23)    does the following infinite geometric series diverge or converge? explain. 1/7+1/28+1/112+1/448+ it diverges; it has a sum. it converges; it does not have a sum. it diverges; it does not have a sum. it converges; it has a sum.

 The correct option is (D) It converges; it has a sum.

Step-by-step explanation:  We are given to check whether the following infinite geometric series diverge or converge :

We know that

an infinite geometric series converges if the modulus of the common ratio is less than 1.

For the given geometric series, the common ratio r is given by

So, we get

Therefore, the given infinite geometric series converges.

Also, we know that the sum of a convergent infinite geometric series with first term a and common ratio r is given by

For the given series,

Therefore, the required sum will be

Thus, the given series is convergent and it has a sum of

Option (D) is CORRECT.

c. (3,2,6) is the answer.

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: