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Svetradugi [14.3K]
3 years ago
13

Complete the square of x^2+16x=1

Mathematics
1 answer:
Rus_ich [418]3 years ago
5 0
The answer is approximately .062 and -16.06

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A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if
topjm [15]

Answer:

a) The expected value is \frac{-1}{15}

b) The variance is  \frac{49}{45}

Step-by-step explanation:

We can assume that both marbles are withdrawn at the same time. We will define the probability as follows

#events of interest/total number of events.

We have 10 marbles in total. The number of different ways in which we can withdrawn 2 marbles out of 10 is \binom{10}{2}.

Consider the case in which we choose two of the same color. That is, out of 5, we pick 2. The different ways of choosing 2 out of 5 is \binom{5}{2}. Since we have 2 colors, we can either choose 2 of them blue or 2 of the red, so the total number of ways of choosing is just the double.

Consider the case in which we choose one of each color. Then, out of 5 we pick 1. So, the total number of ways in which we pick 1 of each color is \binom{5}{1}\cdot \binom{5}{1}. So, we define the following probabilities.

Probability of winning: \frac{2\binom{5}{2}}{\binom{10}{2}}= \frac{4}{9}

Probability of losing \frac{(\binom{5}{1})^2}{\binom{10}{2}}\frac{5}{9}

Let X be the expected value of the amount you can win. Then,

E(X) = 1.10*probability of winning - 1 probability of losing =1.10\cdot  \frac{4}{9}-\frac{5}{9}=\frac{-1}{15}

Consider the expected value of the square of the amount you can win, Then

E(X^2) = (1.10^2)*probability of winning + probability of losing =1.10^2\cdot  \frac{4}{9}+\frac{5}{9}=\frac{82}{75}

We will use the following formula

Var(X) = E(X^2)-E(X)^2

Thus

Var(X) = \frac{82}{75}-(\frac{-1}{15})^2 = \frac{49}{45}

7 0
3 years ago
Solve this pls<br><br> 6i&lt;5i+3u
lions [1.4K]

i < 3u

Step-by-step explanation:

6i < 5i + 3u

6i - 5i < 3u

i < 3u

8 0
2 years ago
A) Work out the value of angle x.<br>X<br>X=<br>b) Give reasons for your answer.​
Dmitriy789 [7]

Answer:

x = 60° (Alternate angles)

Step-by-step explanation:

a) x = 60°

b) Reason: Alternate angles

5 0
3 years ago
What is the Difference between 8 and -4
pav-90 [236]

Answer:

One is postive and the other is negative but both are integers and whole numbers

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Which is bigger 0.17 or 0.165
Bogdan [553]
0.17 is bigger because you compare the values of the number in each place. There is no whole number, the tenths place is equal. Then in the hundredths place you have a 6 and a 7. 6<7 so therefore 0.17> 0.165. To help yourself out u can add a 0 at the end to then more easily compare .170 to .165
5 0
3 years ago
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