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3 years ago

The set of ordered pairs (-1,8), (0, 3), (1, -2), and (2-7) represent a function. What is the range of the function?

Mathematics

1 answer:

Rama09 [41]3 years ago

4 0

Answer:

Range is given by the second option: $y=$ { $-7,-2,3,8$ }.

Step-by-step explanation:

Range is the set of possible $y$ values in a given function.

Here, the function is defined by the following ordered pairs:

$(-1,8),(0,3),(1,-2),(2,-7)$

The y values of the function are $y=$ { $-7,-2,3,8$ }

Therefore, the range is given as $y=$ { $-7,-2,3,8$ }.

So, the second option is correct.

You might be interested in

A 400 pound metal star is hanging on two cables which are attached to the ceiling. The left hand cable makes a 18° angle with th

notka56 [123]

Answer:

left: 123.607 lb
right: 380.423 lb

Step-by-step explanation:

By balancing horizontal and vertical forces, we find the cable tensions to be ...

Ta = W·sin(b)/sin(a+b) . . . . . where W is the weight being held

Tb = W·sin(a)/sin(a+b)

Where Ta is the tension in the cable that makes an angle of 'a' with respect to the vertical, and Tb is the tension in the cable that makes an angle of 'b' with respect to the vertical.

The given angles are with respect to the ceiling, so the angles with respect to the vertical will be their compmements.

<h3>left cable (a)</h3>

angle 'a' is 90° -18° = 72°

angle 'b' is 90° -72° = 18°

a+b = 72° +18° = 90°

Ta = (400 lb)sin(18°)/sin(90°) = 123.607 lb

<h3>right cable (b)</h3>

Tb = (400 lb)sin(72°)/sin(90°) = 380.423 lb

_____

<em>Additional comment</em>

The nice expressions for cable tension come from the balance of forces.

vertical: Ta·cos(a) +Tb·cos(b) = W

horizontal: Ta·sin(a) = Tb·sin(b)

Solving the horizontal equation for Ta, we get ...

Ta = Tb·sin(b)/sin(a)

Substituting into the vertical equaiton gives ...

Tb·sin(b)cos(a)/sin(a) +Tb·cos(b) = W

Multiplying by sin(a) gives ...

Tb(sin(b)cos(a) +sin(a)cos(b)) = W·sin(a)

Using the trig identity for the sine of the sum of angles, we can rewrite this in the form shown above:

Tb = W·sin(a)/sin(a+b)

The problem is symmetrical with respect to 'a' and 'b', so the other tension is found by interchanging 'a' and 'b' in the equation:

Ta = W·sin(b)/sin(a+b)

4 0

2 years ago

Consider the relationship between the number of bids an item on eBay received and the item's selling price. The following is a s

n200080 [17]

Answer:

Let's assume the following data:

Price in Dollars (X) 26 29 32 38 47

Number of Bids (Y) 12 13 15 16 18

For our case we have this:

n=10 $\sum x = 172, \sum y = 74, \sum xy = 2623, \sum x^2 =6194, \sum y^2 =1118$

$r=\frac{5(2623)-(172)(74)}{\sqrt{[5(6194) -(172)^2][5(1118) -(74)^2]}}=0.974$

So then the correlation coefficient would be r =0.974

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

Solution to the problem

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$