Answer:
Final answer is
.
Step-by-step explanation:
Given problem is
.
Now we need to simplify this problem.
![\sqrt[3]{x}\cdot\sqrt[3]{x^2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D%5Ccdot%5Csqrt%5B3%5D%7Bx%5E2%7D)
![\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E1%7D%5Ccdot%5Csqrt%5B3%5D%7Bx%5E2%7D)
Apply formula
![\sqrt[n]{x^p}\cdot\sqrt[n]{x^q}=\sqrt[n]{x^{p+q}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5Ep%7D%5Ccdot%5Csqrt%5Bn%5D%7Bx%5Eq%7D%3D%5Csqrt%5Bn%5D%7Bx%5E%7Bp%2Bq%7D%7D)
so we get:
![\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{1+2}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E1%7D%5Ccdot%5Csqrt%5B3%5D%7Bx%5E2%7D%3D%5Csqrt%5B3%5D%7Bx%5E%7B1%2B2%7D%7D)
![\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E1%7D%5Ccdot%5Csqrt%5B3%5D%7Bx%5E2%7D%3D%5Csqrt%5B3%5D%7Bx%5E%7B3%7D%7D)
![\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E1%7D%5Ccdot%5Csqrt%5B3%5D%7Bx%5E2%7D%3Dx)
Hence final answer is
.
Answer:
There is a 2/3 probability that the other side is also black.
Step-by-step explanation:
Here let B1: Event of picking a card that has a black side
B2: Event of picking a card that has BOTH black side.
Now, by the CONDITIONAL PROBABILITY:

Now, as EXACTLY ONE CARD has both sides BLACK in three cards.
⇒ P (B1 ∩ B2) = 1 /3
Also, Out if total 6 sides of cards, 3 are BLACK from one side.
⇒ P (B1 ) = 3 /6 = 1/2
Putting these values in the formula, we get:

⇒ P (B2 / B1) = 2/3
Hence, there is a 2/3 probability that the other side is also black.
Hi!
If the perimeter of the triangle is 41, then x is:
5x + 2 + 6x - 3 + 3x = 41
5x + 6x + 3x = 41 + 3 - 2
14x = 42
x = 42/14
x = 3
The x is 3.
Solving for y:
4x-3y=10. (subtract 4x on both sides)
-3y=-4x+10. (divide by -3 on both sides)
y=4/3 x+10/3
Answer:
If the observed sample mean is greater than 17.07 minutes, then we would reject the null hypothesis.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 15 minutes
Sample size, n = 10
Alpha, α = 0.05
Population standard deviation, σ = 4 minutes
First, we design the null and the alternate hypothesis
Since the population standard deviation is given, we use one-tailed z test to perform this hypothesis.
Formula:
Now,
Thus, we would reject the null hypothesis if the z-statistic is greater than this critical value.
Thus, we can write:

Thus, the decision rule would be if the observed sample mean is greater than 17.07 minutes, then we would reject the null hypothesis.