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3 years ago

F(x)=(x^3+4x^2+7x-9) d(x)=(x+3) divide using long division

Mathematics

1 answer:

Alchen [17]3 years ago

7 0

The result is x^2 +x +4 -21/(x+3).

_____

Polynomial long division tends to be easier than numerical long division because the quotient term never needs adjustment. It is always the ratio of the highest degree terms of the dividend and divisor.

See the attachment for the intermediate steps.

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An automobile club reported that the average price of regular gasoline in a certain state was $2.61 per gallon. The following d

laila [671]

Answer:

$2.618-2.98\frac{0.078}{\sqrt{15}}=2.56$

$2.618+2.98\frac{0.078}{\sqrt{15}}=2.68$

So on this case the 99% confidence interval would be given by (2.56;2.68)

Step-by-step explanation:

Previous concepts

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=2.618$

The sample deviation calculated $s=0.078$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=15-1=14$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,14)".And we see that $t_{\alpha/2}=2.98$

Now we have everything in order to replace into formula (1):

$2.618-2.98\frac{0.078}{\sqrt{15}}=2.56$

$2.618+2.98\frac{0.078}{\sqrt{15}}=2.68$

So on this case the 99% confidence interval would be given by (2.56;2.68)

5 0

3 years ago

How do I simplify this (sinx)/(secx+1)

pochemuha

Answer:

Step-by-step explanation:

$\frac{sin~x}{sec~x+1} =\frac{sin~x}{\frac{1}{cos~x}+1 } =\frac{sin~x~cos~x}{1+cos~x} \\=\frac{sin~x~cos~x}{1+cos~x} \times \frac{1-cos~x}{1-cos~x} \\=\frac{sin~x~cos~x(1-cos~x)}{1-cos^2 x} \\=\frac{sin~x~cos~x(1-cos~x)}{sin^2x} \\=\frac{cos~x(1-cos~x)}{sin~x} \\=cos ~x(csc~x-cot~x)\\or\\=cot~x(1-cos~x)$

6 0

3 years ago

Which of the following is the solution for 6x + 3 ≤ 27

postnew [5]

Answer:

x ≤ 4

Step-by-step explanation:

6x + 3 ≤ 27 subtract 3 both sides

6x ≤ 24 divide 6 both sides

x ≤ 4 There's your answer

5 0

3 years ago

2x + 5y = 16<br> y + 4x = 3

masha68 [24]

Answer:

If your solving for x on the first one it’s x =−5/2y+8

If your solving for y on the second one it’s y =−4x+3

Step-by-step explanation:

5 0

3 years ago

Can someone help me figure out what 40% of 65 is?

Akimi4 [234]

Answer:

Step-by-step explanation:

Convert 40% to a decimal

40% = 0.4

Multiply 0.4 with 65

0.4 • 65 = 26

40% of 65 is 26

7 0

3 years ago

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