1) Determine the value written as a fraction , decimal & a percent. fraction decimal percent

The vertex of this parabola is at (-3, 6). Which of the following could be its equation?

pishuonlain [190]

Since the vertex is at (-3, 6), the equation is given by
y = a(x + 3) + 6

Therefore, option A is the correct answer.

6 0

3 years ago

The weights of packets of cookies produced by a certain manufacturer have a Normal distribution with a mean of 202 grams and a s

Evgen [1.6K]

Answer:

209.005 gms

Step-by-step explanation:

Given that the weights of packets of cookies produced by a certain manufacturer have a Normal distribution with a mean of 202 grams and a standard deviation of 3 grams.

Let X be the weight of packets of cookies produced by manufacturer

X is N(202, 3) gms.

To find the weight that should be stamped on the packet so that only 1% of the packets are underweight

i.e. P(X<c) <0.01

From std normal table we find that z value = 2.335

Corresponding x value = 202+3(2.335)

=209.005 gms.

5 0

2 years ago

A circle has the equation 2x²+12x+2y²−16y−150=0.

KonstantinChe [14]

Answer: B. The coordinates of the center are (-3,4), and the length of the radius is 10 units.

Step-by-step explanation:

The equation of a circle in the center-radius form is:

$(x-h)^{2} +(y-k)^{2}=r^{2}$ (1)

Where $(h,k)$ are the coordinates of the center and $r$ is the radius.

Now, we are given the equation of this circle as follows:

$2x^{2}+12x+2y^{2}-16y-150=0$ (2)

And we have to write it in the format of equation (1). So, let's begin by applying common factor 2 in the left side of the equation:

$2(x^{2}+6x+y^{2}-8y-75)=0$ (3)

Rearranging the equation:

$x^{2}+6x+y^{2}-8y=75$ (4)

$(x^{2}+6x)+(y^{2}-8y)=75$ (5)

Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of $(a\pm b)^{2}=a^{2}\pm+2ab+b^{2}$ :