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Ostrovityanka [42]
3 years ago
12

What is the scale factor of the dilation?

Mathematics
1 answer:
Mars2501 [29]3 years ago
5 0

Answer:

Step-by-step explanation:

2/5

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The arithmetic sequence a; is defined by the formula:
Morgarella [4.7K]

Answer:

The sum of the first 650 terms of the given arithmetic sequence is 2,322,775

Step-by-step explanation:

The first term here is 4

while the nth term would be ai = a(i-1) + 11

Kindly note that i and 1 are subscript of a

Mathematically, the sum of n terms of an arithmetic sequence can be calculated using the formula

Sn = n/2[2a + (n-1)d)

Here, our n is 650, a is 4, d is the difference between two successive terms which is 11.

Plugging these values, we have

Sn = (650/2) (2(4) + (650-1)11)

Sn = 325(8 + 7,139)

Sn = 325(7,147)

Sn = 2,322,775

6 0
3 years ago
Which set of numbers could be the length of the sides of a triangle?
san4es73 [151]

3. {6,9,15)

for these u have use Pythagoras theorem

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3 years ago
What is the tru solution to the logarithmic equation below? Log4[log4(2x)]=1
zaharov [31]

\log_4(\log_42x)=1

Take both sides as powers of 4:

4^{\log_4(\log_42x)}=4^1\implies\log_42x=4

Do it again:

4^{\log_42x}=4^4\implies2x=(2^2)^4=2^8\implies x=2^7=128

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What does write two addition sentences where the sum is zero mean
Alex777 [14]
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6 0
3 years ago
Read 2 more answers
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.3 minutes and a standard deviation of 3.3
In-s [12.5K]

Answer:

a) There is a 74.22% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

b) There is a 1-0.0548 = 0.9452 = 94.52% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.

c) There is a 68.74% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}.

Problems of normally distributed samples can be solved using 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.

In this problem, we have that:

The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.3 minutes and a standard deviation of 3.3 minutes. This means that \mu = 8.3, \sigma = 3.3.

(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?

We are working with a sample mean of 37 jets. So we have that:

s = \frac{3.3}{\sqrt{37}} = 0.5425

Total time of 320 minutes for 37 jets, so

X = \frac{320}{37} = 8.65

This probability is the pvalue of Z when X = 8.65. So

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

Z = \frac{8.65 - 8.3}{0.5425}

Z = 0.65

Z = 0.65 has a pvalue of 0.7422. This means that there is a 74.22% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?

Total time of 275 minutes for 37 jets, so

X = \frac{275}{37} = 7.43

This probability is subtracted by the pvalue of Z when X = 7.43

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

Z = \frac{7.43 - 8.3}{0.5425}

Z = -1.60

Z = -1.60 has a pvalue of 0.0548.

There is a 1-0.0548 = 0.9452 = 94.52% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.

(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?

Total time of 320 minutes for 37 jets, so

X = \frac{320}{37} = 8.65

Total time of 275 minutes for 37 jets, so

X = \frac{275}{37} = 7.43

This probability is the pvalue of Z when X = 8.65 subtracted by the pvalue of Z when X = 7.43.

So:

From a), we have that for X = 8.65, we have Z = 0.65, that has a pvalue of 0.7422.

From b), we have that for X = 7.43, we have Z = -1.60, that has a pvalue of 0.0548.

So there is a 0.7422 - 0.0548 = 0.6874 = 68.74% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes.

7 0
3 years ago
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