Answer:
(-15)/3 = -5
Step-by-step explanation:
(-15)/3
Assume that your positive tiles are yellow, and your negative tiles are red.
The question is asking, "if you take 15 red tiles and split them into three equal groups, how many will you have in each group?"
How can you model the first value of -15? With 15 red tiles.
Let’s model how to divide the tiles into three equal groups by moving one tile at a time into three separate groups until all 15 tiles have been moved.
Step 1.
Start with 15 red tiles, as in the first picture.
Step 2.
Start by moving tiles one at a time to begin creating three new groups.
The middle picture shows the situation after you have moved the first three tiles.
Step 3.
Continue moving tiles one at a time from the original group and stacking them evenly in the three new groups until you have no more tiles to move.
The third picture shows the situation when you have finished.
How many red tiles are in each group? There are five.
Is the answer positive or negative? The answer is negative, because there are five red negative tiles in each group.
Conclusion? (-15)/3 = -5
Answer:
0.536 is the required probability.
Step-by-step explanation:
We have been given the word the word "GEOMETRY"
we have to find the probability that two consonants and one vowel are chosen:
Number of consonants are: 5
Number of vowels are: 3
Hence, The required probability is: 
Using: 
Simplifying the above expression:
Further simplification after cancelling out the common terms we get:
Hence, Option 1 is correct.
Answer:
And when we apply the limit we got that:
Step-by-step explanation:
Assuming this complete problem: "The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit . 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2"
We have the following formula in order to find the sum of cubes:
We can express this formula like this:
![\lim_{n\to\infty} \sum_{n=1}^{\infty}i^3 =\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2](https://tex.z-dn.net/?f=%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7Di%5E3%20%3D%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5B%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%5D%5E2)
And using this property we need to proof that: 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2
![\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2](https://tex.z-dn.net/?f=%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5B%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%5D%5E2)
If we operate and we take out the 1/4 as a factor we got this:
We can cancel 
and we got
We can reorder the terms like this:
We can do some algebra and we got:
We can solve the square and we got:
And when we apply the limit we got that:
Answer: find the answers in the explanation.
Step-by-step explanation:
Given that the predicted Number of Text Messages Sent = 60 – 0.8 • Age
Where the slope = - 0.8
The intercept = 60
1) the slope of the least regression line is -0.8
2.) The unit of the slope of the line is text per year
3.) Therefore, the slope of the line tells you that for every year older the smart phone user is, you can expect a typical average in text messages sent of - 0.8
4.) The y - intercept of the least square regression line is 60
5.) The unit of the y - intercept of the line are text sent
6.) The y - intercept of the line tells you the starting point. The first number of text messages sent.
