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xxMikexx [17]
3 years ago
6

So far, Ricardo has scores of 13, 17, 19 and 21 points for the first four rounds of a dice game. What does he need the total sco

re to be for the next two rounds combined in order to achieve an average score of 20 points per round for all six rounds?
Mathematics
1 answer:
posledela3 years ago
3 0

Answer:

40 points

Step-by-step explanation:

The score for the first four rounds of the game is 13, 17, 19, and 21 points.

Let S_5 and S_6 be the scores of the fifth and sixth games respectively in order to achieve an average score of 20 points per round for all six rounds.

\text{Average score} = \frac{\text{Sum of the scores of all the rounds}}{\text{Total number of the rounds}}

\Rightarrow 20=\frac{13+17+19+21+S_5+S_6}{6}

\Rightarrow 20\times6=80+S_5+S_6

\Rightarrow S_5+S_6=120-80=40.

Hence, the combined score of the fifth and sixth rounds are 40 points.

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The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation
balu736 [363]

Answer: 0.16

Step-by-step explanation:

Given that the run times provided are normally distributed ;

Mean(x) of distribution = 3 hours 50 minutes

Standard deviation(s) = 30 minutes

The probability that a randomly selected runner has a time less than or equal to 3 hours 20 minutes

3 hours 20 minutes = (3 hrs 50 mins - 30 mins):

This is equivalent to :

[mean(x) - 1 standard deviation]

z 1 standard deviation within the mean = 0.84

z, 1 standard deviation outside the mean equals:

P(1 - z value , 1standard deviation within the mean)

1 - 0.8413 = 0.1587

= 0.16

7 0
3 years ago
John wants to make a 100 ml of 6% alcohol solution mixing a quantity of a 3% alcohol solution with an 8% alcohol solution. What
mart [117]

Answer:

-50 ml of 3% alcohol solution and 150 ml of 8% alcohol solution

Step-by-step explanation:

For us to solve this type of mixture problem, we must represent the problem in equations. This will be possible by interpreting the question.

Let the original volume of the first alcohol solution be represented with x.

The quantity of the first alcohol solution needed for the mixture is 3% of x

                   ⇒ \frac{3}{100} * x

                       = 0.03x

Let the original volume of the second alcohol solution be represented with y.

The quantity of the second alcohol solution needed for the mixture is 5% of y

                   ⇒ \frac{5}{100} * y

                       = 0.05y

The final mixture of alcohol solution is 6% of 100 ml

                 ⇒ \frac{6}{100} * 100 ml

                       = 6 ml

Sum of values of two alcohol solutions = Value of the final mixture

                     0.03x + 0.05y = 6 ml               ..........(1)

Sum of original quantity of each alcohol solution = Original volume of the of mixture

                     x + y = 100 ml                          ..........(2)      

For easy interpretation, I will be setting up a table to capture all information given in the question.

Component                       Unit Value      Quantity(ml)       Value

3% of Alcohol solution        0.03                 x                     0.03x

8% of Alcohol solution        0.08                 y                     0.08y

Mixture of 100ml of 6%        0.06               100                       6    

                                                                x + y = 100       0.03x + 0.08y =6

Looking at the equations we derived, we have two unknowns in two equations which is a simultaneous equation.

                                0.03x + 0.05y = 6 ml               ..........(1)

                                x + y = 100 ml                           ..........(2)    

Using substitution method to solve the simultaneous equation.

Making x the subject of formula from equation (2), we have,

                                x  = 100 - y                                 ..........(3)

Substituting  x  = 100 - y from equation (3) into equation (1)

                               0.03(100 - y) + 0.05y = 6  

                               3 - 0.03y + 0.05y = 6  

Rearranging the equation,            

                               0.05y - 0.03y = 6 - 3

                               0.02y = 3

                               y = \frac{3}{0.02}

                               y = 150 ml

Substituting y = 150 ml into equation (3) to get x

                              x  = 100 - 150 ml

                              x = - 50 ml

The quantity of the first alcohol solution needed for the mixture for 3% is - 50 ml

The quantity of the second alcohol solution needed for the mixture for 5% is 150 ml

This solution means 50 ml of the first alcohol solution must be removed from the mixture with 150 ml of the second alcohol solution to get a final mixture of 100 ml of 6% alcohol solution.

3 0
3 years ago
Which represents the number 16,807 in exponential form
Naya [18.7K]
7^5. Found by trial and error.
3 0
3 years ago
QUESTION ON PIC !THX
Aliun [14]

Answer:

Step-by-step explanation:

The original price was 43 dollars

The new price is 55/100 * 43

The new price is 2365/100

The new price is 23.65 dollars

2365 came from multiplying 43 * 55 which is 2365

4 0
2 years ago
Can someone help me please
Neporo4naja [7]

If Deliah does jumping jacks at a constant rate, this means that she does them at the same pace or you could say that she does the same amount of jumping jacks in a specified amount of time, ie. if you counted how many jumping jacks she did in one minute, it would be same as how many she would complete in the next minute, and the next, and so on.

Now given that she does 184 jumping jacks in four minutes, and she has kept a constant pace throughout, to find out how many she does each minute, we simply need to divide the number of jumping jacks she does in 4 minutes by 4. Thus:

Jumping jacks in 1 minute = Jumping jacks in 4 minutes / 4

= 184 / 4

= 46

Thus, Deliah can do 46 jumping jacks per minute.

5 0
3 years ago
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