Hanna is driving 480 miles. She has already driven 312 miles. What percent of her trip has she completed?

Mrs. Owens was making Thanksgiving dinner for 10

saul85 [17]

Well if she is making dinner for 10 people and each person want 2 pieces then you need to multiple 10 x 2 = 20. So she is going to need to make 20 pieces.

If each of her pumpkin pies only has 8 pieces then she is going to have to make 3 pies.

3 pies x 8 pieces = 24 pieces of pumpkin pie. So she has to make 3 pies because she needs 20 pieces since everyone wants 2.

In conclusion Mrs. Owens has to make 3 pies and she is going to have 4 pieces left over.

7 0

3 years ago

Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

DiKsa [7]

Answer:

The standard equation of the sphere is $(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Let the first endpoint be represented as $(x_{1}, y_{1}, z_{1})$ and the second endpoint be $(x_{2}, y_{2}, z_{2})$ .

Hence,

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Midpoint = $(\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})$

Midpoint = $(\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\$

Midpoint = $(5, 5, 4)$

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

$d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }$

$d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}$

$d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}$

$d = \sqrt{16 +196 + 0$

$d =\sqrt{212}$

$d = 2\sqrt{53}$

This is the diameter

To find the radius, r

From $Radius = \frac{Diameter}{2}$

$Radius = \frac{2\sqrt{53} }{2}$

∴ $Radius = \sqrt{53}$

r = $\sqrt{53}$

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is $(5, 5, 4)$

Radius of the sphere is $\sqrt{53}$

The equation of a sphere of radius r and center $(h,k,l)$ is given by

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

Hence, the equation of the sphere of radius $\sqrt{53}$ and center $(5, 5, 4)$ is

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}$

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

This is the standard equation of the sphere

6 0

3 years ago

HALP Can someone explain why this is a math question

erica [24]

Answer:

If the robot has more mass, then it will take a bigger force to lift up another object. If the robot is going to lift something up, it will use its arms, and its arms have mass, and the object has a mass as well. If the robot's arms have a mass of 10kg, and the object has a mass of 12kg, it will use a certain amount of force to lift up the object using it's arms. If the the robots arms were 5kg instead, it would take less force to lift of the same object using its arms.

4 0

3 years ago

A baseball player comes up to bat 3 times during a league game. He either gets a hit or gets an out. What is the probability tha

KiRa [710]

Answer:

Since there are 2 possibilities for each bat (hit or out), the amount of total possibilities is 2 * 2 * 2 = 8. There is only one possibility out of those eight that gives us three hits, therefore the probability is 1 / 8 or 0.125.

4 0

3 years ago

You are making a scaledrawing of a room using a scale of1 inch : 4 feet.a. The room is 14 feet by 18 feet. Find itsdimensions in

lilavasa [31]

Answer:

a. 3.5 inches by 4.5 inches

b. 1.5 inches

c. Divide 48 inches by 2 and multiply 1 inch by 12 to get a scale of 1 : 2

Step-by-step explanation:

A scale is a representative fraction showing the relationship between length on a drawing and actual length.

i.e scale = $\frac{length on a drawing}{actual length}$

scale = 1 inch : 4 feet

a. The dimensions in the drawing can be determined as;

1 inch : 4 feet implies an inch on the drawing equates 4 feet on actual length.

$\frac{14}{4}$ = 3.5 inches

$\frac{18}{4}$ = 4.5 inches

Dimensions on drawing is 3.5 inches by 4.5 inches.

b. The length of the sofa is 6 feet, its length on the drawing is;

$\frac{6}{4}$ = 1.5 inches

c. To enlarge the scale so as to double the dimensions of the drawing, we have;

12 inches = 1 feet

4 feet = 4 × 12 = 48 inches

given scale = 1 inch : 48 inches

Thus, divide 48 inches by 2 and multiply 1 inch by 12.

scale = 12 inch : 24 inch

scale = 1 : 2

To double the dimensions of the drawing, the scale required is 1 : 2. This implies that a unit measure on the drawing is synonymous to 2 measures on the actual reading.

6 0

3 years ago