2x^2-8x-24=0
Divide the whole equation by 2.
x^2-4x-12=0
Complete the square
x^2-4x+4-16=0
(x-2)^2 -16=0
(x-2)^2=16
Take the square root of each side.
(x-2)=4 and (-(x-2))=4
x=6 and x=-2
Answer:
B.
Step-by-step explanation:
Total coins = 11 ( 3 + 4 + 4 = 11).
The probability of picking a nickel first = 3/11 ( 4 nickels out of 11 total).
The probability of picking a dime second = 4/10 = 2/5 ( 3 dimes out of 10 coins left).
The probability of picking the third coin as a quarter = 4/9 ( 3 quarters out of 9 coins left).
The probability of picking all three in that order = 3/11 x 2/5 x 4/9 = 8/165
Part A:
Given the ratio 1 : 2, we can describe this ratio with the following situation.
The number of green balls to orange balls in the bag is in the ratio of 1 : 2. For every green ball in the bag, there are 2 corresponding orange ball.
Part B:
Given the ratio 29 : 30, we can describe this ratio with the following situation.
The ratio of the amount of sugar used to the amount of salt used to prepare the sugar-salt solution is 29 : 30. For every teaspoons of sugar used in the solution, 30 teaspoons of salt needs to be used.
Part C:
Given the ratio 52 : 12, we can describe this ratio with the following situation.
The
number of kilometers travelled by the car and the bicycle is in the ratio of 52 :
12. For every 52 kilometers travelled by the car, the bicycle travelled 12 kilometers.
45th percentile means that 45% of the data fall below that number while 55% (that is, 100-45) fall above it.
Now, arranging the number in ascending order;
$60, $85, $95, $105, $120, $145, $155, $175, $190, $215, $235, $240, $260, $285, $325
The total number of counts = 15
Then,
Index = 15*45% = 15*0.45 = 6.75
Round up,
Index = 7
The,
7th number = $155
Therefore, 45th percentile value of the data = $155
