1 7/10 is equivalent to the improper fraction 17/10
Answer:
Adult tickets =125
Child tickets = 128
Step-by-step explanation:
Let the number of adult and children tickets sold be x and y respectively
So that
x+y= 253--------1
Since total sales/receipt is $2,771
And given that tickets for a dance recital cost $15 for adults and $7 for children hence
15x+7y= 2771-------2
Solving equation 1 and 2 simultaneously we have
x+y= 253---------------1
15x+7y= 2771----------2
Let us multiply equation 1 by 15 to get equation 3 to eliminate x and subtract equation 2 from 3
15x+15y=3795---------3
-{15x+7y= 2771----------2
0+8y=1024
8y= 1024
y= 1024/8
y= 128 tickets
So solve for x let us put y= 128 in equation 1
x+ 128=253
x=253-128
x= 125 tickets
The numbers between 30 and 40 whose only factors are one and themselves, also called prime numbers, are 31 and 37.<span> Prime numbers are useful in generating numerical passwords or codes that are difficult to crack. so A) is the answer
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Answer:
24 Combinations Total
Step-by-step explanation:
METHOD 1 (no advanced math skills needed)
i. Number the friends: a, b, c, and d
ii. List all possible combinations...
- a b c d
- a b d c
- a c b d
- a c d b
- a d b c
- <u>a d c b</u>
- b a c d
- b a d c
- b c a d
- b c d a
- b d a c
- <u>b d c a</u>
- c a b d
- c a d b
- c b a d
- c b d a
- c d a b
- <u>c d b a</u>
- d a b c
- d a c b
- d b a c
- d b c a
- d c a b
- <u>d c b a</u>
To speed up the process instead of sitting here and listing 24 combinations, after two sections you can see that with friend "a" sitting all the way at the left there are six combinations and the same goes for friend "b". You can then multiply 6 (number of combinations with that friend <em>first</em>) and 4 (friends) to get 24.
METHOD 2
n! means the total number for permutations calculation (1 x 2 x ... until you reach <u><em>n</em></u><em> </em>) = 24
Let the square base of the container be of side s inches and the height of the container be h inches, then
Surface are of the container, A = s^2 + 4sh
For minimum surface area, dA / ds + dA / dh = 0
i.e. 2s + 4h + 4s = 0
6s + 4h = 0
s = -2/3 h
But, volume of container = 62.5 in cubed
i.e. s^2 x h = 62.5
(-2/3 h)^2 x h = 62.5
4/9 h^2 x h = 62.5
4/9 h^3 = 62.5
h^3 = 62.5 x 9/4 = 140.625
h = cube root of (140.625) = 5.2 inches
s = 2/3 h = 3.47
Therefore, the dimensions of the square base of the container is 3.47 inches and the height is 5.2 inches.
The minimum surface area = s^2 + 4sh = (3.47)^2 + 4(3.47)(5.2) = 12.02 + 72.11 = 84.13 square inches.
