712,684.506 word form

Mathematics

1 answer:

8_murik_8 [283]2 years ago

5 0

Answer:

seven-hundred and tweleve thousand, six-hundred and eighty-four point five-hundred and six

Step-by-step explanation:

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What is the common difference of 80,60,45,33.75

GenaCL600 [577]

Answer:

The common difference (or common ratio) = 0.75

Step-by-step explanation:

i) let the first term be $a_{1}$ = 80

ii) let the second term be $a_{2}$ = $a_{1}$ . r = 80 × r = 60 ∴ r = $\frac{60}{80}$ = 0.75

iii) let the third term be $a_{3}$ = $a_{2}$ . r = 60 × r = 45 ∴ r = $\frac{45}{60}$ = 0.75

iv) let the fourth term be $a_{4}$ = $a_{3}$ . r = 45 × r = 33.75 ∴ r = $\frac{33.75}{45}$ = 0.75

Therefore we can see that the series of numbers are part of a geometric progression and the first term is 80 and the common ratio = 0.75.

4 0

2 years ago

A small combination lock on a suitcase has 55 wheels, each labeled with the 10 digits 0 to 9. How many 55 digit combinations ar

den301095 [7]

Suppose $a_n$ is the number of possible combinations for a suitcase with a lock consisting of $n$ wheels. If you added one more wheel onto the lock, there would only be 9 allowed possible digits you can use for the new wheel. This means the number of possible combinations for $n+1$ wheels, or $a_{n+1}$ is given recursively by the formula

$a_{n+1}=9a_n$

starting with $a_1=10$ (because you can start the combination with any one of the ten available digits 0 through 9).

For example, if the combination for a 3-wheel lock is 282, then a 4-wheel lock can be any one of 2820, 2821, 2823, ..., 2829 (nine possibilities depending on the second-to-last digit).

By substitution, you have

$a_{n+1}=9a_n=9^2a_{n-1}=9^3a_{n-2}=\cdots=9^na_1=10\times9^n$

This means a lock with 55 wheels will have

$a_{55}=10\times9^{54}$

possible combinations (a number with 53 digits).

7 0

2 years ago

Suppose you want to accumulate $25,000 as down payment on a house and the best you can do is to put aside $200 a month. If you d

Sunny_sXe [5.5K]

Answer:

It will take 88.2 months to accumulate the amount

Step-by-step explanation:

Given;

Future value of money, FV = $25,000

investment per compound period, P = $200

interest rate, i = 0.75% x 12 = 9%

The number of monthly installments required to amount to FV is given by;

$n = \frac{ln(FVi +cp)-ln(cp)}{ln(c+i)-ln(c)}\\\\ n = \frac{ln(25000*0.09 +200*12)-ln(200*12)}{ln(12+0.09)-ln(12)}\\\\n = \frac{8.4446 -7.7832}{2.4924-2.4849}\\\\n = 88.2 \ months$