H=45+M
78 is the total
78=45+33(1)
67 is the mode because it appears the most.
Answer:
i dont know but i have a pic for u
Step-by-step explanation:
Given:
16 emails to 6 text messages- 10 emails to 4 text messages
To find:
Whether 16 emails to 6 text messages- 10 emails to 4 text messages proportional or not.
Solution:
Check the ratio of emails to text. If the ratios are equal then the relation is proportional.
16 emails to 6 text messages.
![\dfrac{Emails}{Text}=\dfrac{16}{6}](https://tex.z-dn.net/?f=%5Cdfrac%7BEmails%7D%7BText%7D%3D%5Cdfrac%7B16%7D%7B6%7D)
![\dfrac{Emails}{Text}=\dfrac{8}{3}](https://tex.z-dn.net/?f=%5Cdfrac%7BEmails%7D%7BText%7D%3D%5Cdfrac%7B8%7D%7B3%7D)
![\dfrac{Emails}{Text}=8:3](https://tex.z-dn.net/?f=%5Cdfrac%7BEmails%7D%7BText%7D%3D8%3A3)
10 emails to 4 text messages.
![\dfrac{Emails}{Text}=\dfrac{10}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7BEmails%7D%7BText%7D%3D%5Cdfrac%7B10%7D%7B4%7D)
![\dfrac{Emails}{Text}=\dfrac{5}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7BEmails%7D%7BText%7D%3D%5Cdfrac%7B5%7D%7B2%7D)
![\dfrac{Emails}{Text}=5:2](https://tex.z-dn.net/?f=%5Cdfrac%7BEmails%7D%7BText%7D%3D5%3A2)
Since
or
, therefore, it is not proportional.
Answer:
![\large \boxed{y = - \frac{1}{9} x - \frac{5}{9} }](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7By%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20x%20-%20%20%5Cfrac%7B5%7D%7B9%7D%20%7D)
Step-by-step explanation:
In order to find an equation of a line with two given ordered pairs. We have to find a slope first which we can do by using the formula below.
![\large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7Bm%20%3D%20%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%20%7D)
m-term is defined as slope in y = mx+b form which is slope-intercept form.
Now we substitute these ordered pairs (x, y) in the formula.
![\large{m = \frac{1 - ( - 2)}{ -14 - 13} } \\ \large{m = \frac{1 + 2}{ - 27} } \\ \large{m = \frac{3}{ - 27} = - \frac{1}{9} }](https://tex.z-dn.net/?f=%20%5Clarge%7Bm%20%3D%20%20%5Cfrac%7B1%20-%20%28%20-%202%29%7D%7B%20-14%20-%2013%7D%20%7D%20%5C%5C%20%20%5Clarge%7Bm%20%3D%20%20%5Cfrac%7B1%20%2B%202%7D%7B%20-%2027%7D%20%7D%20%5C%5C%20%20%5Clarge%7Bm%20%3D%20%20%5Cfrac%7B3%7D%7B%20-%2027%7D%20%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20%7D)
After we calculate for slope, we substitute m-value in slope-intercept form. The slope-intercept form is
![\large \boxed{y = mx + b}](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7By%20%3D%20mx%20%2B%20b%7D)
We already know m-value as we substitute it.
![\large{y = - \frac{1}{9} x + b}](https://tex.z-dn.net/?f=%20%5Clarge%7By%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20x%20%20%2B%20b%7D)
We are not done yet because we need to find the b-term which is our y-intercept. (Note that m-term is slope while b-term is y-intercept)
We can find the y-intercept by substituting either (-14,1) or (13,-2) in the equation. I will be using (13,-2) to substitute in the equation.
![\large{y = - \frac{1}{9} x + b} \\ \large{ - 2 = - \frac{1}{9} (13) + b} \\ \large{ - 2 = - \frac{13}{9} + b} \\ \large{ - 2 + \frac{13}{9} = b} \\ \large{ - \frac{5}{9} = b}](https://tex.z-dn.net/?f=%20%5Clarge%7By%20%3D%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20x%20%2B%20b%7D%20%5C%5C%20%20%5Clarge%7B%20-%202%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20%2813%29%20%2B%20b%7D%20%5C%5C%20%20%5Clarge%7B%20-%202%20%3D%20%20-%20%20%5Cfrac%7B13%7D%7B9%7D%20%20%2B%20b%7D%20%5C%5C%20%20%5Clarge%7B%20-%202%20%2B%20%20%5Cfrac%7B13%7D%7B9%7D%20%20%3D%20b%7D%20%5C%5C%20%20%5Clarge%7B%20-%20%20%5Cfrac%7B5%7D%7B9%7D%20%20%3D%20b%7D)
Finally, we know b-value. Then we substitute it in our equation.
![\large{y = - \frac{1}{9} x + b} \\ \large{y = - \frac{1}{9} x - \frac{5}{9} }](https://tex.z-dn.net/?f=%20%5Clarge%7By%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20x%20%2B%20b%7D%20%5C%5C%20%20%5Clarge%7By%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20x%20-%20%20%5Cfrac%7B5%7D%7B9%7D%20%7D)