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NISA [10]
3 years ago
13

for the polynomial P(x)=4x^2-5x+6 and c =1, find p(c) by (a. direct substitution and (b. the remainder theorem

Mathematics
1 answer:
nata0808 [166]3 years ago
8 0
p(x)=4x^2-5x+6

c=1\implies p(c)=4(1)^2-5(1)+6=5

By the remainder theorem, the remainder upon dividing a polynomial p(x) by a linear binomial x-c is equal to p(c). Via synthetic division, we get

1   |  4   -5   6
.    |        4  -1
- - - - - - - - - - -
.    |  4   -1   5

which translates to

\dfrac{4x^2-5x+6}{x-1}=4x-1+\dfrac5{x-1}

or

4x^2-5x+6=(4x-1)(x-1)+5

Indeed, when x=1, the first term on the right hand side vanished and we're left with 5.
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18a - 24ay + 48b - 64by​
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Determine the sample size needed to construct a 90% confidence interval to estimate the population proportion when p = 0.65 and
WINSTONCH [101]

Answer:

n=170

Step-by-step explanation:

1) Notation and definitions

n random sample taken (variable of interest)

\hat p=0.65 estimated proportion.

p true population

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by \alpha=1-0.90=0.1 and \alpha/2 =0.05. And the critical value would be given by:

z_{\alpha/2}=\pm 1.64

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.06 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.65(1-0.65)}{(\frac{0.06}{1.64})^2}=169.968  

And rounded up we have that n=170

6 0
3 years ago
A data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a maximum of 20. Which state
ololo11 [35]

Given:

A data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a maximum of 20.

To find:

The correct statement for the box plot.

Solution:

Lower quartile is 10 and upper quartile is 15, so the box will go from 10 to 15.

Median of the data set is 12, so a line dividing the box will be at 12.

Minimum value is 4 and lower quartile is 10, so the left whisker will go from 4 to 10.

Upper quartile is 15 and maximum value is 20, so the right whisker will go from 15 to 20.

Therefore, the correct option is B.

8 0
3 years ago
Read 2 more answers
A collection of coins contains a total of sixteen dimes and quarters. It is worth $2.20 in all. How many dimes are in the collec
grin007 [14]

9514 1404 393

Answer:

  12 dimes

Step-by-step explanation:

Let q represent the number of quarters. Then the number of dimes is 16-q and the total value is ...

  0.25q +0.10(16 -q) = 2.20

  0.15q +1.60 = 2.20 . . . . . . . simplify

  0.15q = 0.60 . . . . . . . . subtract 1.60

  q = 4 . . . . . . . . . . . divide by 0.15

  16-q = 12

There are 12 dimes in the collection.

5 0
3 years ago
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