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3 years ago

Solve the quadratic equation. (a + 5)2 +36 = 9

Mathematics

1 answer:

Andrej [43]3 years ago

6 0

Answer:

No solution unless you want to solve for an imaginary number which in that case $a=27i-5$

Step-by-step explanation:

$(a+5)^{2} +36=9$

$(a+5)^2=-27$

$a+5=\sqrt{-27}$

Here you can stop and say "no solution" since you cannot square root a negative number, but if you want you can still solve for an imaginary number:

$a+5=\sqrt{-1} \sqrt{27}$

$a+5=27i$

$a=27i-5$

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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

4 years ago

An arithmetic sequence is represented in the following table. Enter the missing term of the sequence.

boyakko [2]

Answer:

17 is the answer

Step-by-step explanation:

-7 + 6 = -1

-1 + 6 = 5

5 + 6 = 11

11 + 6 = 17

3 0

3 years ago

Read 2 more answers

How many seconds are in 10 hours

enot [183]

There are 60 seconds in a minute.

There are 60 minutes in an hour.

This means that there'd be 600 minutes in 10 hours.

And if there are 60 seconds in a minute, there are 600 x 60 seconds in 600 minutes.

600 x 60 = 600 x 10 x 6 = 6000 x 6 = 36000

So we know that there are 36000 seconds in 10 hours.

5 0

4 years ago

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the cable of a hoist has a cross-section of 80 mm2. the hoist is used to lift a crate weighing 500 kg. what is the stress in the

Daniel [21]

Answer:

stress on the cable is 61.312mpa

If steel is used, extension will be 0.91968mm

If polypropylene is used, extension will be 0.1532mm

Step-by-step explanation: detailed explanation and calculation is shown in the image below

3 0

3 years ago

The table shows the height of a plant as it grows. Which equation in point slope form gives the plant’s height at any time

vodka [1.7K]

Answer:

Option A is correct.

$y-16=8(x-2)$ is the equation represent the point slope form gives the plant's height at any time.

Step-by-step explanation:

Point slope intercept form: For any two points $(x_1, y_1)$ and $(x_2, y_2)$ then,

the general form

$y-y_1=m(x-x_1)$ for linear equations; where m is the slope given by:

$m =\frac{y_2-y_1}{x_2-x_1}$

Consider any two points from the table;

let A= (2 , 16) and B =(4, 32)

First calculate the slope of the line AB:

$m =\frac{y_2-y_1}{x_2-x_1}=\frac{32-16}{4-2}=\frac{16}{2}$ = 8

Therefore, slope of the line m = 8

Then,

the equation of line is:

$y-y_1=m(x-x_1)$

Substitute the value of m=8 and (2, 16) above we get;

$y-16=8(x-2)$

Therefore, the equation in point slope form which gives the plant's height at any time is; $y-16=8(x-2)$ , where x is the time(months) and y is the plant height (cm)

5 0

3 years ago

Read 2 more answers