The equation y−5=−2(x−3) is in point-slope form. Which shows this equation in slope-intercept form?

Mathematics

1 answer:

Tatiana [17]3 years ago

8 0

Add 5 and eliminate parentheses

... y = -2x +6 +5

Simplifying, you get

... B. y = -2x +11

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1.44 Make-up exam: In a class of 28 students, 27 of them took an exam in class and 1 student took a make-up exam the following d

Olenka [21]

Answer:

a) Decrease

b) New mean = 78.43

c) Decrease

Step-by-step explanation:

We are given the following in the question:

Total number of students in class = 28

Average of 27 students = 79

Standard Deviation of 27 students = 6.5

New student's score = 63

a) The new student's score will decrease the average.

b) New mean

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean = \dfrac{\displaystyle\sum x_i}{27} = 79\\\\\sum x_i = 27\times 79 = 2133$

New mean =

$\text{ New mean} =\dfrac{ \displaystyle\sum x_i +63}{28}\\\\ =\dfrac{2133+63}{28}= \dfrac{2196}{28} = 78.43$

Thus, the new mean is 78.43

c) Since the new mean decreases, standard deviation for new scores will decrease.

This is because the new value is within the usual values i.e. within two standard deviations of the mean. So, this wont cause a lot of variation as this value will be closer to already available data values. Also number of observations (n) in the denominator is increasing. Based on both these points we can conclude that standard deviation will decrease

Formula for Standard Deviation:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}$