Answer:
C.) ![x^{\frac{3}{2} } y^{\frac{19}{2} }](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7B3%7D%7B2%7D%20%7D%20y%5E%7B%5Cfrac%7B19%7D%7B2%7D%20%7D)
Step-by-step explanation:
To simplify the expression, you need to:
1.) Rewrite ![\sqrt{xy^{3} }](https://tex.z-dn.net/?f=%5Csqrt%7Bxy%5E%7B3%7D%20%7D)
-----> ![\sqrt{x} = x^{\frac{1}{2} }](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D)
2.) Distribute the exponents
-----> When an exponent is raised to another exponent, they should be multiplied
3.) Create common denominators
4.) Combine the variables
-----> When two variables with exponents are being multiplied, the exponents should be added
It has to be B is the one that has to ne correct
9514 1404 393
Answer:
21 in²
Step-by-step explanation:
The net consists of a square and 4 triangles. The relevant dimensions of each are given, so the appropriate area formulas can be used.
Area of one triangle:
A = 1/2bh
A = 1/2(3 in)(2 in) = 3 in²
Area of the square:
A = s²
A = (3 in)² = 9 in²
__
Total net area (surface area of the pyramid):
square area + 4 × triangle area
9 in² + 4 × 3 in² = 21 in² . . . . surface area
The quick and easy answer is 3/100
Answer: 0.4402
Step-by-step explanation:
Given : The proportion of the registered voters in a country are Republican = P=0.50
Sample space = 36
The test statistic for proportion :-
![z=\dfrac{p-P}{\sqrt{\dfrac{P(1-P)}{n}}}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7Bp-P%7D%7B%5Csqrt%7B%5Cdfrac%7BP%281-P%29%7D%7Bn%7D%7D%7D)
For p= 0.477
![z=\dfrac{0.477-0.50}{\sqrt{\dfrac{0.50(1-0.50)}{36}}}\approx-0.276](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B0.477-0.50%7D%7B%5Csqrt%7B%5Cdfrac%7B0.50%281-0.50%29%7D%7B36%7D%7D%7D%5Capprox-0.276)
For p= 0.58
![z=\dfrac{0.58-0.50}{\sqrt{\dfrac{0.50(1-0.50)}{36}}}\approx0.96](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B0.58-0.50%7D%7B%5Csqrt%7B%5Cdfrac%7B0.50%281-0.50%29%7D%7B36%7D%7D%7D%5Capprox0.96)
Now, the probability that the proportion of freshmen in the sample is between 0.477 and 0.58 (by using the standard normal distribution table):-
![P(0.477](https://tex.z-dn.net/?f=P%280.477%3Cx%3C0.58%29%3DP%28-0.276%3Cz%3C0.96%29%5C%5C%5C%5C%3DP%28z%3C0.96%29-P%28z%3C-0.276%29%5C%5C%5C%5C%3D0.8314724-%200.391274%3D0.4401984%5Capprox0.4402)
Hence, the probability that the proportion of freshmen in the sample is between 0.477 and 0.580 = 0.4402