Answer: The central limit theorem tells us that when random samples are chosen the results tend to approach a normal distribution.
The basic idea is that the more random samples that you select, the closer you should get to the mean. In most cases, 30 or more samples is regarded as a large enough sample to get close to the mean. Our sample is 48, so we should be close to the mean.
Answer:
A
Step-by-step explanation:
Both are ten numbers apart
Sin 2x - sin 4x = 0
sin 2x - 2sin 2x cos 2x = 0
sin x(1 - 2cos 2x) = 0
sin x = 0 or 1 - 2cos 2x = 0
sin x = 0 or 2cos 2x = 1
sin x = 0 or cos 2x = 1/2
x = arc sin 0 or 2x = arc cos (1/2)
x = arc sin 0 or x = 1/2 arc cos (1/2)
x = 0, π, 2π or x = π/6, 7π/6
Answer:
6.75 or 6 3/4
Step-by-step explanation:
First take the whole number and multiply that by 3.
2*3=6
Now, take the fraction and multiply that times 3.
1/4 as a decimal is 0.25. You can ignore the decimal point right now, but you have to remember it is there later.
So, whithout the decimal point, 25*3= 75.
Now, you add the decimal. The 75 is now 0.75, with the decimal.
Add the whole number and the decimal, and you have your answer!
6+0.75=6.75. As a fraction this is 6 3/4
Answer:
y"(2, 1) = -5
Step-by-step explanation:
Step 1: Define implicit differentiation
5 - y² = x²
Step 2: Find dy/dx
- Take implicit differentiation: -2yy' = 2x
- Isolate y': y' = 2x/-2y
- Isolate y': y' = -x/y
Step 3: Find d²y/dx²
- Quotient Rule: y'' = [y(-1) - y'(-x)] / y²
- Substitute y': y" = [-y - (-x/y)(-x)] / y²
- Simplify: y" = [-y - x²/y] / y²
- Multiply top/bottom by y: y" = (-y² - x²) / y³
- Factor negative: y" = -(y² + x²) / y³
Step 4: Substitute and Evaluate
y"(2, 1) = -(1² + 2²) / 1³
y"(2, 1) = -(1 + 4) / 1
y"(2, 1) = -5/1
y"(2, 1) = -5
