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2 years ago

Given a population mean of 53.7 with a standard deviation of 1.3 and a sample size

Mathematics

1 answer:

a_sh-v [17]2 years ago

3 0

Answer: A. 0.4899 B. 14

Step-by-step explanation:

If X = random variable

then, the standard deviation of the sampling distribution of X = $\dfrac{\sigma}{\sqrt{n}}$

GIven: $\sigma= 1.2, \n= 6$

The standard deviation of the sampling distribution of X = $\dfrac{1.2}{\sqrt{6}}=0.4899$

B. Let n be the sample size,

$0.325=\dfrac{1.2}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=\dfrac{1.2}{0.325}\\\\\Rightarrow\ \sqrt{n}=3.69230769231\\\\\Rightarrow\ n= (3.69230769231)^2=13.6331360947\approx 14$

Hence, the required sample size = 14

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The half price of helium-5 is 7.6 X 10 to the power of negative 22 seconds and the half-life helium -9 is 7 x 10 to the power of

Digiron [165]

Answer:

Approximately 9.211 times

Step-by-step explanation:

Given

$x = 7.6 * 10^{-22}s$ --- half life of helium-5

$y = 7 * 10^{-21}s$ --- half life of helium-9

Required

How many times greater is y than x

To do this, we simply divide y by x

$\frac{y}{x} = \frac{7 * 10^{-21}s}{7.6 * 10^{-22}s}$

$\frac{y}{x} = \frac{7 * 10^{-21}}{7.6 * 10^{-22}}$

Apply law of indices

$\frac{y}{x} = \frac{7 * 10^{-21--22}}{7.6}$

$\frac{y}{x} = \frac{7 * 10^{-21+22}}{7.6}$

$\frac{y}{x} = \frac{7 * 10}{7.6}$

$\frac{y}{x} = \frac{70}{7.6}$

$\frac{y}{x} = 9.211$

5 0

2 years ago

Let θ (in radians) be an acute angle in a right triangle, and let x and y, respectively, be the lengths of the sides adjacent an

Fed [463]

Explanation is given step by step just below:
tan(theta(t))=y(t)/x(t)

differentiate
sec^2(theta(t))*theta'(t)=y'(t)x(t)-y(t)x'(t)/x^2(t)
thus
theta'(t)=(y'(t)x(t)-y(t)x'(t))
divided by (x^2(t)*sec^2(θ(t))

8 0

2 years ago

Read 2 more answers

Complete the sequence: 1, 1, 2, 3, 5, ____, ____, ____.

Elza [17]

Answer:

8, 13, 21

Step-by-step explanation:

This is a part of the Fibonacci sequence. it is where you add the two previous numbers together to get the third.

Ex.

1+1 = 2

1+2 = 3