Answer:
6
Step-by-step explanation:
first, we need to find the GCF (Greatest Common Factor) which is the highest number that can go into every number in the equation (In this case, those numbers are 24 and 30)
The GCF for this would be 6, meaning that there would be 6 bags with and equal amount of granola bars and protein bars.
To be more specific, every bag would have 4 granola bars and 5 protein bars.
Answer:
The area of the circular ring is 53.73 π sq. yards
Step-by-step explanation:
The diameter of the skating ring = 44 ft
Diameter = 2 x Radius
⇒Radius of the ring = 44 / 2 = 22 ft
Now, 1 ft = 0.333333 yards
⇒22 ft = 22 x 0.333333 yards = 7.3333 yards
Now, Area of the circular Ring = 
or, 
= 53.73 π sq. yards
or, the area of the circular ring is 53.73 π sq. yards
Answer:
The answer is A:More than 75% of the students prefer Alternative or Hip Hop music.
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k )² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² - 8x + 8y + 23 = 0
collect the x and y terms together and subtract 23 from both sides
x² - 8x + y² + 8y = - 23
using the method of completing the square
add ( half the coefficient of the x / y terms )² to both sides
x² + 2(- 4)x + 16 + y² + 2(4)y + 16 = - 23 + 16 + 16
(x - 4)² + (y + 4)² = 9 ← in standard form
with centre = (4, - 4 ) and r =
= 3
this is shown in graph b
Answer:
Step-by-step explanation:
Since the cube fits perfectly in the sphere, it means that the diagonal of the cube will form the diameter of the sphere. In a cube, all sides are equal. To determine the length of its diagonal, d, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
d² = 10² + 10² = 200
d = √200 = 14.14cm
Formula for finding the volume of a sphere is expressed as
Volume = 4/3 × π × r³
Radius of sphere = diameter/2 = 14.14/2 = 7.07cm
Volume = 4/3 × π × 7.07³ = 471.19π cm³