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lianna [129]
3 years ago
14

What is the coefficient of the term x5y7 in the expansion of (x - y)12 ?

Mathematics
1 answer:
lozanna [386]3 years ago
6 0

Answer:

12 and -12

Step-by-step explanation:

12x-12y is the expansion using the distributive property, so the coefficient of x is 12 and the coefficient of y is -12

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30x297 in distributive property
Vedmedyk [2.9K]

Answer:

8910

Step-by-step explanation:

30x297 = 8910

4 0
3 years ago
The time for a visitor to read health instructions on a Web site is approximately normally distributed with a mean of 10 minutes
klio [65]

Answer:

a) The mean is 10 and the variance is 0.0625.

b) 0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.

c) 10.58 minutes.

Step-by-step explanation:

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

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Normally distributed with a mean of 10 minutes and a standard deviation of 2 minutes.

This means that \mu = 10, \sigma = 2

Suppose 64 visitors independently view the site.

This means that n = 64,  = \frac{2}{\sqrt{64}} = 0.25

a. The expected value and the variance of the mean time of the visitors.

Using the Central Limit Theorem, mean of 10 and variance of (0.25)^2 = 0.0625.

b. The probability that the mean time of the visitors is within 15 seconds of 10 minutes.

15 seconds = 15/60 = 0.25 minutes, so between 9.75 and 10.25 seconds, which is the p-value of Z when X = 10.25 subtracted by the p-value of Z when X = 9.75.

X = 10.25

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

By the Central Limit Theorem

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

Z = \frac{10.25 - 10}{0.25}

Z = 1

Z = 1 has a p-value of 0.8413.

X = 9.75

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

Z = \frac{9.75 - 10}{0.25}

Z = -1

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826.

0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.

c. The value exceeded by the mean time of the visitors with probability 0.01.

The 100 - 1 = 99th percentile, which is X when Z has a p-value of 0.99, so X when Z = 2.327.

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

2.327 = \frac{X - 10}{0.25}

X - 10 = 2.327*0.25

X = 10.58

So 10.58 minutes.

6 0
3 years ago
Find the volume of the cylinder to the nearest tenth use 3.14
Maurinko [17]

the answer is 3.14 r^2 h

the h is the height

3 0
3 years ago
Read 2 more answers
URGENT kaser needs $155 to pay for a new mouth piece for her saxophone she has $35 already and save $15 a week that she earns wa
yulyashka [42]

Answer:

A) she needs to earn $120 for her mouth piece

B) it will taker kaser 8 weeks to get enough money for the mouthpiece

Step-by-step explanation:

whats a segment tool? no idea but i can help solve this so you can attempt that part

explaining

so kaser needs $155, she already has $35 and gains $15 a week. i will be assisting you with how to solve for how much she has when she starts saving and how long until she saves it all

process A

155-35 = 120

answer A

she needs to earn $120 for her mouth piece

process B

120 divided by 15 = 8

answer B

it will taker kaser 8 weeks to get enough money for the mouthpiece

8 0
3 years ago
Lila hired a chainsaw for a week.
Allisa [31]

Answer:

She payed $269 for the chainsaw :)

4 0
3 years ago
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