Answer:
88
Step-by-step explanation:
Write the expression for the sum in the relation you want.
Sn = u1(r^n -1)/(r -1) = 2.1(1.06^n -1)/(1.06 -1)
Sn = (2.1/0.06)(1.06^n -1) = 35(1.06^n -1)
The relation we want is ...
Sn > 5543
35(1.06^n -1) > 5543 . . . . substitute for Sn
1.06^n -1 > 5543/35 . . . . divide by 35
1.06^n > 5578/35 . . . . . . add 1
n·log(1.06) > log(5578/35) . . . take the log
n > 87.03 . . . . . . . . . . . . . . divide by the coefficient of n
The least value of n such that Sn > 5543 is 88.
Answer:
Part c: Contained within the explanation
Part b: gcd(1200,560)=80
Part a: q=-6 r=1
Step-by-step explanation:
I will start with c and work my way up:
Part c:
Proof:
We want to shoe that bL=a+c for some integer L given:
bM=a for some integer M and bK=c for some integer K.
If a=bM and c=bK,
then a+c=bM+bK.
a+c=bM+bK
a+c=b(M+K) by factoring using distributive property
Now we have what we wanted to prove since integers are closed under addition. M+K is an integer since M and K are integers.
So L=M+K in bL=a+c.
We have shown b|(a+c) given b|a and b|c.
//
Part b:
We are going to use Euclidean's Algorithm.
Start with bigger number and see how much smaller number goes into it:
1200=2(560)+80
560=80(7)
This implies the remainder before the remainder is 0 is the greatest common factor of 1200 and 560. So the greatest common factor of 1200 and 560 is 80.
Part a:
Find q and r such that:
-65=q(11)+r
We want to find q and r such that they satisfy the division algorithm.
r is suppose to be a positive integer less than 11.
So q=-6 gives:
-65=(-6)(11)+r
-65=-66+r
So r=1 since r=-65+66.
So q=-6 while r=1.
P = $2000
R = 5.4%
T = 2 yrs
Interest = PTR/100 = 2000*2*5.4/100 = $216
Balance = $2000 + $216 = $2216
There's a simple formula for finding the arc length.
In radians:<span>
A = θ*r = (2pi/3) x 4 cm = 8*pi/3 cm
Therefore, the answer is letter A </span> <span>8*pi/3 cm.
I hope my answer has come to your help. God bless and have a nice day ahead!
</span>
The probability that a randomly selected customer takes more than 10 minutes will be 8.38%
<em><u>Explanation</u></em>
The average or mean
is 8.56 minutes and standard deviation
is 1.04 minutes.
<u>Formula for finding the z-score</u> is: 
So, the z-score for
10 minutes will be.....

Now, according to the standard normal distribution table,
. So.....

So, the probability that a randomly selected customer takes more than 10 minutes will be 8.38%