years ago
3 0

Answer:

The mean of the total number of students is 85.5

Step-by-step explanation:

REcall that given n data pointsx_1, \dots, x_n, the mean is given by

\frac{\sum_{i=1}^n x_i}{n}.

Let us number the students of the 24 students' class from 1 to 24 and the let us number the students of the other class from 25 to 47.

The question is to find the following

\frac{\sum_{i=1}^{47} x_i}{47}

REcall the following

\frac{\sum_{i=1}^{24}x_i}{24} =86

\frac{\sum_{i=25}^{47}x_i}{23} =85

Then, from this equations we can deduce that

\sum_{i=1}^{47}x_i = \sum_{i=1}^{24}x_i + \sum_{i=25}^{47}x_i = 86\cdot 24 + 85\cdot 23

Therefore,

\frac{\sum_{i=1}^{47} x_i}{47}= \frac{86\cdot 24 + 85\cdot 23}{47}= 85.5

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2 years ago
Match the features of the graph of the rational function.
Sunny_sXe [5.5K]

After applying <em>algebraic</em> analysis we find the <em>right</em> choices for each case, all of which cannot be presented herein due to <em>length</em> restrictions. Please read explanation below.

<h3>How to analyze rational functions</h3>

In this problem we have a rational function, whose features can be inferred by algebraic handling:

Holes - x-values that do not belong to the domain of the <em>rational</em> function:

x³ + 8 · x² - 9 · x = 0

x · (x² + 8 · x - 9) = 0

x · (x + 9) · (x - 1) = 0

x = 0 ∨ x = - 9 ∨ x = 1

But one root is an evitable discontinuity as:

y = (9 · x² + 81 · x)/(x³ + 8 · x² - 9 · x)

y = (9 · x + 81)/(x² + 8 · x - 9)

Thus, there are only two holes. (x = - 9 ∨ x = 1) Besides, there is no hole where the y-intercept should be.

Vertical asymptotes - There is a <em>vertical</em> asymptote where a hole exists. Hence, the function has two vertical asymptotes.

Horizontal asymptotes - <em>Horizontal</em> asymptote exists and represents the <em>end</em> behavior of the function if and only if the grade of the numerator is not greater than the grade of the denominator. If possible, this assymptote is found by this limit:

y = \lim_{x \to \pm \infty} \frac {9\cdot x + 81}{x^{2}+8\cdot x - 9}

y = 0

The function has a horizontal asymptote.

x-Intercept - There is an x-intercept for all x-value such that numerator is equal to zero:

9 · x + 81 = 0

x = - 9

There is a x-intercept.

Lastly, we have the following conclusions:

  1. How many holes? 2
  2. One <em>horizontal</em> asymptote along the line where y always equals what number: 0
  3. This function has x-intercepts? True
  4. One <em>vertical</em> asymptote along the line where x always equals what number: 1
  5. There is a hole where the y-intercept should be? False

To learn more on rational functions: brainly.com/question/27914791

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