1. Which events are dependent? I. flipping a coin multiple times II. picking even numbers,with replacement. III. picking odd numbers,without replacement. A. I only B. III only C. I and II D. II and III. 2.Which events are independent? I. flipping a coin multiple times II. picking coins, with replacement III. picking coins ,without replacement. A. I only B. II only C. I and II D. II and III and last one A spinner numbered 1 through 8 is spun 3 times. what is the probability of spinning an even number, then an odd number, and then an 8? Write your answer as a decimal. do not round. Please help me
Answers
Answer 1
Answer:
1). Flipping a coin or picking a number are not dependent. The probability of the result is the same every time. It only changes if you leave out what you picked the first time, because then the total number of possibilities is different. With this reasoning, they might say that iii. is dependent because you don't replace what you draw the first time. I'm not comfortable with that. Sure, you don't replace the first number you picked, but how many odd numbers are left ? Still an infinite number. So I think iii. is the answer they want here, but I don't think any of the choices is really dependent.
2). By the same reasoning, i. and ii. are independent. The coins have no memory. They don't remember what happened last time.
3). The probability of any result is
(number of successes)/(number of possibilities).
Total number of possibilities each time is 8.
Probability of an even number (2, 4, 6, or 8) the first time = 4/8 = 0.5
Probability of an odd number (1, 3, 5, or 7) the second time = 4/8 = 0.5
Probability of an 8 the third time = 1/8 = 0.125 .
Probability of all 3 events = (0.5) x (0.5) x (0.125) = 0.03125 (3.125%)
What is the least common denominator for adding the fractions 4/15, 1/12, and 3/8
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I think you want the least common multipule (exg LCM of 2,3,4 is 12)
so we find the factors and include all of them so like this
15=3 times 5 12=2 times 2 times 3 8=2 times 2 times 2
so to include all of them we include 3 2's, 1 3 and 1 5 or 2 times 2 times 2 times 3 times 5 or 8 times 15 or 4 times 30 or 120
the LCM is 120
so 4/15=32/120 1/12=10/120 3/8=45/120
add 32/120+10/120+45/120=(32+10+45)/120=87/120
The least common denominator would be the least common multiple (LCM) of the denominators, 15 12 and 8.
To find the LCM, multiply two of the numbers together and test to see if the third one divides evenly into it.
15 x 8 = 120
120 ÷ 12 = 10
Because all three numbers go evenly into 120 (and 120 is the smallest number for which that is true), the least common denominator would be 120.
To clean a tank, 3/4 cup of disinfectant is needed for every 2 gallons of water. How many cups of disinfectant are needed for 20 gallons of water?A. 7 1/2 B. 15 C. 22 1/2 D. 30
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Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of gallons of water.”How many cups of disinfectant are needed for 20 gallons of water so c is
I use ratio and proportionchanges 3/4= .75.75 cups/2 gallons= x cups/2o gallonscross multiply2x= 15x= 7 1/2 cupsalso there are 10 gallons for every 3/4 cup10 x 3/4= 30/4= 7 1/2I like ratio and proportion it's more consistent in solving lots of problemshope this helps
Please help asap Make sure to draw a table to visualize your data.You can use desmos to check your answers as well. When putting in the function into desmos, you must put it as (ex: y=30000*(1.04)^x) Desmos does not recognize other letters than x and y.