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3 years ago

Is the given question a statistical question? Explain. (NOT A MULTIPLE CHOICE)

Mathematics

1 answer:

zimovet [89]3 years ago

4 0

Answers:

a) <u>Yes</u>, it is a statistical question
b) <u>No</u>, it is not a statistical question

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Explanations:

a) We have a statistical question here because the population is the set of children's literature readers. We then gather a sample of readers (some subset of the population) and ask what their most favorite genre is of the children's literature category. As expected, we're dealing with a categorical variable and it's also qualitative. Each choice "biography", "science fiction", "fantasy", and "mystery" are categories, names or labels. There is no inherent order to any of these, other than alphabetical order, so we consider this a nominal variable.
b) J.K. Rowling is best known for writing the Harry Potter series, which belongs in the fantasy section. There is no randomness to this answer and it's a single answer that does not change. You could have some people say that perhaps the genre is action/adventure, though I think "fantasy" is the better fit. We don't have a statistical question because we don't need to gather a sample and conduct a survey to answer this. Part (a) can vary randomly, which is one way to help see that part (a) is a statistical question; however, part (b) is fixed and constant.

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What is y in the first line if the line passing though (-1,y) and (1,0) perpendicular to the line passing (8,4) and (-1,1) ?

malfutka [58]

Answer:

$6$ .

Step-by-step explanation:

A line that goes through $(x_{0},\, y_{0})$ and $(x_{1},\, y_{1})$ where $x_{0} \ne x_{1}$ would have a slope of $m = (x_{1} - x_{0}) / (y_{1} - y_{0})$ .

The slope of the line that goes through $(8,\, 4)$ and $(-1,\, 1)$ would thus be:

$\begin{aligned}m_{2} &= \frac{1 - 4}{(-1) - 8} \\ &= \frac{(-3)}{(-9)} \\ &= \frac{1}{3}\end{aligned}$ .

Two lines in a cartesian plane are perpendicular to one another if and only if the product of their slopes is $(-1)$ .

Thus, if $m_{1}$ and $m_{2}$ denote the slope of the first and second lines in this question, $m_{1}\, m_{2} = (-1)$ since the two lines are perpendicular to one another. Since $m_{2} = (1/3)$ , the slope of the first line would be:

$\begin{aligned} m_{1} &= \frac{(-1)}{m_{2}} \\ &= \frac{(-1)}{(1/3)} \\ &= (-3)\end{aligned}$ .

Given that the first line goes through the point $(1,\, 0)$ , the point-slope equation of that line would be:

$(y - 0) = (-3)\, (x - 1)$ .

$y = -3\, x + 3$ .

Substitute in $x = (-1)$ to find the $y$ -coordinate of the point in question:

$y = -3\times (-1) + 3 = 6$ .

4 0

2 years ago

Consider the line 4x + 8y = -4.

goldfiish [28.3K]

A) -2

a slope of a line perpendicular is it’s opposite and reciprocal.

Therefore you want to find the slope. You can do this by writing it in intercept form, or just knowing A/B since it’s in standard form.

slope form: y= mx + b

8y = -4 -4x

y = -1/2x -1/2

So the slope is -1/2 so it’s opposite and reciprocal would be 2. So a slope of a line perpendicular is -2.

b) -1/2

A line parallel would have the same slope as your equation. Since you know the slope -1/2 you know whatever your b value is, that line would be parallel as long as it has the same slope.

3 0

3 years ago

Write the slope-intercept form of the equation for the line that passes through the point (-1,3) and has a slope of 5/3

cricket20 [7]

Answer:

$y=\frac{5}{3}x+4\frac{2}{3}$

Step-by-step explanation:

slope-intercept form: y = mx + b

Given:

Slope(m) = $\frac{5}{3}$

Point = (-1, 3)

To write the equation in slope-intercept form we need to know the slope(m) and the y-intercept(b). Since we already know the value of m, we can use it and the given point to find b:

$3=\frac{5}{3}(-1)+b$