Show ~(P^q) ~PVq ~q is tautology ​

Eight people were asked what the balance of their savings account at the beginning of the month was and how much it increased or decreased by the end of the month. create a scatter plot that represents the data that is shown in the table. the x-axis represents the beginning balance in thousands of dollars and the y-axis represents the change in the savings account in hundreds of dollars. name beginning balance (in thousands of dollars) change in savings account (in hundreds of dollars) jimmy 5 3 kendra 4 7 carlos 5 4 yolanda 3 1 shawn 2 5 laura 3 2 andy 5 6 georgia 4 3

Jabari is power washing houses for a summer job. for every job, he charges an initial fee plus $30 for each hour of work. his total fee for a 4 -hour job, for instance, is $170 . jabari's total fee,f, for a single job is a function of the number,t, of hours it takes him to complete the job. write the function's formula.

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.