Answer:
$14.39
Step-by-step explanation:
The formula for continuous compounding of interest is:
A = Pe^(rt), were P is the initial dollar amount, A is the final amount, r is the interest rate as a decimal fraction, and t is the time in years.
Here we have $2109 = $500e^(10r) and need to solve for r.
To do this, take the natural log of both sides, obtaining:
ln 2109 = ln 500+ 10r.
Then 10r = ln 2109 - ln 500, and
ln 2109 - ln 500
r = --------------------------------------------
10
= .1439
The interest rate was 14.39%.
{<em>q</em>, <em>r</em>, <em>s</em>} consists of 3 elements, so there are 2³ = 8 possible subsets.
• empty set: { }
• every possible singleton set: {<em>q</em>}, {<em>r</em>}, {<em>s</em>}
• every possible pair: {<em>q</em>, <em>r</em>}, {<em>q</em>, <em>s</em>}, {<em>r</em>, <em>s</em>}
• the set itself: {<em>q</em>, <em>r</em>, <em>s</em>}
Answer:
Step-by-step explanation:
First, find the <em>rate of</em><em> </em><em>change</em><em> </em>[<em>slope</em>]:
Then, plug these coordinates into the <em>Slope-Intercept Formula</em> instead of the <em>Point-Slope Formula</em> because you get it done much swiftly. It does not matter which ordered pair you choose:
35 = 4[3] + b
12
Then convert to <em>Standard</em><em> </em><em>Form</em>:
y = 4x + 23
- 4x - 4x
__________
_______________________________________________
19 = 4[−1] + b
−4
Then convert to <em>Standard Form</em>:
y = 4x + 23
- 4x - 4x
__________
** You see? I told you it did not matter which ordered pair you choose because you will ALWAYS get the exact same result.
I am joyous to assist you anytime.
Answer:
7.9.
Step-by-step explanation:
Use the Pythagorean Theorem.
√((-5)^2 + (6)^2 + (-1)^2) = √62 = 7.87 = 7.9.