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Rashid [163]
3 years ago
10

Find the equation of a parabola that has a vertex of (3,2) and contains the point (4,7)

Mathematics
1 answer:
zvonat [6]3 years ago
7 0

Answer:

y = 5(x - 3)² + 2

Step-by-step explanation:

y = a(x - h)² + k

y = a(x - 3)² + 2

7 = a(4 - 3)² + 2

a = 5

y = 5(x - 3)² + 2

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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
Find the percent of change. Where necessary, round to the nearest percent. Describe the percent of change as a percent of increa
deff fn [24]
70.17543859649122 percent change , rounded would be 70%, it is a 70% increase, as it goes to 57,000 to 97,000
6 0
3 years ago
What is the perimeter of the rectangle? one side is 6in. and the A=30 sq in.
monitta
The perimeter of a rectangle can be found by dividing the area by one side.
30/6=5
Then, add the sides up and you get the perimeter.
5+5+6+6=22

The answer is 22 inches.
3 0
3 years ago
Read 2 more answers
On the 25th of every month, Tamesha pays her rent
Alchen [17]
Ok? What’s the question?
3 0
3 years ago
What problem cannot be solved using the law of sines?
Radda [10]
<span>When to use the law of sines formula. You should use the law of sines when you know 2 sides and an angle and you want to find the measure of an angle opposite a known side. Or when you know 2 angles and 1 side and want to get the side opposite a known angle.</span>
3 0
3 years ago
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