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1. A game is set up as follows: All the diamonds are removed from a deck of cards, and these 13 cards are placed in a bag. The c

Maurinko [17]

Answer:

the game must be played in groups of 13 draws, with a cost of $28 for the 13 draws.

Step-by-step explanation:

Probability of drawing any of the 13 balls is the same. So the expected value of play is the average of the values of each card.

The only losing card is the ace; the player loses $20 if that card is drawn.

Each of the 3 face cards wins $10; each of the remaining 9 cards wins $2.

So the average value of each draw is

$\frac{-20+3\times10+9\times2}{13}$

= 28/13

Therefore, on average the player will win $ 28/13. to be a fair game the player must pay $28/13 for a game.

that is not possible, unless the game must be played in groups of 13 draws, with a cost of $28 for the 13 draws.

7 0

3 years ago

A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 4 hot dogs, 3 bags of potato chips, and 4 soft d

GuDViN [60]

The price of chips is $ 0.75, the price of a hot dog is $ 2 and the price of a soft drink is $ 1.25.

Step-by-step explanation:

Given,

A customer buys 4 hot dogs, 3 bags of potato chips, and 4 soft drinks for $15.25.

The price of a hot dog is $1.25 more than the price of a bag of potato chips.

The cost of a soft drink is $2.75 less than the price of two hot dogs.

To find the cost of each item.

Let,

The price of chips = x

The price of a hot dog = x+1.25

Price of two hot dog = 2(x+1.25) = 2x+2.5

The price of a soft drink = 2x+2.5-2.75 = 2x-0.25

Now,

According to the problem,

4(x+1.25)+3x+4(2x-0.25) = 15.25

or, 15x+5-1 = 15.25

or, 15x = 11.25

or, x = 0.75

Hence,

The price of chips = $ 0.75

The price of a hot dog = $ 0.75+1.25 = $ 2

The price of a soft drink = $ 2×0.75-0.25 = $ 1.25

5 0

3 years ago

In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t 2 , 2 + t − 5t 2 , 1 + 2t} to the standard basis of P2.

Serjik [45]

Complete Question:

In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t² , 2+t− 5t² , 1 + 2t} to the standard basis C = {1, t, t²}. Then, write t² as a linear combination of the polynomials in B.

Answer:

The change of coordinate matrix is :

$M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]$

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

Step-by-step explanation:

Let U = {D, E, F} be any vector with respect to Basis B

U = D [1 − 3t²] + E [2+t− 5t²] + F[1 + 2t]..............(*)

U = [D+2E+F]+ t[E+2F] + t²[-3D-5E]...................(**)

In Matrix form;

$\left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right] \left[\begin{array}{ccc}D\\E\\F\end{array}\right] = \left[\begin{array}{ccc}D+2E+F\\E+2F\\-3D-5E\end{array}\right]$

The change of coordinate matrix is therefore,

$M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]$

To find D, E, F in (**) such that U = t²

D + 2E + F = 0.................(1)

E + 2F = 0.........................(2)

-3D -5E = 1........................(3)

Substituting eqn (2) into eqn (1 )

D=3F...................................(4)

Substituting equations (2) and (4) into eqn (3)

-9F+10F=1

F = 1

Put the value of F into equations (2) and (4)

E = -2(1) = -2

D = 3(1) = 3

Substituting the values of D, E, and F into (*)

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

3 0

3 years ago

Initially, there were equal amount of roses and tulips at a store. Each bouquet was made with 3 roses and 4 tulips. After the bo

egoroff_w [7]

Answer:

12 bouquets

Step-by-step explanation:

Let there be x number of roses and x number of tulips initially at the store. Each bouquet was made with 3 roses and 4 tulips. Assume that y bouquets were made in total.

If each bouquet was made with 3 roses and 4 tulips, then y bouquets will be made with 3y roses and 4y tulips.

After the bouquets were all made, there were 30 roses and 18 tulips left in the store. This means, if we subtract number of roses that were used in bouquets from total number of roses, the result must be 30. Likewise, for tulips the result would be 18. This can be represented as:

x - 3y = 30 Equation 1

x - 4y = 18 Equation 2

Subtracting Equation 2 from Equation 1, we get:

x - 3y - (x - 4y) = 30 - 18

x - 3y - x + 4y = 12

y = 12

Since y represents the number of bouquets made, we can conclude that 12 bouquets were made in the store.

5 0

3 years ago

Read 2 more answers

In a class test of 15 questions, (+4) marks are given for every correct answer, (– 2) marks are

romanna [79]

If he answered 3 questions correctly, then the number of questions is got wrong is 7 and the number of questions that he did not attempt is 5.

<h3>What is the linear system?</h3>

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

In a class test of 15 questions, (+4) marks are given for every correct answer, (– 2) marks are given for every incorrect answer, and 0 marks are given for questions that are not attempted. Punit scored (– 2) marks.

If he answered 3 questions correctly, then the number of the question are got wrong and the number of the question that he did not attempt.

Let x be the correct question and y be the incorrect question, z be the number of questions that he did not attempt, and A be the number of the total score. Then we have

4x – 2z = A

x + y + z = 15

If A = -2 and x = 3, then we have

4 × 3 – 2z = -2

12 + 2 = 2z

z = 7

Then the value of y will be

3 + y + 7 = 15

y = 5

More about the linear system link is given below.

brainly.com/question/20379472

#SPJ1

3 0

2 years ago