Answer:
a. Present value of a lump sum =
PV = FV / ( 1 + i )ⁿ
b. Present value of an annuity =
P = PMT x ((1 – (1 / (1 + r)⁻ⁿ )) / r)
Step-by-step explanation:
a. Present Value of a Lump sum =
PV = FV / ( 1 + i )ⁿ
Where variables in the formula are explained as follows
PV = Present Value of the given amount today
FV = Future Value of the given amount
i = Discount rate
n = Number of periods
b. Present value of an annuity is given as:
P = PMT x ((1 – (1 / (1 + r)⁻ⁿ)) / r)
The variables in the equation are explained as the follows:
P = the present value of annuity
PMT = Payment per period or the amount in each annuity payment
r = the interest or discount rate
n = total number of periods or the number of payments left to receive
Answer:
B
Step-by-step explanation:
Using the determinant to determine the type of zeros
Given
f(x) = ax² + bx + c ( a ≠ 0 ) ← in standard form, then the discriminant is
Δ = b² - 4ac
• If b² - 4ac > 0 then 2 real and distinct zeros
• If b² - 4ac = 0 then 2 real and equal zeros
• If b² - 4ac < 0 then 2 complex zeros
Given
f(x) = (x - 1)² + 1 ← expand factor and simplify
= x² - 2x + 1 + 1
= x² - 2x + 2 ← in standard form
with a = 1, b = - 2, c = 2, then
b² - 4ac = (- 2)² - (4 × 1 × 2) = 4 - 8 = - 4
Since b² - 4ac < 0 then the zeros are complex
Thus P(x) has no real zeros
Answer:
h = 10 m
Step-by-step explanation:
The formula for area of a trapezoid is
A = (1/2)(B + b)h where B is the bottom base, b is the top base, and h is the height.
We are given B = 16, b = 14, and A = 15, plug those values in and simplify
150 = (1/2)(16 + 14)(h)
150 = (1/2)(30)(h)
150 = (15)h (half of 30 is 15)
10 m = h (divide both sides by 15 to isolate h)
Try using a calculator i don't have one on me sorry :(
Answer:
17
Step-by-step explanation:
85 divided by 5 in distributive property
85 can be break into 80 and 5
80+5 is 85
Now we divide each term by 5
Denominator 5 is distributed 5 inside the numerator
17 is the final answer
