Algebra I test 10 problems explained

#7 A jar contains several marbles: 4 pink, 3 black, 5 purple, and 8 white. What fraction would represent the white marbles?

# of white = 8 total number = 4+3+5+8 = 20 8/20 reduces to 2/5

#20 If the required value of y is -108.5, use the fit line equation y = -2.61x + 152.51 to determine the needed x-value. Round to the nearest whole number.

-108.5 = -2.61x + 152.51 2.61x = 261.01 x = 100

A drawer contains 30 pens of various colors: 4 are black, 10 are blue, 3 are red, 6 are green, 6 are blue and red, and 1 is white #31 A black pen is removed from the drawer and is not replaced before a white pen is taken

P(black and white) = P(black) * P(white|black) = 4/30 * 1/29 =2/15 * 1/29 = 2/435

A drawer contains 30 pens of various colors: 4 are black, 10 are blue, 3 are red, 6 are green, 6 are blue and red, and 1 is white #29 A pen having blue or red is taken out of the drawer.

P(blue or red) = P(blue) + P(red) - P(blue or red) P(blue or red) = 16/30 + 9/30 - 6/30 = 19/30

A drawer contains 30 pens of various colors: 4 are black, 10 are blue, 3 are red, 6 are green, 6 are blue and red, and 1 is white #30 A green pen is removed from the drawer and replaced before a black pen is removed

P(green and black) = P(green) * P(black) = 6/30 * 4/30 = 1/5 * 2/15 = 2/75

#24 Determine the five-number summary of the data set: 10 11 15 19 21 23 24 25 25 28 32 33 36 38 38 43 45 46 47 49

five-number summary is: min-Q1-median-Q3-max min = 10 max = 49 median=30 [median is the center number of the data set; because the set is an even number, take the two center numbers (28, 32) and find their average (28+32=60 60/2=30)] Q1 = 22 [to find Q1, put parenthesis around all numbers below the median (10 11 15 19 21 23 24 25 25 28) and find the median of this set--it is an even number, so find the average of the two center numbers (21+23=44 44/2=22)] Q3 = 40.5 [this is the same process as used to find Q1, except you'll use the data above the median (32 33 36 38 38 43 45 46 47 49) 38+43=81 81/2=40.5

#19 The fit line equation for the scatterplot is y = -2.61x + 152.51 where x is Variable 1 and y is Variable 2. According to the equation, what is the expected value of y when the x-value is 45?

y = -2.62(45) + 152.51 y = -117.45 + 152.51 y = 35.06