Answer:
29.11
Step-by-step explanation:
This is clearly cos. So make an equation of cos equals 9 / x. Then use cross product to get x times cos equals 9. Finally divide by cos and use the calcuator to get x equals 29.11.
No. of children in lamb, chicken, duck, and turkey category is 66, 24, 18 and 12 respectively.
<h3>What is percentage ?</h3>
Percentage is the value per hundredth.
According to the given question a survey was carried out among 120 school children looked at which type of meat they preferred. 55% said they preferred lamb,20% said they preferred chicken, 15% preferred duck and 10% turkey and we have to calculate no. of children in each category.
55% said they preferred lamb, So the no. of students i this category is
= (55/100)×120
= 66 children.
20% said they preferred chicken, So the no. of children in this category is
= (20/100)×120
= 24 children.
15% said they preferred duck, So the no. of children in this category is
= (15/100)×120
= 18 children.
10% said they preferred turkey, So the no. of children in this category is
= (10/100)×120
= 12 children.
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Answer:
a) P ( E | F ) = 0.54545
b) P ( E | F' ) = 0
Step-by-step explanation:
Given:
- 4 Coins are tossed
- Event E exactly 2 coins shows tail
- Event F at-least two coins show tail
Find:
- Find P ( E | F )
- Find P ( E | F prime )
Solution:
- The probability of head H and tail T = 0.5, and all events are independent
So,
P ( Exactly 2 T ) = ( TTHH ) + ( THHT ) + ( THTH ) + ( HTTH ) + ( HHTT) + ( HTHT) = 6*(1/2)^4 = 0.375
P ( At-least 2 T ) = P ( Exactly 2 T ) + P ( Exactly 3 T ) + P ( Exactly 4 T) = 0.375 + ( HTTT) + (THTT) + (TTHT) + (TTTH) + ( TTTT)
= 0.375 + 5*(1/2)^4 = 0.375 + 0.3125 = 0.6875
- The probabilities for each events are:
P ( E ) = 0.375
P ( F ) = 0.6875
- The Probability to get exactly two tails given that at-least 2 tails were achieved:
P ( E | F ) = P ( E & F ) / P ( F )
P ( E | F ) = 0.375 / 0.6875
P ( E | F ) = 0.54545
- The Probability to get exactly two tails given that less than 2 tails were achieved:
P ( E | F' ) = P ( E & F' ) / P ( F )
P ( E | F' ) = 0 / 0.6875
P ( E | F' ) = 0
(a) 3x=4(x-2.25) (or simplified: 3x=4x-9)
(b) 3x=4x-9
0=x-9
x=$9
(c) 3x9=27
4x9=36
36-9=27
and 27=27 therefore they spent the same and it is correct
(d) Tanya's items cost $9 each and Tony's items cost $2.25 less than this, or $6.75
Let the first number be represented by "x".
Let the second number be represented by "y".
"Four times a number..." = 4x
"... minus 5..." = 4x - 5
"... times another number..." = y(4x - 5)
"... is equal to 21." = y(4x - 5) = 21
y(4x - 5) = 21
"Three times the sum of the two numbers (x & y) is 36." = 3(x +y) = 36
3(x + y) = 36
y(4x - 5) = 21
1) solve for "y"
1) y(4x - 5) = 21
2) 4xy - 5y = 21
3) 4xy/4x - 5y = 21/4x
(what you do to one side of the equals sign, you must do to the other so 4x cancels out on the left side, and on the right side you have to divide 21 by 4x)
4) y - 5y/-5 = 5.25x/-5
5) y + y = -1.05x
6) 2y = -1.05x
7) 2y/2 = -1.05x/2
8) y = -.525x
2) substitute "y" in for the second equation
1) 3(x + (-.525x)) = 36
(notice how you now only have x's in this equation)
3) solve for x
1) 3x - 1.575x = 36
2) 1.425x = 36
3) 1.425x/1.425 = 36/1.425
4) x = 25.3
4) finish finding "y" in either one of the equations using the answer you got for "x"
1) y(4(25.3) - 5) = 21
2) y(101.2 - 5) = 21
3) y(96.2) = 21
4) 96.2y = 21
5) 96.2y/96.2 = 21/96.2
6) y = .22
5) check your work by substituting the two answers back into one of the equations
1) .22(4(25.3) - 5) = 21
2) .22(101.2 - 5) = 21
3) .22(96.2) = 21
4) 21.164 = 21
(round down to get the answer)
