MATHEMATICS HIGH SCHOOL

Which of the following equations is an equation formed when completing the square on y 2 - 12y = -27?(y - 6) 2 = -27
(y - 6) 2 = 9
(y + 6) 2 = 9

Answers

Answer 1
Answer:

Answer:  The correct option is

(B) (y-6)^2=9.

Step-by-step explanation:  We are given to select the equation that is formed when completing the square on the following equation :

y^2-12y=-27~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

We will be using the following formula :

a^2-2ab+b^2=(a-b)^2.

From equation (i), we have

y^2-12y=-27\n\n\Rightarrow y^2-2* x*6=-27\n\n\Rightarrow y^2-2* x* 6+6^2=-27+6^2\n\n\Rightarrow (y-6)^2=-27+36\n\n\Rightarrow (y-6)^2=9.

Thus, the required equation that is formed is(y-6)^2=9.

Option (B) is CORRECT.
Answer 2
Answer: Hello,

You should write y²-12y=-27 or y^2-12y=-27

y²-12y=-27
==>y²-2*6y+6²=-27+36
==>(y-6)²=9
(second answer)

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Answers

Answer: The population of the survey includes everyone the farmer called.

Step-by-step explanation:

10.5 in the form a/b

Answers

10.5 in the form of a/b = 105/10 = 21/2

Find all relative extrema of the function. use the second derivative test where applicable. (if an answer does not exist, enter dne.) f(x) = x3 − 9x2 + 2

Answers

First find the derivative of the function.  The derivative is f'(x)=3 x^(2) -18x.  Now set it equal to 0 to find the critical numbers.  0=3 x^(2) -18x.  Factor to solve for the zeros of the derivative.  0=3x(x-6).  So 3x = 0, and x = 0, or x - 6 = 0 and x = 6.  We will make a table with values for -∞<x<0, 0<x<6, 6<x<∞.  Pick a value within those boundaries for each interval and find the sign, positive or negative, that results from subbing that number into the derivative.  If we choose -1 in the first interval f'(-1)=21, so the function is increasing from negative infinity to 0.  If we choose 1 in the second interval, f'(1)=-15, so the function is decreasing from 0 to 6.  If we choose 10 in the last interval, f'(10)=120, so the function is increasing from 6 to infinity.  The points of extrema are found by subbing the critical x values into the original function. We know the function is increasing from negative infinity to 0, so f(0)=2, and our max point is (0, 2).  We know the function is decreasing from 6 to infinity, so f(6)=-106, and our min point is (6, -106).  I do this instead of the second derivative test, but they both work.

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. To determine the effectiveness of the advertising campaign, a sample of 49 days of sales were taken. They found that the average daily sales were $6,300 per day. From past history, the restaurant knew that its population standard deviation is about $1,000. If the level of significance is 0.01, have sales increased as a result of the advertising campaign? Multiple Choice A. Reject the null hypothesis and conclude that the mean is equal to $6,000 per day.
B. Fail to reject the null hypothesis.
C. Reject the null hypothesis and conclude the mean is lower than $6,000 per day.
D. Reject the null hypothesis and conclude the mean is higher than $6,000 per day.

Answers

Answer:

Option B) Fail to reject the null hypothesis.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $6,000

Sample mean, \bar{x} = $6,300

Sample size, n = 49

Alpha, α = 0.01

Population standard deviation, σ = $1,000

First, we design the null and the alternate hypothesis

H_(0): \mu = 6000\text{ dollars per week}\nH_A: \mu > 6000\text{ dollars per week}

We use one-tailed(right) z test to perform this hypothesis.

Formula:

z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }

Putting all the values, we have

z_(stat) = \displaystyle(6300 - 6000)/((1000)/(√(49)) ) = 2.1

Now, z_(critical) \text{ at 0.01 level of significance } = 2.33

Since,  

z_(stat) < z_(critical)

We fail to reject the null hypothesis and accept the null hypothesis. Thus, we conclude that sales have not increased as a result of the advertising campaign

Option B) Fail to reject the null hypothesis.

How to change 4.1 into a decimal?

Answers

Well you can't change 4.1 into a decimal because it's already a decimal with a decimal point included in it, so there's really no point of asking that question when you've already done it yourself! Just wanted to notify you on that point.
You can't change it to a decimal because it is already a decimal.

OK I need help the answer is c but I didn't understand the teacher explanation pls help me

Answers

9 - 6 + 4 - 8/3 ..,
geometric series a(n) = a1r^(n-1)

r = a(n+1)/a(n)
-6/9 = -2/3
4/-6 = -2/3
-8/3/4 = -2/3
so r = -2/3 and a1 = 9

Sn = a1(1-r^n)/(1-r) = 9(1-(-2/3)^n)/(1-(-2/3))
n is infinite Sn = 9/(5/3) = 27/5
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