Let a ault tickets and s student tickets be sold.
a+s=56
13a+8s=568
s=56-a
13a+8(56-a)=568
13a+448-8a=568
5a+448=568
5a=120
a=24
s=56-24=32
24 adult tickets and 32 student tickets are sold.
Given:
The expression is
![\dfrac{\sqrt[3]{9}}{\sqrt[3]{4}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B3%5D%7B9%7D%7D%7B%5Csqrt%5B3%5D%7B4%7D%7D)
To find:
The simplified form of given expression.
Solution:
We have,
It can be written as
![\dfrac{\sqrt[3]{9}}{\sqrt[3]{4}}=\sqrt[3]{\dfrac{9}{4}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B3%5D%7B9%7D%7D%7B%5Csqrt%5B3%5D%7B4%7D%7D%3D%5Csqrt%5B3%5D%7B%5Cdfrac%7B9%7D%7B4%7D%7D)
![\left[\because \dfrac{\sqrt[a]{x}}{\sqrt[a]{y}}=\sqrt[a]{\dfrac{x}{y}}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbecause%20%5Cdfrac%7B%5Csqrt%5Ba%5D%7Bx%7D%7D%7B%5Csqrt%5Ba%5D%7By%7D%7D%3D%5Csqrt%5Ba%5D%7B%5Cdfrac%7Bx%7D%7By%7D%7D%5Cright%5D)
Therefore, the simplified form of given expression is ![\sqrt[3]{\dfrac{9}{4}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cdfrac%7B9%7D%7B4%7D%7D)
.
Note: We can further simplify this expression but be need use exponential properties.
Answer:
1) 147
2) 87
Step-by-step explanation:
1) Area of triangle = × base length × height
= 
× 14 × 10
= 70
Area of a semicircle = 
( r is the radius)
Radius = half of diameter = 
= 7m
Area of semicircle = 
= 77 ( Nearest whole number )
Total area = 77 + 70 = 147
2) Divide the shape into 2 rectangles
Area of a rectangle = length × width
Rectangle 1 = 7 × ( 3+3+5 )
= 7 × 11 = 77
Rectangle 2 = 2 × 5
= 10
Total Area = 77 + 10 = 87
Answer:
0.10512
Step-by-step explanation:
Given the following :
Mean number of calls(μ) in 2 hours = 14
2 hours = 60 * 2 = 120 minutes
Average number of calls in 45 minutes :
= (45 / 120) * 14
= 0.375 * 14
= 5.25
Now find P( x ≤ 2) = p(x = 0) + p( x = 1) + p(x = 2)
Using the poisson probability formula:
P(x, μ) = [(e^-μ) * (μ^x)] / x!
Where :
e = euler's constant
μ = 5.25
x = 0, 1, 2
Using the online poisson probability calculator :
P(x, 5.25) = P( x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)
P(x, 5.25) = P( x ≤ 2) = 0.00525 + 0.02755 + 0.07232 = 0.10512
Answer:
b^2 + 4 a b - 2 b - 2 a^2 + -5 a
Step-by-step explanation:
Simplify the following:
-2 a (a + b - 5) + 3 (2 b - 5 a) + b (6 a + b - 8)
-2 a (-5 + a + b) = 10 a - 2 a^2 - 2 a b:
10 a - 2 a^2 - 2 a b + 3 (2 b - 5 a) + b (6 a + b - 8)
3 (2 b - 5 a) = 6 b - 15 a:
10 a - 2 a^2 - 2 a b + 6 b - 15 a + b (6 a + b - 8)
b (-8 + 6 a + b) = -8 b + 6 a b + b^2:
10 a - 2 a^2 - 2 a b - 15 a + 6 b + -8 b + 6 a b + b^2
Grouping like terms, 10 a - 2 a^2 - 2 a b - 15 a + 6 b - 8 b + 6 a b + b^2 = b^2 + (6 a b - 2 a b) + (6 b - 8 b) - 2 a^2 + (10 a - 15 a):
b^2 + (6 a b - 2 a b) + (6 b - 8 b) - 2 a^2 + (10 a - 15 a)
a b 6 + a b (-2) = 4 a b:
b^2 + 4 a b + (6 b - 8 b) - 2 a^2 + (10 a - 15 a)
6 b - 8 b = -2 b:
b^2 + 4 a b + -2 b - 2 a^2 + (10 a - 15 a)
10 a - 15 a = -5 a:
Answer: b^2 + 4 a b - 2 b - 2 a^2 + -5 a
