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Crazy boy [7]
3 years ago
9

In an arithmetic sequence, the 10th term is 37, and the 21st term is 4. Find the common difference and the first term

Mathematics
1 answer:
Masja [62]3 years ago
3 0

Answer:

Common difference is 3. And the first term is 64.

Step-by-step explanation:

The differnce between 21 and 10 is 11. So there are 11 unknown numbers in between.  And the difference between 37 and 4 is 33. 33/11 is equal to 3. So the pattern is minus three. the first term is 9 terms before 37. 9 times 3 is 27. 37+27 is equal to 64. so the first term is 64

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If a number has 2 and 6 as factors then it has 12 as a factor
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Answer:

yes

Step-by-step explanation:

2,4,6,8,10,12 so on

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: A theater sells tickets for a concert. Adult tickets sell for $6.50 each, and children's tickets sell for $3.50 each. The thea
BARSIC [14]

Answer: 321 adult tickets and 227 children tickets were sold.

Step-by-step explanation:

Let x represent the number of adult tickets that were sold.

Let y represent the number of children tickets that were sold.

The total number of tickets that the theatre sold is 548. This means that

x + y = 548

Adult tickets sell for $6.50 each, and children's tickets sell for $3.50 each. The total ticket sales was $2881. This means that

6.5x + 3.5y = 2881 - - - - - - - - - - -1

Substituting x = 548 - y into equation 1, it becomes

6.5(548 - y) + 3.5y = 2881

3562 - 6.5y + 3.5y = 2881

- 6.5y + 3.5y = 2881 - 3562

- 3y = - 681

y = - 681/ -3

y = 227

x = 548 - y = 548 - 227

x = 321

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Find the slope of the line containing the points (5, -1) and (-8, -4).
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Test scores of the student in a school are normally distributed mean 85 standard deviation 3 points. What's the probability that
Mrrafil [7]

Answer:

The probability that a random selected student score is greater than 76 is \\ P(x>76) = 0.99865.

Step-by-step explanation:

The Normally distributed data are described by the normal distribution. This distribution is determined by two <em>parameters</em>, the <em>population mean</em> \\ \mu and the <em>population standard deviation</em> \\ \sigma.

To determine probabilities for the normal distribution, we can use <em>the standard normal distribution</em>, whose parameters' values are \\ \mu = 0 and \\ \sigma = 1. However, we need to "transform" the raw score, in this case <em>x</em> = 76, to a z-score. To achieve this we use the next formula:

\\ z = \frac{x - \mu}{\sigma} [1]

And for the latter, we have all the required information to obtain <em>z</em>. With this, we obtain a value that represent the distance from the population mean in standard deviations units.

<h3>The probability that a randomly selected student score is greater than 76</h3>

To obtain this probability, we can proceed as follows:

First: obtain the z-score for the raw score x = 76.

We know that:

\\ \mu = 85

\\ \sigma = 3

\\ x = 76

From equation [1], we have:

\\ z = \frac{76 - 85}{3}

Then

\\ z = \frac{-9}{3}

\\ z = -3

Second: Interpretation of the previous result.

In this case, the value is <em>three</em> (3) <em>standard deviations</em> <em>below</em> the population mean. In other words, the standard value for x = 76 is z = -3. So, we need to find P(x>76) or P(x>-3).

With this value of \\ z = -3, we can obtain this probability consulting <em>the cumulative standard normal distribution, </em>available in any Statistics book or on the internet.

Third: Determination of the probability P(x>76) or P(x>-3).

Most of the time, the values for the <em>cumulative standard normal distribution</em> are for positive values of z. Fortunately, since the normal distributions are <em>symmetrical</em>, we can find the probability of a negative z having into account that (for this case):

\\ P(z>-3) = 1 - P(z>3) = P(z

Then

Consulting a <em>cumulative standard normal table</em>, we have that the cumulative probability for a value below than three (3) standard deviations is:

\\ P(z

Thus, "the probability that a random selected student score is greater than 76" for this case (that is, \\ \mu = 85 and \\ \sigma = 3) is \\ P(x>76) = P(z>-3) = P(z.

As a conclusion, more than 99.865% of the values of this distribution are above (greater than) x = 76.

<em>We can see below a graph showing this probability.</em>

As a complement note, we can also say that:

\\ P(z3)

\\ P(z3)

Which is the case for the probability below z = -3 [P(z<-3)], a very low probability (and a very small area at the left of the distribution).

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To make a profit. The store needs to make a profit. Buy something from Walmart cheap, sell it for 60% percent more to make a 'good' profit.

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