Using the z-distribution, it is found that a sample of 171 should be selected.
<h3>What is a z-distribution confidence interval?</h3>
The confidence interval is:
The margin of error is:
In which:
is the sample mean.
is the standard deviation for the population.
For this problem, the parameters are:
Hence we solve for n to find the needed sample size.
n = 170.7.
Rounding up, a sample of 171 should be selected.
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Answer:
5 in 12 chance or 42% probability of happening
Solve for x over the real numbers using factor method:
10 x^2 + 19 x - 15 = 0
The left hand side factors into a product with two terms:
(2 x + 5) (5 x - 3) = 0
Split into two equations:
2 x + 5 = 0 or 5 x - 3 = 0
Subtract 5 from both sides:
2 x = -5 or 5 x - 3 = 0
Divide both sides by 2:
x = -5/2 or 5 x - 3 = 0
Add 3 to both sides:
x = -5/2 or 5 x = 3
Divide both sides by 5:
Answer: x = -5/2 or x = 3/5
The perimeter of the entire figure is 62.8 cm.
Given, that the diameter of the inner semicircles is 9 cm and the width between the outer and inner semicircles is 2 cm.
The radius of the inner semicircle =4.5 cm and the radius of outer semicircle =5.5 cm (∵Diameter=9+2=11 cm)
We need to find the perimeter of the entire figure.
<h3>What is the perimeter?</h3>
A perimeter is a closed path that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.
We know that, the circumference of a semicircle=πr and the circumference of two semicircles=2πr
Thus, the circumference of inner semicircles=2×3.14×4.5=28.26 cm
The circumference of outer semicircles=2×3.14×5.5=34.54 cm
The perimeter of the entire figure=28.26+34.54=62.8 cm
Therefore, the perimeter of the entire figure is 62.8 cm.
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Answer:
0.7361
Step-by-step explanation:
In this question we have
number to be 10
Then we have a probability of 10% = 0.10
We have q = 1-p
= 1-0.10 = 0.90
Then the probability of not more than 1 being defective:
P(x=0) + p(x= 1)
(10C0 x 0.1⁰ x 0.9^10-0)+(10C1 x 0.1¹ x 0.9^10-1)
= 1 x1 x0.3487 + 10 x 0.1 x 0.3874
= 0.3487 + 0.3874
= 0.7361
This is the the required probability and this answers the question.
probability = 10 percent = 0.1
q= 1- 10percent = 90% = 0.9
n = 4
To get the required probabiltiy for this question is
P(not greater than one is defective )=P(x=0)+P(x=1)
= 4C0x(0.1)⁰x(0.9)⁴+4C1x(0.1)¹x(0.9)³
= 0.9477
The required probability is 0.9477
