Answer:
Sharing cone holds 9 times more popcorn than a skinny cone.
Step-by-step explanation:
Height of each cone = 9 inches
Radius of the sharing size cone = 3 times radius of the skinny size cone
Let the radius of skinny size cone = r
Then radius of the sharing size cone = 3r
Volume of the sharing size cone = ![\frac{1}{3}(\pi )(\text{Radius})^{2}(\text{Height})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%28%5Cpi%20%29%28%5Ctext%7BRadius%7D%29%5E%7B2%7D%28%5Ctext%7BHeight%7D%29)
= ![\frac{1}{3}(\pi )(3r)^{2}(9)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%28%5Cpi%20%29%283r%29%5E%7B2%7D%289%29)
= 27πr²
Volume of the skinny size cone = ![\frac{1}{3}(\pi )(\text{Radius})^{2}(\text{Height})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%28%5Cpi%20%29%28%5Ctext%7BRadius%7D%29%5E%7B2%7D%28%5Ctext%7BHeight%7D%29)
= ![\frac{1}{3}(\pi )(r)^{2}(9)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%28%5Cpi%20%29%28r%29%5E%7B2%7D%289%29)
= 3πr²
Ratio of the volumes = ![\frac{\text{Volume of sharing size cone}}{\text{Volume of skinny size cone}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BVolume%20of%20sharing%20size%20cone%7D%7D%7B%5Ctext%7BVolume%20of%20skinny%20size%20cone%7D%7D)
=
= 9
Therefore, sharing cone holds 9 times more popcorn than a skinny cone.
f(x) = (x -
)² - ![\frac{85}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B85%7D%7B4%7D)
the equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
given a quadratic in standard form : y = ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
= - ![\frac{b}{2a}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7B2a%7D)
f(x) = x² - 11x + 9 is in standard form
with a = 1, b = - 11 and c = 9
= -
= ![\frac{11}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B11%7D%7B2%7D)
substitute this value into the equation for y- coordinate
y = (
)² - 11(
) + 9
=
-
+
= - ![\frac{85}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B85%7D%7B4%7D)
f(x) = (x -
)² -
← in vertex form
Answer:
13,I
Step-by-step explanation:
set the 3 number is 3/5, x,y
product of them
3 /5 xy = 7:6
xy = 7:6 x 5 /3
Xy = 13
So the two number is 13, 1
Answer:
No, Jason did not solve correctly
Step-by-step explanation:
Jason has saved 41% of what he needs to buy a 73$ skateboard.
Jason found out 50% of 70 is the same things as 70 divided by .50= 140. So he has more than enough to purchase the skateboard. Did he solve correctly
Let compare both statements
50% of 70 = 70 ÷ 0.5 (140)
50% × 70 = 140
50/100 × 70 = 140
35 ≠ 140
JASON DID NOT SOLVE CORRECTLY
This is because the left-hand side used the operation of multiplication while the right-hand side used the operation of division.
Answer:
115 mg
Step-by-step explanation:
The 50th percentile has a corresponding z-score of z = 0. The z-score, for any given value of caffeine, X, is given by:
![z = \frac{X-mean}{SD}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX-mean%7D%7BSD%7D)
Therefore, if z=0, then X must be equal to the mean value of the normal distribution, which is 115 mg. Thus, the 50th percentile value of caffeine content is 115 mg.