$\displaystyle\bf\\a_{35}=57\\r=5\\----\\a_1=?\\S_{61}=?\\----\\Solve:\\1)\\a_1=a_{35}-(35-1)\times r=57-34\times 5=57-170=-113\\\boxed{\bf a_1=-113}\\\\$

$\displaystyle\bf\\2)\\A_{61}=a_1+(61-1)\times r=-113+60\times5=-113+300=187\\\\S_{61}=(-113)+(-108)+(-103)+...+(-8)+(-3)+2+7+12+...+187\\\\S_{61}=SA+SB\\\\SA=(-113)+(-108)+(-103)+...+(-8)+(-3)=-(3+8+103+108+113)\\\\n=\frac{113-8}{5}+1=\frac{105}{5}+1=21+1=22~terms\\SA=-\Big( \frac{n(113+3)}{2} \Big)=-\Big( \frac{22\times116}{2} \Big)=-11\times116 =-1276$

$\displaystyle\bf\\SB=2+7+12+...+187\\\\n=\frac{187-2}{5}+1=\frac{185}{5}+1=37+1=38~terms\\\\SB=\frac{n(187+2)}{2}=\frac{38\times189}{2}=19\times189=3591\\\\S_{61}=SA+SB=-1276+3591=2315\\\\\boxed{\bf S_{61}=2315}$

8 0

2 years ago

Does a plane have a definite beginning and end?

Lorico [155]

Technically no. It extends forever in the X and Y axis, but does not have a Z axis.

5 0

3 years ago

Given the Venn diagram below, if a student is randomly selected, what is the probability that he or she is attending both colleg

guajiro [1.7K]

Add up all the values shown:
64+28+52+56 = 200

This result indicates that there are 200 students total.

Of these 200 total people, there are 28 who are attending both colleges. This is the value shown in the overlapping region of the two circles.

Divide the two values (28 and 200) to get...
28/200 = 0.14 = 14%

The probability as a decimal value is 0.14 which is saying there's a 14% chance of picking someone who goes to both colleges.

3 0

3 years ago

Read 2 more answers

I NEED HELP PLZZZZZZ THIS IS MAJOR PLZZZZZZ HELP ! ! !

Anettt [7]

The possibility of landing on yellow would be 8/72 times because 1/9=x/72.
9 times 8 is 72 so 8 times 1 is 8/72. 1/9 is from the 1+7+1=9. 1/9.
The answer is 8/72 or 1/9.

6 0

3 years ago