In this card game, a player is dealt 10 cards. A player wins $1,000,000 if he is dealt 8 hearts. Use combinatorics to set up your problem a. Calculate the probability a player is dealt exactly 8 hearts b. Calculate the probability a player is dealt exactly 8 hearts if the first tweo cards he was dealt were diamonds. 2

Answers

Answer 1

Answer:

Assume a standard deck of 52 cards with 4 suits of 13 cards each.

a. There are $\dbinom{13}8\dbinom{39}2$ ways of being dealt a hand consisting of 8 hearts and 2 non-hearts, so the probability of being dealt such a hand is

$\frac{\dbinom{13}8\dbinom{39}2}{\dbinom{52}{10}}\approx0.0000602823$

b. This time, the non-hearts specifically belong to the suit of diamonds, for which there are $\dbinom{13}2$ ways of getting drawn, so the probability is

$\frac{\dbinom{13}8\dbinom{13}2}{\dbinom{52}{10}}\approx0.0000063455$

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The salary of members of two governing bodies in 2008 was $167.2

167.2 thousand, and has increased by approximately $

2

2 thousand per year since then.

Complete parts a. and b.

Answers

Complete Question

The salary of members of two governing bodies in 2008 was $167.2 thousand, and has increased by approximately $2 thousand per year since then. Complete parts (a) and (b).

(a) Complete the following table to help find an expression that stands for the the salary (in thousands of dollars) of members of the two governing bodies t years since 2008.

Number of years and salaries of members of the two governing bodies

$\left|\begin{array}{c|c}-------&------\n$Years since 2008&$Salary (thousands of dollars)\n-------&------\n0&(2*--) + --\n1&(2*--) + --\n2&(2*--) + --\n3&(2*--) + --\n4&(2*--) + --\nt&(2*--) + --\end{array}\right| \n$

(b) Evaluate the expression that is found in part (a) for t = 5. What does the result means in this situation?

Answer:

(a) $S(t)=2t+167.2$

(b) S(5)=$177.2 thousand.

Step-by-step explanation:

(a)

The salary increases by $2 thousand per year since 2008. Therefore, the completed table is below:

$\left|\begin{array}{c|c}-------&------\n$Years since 2008&$Salary (thousands of dollars)\n-------&------\n0&(2\cdot 0) + 167.2\n1&(2\cdot 1) + 167.2\n2&(2\cdot 2) + 167.2\n3&(2\cdot 3) + 167.2\n4&(2\cdot 4) + 167.2\nt&(2\cdot t) + 167.2\end{array}\right| \n$

Therefore, an expression that gives the salary (in thousands of dollars) of members of the two governing bodies t years since 2008 is:

$S(t)=2t+167.2$

(b)

When t=5

$S(5)=2*5+167.2\nS(5)=177.2$

This means that 5 years after 2008 (i.e Year 2013) the salary of members of the two governing bodies will be approximately$177.2 thousand.

Find the missing segment in the image below

Answers

the missing segment is 25

The missing segment is 25

Julio has $2.75 in his pocket in nickels and dimes. The number of dimes is 10 less than twice the number of nickels. Find the number of each type of coin.

Answers

Answer: Dimes= 20, Nickels= 15

Step-by-step explanation:

Since we are looking for the amount of coins, we can use system of equations to solve for the amount of coins.

Equation 1:

0.1x+0.05y=2.75

This equation comes from the total cost. x stands for dimes and y stands for nickels. 0.1 is the worth of a dime and 0.05 is the worth of a nickel.

Equation 2:

x=2y-10

This equation comes from 10 less than twice the number of nickels.

We can use substitution to find x and y.

0.1(2y-10)+0.05y=2.75

0.2y-1+0.05y=2.75

0.25y-1=2.75

0.25y=3.75

y=15

There are 15 nickels.

Now that we have y, we can plug it back into the equation to find x.

x=2(15)-10

x=30-10

x=20

There are 20 dimes.

Can some tell me how to do these

Answers

Never forget propertie of indices

The opening prices per share Y1 and Y2 of two similar stocks are independent random variables, each with a density function given by

Answers

Answer:given by what?

Choose correct way to rewrite 56% as a decimal number.A.
0.056
B.
0.56
C.
5.6

Answers

Answer:

The correct answer is: [B]: " 0.56 " .

Step-by-step explanation:

Note:

" 56% = " $((56)/(100))$ " ;

= (56) ÷ (100) = 0.56 ;

→ which corresponds to: " Answer choice: [B]: " 0.56 " .

______________________________________________

You would write 56% as 0.56.

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