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Alexeev081 [22]
3 years ago
13

Suppose you have a 6-face unfair dice with numbers 1,2,3,4,5,6 on each of its faces. If the probability distribution of throwing

a number up is as follows:
1 with probability 1/12
2 with probability 1/12
3 with probability 1/12
4 with probability 1/12
5 with probability 1/12
6 with probability 1/2

Which of the following statement is correct?

a. The mathematical expectation of the dice throwing a number up is 3.5
b. The mathematical expectation of the dice throwing a number up is 6
c. The mathematical expectation of the dice throwing a number up is 4.25
d. This is not a proper probability distribution because all the probabilities do not sum up to one
Mathematics
1 answer:
kotegsom [21]3 years ago
4 0

Answer:

D is correct

Step-by-step explanation:

Here, we want to select which of the options is correct.

The correct option is the option D

Since the die is unfair, we expect that the probability of each of the numbers turning up

will not be equal.

However, we should also expect that if we add the chances of all the numbers occurring together, then the total probability should be equal to 1. But this does not work in this case;

In this case, adding all the probabilities together, we have;

1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/2

= 5(1/12) + 1/2 = 5/12 + 1/2 = 11/12

11/12 is not equal to 1 and thus the probability distribution cannot be correct

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Maria scored 72, 97, and 82 on her first three math tests. She wants to have a mean score of 82 for the quarter. How many points
Rom4ik [11]

Answer:

<em>She needs </em><em>77 </em><em>on her last test to earn an 82 for the quarter.</em>

Step-by-step explanation:

Maria scored 72, 97, and 82 on her first three math tests.

She wants to have a mean score of 82 for the quarter.

Let us assume that she must score x on her last test to earn an 82 for the quarter.

So the average score will be,

=\dfrac{72+97+82+x}{4}

But the average score is given as 82, so

\Rightarrow \dfrac{72+97+82+x}{4}=82

\Rightarrow 72+97+82+x=82\times 4

\Rightarrow 72+97+82+x=328

\Rightarrow x=328-72-97-82

\Rightarrow x=77

3 0
3 years ago
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What is the solution to the equation x + 7.5 = 21.5? A.x = 2.9 B.x = 7.8 C.x = 14 D.x = 29
dedylja [7]
X+7.5=21.5
Subtract 7.5 from both sides
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3 years ago
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Describe how you would find the sum of 24,36,and 13.
fenix001 [56]
I would add 24 and 36, to make 60, then I would tack on 13 and get 73.
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3 years ago
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How much material was required for each dresses of the same size if it took 5 1/2 yards for both ?
ki77a [65]

Answer:

2.75 yards

Step-by-step explanation:

If it took both (meaning 2) dresses a certain amount, half of that amount is one dress. So, we need to divide 5 1/2 by 2

*1/2 of 1 = 0.5

0.5 + 5 = 5.5

5.5 / 2 = 2.75

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7 0
2 years ago
Worth 17 points! Help me please!!! Look in the picture
ivanzaharov [21]

Answer:

Part A

1. After 4 weeks of work, Jeremy has saved <u>300</u>

2. Jeremy worked <u>8</u> weeks in order to save $600

3. For every one week of work, Jeremy saved <u>75</u> dollars

4. If Jeremy works 15 weeks, then he can expect to save <u>1,125</u> dollars

Part B

1. Saeed orders 15 meals and his total cost of delivery is <u>$24</u>

2. Saeed paid $32 to have <u>20</u> meals delivered

3. For every meal delivered, Saeed is charged <u>$1.6</u>

4. If Saeed pays $19.20 in delivery fees then he ordered <u>12</u> meals

Step-by-step explanation:

Part A

The given graph gives the proportional relationship between total amount saved and the number of weeks worked

1. Reading from the graph, at the point where the vertical line from point 4 touches the line of the graph, an horizontal line to the vertical y-axis touches the y-axis at 300

Therefore;

After 4 weeks of work, Jeremy has saved <u>300</u>

2. The point where an horizontal line from point 600 on the vertical y-axis touches the line of the graph, a vertical line drawn to the horizontal, x-axis touches the x-axis at 8

Therefore;

Jeremy worked <u>8</u> weeks in order to save $600.

3. The rate of change of the amount saved to the number of weeks worked, 'm', for the given proportional relationship (straight line relationship, passing through the origin) is given as follows;

Rate of change, m = Constant = y/x

∴ Rate of change of the amount saved to the number of weeks worked = (300-0)/(4 weeks- 0 week) = 75/week

Therefore;

For every one week of work, Jeremy saved <u>75</u> dollars

4. The amount Jeremy would have saved in 15 weeks, 'A', is given as follows;

A = m × n

Where;

m = The rate of change of the amount saved to the number of weeks worked = 75/week

n = The number of weeks worked

∴ A = 75/week × 15 = $1,125

Therefore;

If Jeremy works 15 weeks, then he can expect to save <u>1,125</u> dollars

Part B

From the graph, we have;

1. From the graph there is a proportional relationship between the total cost of delivery and the number of meals

At the point a vertical line drawn to the line of the graph from 15 on the horizontal axis (number of meals), a horizontal line drawn to the vertical y-axis touches the y-axis at 24

Therefore;

1. Saeed orders 15 meals and his total cost of delivery is <u>$24</u>

2. From the point where the horizontal line from 32 on the vertical axis touches the linear graph of the relationship between the total cost of delivery and the number of meals, a vertical line drawn down to the horizonal axis touches the horizontal x-axis at 20

Therefore;

Saeed paid $32 to have <u>20</u> meals delivered

3. The rate of change of the total cost of delivery to the number of meals, 'm', is given as follows;

m = y/x (for proportional relationships)

Taking any corresponding 'x' and y-values

m = 16/10 = 32/20 = 24/15 = 1.6 Dollars/meal

Therefore;

For every meal delivered, Saeed is charged <u>$1.6</u>

4. From m = y/x = 1.6

When y = $19.20

x = y/m = $19.20/($1.6/meal) = 12 meals

Therefore;

If Saeed pays $19.20 in delivery fees then he ordered <u>12</u> meals.

3 0
3 years ago
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