This is an exponential decay problem.
Using the equation Y = a *(1-rate)^time
where Y is the future value given as 12,000 and a is the starting value given as 13,000.
The rate is also given as 5%.
The equation becomes:
12,000 = 13,000(1-0.05)^x
12,000 = 13,000(0.95)^x
Divide each side by 13000:
12000/13000 = 0.95^x/13000
12/13 = 0.95^x
Use the natural log function:
x = ln(12/13) / ln(0.95)
x = 1.56 years. ( this will equal 12,000
Round to 2 years it will be less than 12000.
Answer:
The measure of arc a is 86°
Step-by-step explanation:
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
so
86°=(1/2)[arc c+arc a]
see the attached figure with letters to better understand the problem
In this problem
Triangles ABO and CDO are congruent by SSS postulate theorem
∠AOB=∠COD
∠AOB=arc a -----> by central angle
∠COD=arc c -----> by central angle
therefore
The measure of arc a is congruent with the measure of arc c
arc a=arc c
so
86°=(1/2)[2arc a]
86°=[arc a]
arc a=86°
Answer:
34 is 85% of 40
Step-by-step explanation:
6
6 * 0.7 = 4.2
4.2 * 0.7 = 2.94
2.94 * 0.7 = 2.058
2.058 * 0.7 = 1.4406
1.4406 * 0.7 = 1.00842
4.2 + 4.2 + 2.94 + 2.94 + 2.058 + 2.058 + 1.4406 + 1.4406 =
Y = kx is the direct variation equation, where 'k' is the constant of variation.
12 = 7(x)
Divide both sides by 7
12/7 = x