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Alexus [3.1K]
3 years ago
5

As the limit of x goes to 3 from the left find the limit of (x/ sqrt x^2 -9)

Mathematics
1 answer:
Dimas [21]3 years ago
8 0
\displaystyle\lim_{x\to3^-}\frac x{\sqrt{x^2-9}}=\lim_{x\to3^-}\frac x{\sqrt{x^2}\sqrt{1-\frac9{x^2}}}=\lim_{x\to3^-}\frac x{|x|\sqrt{1-\frac9{x^2}}}

Since x>0, you have |x|=x and the limand reduces to

\displaystyle\lim_{x\to3^-}\frac1{\sqrt{1-\frac9{x^2}}}

For x>3, you have \sqrt{1-\frac9{x^2}}>0 since \dfrac9{x^2} will always be smaller than 1, which means \dfrac1{\sqrt{1-\frac9{x^2}}}\to+\infty
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A Government company claims that an average light bulb lasts 270 days. A researcher randomly selects 18 bulbs for testing. The s
Fofino [41]

Answer:

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In this question, we have that:

\mu = 270, \sigma = 90, n = 18, s = \frac{90}{\sqrt{18}} = 21.2

What is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days?

This is the pvalue of Z when X = 260. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{260 - 270}{21.2}

Z = -0.47

Z = -0.47 has a pvalue of 0.3192.

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

5 0
3 years ago
A store is selling cookies for $8 for 12 bags how much will it cost if you want to buy 30 for your class?
sveticcg [70]

Answer: $20

Step-by-step explanation:

8 divided by 12 = .67

.67 times 30

7 0
3 years ago
Read 2 more answers
4x−1<11 answer my question
Hitman42 [59]

Answer:

Step-by-step explanation:

4 0
2 years ago
Assume every 10-digit natural number is a possible telephone number except those that begin with 0, 1 or 2. What fraction of tel
lana [24]

Answer: 1/70

Step-by-step explanation:

This is a question that can also be interpreted as what is the probability of having the first number of a phone number to be 8 and the last number of the phone number to also be 8. This answer gives the fraction of the phone numbers that starts with 8 and end with 8.

Since three numbers (0,1,2) cannot start a phone number and we are left to pick from 7 numbers,

then the probability of figure "8" starting phone number = 1/7

Since all 10 numbers can possibly end a phone number,

then the probability of having figure "8" as the last digit of a phone number = 1/10

Hence probability of having "8" as the first and last digit of a phone number = fraction of total telephone numbers that begin with digit 8 and end with digit 8 = 1/7 × 1/10 = 1/70.

5 0
3 years ago
If B = w + 10 and C = -w - 1, find an expression that equals B + 2C in standard form
enot [183]

Answer:

Step-by-step explanation:

B + 2C

= w + 10 + 2(-w - 1)

= w + 10 -2w - 2

= -w + 8

8 0
2 years ago
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