Of the three digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?
a) 90
b) 82
c) 80
d) 45
e) 36

80.

Step-by-step explanation:

Three digit number can only have three patterns

A. All digits are distinct

B. Two digits are same and third is different

C. All three digits are alike.

We need to calculate B

that is B= Total- A-C

Total numbers from 700 to 999= 299.

Number numbers having all digits distinct = 3×9×8= 216 ( first digit can have only three digits 7,8,9)

All three are alike = 3 ( 777,888,999).

So, 299 -216-3= 80.

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).