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Mariana [72]
3 years ago
5

i need help on a story problem? Jason ran 5/7 of the distance around the school track. Sara ran 4/5 of Jason's distance. What fr

action of the total distance around the track did Sara run?
Mathematics
1 answer:
julia-pushkina [17]3 years ago
3 0
The first thing you do is to find the lowest common multiple of 5 and 7.What you do on the bottom, you must do on the top 25/35 / 28/35.  The answer is 25/28.  Sara ran 25/28 of the total distance around the track. 
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12% of what number is 180? <br> A.<br> 15<br> B.<br> 150<br> C.<br> 1500<br> D.<br> 21.6
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The correct answer is C
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The game of European roulette slots: 18 red, 18 black, and I green. A ball is spun onto the wheel and will eventually land ina s
Anestetic [448]

Answer:

(a) E(x) = -0.081  S.D = 3

(b) E(x) = -0.081  S.D = 1.73

(c) it is less risky to bet $1 in three different rounds as compared to betting $3 in a single round.    

Step-by-step explanation:

(a) You bet $3 on a single round which means that if you win the game, your amount will double ($6), your profit will be $3. Whereas, if you lose the round, your profit will be -$3. You can only bet on red or black and both have 18 slots each.

So, the probability of landing the ball in a red/black slot = 18/37. This is the probability of winning. The probability of losing can be calculated as 1-18/37 = 19/37.

We can make a probability distribution table:

x                    3             -3

P(X=x)         18/37      19/37

Expected value E(x) can be calculated as:

E(x) = ∑ x.P(x)

      = (3)(18/37) + (-3)(19/37)

E(x) = -0.081

Standard deviation can be calculated by the following formula:

Var(x) = E(x²) - E(x)²

S.D = √Var(x)

We need to first calculate E(x²).

E(x²) = ∑x².P(x)

       = (3)²(18/37) + (-3)²(19/37)

       = (9)(18/37) + (9)(19/37)

E(x²) = 9

Var(x) = E(x²) - E(x)²

         = 9 - (-0.081)²

Var(x) = 8.993

S.D = √8.993

S.D = 2.99 ≅ 3

(b) Now, the betting price is $1 and 3 rounds are played. We will compute the expectation for one round and then add it thrice to find the expectation for three rounds. Similarly, for the standard deviations, we will add the individual variances and then consider the square root of it.

E(x) = ∑ x.P(x)

      = (1)(18/37) + (-1)(19/37)

E(x) = -0.027

Standard deviation can be calculated by the following formula:

Var(x) = E(x²) - E(x)²

S.D = √Var(x)

We need to first calculate E(x²).

E(x²) = ∑x².P(x)

       = (1)²(18/37) + (-1)²(19/37)

       = (1)(18/37) + (1)(19/37)

E(x²) = 1

Var(x) = E(x²) - E(x)²

         = 1 - (-0.027)²

Var(x) = 0.9992

The expectation for one round is -0.027

For three rounds,

E(x₁ + x₂ + x₃) = E(x₁) + E(x₂) + E(x₃)

                     = (-0.027) + (-0.027) + (-0.027)

E(x₁ + x₂ + x₃) = -0.081

Similarly, the variance for one round is 0.9992.

Var (x₁ + x₂ + x₃) = Var(x₁) + Var(x₂) + Var(x₃)

                           = 0.9992 + 0.9992 + 0.9992

Var (x₁ + x₂ + x₃) = 2.9976

S.D = √2.9976

S.D = 1.73              

(c) The expected values for both part (a) and (b) are the same but the standard deviation is lower in part (c) as compared to (b). Since the standard deviation is less in part (c), it means that it is <u>less risky to bet $1 in three different rounds as compared to betting $3 in a single round.</u>            

5 0
3 years ago
the height y of a ball thrown by a child is given by y = -1/12x^2 + 2x + 4. how high is the ball when it is at its maximum heigh
zhuklara [117]

Answer:

The height of ball when it is at maximum height is 12  unit

Step-by-step explanation:

Given as :

A ball is thrown by child to height y

And y as a function  x is y = -\frac{1}{12}x^{2}+2x+4

So, for maximum value of height ,

\frac{\partial y}{\partial x}  = 0

Or , \frac{\partial (-\frac{1}{12}x^{2}+2x+4)}{\partial x} = 0

Or, -\frac{1}{12}(2x)+2 = 0

Or, \frac{1}{12}(2x) = 2

or,  x = 12

Hence The height of ball when it is at maximum height is 12  unit  Answer

3 0
3 years ago
Explain how to determine the
Paladinen [302]

Answer: Compound probability is equal to the probability of the first event multiplied by the probability of the second event

HOPE THIS HELPS

3 0
3 years ago
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