Answer:
x = 34
Step-by-step explanation:
complementary angle sum to 90°
sum the 2 angles and equate to 90
x + x + 22 = 90
2x + 22 = 90 ( subtract 22 from both sides )
2x = 68 ( divide both sides by 2 )
x = 34
Given rate is = 7% or 0.07
Total amount needed = $12000
Time = 4 years
Here, the deposit is compounded semiannually, means twice per year and this gives 8 annual compounding periods in 4 years.
The equation becomes:
P= 
P = 
Solving it, we get P = $ 9112.93
Hence $9112.93 should be deposited today.
The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of cos(28°) is -0.9626.
<h3>What are Trigonometric functions?</h3>
The trigonometric function gives the ratio of different sides of a right-angle triangle.

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
The cosine is the ratio of the base of the triangle and the hypotenuse of the triangle. Therefore, The value of cos(28°) is -0.9626.
Learn more about Trigonometric functions:
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For this case we have that each student takes 8 \ frac {3} {4} minutes to perform and play 3 songs. Then, we convert the mixed number to a fraction:

Thus, each student takes
minutes.
If there are 9 students in the recital then we have:
minutes.
Thus, the recital lasts at least 78.75 minutes.
Answer:
The recital lasts at least 78.75 minutes.