Answer:
x = 102 , y = 35
Step-by-step explanation:
x and 78 are same- side interior angles and sum to 180° , that is
x + 78 = 180 ( subtract 78 from both sides )
x = 102
x and 6y - 108 are vertically opposite angles and are congruent , so
6y - 108 = 102 ( add 108 to both sides )
6y = 210 ( divide both sides by 6 )
y = 35
Answer:
V = 54π in³
Step-by-step explanation:
Volume of cylinder = <em>h * πr² --> b * h</em>, where b = area of circle
Substitute: V = 6 * π(3)²
Exponents: V = 6 * 9π
Multiply: V = 54π in³
38-15= 23. I’m guessing this is what you meant. If not please correct me.
Answer: D) cube root of 16
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Explanation:
The rule we use is
![x^{m/n} = \sqrt[n]{x^m}](https://tex.z-dn.net/?f=x%5E%7Bm%2Fn%7D%20%3D%20%5Csqrt%5Bn%5D%7Bx%5Em%7D)
In this case, x = 4, m = 2 and n = 3.
So,
![x^{m/n} = \sqrt[n]{x^m}\\\\\\4^{2/3} = \sqrt[3]{4^2}\\\\\\4^{2/3} = \sqrt[3]{16}\\\\\\](https://tex.z-dn.net/?f=x%5E%7Bm%2Fn%7D%20%3D%20%5Csqrt%5Bn%5D%7Bx%5Em%7D%5C%5C%5C%5C%5C%5C4%5E%7B2%2F3%7D%20%3D%20%5Csqrt%5B3%5D%7B4%5E2%7D%5C%5C%5C%5C%5C%5C4%5E%7B2%2F3%7D%20%3D%20%5Csqrt%5B3%5D%7B16%7D%5C%5C%5C%5C%5C%5C)
Showing that the original expression turns into the cube root of 16.
Answer:
Probability that average height would be shorter than 63 inches = 0.30854 .
Step-by-step explanation:
We are given that the average height of 20-year-old American women is normally distributed with a mean of 64 inches and standard deviation of 4 inches.
Also, a random sample of 4 women from this population is taken and their average height is computed.
Let X bar = Average height
The z score probability distribution for average height is given by;
Z =
~ N(0,1)
where,
= population mean = 64 inches
= standard deviation = 4 inches
n = sample of women = 4
So, Probability that average height would be shorter than 63 inches is given by = P(X bar < 63 inches)
P(X bar < 63) = P(
<
) = P(Z < -0.5) = 1 - P(Z <= 0.5)
= 1 - 0.69146 = 0.30854
Hence, it is 30.85% likely that average height would be shorter than 63 inches.