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3 years ago

What are the vertex, focus, and directrix of the parabola with the equation x2+8x+4y+4=0

1 answer:

7 0

x2 +8x +4y +4 = 0
4y= -x2 -8x -4y = -.25*x^2 -2x -1
a = -.25b = -2c = -1
x position of vertex:
h = -b / 2a
h = 2 / 2*-.25h = 2 / -.5h = -4
y position of vertex:
k = ah^2 + bh + ck = -.25*-4^2 + -2*-4 + -1k = -4 +8 -1k = 3
VERTEX = (-4, 3)**************************************************************************
x value of focus =x value of vertex = -4
y value of focus =(1 (-b^2 -4ac)) / 4a

a = -.25 b = -2 c =-1
y value = (1 (-4 -4*-.25*-1)) / 4*-.25
y value = (1 (-4 -4*-.25*-1)) / -1
y value = (1 -4 +1) / -1y value = (-2 / -1)y value = 2
focus value = (-4, 2)
Answer is the last one.

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In the U.S., 51% of all births are boys, and 49% are girls. Use the binomial model to find the probability that 6 out of 10 birt

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Answer: The correct answer is B) 21%

Step-by-step explanation:

This is a binomial model probability problem. We need to find the probability of 6 out of 10 new births at a hospital being boys. The information we need is the number of trials observed, the number of successes and the percentage chance you have of any birth being a boy. The number of trials are 10, with the number of successes being 6 (the number of trials we want to be boys) It states that 51% or 0.51 of all births in the US are boys so we can use this value to determine our answer using our binomial model formula. After simplifying we get our answer of 21% I hope this has been of use to you :)

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3 years ago

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4 years ago

Hot chocolate sales and outside temperatures sales $100 $213 $830 $679 $209 $189 $1110 $456 $422 $235 $199 Temperature 92 88 54

Tomtit [17]

Answer:

(A) The scatter plot is attached below.

(B) The outlier is at (189, 16°F).

(D) The dependent variable is sales and independent variable is the temperature.

Step-by-step explanation:

The data provided for Hot chocolate sales and outside temperatures is as follows:

Sales (Y) Temperature (X)

100 92

213 88

830 54

679 62

209 85

189 16

1110 52

456 65

422 68

235 89

199 91

(A)

The scatter plot is attached below.

(B)

A cluster is a collection of points or values at one place.

On the scatter plot there is a cluster of three values between the temperatures 80°F to 100°F.

An outlier is a value that is very different from the other values in a data set. It is either too small or too large.

There is an outlier present in the provided data set.

The outlier is at (189, 16°F).

(C)

The point on the scatter plot are downwards sloping.

This implies that there is a negative relationship between the variables temperature and sales.

Thus, there is a negative correlation.

(D)

Dependent variables are those variables that are under study, i.e. they are being observed for any changes when the other variables in the model are changed.

Independent variables are the variables that are being altered to see a proportionate change in the dependent variable.

In this case the data represents the sales of hot chocolate according to the temperature outside.

So, the dependent variable is sales and independent variable is the temperature.

This is because as the temperature decreases the sales of hot chocolate increases.