Answer:
The probability that more than 10 parts will be defective is 0.99989.
Step-by-step explanation:
Let <em>X</em> = a part in the shipment is defective.
The probability of a defective part is, P (Defect) = <em>p</em> = 0.03.
The size of the sample is: <em>n</em> = 1000.
Thus, the random variable .
But the sample size is very large.
The binomial distribution can be approximated by the Normal distribution if the following conditions are satisfied:
- np ≥ 10
- n (1 - p) ≥ 10
Check the conditions:
Thus, the binomial distribution can be approximated by the Normal distribution.
The sample proportion (<em>p</em>) follows a normal distribution.
Mean:
Standard deviation:
Compute the probability that there will be more than 10 defective parts in this shipment as follows:
The proportion of 10 defectives in 1000 parts is:
The probability is:
Use the standard normal table for the probability.
Thus, the probability that more than 10 parts will be defective is 0.99989.
Answer:
2 1/6
Step-by-step explanation:
reduce 130/60 to its lowest form
Answer:
m∠x = 10°
Step-by-step explanation:
Since we are dealing with a <u>right triangle</u> and its two sides and one angle, we can use <u>trigonometry ratios</u>. Remember them all with the acronym SohCahToa.
"o" is for opposite side, "a" is for adjacent side, "h" is for hypotenuse side.
The ratios are:
sinθ = opposite/hypotenuse
cosθ = adjacent/hypotenuse
tanθ = opposite/adjacent
θ means the "angle of reference", or the angle you know or want to find. This determines which side is adjacent (touching) or opposite (not touching). The hypotenuse (longest side) does not change.
In this triangle, θ = x. The sides we know are hypotenuse and opposite. Therefore, we will use the sinθ ratio.
sinθ = opposite/hypotenuse
sinx = CB/AB Substitute the labels in the diagram
sinx = 4/23 Substitute known values (side lengths)
x = sin⁻¹(4/23) Isolate 'x'. Use calculator to solve.
x = 10.015....° Exact answer
x ≈ 10° Round to the nearest degree
Therefore the measure of angle x (m∠x) is 10°.
Answer: (3,4) (-3,4) (3,-3) (-3,-2)
Step-by-step explanation:
Answer:
p(x) = 7x - 20
Step-by-step explanation:
A company makes a profit selling goods when the revenue taken in from the sales is greater than the cost of those goods: p(x) = r(x) - c(x) > 0.
In this case the revenue function is r(x) = 12x; the cost function is c(x) = 5x + 20, and the profit function is p(x) = 12x - (5x + 20), or:
p(x) = 12x - 5x - 20, or
p(x) = 7x - 20