Can someone check these answers for me

The principal amount in the loan taken by Sharon is $750 . Note hat the $20 processing fee is a one time cost and is not included in the interest calculation.

Annual Rate of interest offered to Sharon is 12%

Time interval for the loan transaction is 1 year.

So the interest for 1 year is given by \[Principal * Rate * Year /100\]

\[750 * 12 * 1 /100\] = $90

So, Sharon will have to pay $90 as interest for the loan amount $750 borrowed for one year at the rate 12%.

8 0

2 years ago

A researcher asks random samples of residents of two separate counties as to whether they had purchased organically grown food i

Leni [432]

Answer:

2 proportions z test

The two populations are named as residents from the first county and residents from the second county.

Step-by-step explanation:

This is testing hypothesis about the difference between two proportions.

When the proportions are tested if they are the test statistic

z= ( p^1-p^2)- (p1-p2) / √p₁q₁/n₁ + p₂q₂/ n₂

where p^1 is the proportion of success in the first sample and p^2 of size n₁ is the proportion of success in the second sample of size n₂ with unknown proportions of successes p1 and p2 respectively.

When the sample sizes are sufficiently large

z= ( p^1-p^2)- (p1-p2) / √p₁q₁/n₁ + p₂q₂/ n₂ is approximately standard normal.

The two populations are named as residents from the first county and residents from the second county.

7 0

2 years ago

Your friend asks if you would like to play a game of chance that uses a deck of cards and costs $1 to play. They say that if you

gtnhenbr [62]

Answer:

Expected value = 40/26 = 1.54 approximately

The player expects to win on average about $1.54 per game.

The positive expected value means it's a good idea to play the game.

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Further Explanation:

Let's label the three scenarios like so

scenario A: selecting a black card
scenario B: selecting a red card that is less than 5
scenario C: selecting anything that doesn't fit with the previous scenarios

The probability of scenario A happening is 1/2 because half the cards are black. Or you can notice that there are 26 black cards (13 spade + 13 club) out of 52 total, so 26/52 = 1/2. The net pay off for scenario A is 2-1 = 1 dollar because we have to account for the price to play the game.

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Now onto scenario B.

The cards that are less than five are: {A, 2, 3, 4}. I'm considering aces to be smaller than 2. There are 2 sets of these values to account for the two red suits (hearts and diamonds), meaning there are 4*2 = 8 such cards out of 52 total. Then note that 8/52 = 2/13. The probability of winning $10 is 2/13. Though the net pay off here is 10-1 = 9 dollars to account for the cost to play the game.

So far the fractions we found for scenarios A and B were: 1/2 and 2/13

Let's get each fraction to the same denominator

1/2 = 13/26
2/13 = 4/26

Then add them up

13/26 + 4/26 = 17/26

Next, subtract the value from 1

1 - (17/26) = 26/26 - 17/26 = 9/26

The fraction 9/26 represents the chances of getting anything other than scenario A or scenario B. The net pay off here is -1 to indicate you lose one dollar.

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Here's a table to organize everything so far

$\begin{array}{|c|c|c|}\cline{1-3}\text{Scenario} & \text{Probability} & \text{Net Payoff}\\ \cline{1-3}\text{A} & 1/2 & 1\\ \cline{1-3}\text{B} & 2/13 & 9\\ \cline{1-3}\text{C} & 9/26 & -1\\ \cline{1-3}\end{array}$

What we do from here is multiply each probability with the corresponding net payoff. I'll write the results in the fourth column as shown below

$\begin{array}{|c|c|c|c|}\cline{1-4}\text{Scenario} & \text{Probability} & \text{Net Payoff} & \text{Probability * Payoff}\\ \cline{1-4}\text{A} & 1/2 & 1 & 1/2\\ \cline{1-4}\text{B} & 2/13 & 9 & 18/13\\ \cline{1-4}\text{C} & 9/26 & -1 & -9/26\\ \cline{1-4}\end{array}$

Then we add up the results of that fourth column to compute the expected value.

(1/2) + (18/13) + (-9/26)

13/26 + 36/26 - 9/26

(13+36-9)/26

40/26

1.538 approximately

This value rounds to 1.54

The expected value for the player is 1.54 which means they expect to win, on average, about $1.54 per game.

Therefore, this game is tilted in favor of the player and it's a good decision to play the game.

If the expected value was negative, then the player would lose money on average and the game wouldn't be a good idea to play (though the card dealer would be happy).

Having an expected value of 0 would indicate a mathematically fair game, as no side gains money nor do they lose money on average.

7 0

2 years ago