Answer:
X=17,384.37
Step-by-step explanation:
The present value of the perpetuity can be calculated by discounted for the different interest rates:
![PV_{perpetuity}=[\frac{1}{0.1}+\frac{(\frac{1}{0.08}-\frac{1}{0.1})}{1.1^{10}}]\times 15,000+15000\\\\\\=164,457.87+15,000=179,457.87](https://tex.z-dn.net/?f=PV_%7Bperpetuity%7D%3D%5B%5Cfrac%7B1%7D%7B0.1%7D%2B%5Cfrac%7B%28%5Cfrac%7B1%7D%7B0.08%7D-%5Cfrac%7B1%7D%7B0.1%7D%29%7D%7B1.1%5E%7B10%7D%7D%5D%5Ctimes%2015%2C000%2B15000%5C%5C%5C%5C%5C%5C%3D164%2C457.87%2B15%2C000%3D179%2C457.87)
#Now, we use the annuity-due present value factor to get the present values of the annuity payments, let X be the annual annuity payments;
![X[\ddot a_{10}_|_{0.10}+\frac{\ddot a_{15}|_{0.08}}{1.10^{10}}]=179,457.87\\\\\\X[6.759+\frac{9.244}{1.1^{10}}]=179457.87\\\\\\X=17384.37](https://tex.z-dn.net/?f=X%5B%5Cddot%20a_%7B10%7D_%7C_%7B0.10%7D%2B%5Cfrac%7B%5Cddot%20a_%7B15%7D%7C_%7B0.08%7D%7D%7B1.10%5E%7B10%7D%7D%5D%3D179%2C457.87%5C%5C%5C%5C%5C%5CX%5B6.759%2B%5Cfrac%7B9.244%7D%7B1.1%5E%7B10%7D%7D%5D%3D179457.87%5C%5C%5C%5C%5C%5CX%3D17384.37)
Hence, the value of X is 17,384.37
Answer:
Rotational symmetry
Step-by-step explanation:
The rectangle rotated 180 degrees to get the transformed rectangle.
Answer:
52 inches by 29 inches
Step-by-step explanation:
Let one side by 16x and the other side be 9x
We know the diameter is 60 inches
Using the Pythagorean theorem
a^2 + b^2 = c^2
(16x) ^2 + ( 9x) ^2 = 60 ^2
256 x^2 + 81x^2 = 3600
Combine like terms
337 x^2 = 3600
Divide each side by 337
337x^2 /337 = 3600/337
x^2 =10.68249258
Take the square root of each side
sqrt(x^2) =sqrt(10.68249258)
x =3.268408264
The sides are 16x by 9x
16*(3.268408264) =52.29453223 or 52
9 *(3.268408264)= 29.41567438 or 29
Answer:
0.89
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
The answer is 12 because there are 12 different months in a year and also all the attendees must have birthdays in different months and not in the Same month. Hence 12 the largest possible number of attendees
