# Tutor profile: Deniece W.

## Questions

### Subject: Statistics

A card is drawn randomly from a deck of ordinary playing cards. You win $10 if the card is a spade or a 10. What is the probability that you will win the game?

First we'll assign variables for each event. E - spade card F - 10 card P(E or F) = ? The Addition Rule is as follows: P(E or F) = P(E) + P(F) - P(E and F) Identify the individual components of the formula above: P(E) = 13/52 P(F) = 4/52 P(E and F) = 1/52 Plug in the probabilities into the formula: P(E or F) = (13+4-1)/52 = 16/52 = 0.3077 The probability that you will win the game is 0.3077

### Subject: Statistics

A sample consists of four observations: {1, 3, 5, 7}. Calculate the measures of central tendency: mean, median and mode.

To find the mean we will add the numbers and divide by the sample size. (1 + 3 + 5 + 7)/ 4 = 16/4 = 4 Mean = 4 The median is the midpoint of the data set. Since there are four numbers we will take the average of the two numbers in the middle. 3+5/2 = 4. Median = 4 The mode is the most frequently observed data value. Since there are no numbers that occur more than any other we conclude there is no mode.

### Subject: Algebra

Solve the equation: 5(-3x - 2) - (x - 3) = -4(4x + 13)

Step 1. Multiply to get rid of the parentheses. -3x(5) -2(5) -(x-3) = 4x(-4)+13(-4) -15x-10-x+3 =-16x-52 Step 2. Combine like terms -15x-x-10+3 = -16x-52 -16x-7=-16x-52 Step 3. Isolate the x variable by moving it to the other side of the equation. Then simplify. -16x+16x - 7 = -52 0x-7 = -52 0-7=--52 -7=-52 Step 4. Since the left side and the right side do not match. It is impossible that -7 = -52, we conclude that there is no solution to this problem.

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