Answer:
17. surface area ≈ 441.84
04π m² or 1387.38 m²
18. Ratio of volumes = 8/27
19. volume of the smaller solid = 339 yards³
Step-by-step explanation:
17 .
To find the surface area of the sphere we have to find the radius of the sphere first.
volume of a sphere = 4/3πr³
volume = 1548π m³
r = ?
volume of a sphere = 4/3πr³
1548π = 4/3 × π × r³
multiply both sides by 3/4
1548π × 3/4 = πr³
4644π/4 = πr³
1161π = πr³
divide both sides by π
r³ = 1161
cube root both sides
r = ∛1161
r = 10.5101942
r ≈ 10. 51
surface area of a sphere = 4πr²
surface area = 4 × π × 10.51²
surface area = 4 × 110.4601 × π
surface area = 441.8404π m²
surface area = 441.8404 × 3.14 = 1387.378856 m² ≈ 1387.38 m²
18
If two figure or solid are similar with scale factor or ratio of x/y then the ratio of their volume is (x/y)³. If the ratio of of two similar prism is 2 : 3 the volume will be (2/3)³ = 8/27 .
19
If two solids are similar then the ratio of their surface area is the squared of the scale factor.
121/361 = (x/y)²
square root both sides
x/y = 11/19
If two solids are similar then the ratio of their volume is the cube of the scale factor.
(11/19)³ = a/1747
1331/6859 = a/1747
cross multiply
6859a = 2325257
divide both sides by 6859
a = 2325257/6859
a = 339.008164455
a ≈ 339 yards³
volume of the smaller solid ≈ 339 yards³
Answer:
4/6=t/(t+1)
Step-by-step explanation:
4/6=t/(t+1)
Number of child tickets bought is 20
<h3><u>
Solution:</u></h3>
Given that It cost 5 dollars for a child ticket and 8 dollars for a adult ticket
cost of each child ticket = 5 dollars
cost of each adult ticket = 8 dollars
Let "c" be the number of child tickets bought
Let "a" be the number of adult tickets bought
Total tickets sold were 110 bringing in 820 dollars
<em>Number of child tickets bought + number of adult tickets bought = 110</em>
c + a = 110 ----- eqn 1
<em><u>Also we can frame a equation as:</u></em>
Number of child tickets bought x cost of each child ticket + number of adult tickets bought x cost of each adult ticket = 820

5c + 8a = 820 -------- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "c" and "a"
From eqn 1,
a = 110 - c ------ eqn 3
Substitute eqn 3 in eqn 2
5c + 8(110 - c) = 820
5c + 880 - 8c = 820
-3c = - 60
c = 20
Therefore from eqn 3,
a = 110 - 20 = 90
a = 90
Therefore number of child tickets bought is 20
X-20 = Y+20........ X-Y = 20+20........
X-Y = 40
AND
2Y-44=X+22............. Y-X= 44+22
Y-X=66
NOW, LET'S FIND X AND Y FROM THESE TWO EQUATIONS....
X-Y =40
Y-X= 66
IF WE COLLECT ....... 2Y = 106 AND Y = 53
THEN, USE Y IN ANY EQUATIONS FOR FINDING X
X-53 = 40 ..... X= 53+40 .......... X= 93
X= 93
Y=53
Answer:
There will be 90 ways to reach Greenup from Charleston.
Step-by-step explanation:
<em>Option C: 90 is correct.</em>
Let's name all the ways and try to visualize the roads.
C = Charleston
M = Mattoon
T = Toledo
G = Greenup
Task = Charleston to Greenup. How many different ways to reach?
1 1
2 2 1
C 3 M 3 T 2 G
4 4 3
5 5
6
So, Refer to this above diagram.
If we Start from C then go to 1 and then go to M and then go to 1 and then go to T and then go to 1 and then go G.
If you notice, in this single possibility we have 3 ways: C to 1 to M, M to 1 to T, T to 1 to G.
It means we will have: 5 x 6 x 3 = 90 number of ways to reach greenup from Charleston.