Bruno claims that the solution to the linear equation −3(2x+6)+25=1 is x=1. He shows the steps below to justify his solution.
1 answer:
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Answer:
Step-by-step explanation:
The circumference of a circle can be found using the following formula:
where d is the diameter. We are given the radius, so let's find the diameter.
The diameter is twice the radius.
The radius is 15 feet.
Multiply.
Now we know the diameter. Substitute 30 feet in for d.
We are using 3.14 for pi, so substitute it in.
Multiply.
The circumference of the circle is 94.2 feet.
Answer:
The probability that at most 10 of the next 150 items produced are unacceptable is 0.8315.
Step-by-step explanation:
Let <em>X</em> = number of items with unacceptable quality.
The probability of an item being unacceptable is, P (X) = <em>p</em> = 0.05.
The sample of items selected is of size, <em>n</em> = 150.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 150 and <em>p</em> = 0.05.
According to the Central limit theorem, if a sample of large size (<em>n</em> > 30) is selected from an unknown population then the sampling distribution of sample mean can be approximated by the Normal distribution.
The mean of this sampling distribution is:
The standard deviation of this sampling distribution is:
If 10 of the 150 items produced are unacceptable then the probability of this event is:
Compute the value of as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that at most 10 of the next 150 items produced are unacceptable is 0.8315.