Answer:
3964 in³
Step-by-step explanation:
volume of sphere: V = 4/3 πr³
v₁ = 4/3 x 3.14 x 7³ = 1436
volume of prism: v = Bh B = 15 x 18 = 270 h = 20
v₂ = 270 x 20 = 5400
v₂ - v₁ = 5400 - 1436 = 3964 in³
Answer:
Remember that:
Speed = distance/time.
Then we can calculate the average speed in any segment,
Let's make a model where the average speed at t = t0 can be calculated as:
AS(t0) = (y(b) - y(a))/(b - a)
Where b is the next value of t0, and a is the previous value of t0. This is because t0 is the middle point in this segment.
Then:
if t0 = 100s
AS(100s) = (400ft - 0ft)/(200s - 0s) = 2ft/s
if t0 = 200s
AS(200s) = (1360ft - 50ft)/(300s - 100s) = 6.55 ft/s
if t0 = 300s
AS(300s) = (3200ft - 400ft)/(400s - 200s) = 14ft/s
if t0 = 400s
AS(400s) = (6250s - 1360s)/(500s - 300s) = 24.45 ft/s
So for the given options, t = 400s is the one where the velocity seems to be the biggest.
And this has a lot of sense, because while the distance between the values of time is constant (is always 100 seconds) we can see that the difference between consecutive values of y(t) is increasing.
Then we can conclude that the rocket is accelerating upwards, then as larger is the value of t, bigger will be the average velocity at that point.
Percentage of discount on the Marked price = 35%
Marked price of the pair of red heels that Claire falls in love with = $64.99
Then
Amount of discount on the
marked price of the pair of red heels = (35/100) * 64.99 dollars
= 0.35 * 64.99 dollars
= 22.746 dollars
= 22.75 dollars
Then
Price of the red heels after discount = (64.99 - 22.75) dollars
= 42.24 dollars
Percentage of sales tax that needs to be given by Claire = 7.5%
Amount of sales tax that needs to be given by Claire = (7.5/100) * 42.24 dollars
= 316.80/100 dollars
= 3.168 dollars
= 3.17 dollars
Then
The total price of the
red heels that Claire has to pay = (42.24 + 3.17) dollars
= 45.41 dollars
So Claire has to pay a total of $45.41 for the pair of red heels she has fallen in love with.
Answer:
3x + 6y
x = sliders
y = onion rings
Step-by-step explanation:
2:1 ratio of onion rings to sliders, add them 200+70+70 = 340,
then 1020/340 = 3, then input into an equation remembering the ratio of onion rings to sliders
Answer:
Options (3) and (6)
Step-by-step explanation:
ΔABC is a dilated using a scale factor of 
to produce image triangle ΔA'B'C'.
Since, dilation is a rigid transformation,
Angles of both the triangles will be unchanged or congruent.
m∠A = m∠A' and m∠B = m∠B'
Since, sides of ΔA'B'C' = of the sides of ΔABC
Area of ΔA'B'C' = 
Area of ΔABC > Area of ΔA'B'C'
Since, angles of ΔABC and ΔA'B'C' are congruent, both the triangles will be similar.
ΔABC ~ ΔA'B'C'
Therefore, Option (3) and Option (6) are the correct options.
