What is the mean of the data set in the box below?<br> -8, -6, - 2, 0, -6,

3^2 • 3^-8 • 3^0<br> i need help with this asap

pantera1 [17]

Steps to solve:

3^2 • 3^-8 • 3^0

~Apple exponent rule [ a^b * a^c = a^b+c ]

3^2-8+0

~Simplify

3^-6

~Use exponent rule [ a^-b = 1/a^b ]

1/3^6

~Simplify

1/729

Best of Luck!

6 0

2 years ago

Read 2 more answers

Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

$(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14$ .

(Expand to obtain an equivalent expression for the sphere: $x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between $\left(x_1, \, y_1, \, z_1\right)$ and $\left(x_2, \, y_2, \, z_2\right)$ would be:

$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .

The equation for a sphere of radius $r$ and center $\left(x_0,\, y_0,\, z_0\right)$ would be:

$\left(x - x_0\right)^2 + \left(y - y_0\right)^2 + \left(z - z_0\right)^2 = r^2$ .

In this case, the equation would be:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z - (-6)\right)^2 = \left(\sqrt{56}\right)^2$ .

Simplify to obtain:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z + 6\right)^2 = 56$ .

Expand the squares and simplify to obtain:

$x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ .

8 0

3 years ago

Plzzzzzzzz help this is math

elena-s [515]

The answer would be
m= -25

3 0

2 years ago

Read 2 more answers

40x40x40+26-98+45x78x78x78 then divide by 3

kykrilka [37]

You've written "then" before 3, so i assume the real question is:

(40 * 40 * 40 + 26 - 98 + 45 * 78 * 78 * 78) / 3
Use "PEMDAS" first solve under the parenthesis, then after it.

= (64000 + 26 - 98 + 21354840) / 3
= 21418768 / 3
= 7139589.33

In short, Your Answer would be: 7139589.33

Hope this helps!

7 0

3 years ago

Hot dog buns come in package of 8.for school picnic, mr bught 30 packge of hot dog buns how many hot dog buns did he buy? A,24,b

Oliga [24]

It is 240 because 8 bags of hot dog buns plus 30 packages of hot dog buns would equal 240.

8 0

2 years ago

What is the mean of the data set in the box below? -8, -6, - 2, 0, -6, - 8. 4, 7, 8, 1