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3 years ago

Construct a difference table to predict the next term of the sequence.

Mathematics

1 answer:

sergiy2304 [10]3 years ago

8 0

Answer:

Step-by-step explanation:

8-1=7

18-8=10

31-18=13

47-31=16

66-47 = 19

x - 66 = 22

+66 +66

x= 88

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What is the modulus of 2 – 3i?

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3 years ago

Let Z be the standard normal random variable. Use a probability calculator to answer the following questions: What is the probab

Softa [21]

Answer:

0.6826 = 68.26% probability Z will be within one standard deviation of average.

Step-by-step explanation:

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.

What is the probability Z will be within one standard deviation of average?

This is the p-value of Z = 1 subtracted by the p-value of Z = -1.

Z = 1 has a p-value of 0.8413.

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

0.8413 - 0.1587 = 0.6826

0.6826 = 68.26% probability Z will be within one standard deviation of average.

8 0

3 years ago

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const2013 [10]

Answer:

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6 0

3 years ago

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3 years ago

What number should be added to both sides of the equation to complete the square?<br> x2 - 6x = 5

ikadub [295]

Answer:

First of all, it is better to note that x2 is not equal to x² .In mathematics x2 is equal to 2nd x or 2x i.e. 2 times x=2*x=x*2.

I don't know what this question means ! But if it means to just confine x2 and -6x in a square or to make them part of a square then it could be done as follows.

Assume x2 as x² as per your needs as case may be.

Now use the identity

(a² - 2a×b + b²) =(a - b )²

Here , in LHS

a appears twice as in a² and in 2a×b.

So for given expression (x2 – 6x = 5) or (x² – 6x = 5) or (x² - 6x -5 =0)

Assume x=a

Then,

6x =2*x*3 =2*a*b

=> 3 = b

Thus

(x² - 6x -5 =0)

=> x² - 2*x*3 + 3² -3² -5 =0

=> ( x² - 2*x*3 + 3² ) - 3² -5 =0

=> (x - 3)² - 3² = 5

=> (x - 3)² = 5 + 3²

=> (x - 3)² = 5 + 9 = 14 = ( ±√(14) )²

Now comparing

(x² – 6x = 5) and (x - 3)² = 5 + 9,

it can be said that number 9 should be added to both sides of (x² – 6x = 5) or (x² – 6x) = ( 5 ) to make ( x² ) and (-6x ) as the constituting parts of the square (x-3)² .

I hope it helps.

Thank you for patiently reading it.

6 0

3 years ago