What is the value of X?

The median of the data set is 81 what number is missing in data set 82, 87, 77, 70, 80, 88

Gekata [30.6K]

The number that missing is clearly 81

6 0

3 years ago

a cylinder has a base radius of 2 inches and a height of 9 inches what is the volume in cubic in to the nearest tenth place.

GuDViN [60]

Answer:

113.1 cubic inches

Step-by-step explanation:

The volume of a cylinder is given by the formula:

$V=\pi r^2 h$

Where

V is the volume

r is the radius

h is the height

Given, h = 9 and r = 2, we substitute and find the volume:

$V=\pi r^2 h\\V=\pi (2)^2 (9)\\V=36\pi\\V=113.097$

We need answer to nearest tenth, that is 1 decimal place, so we round of the answer as:

113.1 cubic inches

3 0

3 years ago

What is the distance from m(-1,6) to n(11,1)

NARA [144]

13

The formula for distance is √(x2-x1)^2 + (y2-y1)^2

7 0

3 years ago

Find equations of the spheres with center(3, −4, 5) that touch the following planes.a. xy-plane b. yz- plane c. xz-plane

postnew [5]

Answer:

(a) (x - 3)² + (y + 4)² + (z - 5)² = 25

(b) (x - 3)² + (y + 4)² + (z - 5)² = 9

(c) (x - 3)² + (y + 4)² + (z - 5)² = 16

Step-by-step explanation:

The equation of a sphere is given by:

(x - x₀)² + (y - y₀)² + (z - z₀)² = r² ---------------(i)

Where;

(x₀, y₀, z₀) is the center of the sphere

r is the radius of the sphere

Given:

Sphere centered at (3, -4, 5)

=> (x₀, y₀, z₀) = (3, -4, 5)

(a) To get the equation of the sphere when it touches the xy-plane, we do the following:

i. Since the sphere touches the xy-plane, it means the z-component of its centre is 0.

Therefore, we have the sphere now centered at (3, -4, 0).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, -4, 0) as follows;

$d = \sqrt{(3-3)^2+ (-4 - (-4))^2 + (0-5)^2}$

$d = \sqrt{(3-3)^2+ (-4 + 4)^2 + (0-5)^2}$

$d = \sqrt{(0)^2+ (0)^2 + (-5)^2}$

$d = \sqrt{(25)}$

d = 5

This distance is the radius of the sphere at that point. i.e r = 5

Now substitute this value r = 5 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 5²

(x - 3)² + (y + 4)² + (z - 5)² = 25

Therefore, the equation of the sphere when it touches the xy plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 25

(b) To get the equation of the sphere when it touches the yz-plane, we do the following:

i. Since the sphere touches the yz-plane, it means the x-component of its centre is 0.

Therefore, we have the sphere now centered at (0, -4, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (0, -4, 5) as follows;

$d = \sqrt{(0-3)^2+ (-4 - (-4))^2 + (5-5)^2}$

$d = \sqrt{(-3)^2+ (-4 + 4)^2 + (5-5)^2}$

$d = \sqrt{(-3)^2 + (0)^2+ (0)^2}$

$d = \sqrt{(9)}$

d = 3

This distance is the radius of the sphere at that point. i.e r = 3

Now substitute this value r = 3 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 3²

(x - 3)² + (y + 4)² + (z - 5)² = 9

Therefore, the equation of the sphere when it touches the yz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 9

(b) To get the equation of the sphere when it touches the xz-plane, we do the following:

i. Since the sphere touches the xz-plane, it means the y-component of its centre is 0.

Therefore, we have the sphere now centered at (3, 0, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, 0, 5) as follows;

$d = \sqrt{(3-3)^2+ (0 - (-4))^2 + (5-5)^2}$

$d = \sqrt{(3-3)^2+ (0+4)^2 + (5-5)^2}$

$d = \sqrt{(0)^2 + (4)^2+ (0)^2}$

$d = \sqrt{(16)}$

d = 4

This distance is the radius of the sphere at that point. i.e r = 4

Now substitute this value r = 4 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 4²

(x - 3)² + (y + 4)² + (z - 5)² = 16

Therefore, the equation of the sphere when it touches the xz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 16

3 0

4 years ago

Donald has xxx twenty-dollar bills and 111 ten-dollar bill.

Sloan [31]

Alright, so we have xxx twenty dollar bills. If we have 1 twenty dollar bill, we have 20 dollars=20*1. If we have two twenty dollar bills, we have 20+20=20*2=40 dollars, and so on. Therefore, the amount of money Donald has in twenty dollar bills is 20*the amount of dollar bills = 20*xxx. Similarly with the ten dollar bills, we have 10*the amount of 10 dollar bills = 111*10. To multiply a number by 1 with a number of 0s after it (and no other numbers), we simply add a 0 to the end of the number for the amount of 0s the number you’re multiplying it by has. Therefore, we would then have 111*10=1110. Similarly, when dividing by a number with 1 and the start and such, we move the decimal place one to the left for every 0, so 111/10=11.1 instead of 111.0. Therefore, as the amount of money Donald has is the total amount of money he has in 20 dollar bills added onto the money he has in 10 dollar bills, he has 1110+20*xxx dollars.

Feel free to ask further questions!

4 0

3 years ago

Read 2 more answers