Why is a variable exponent a number plus a variable adds eg: (x)*+(x) =?

3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round

Mariana [72]

The volume of the prop is calculated to be 2,712.96 cubic inches.

Step-by-step explanation:

Step 1:

The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.

The volume of the cone : $V=\pi r^{2} \frac{h}{3}$ = $3.14 \times 9^{2} \times \frac{14}{3}$ = 1,186.92 cubic inches.

Step 3:

The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³).

Here the radius is 9 inches. We take π as 3.14.

The volume of a full sphere = $V=\frac{4}{3} \pi r^{3}$ = $\frac{4}{3} \times 3.14 \times 9^{3}$ = 3,052.08 cubic inches.

The volume of the half-sphere = $\frac{3,052.08}{2}$ = 1,526.04 cubic inches.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume = 1,186.92 + 1,526.04 = 2,712.96 cubic inches.

5 0

3 years ago

Pastries made out of filo dough are brushed with either olive oil or butter (but not both). Pastries made out of shortcrust doug

givi [52]

Answer:

3X/20 (option a) of the pastries submitted by Rashid and Mikhail were brushed with butter

Step-by-step explanation:

Rashid pastries (R)

Mikhail pastries (M)

Rashid and Mikhail submitted a total of x pastries

R+M=x (I)

Rashid made 2/3 as many pastries as Mikhail

(2/3)*R=M (II)

Using II in I

R+(2/3)*R=x

(5/3)*R = x

R=(3/5)*x (III)

Using III in I

(3/5)*x+M=x

M=x-(3/5)*x

M=(2/5)*x (IV)

Mikhail filo dough (MF)

Mikhail shortcrust dough (MS)

Rashid filo dough (RF)

Rashid shortcrust dough (RS)

Mikhail used filo dough for all of his pastries

MF=M

MS=0

Rashid used shortcrust dough for all of his pastries

RS=R

RF=0

Filo dough (FD)

FD=RF+MF=0+MF=MF=M (V)

5/8 of the filo dough pastries were brushed with olive oil

pastries brushed with olive oil (OI)

(5/8)*FD=OI

Using V

(5/8)*M=OI

Using IV

(5/8)*(2/5)*x=OI

(1/4)*x=OI (VI)

pastries brushed with butter (B)

Pastries made out of filo dough are brushed with either olive oil or butter (but not both)

FD=OI+B

B=FD-OI

Using V and VI

B= M - (1/4)*x

Using IV

B = (2/5)*x - (1/4)*x

B= (3/20)*x

3X/20 (option a) of the pastries submitted by Rashid and Mikhail were brushed with butter

5 0

3 years ago

The total number of students enrolled in MATH 123 this semester

Kay [80]

Answer:

5796 people

Step-by-step explanation:

.28 percent of 5780 is 16.184 so added 5,780+16.184=5,796.184 but rounded to a whole person is 5,796!

7 0

3 years ago

One restaurant offers two large pizzas for the same price as two medium pizzas and a $6 pitcher of drinks. The medium pizza cost

STALIN [3.7K]

A large pizza costs $6

3 0

3 years ago

Write the phrase "one more than the product of six and nine" as a mathematical expression.

frosja888 [35]

Answer:

C. 6 ⋅ 9 + 1

Step-by-step explanation:

Start with the multiplication:

"one more than the product of six and nine"

6 ⋅ 9

Now take care of the addition by adding 1 to the product.

"one more than the product of six and nine"

6 ⋅ 9 + 1

Answer: C. 6 ⋅ 9 + 1

4 0

3 years ago

Why is a variable exponent a number plus a variable adds eg: (x)*+(x) =?​

Why is a variable exponent a number plus a variable adds eg: (x)*+(x) =?