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4 years ago

How are experimental and theoretical probability alike?

1 answer:

5 0

The probability is still calculated the same way, using the number of possible ways to outcome can occur divided by the total number of outcomes.

You might be interested in

What is the equation of the line of best fit for the following data? Round the

Svet_ta [14]

Answer:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=438-\frac{44^2}{5}=50.8$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=415-\frac{44*42}{5}=45.4$

And the slope would be:

$m=\frac{45.4}{50.8}=0.8937 \approx 0.894$

Now we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{44}{5}=8.8$

$\bar y= \frac{\sum y_i}{n}=\frac{42}{5}=8.4$

And we can find the intercept using this:

$b=\bar y -m \bar x=8.4-(0.894*8.8)=0.535$

So the line would be given by:

$y=0.894 x +0.535$

And the best option is:

A. y = 0.894x + 0.535

Step-by-step explanation:

We have the following dataset given

x: 5,6,9,10,14

y: 4,6,9,11,12

We want to find the least-squares line appropriate for this data given by this general expresion:

$y = mx +b$

Where m is the slope and b the intercept

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 44$

$\sum_{i=1}^n y_i =42$

$\sum_{i=1}^n x^2_i =438$

$\sum_{i=1}^n y^2_i =398$

$\sum_{i=1}^n x_i y_i =415$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=438-\frac{44^2}{5}=50.8$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=415-\frac{44*42}{5}=45.4$

And the slope would be:

$m=\frac{45.4}{50.8}=0.8937 \approx 0.894$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{44}{5}=8.8$

$\bar y= \frac{\sum y_i}{n}=\frac{42}{5}=8.4$

And we can find the intercept using this:

$b=\bar y -m \bar x=8.4-(0.894*8.8)=0.535$

So the line would be given by:

$y=0.894 x +0.535$

And the best option is:

A. y = 0.894x + 0.535

4 0

4 years ago

The perimeter of a rectangle is 400 yards. What are the dimensions of the rectangle if the length is 90 yards more than the wid

mihalych1998 [28]

X+90 = length
x=width
4x+180=400
4x=220
x=55

The width is 55 yards and the length is 145 yards

6 0

4 years ago

A truck can be rented from Company A for $140 a day plus $0.80 per mile. Company B charges $80 a day plus $0.90 per mile to

natta225 [31]

Answer:

600 miles in a day.

Step-by-step explanation:

Variable x = number of miles

Company A: 140 + 0.80x

Company B: 80 + 0.90x

Set up an equation:

140 + 0.80x = 80 + 0.90x

Isolate variable x:

60 + 0.80x = 0.90x

60 = 0.10x

600 = x

Check your work:

140 + 0.80(600) = 80 + 0.90(600)

140 + 480 = 80 + 540

620 = 620

Correct!

8 0

3 years ago

What is probablity, and how would I be able to find? (Could you also show an example)

Dominik [7]

How many are there then the total amount

7 0

4 years ago

I need the domain range and function. With an explanation

erastovalidia [21]

<h3>Answers:</h3>

Problem 1

Domain = $-3 < x \le 3$ , interval notation (-3, 3]
Range = $-3 \le y < 3$ , interval notation [-3, 3)
Is it a function? Yes

Problem 2

Domain = $x \ge -2$ , interval notation $[-2, \infty)$
Range = All real numbers, interval notation $(-\infty, \infty)$
Is it a function? No

Problem 3

Domain = $-4 \le x < 3$ , interval notation [-4, 3)
Range = $-4 < y \le 3$ , interval notation (-4, 3]
Is it a function? Yes

Problem 4

Domain = All real numbers, interval notation $(-\infty, \infty)$
Range = $y \le 4$ , interval notation $(-\infty, 4]$
Is it a function? Yes

==================================================

Explanations:

The left most point is when x = -3, and we are not including this value due to the open hole. The other endpoint is included because it is a filled in circle. The domain is therefore $-3 < x \le 3$ which in interval notation is (-3, 3]. We have the curved parenthesis meaning "exclude endpoint" and the square bracket says "include endpoint". The range is a similar story but we're looking at the smallest and largest y values. Though be careful about which endpoint is open/closed. We have a function because it passes the vertical line test.
The smallest x value is x = -2. There is no largest x value because the arrows say to go on forever to the right. We can say the domain is $x \ge -2$ which in interval notation is $[-2, \infty)$ . The range is $(-\infty, \infty)$ to indicate "all real numbers". This graph fails the vertical line test, so it is not a function. The vertical line test is where we check to see if we can pass a vertical line through more than one point on the curve. In this case, such a thing is possible which is why it fails the test.
This is the same idea as problem 1, though note the endpoints are flipped in terms of which has an open circle and which doesn't. It is not possible to draw a single vertical line to have it pass through more than one point on the curve, so it passes the vertical line test and we have a function.
This is a function because it passes the vertical line test. The domain is the set of all real numbers due to the arrows in both directions. Any x value is a possible input. The range is $y \le 4$ which is the same as saying $(-\infty, 4]$ in interval notation. This is because y = 4 is the largest y value possible. There is no smallest y value due to the arrows.

7 0

4 years ago