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2 years ago

How many six-digit odd numbers are possible if the leftmost digit cannot be zero

Mathematics

1 answer:

Romashka [77]2 years ago

4 0

For the leftmost digit there are 9 possibilities!

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The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 ci

Olenka [21]

Answer:

The correct answer is

(0.0128, 0.0532)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$

For this problem, we have that:

In a random sample of 300 circuits, 10 are defective. This means that $n = 300$ and $\pi = \frac{10}{300} = 0.033$

Calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool.

So $\alpha$ = 0.05, z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 - 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0128$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 + 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0532$

The correct answer is

(0.0128, 0.0532)

4 0

2 years ago

Consider the incomplete paragraph proof. Given: Isosceles right triangle XYZ (45°–45°–90° triangle) Prove: In a 45°–45°–90° tria

Norma-Jean [14]

Answer:

(C)Determine the principal square root of both sides of the equation.

Step-by-step explanation:

Given: Isosceles right triangle XYZ (45°–45°–90° triangle)

To Prove: In a 45°–45°–90° triangle, the hypotenuse is $\sqrt{2}$ times the length of each leg.

Proof:

$\angle XYZ$ is 90^\circ$ and the other 2 angles are 45^\circ. \\\overline{XY} = a, \overline{YZ}= a, \overline{XZ}= c.\\$

Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, $a^2 + b^2 = c^2$

Since a=b in an isosceles triangle:

$a^2 + a^2 = c^2\\$Combining like terms\\2a^2 = c^2\\$Determine the principal square root of both sides of the equation.\\\sqrt{c^2}=\sqrt{2a^2} \\\\c=a\sqrt{2} \\$