Answer:
-32
Step-by-step explanation:
Answer: ![S_{12}=399.90](https://tex.z-dn.net/?f=S_%7B12%7D%3D399.90)
Step-by-step explanation:
You know that the formula to find the sum of a finite geometric series is:
![S_n=\frac{a_1(1-r^n)}{1-r}](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Ba_1%281-r%5En%29%7D%7B1-r%7D)
Where
is the number of terms,
is the first term and
is the common ratio (
).
The steps to find the sum of the first 12 terms of the given geometric serie, are:
1. Find the common ratio "r". By definition:
![r=\frac{a_2}{a_1}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_2%7D%7Ba_1%7D)
Then:
![r=\frac{100}{200}\\\\r=\frac{1}{2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B100%7D%7B200%7D%5C%5C%5C%5Cr%3D%5Cfrac%7B1%7D%7B2%7D)
2. Finally, knowing that:
![a_1=200\\\\n=12](https://tex.z-dn.net/?f=a_1%3D200%5C%5C%5C%5Cn%3D12)
You must substitute values into the formula.
Then you get:
![S_{12}=\frac{200(1-(\frac{1}{2})^{12})}{1-\frac{1}{2}}\\\\S_{12}=399.90](https://tex.z-dn.net/?f=S_%7B12%7D%3D%5Cfrac%7B200%281-%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B12%7D%29%7D%7B1-%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%5C%5CS_%7B12%7D%3D399.90)
To find the decimal expansion of a fraction, we put the denominator in proportion to 100. One fraction we can do this for is 2/5:
5 x 20 = 100, so now our denominator is 100. Because we multiplied 5 by 20, we also have to multiply 2 by 20. This means that 2/5 is equal to 40/100. 40/100 is representative as 0.4.
3/9 as a decimal can convert to 33/99, which would give us 0.3333 as a repeating decimal.
7/8 as a decimal expansion would give us 0.875 because 100 divided by 8 is equal to 12.5 (which is representative of 1/8), and 12.5 x 7 is equal to 87.5. Because we multiplied 1/8 x 7, we get 7/8 which is less than a whole. Therefore, the only number to the left of the decimal point should be 0. Hence, we divide 87.5 by 100 and we get 0.875. That is our decimal conversion.
4/6 as a decimal expansion would be 0.6666. Why? Well, first we would divide 100 by 6 to get approximately 16.6666. Then, because this represents 1/6, we can multiply it by 4 to get 4/6, which equals about 66.6664. Again, 4/6 is not a whole number and is less than a whole number. Because of this, the only digit to the left of the decimal point would be 0. When we divide 66.6664 by 100, we get 0.6666 as a repeating decimal.
If you need to better understand, let me know and I will gladly assist you.
Answer:
CosA = 4/5
Step-by-step explanation:
The acute angle with cosine of 4/5
Recall from trigonometry ;
Cosine = Adjacent / hypotenus
From the right angled triangle Given:
For angle A :
Opposite = BC = 8
Hypotenus = AC = 10
Cos A = BC / AC = 8 /10 = 4 /5
CosA = 4/5
For C :
Opposite = AB = 6
Hypotenus = AC = 10
Cos C = 6 /10 = 3 /5
Answer:
Simple interest of Ben :
![\frac{\$650 \times 3.5\% \times 4years}{100} = \frac{9100}{100} = \$91 \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5C%24650%20%5Ctimes%203.5%5C%25%20%5Ctimes%204years%7D%7B100%7D%20%20%3D%20%20%5Cfrac%7B9100%7D%7B100%7D%20%20%3D%20%5C%2491%20%5C%5C%20)
Ben earn <em><u>$91</u></em> in 4 years.