By remainder theorem:
f(x) = x³ - 2
factor, x - 1 = 0
x = 1,
Remainder = f(1)
f(x) = x³ - 2
f(1) = 1³ - 2 = 1 - 2 = -1.
Hence remainder is = -1.
Experimental probability = 1/5
Theoretical probability = 1/4
note: 1/5 = 0.2 and 1/4 = 0.25
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How I got those values:
We have 12 hearts out of 60 cards total in our simulation or experiment. So 12/60 = (12*1)/(12*5) = 1/5 is the experimental probability. In the simulation, 1 in 5 cards were a heart.
Theoretically it should be 1 in 4, or 1/4, since we have 13 hearts out of 52 total leading to 13/52 = (13*1)/(13*4) = 1/4. This makes sense because there are four suits and each suit is equally likely.
The experimental probability and theoretical probability values are not likely to line up perfectly. However they should be fairly close assuming that you're working with a fair standard deck. The more simulations you perform, the closer the experimental probability is likely to approach the theoretical one.
For example, let's say you flip a coin 20 times and get 8 heads. We see that 8/20 = 0.40 is close to 0.50 which is the theoretical probability of getting heads. If you flip that same coin 100 times and get 46 heads, then 46/100 = 0.46 is the experimental probability which is close to 0.50, and that probability is likely to get closer if you flipped it say 1000 times or 10000 times.
In short, the experimental probability is what you observe when you do the experiment (or simulation). So it's actually pulling the cards out and writing down your results. Contrast with a theoretical probability is where you guess beforehand what the result might be based on assumptions. One such assumption being each card is equally likely.
If you finish the question I may be able to answer it. ^^
Answer:
The total numbers of possible combinations are 3430.
Step-by-step explanation:
Consider the provided information.
A combination for 0 1 2 3 4 6 5 7 8 9 this padlock is four digits long. Because of the internal mechanics of the lock, no pair of consecutive numbers in the combination can be the same or one place apart on the face.
Here, for the first digit we have 10 choices.
For the second digit we have 7 choices, as the digit can't be the same nor adjacent to the first digit.
For the third digit we have 7 choices, as the digit can't be the same nor adjacent to the second digit.
For the fourth digit we have 7 choices, as the digit can't be the same nor adjacent to the third digit.
So the number of choices are:
Hence, the total numbers of possible combinations are 3430.
Considering the definition of an inequality, the maximum number of tickets that they can buy is 10.
<h3>Definition of inequality</h3>
An inequality is the existing inequality between two algebraic expressions, connected through the signs:
- greater than >.
- less than <.
- less than or equal to ≤.
- greater than or equal to ≥.
An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
<h3>Maximum number of tickets that they can buy</h3>
In this case, you know that
- One ticket to a ride of the merry-go-round at the Sunday Fair costs $2.
- Jenny and her friends have $36 with them.
- After buying tickets to the merry-go-round, they want to be left with no less than $15.
So, they want to spend on the purchase of tickets for the merry-go-round a value less than or equal to $36 - $15= $21.
Being "x" the maximum number of tickets that they can buy, the inequality that expresses the previous relationship is
2x≤ 21
Solving:
x≤ 21÷2
<u><em>x≤ 10.5</em></u>
Then, the maximum number of tickets that they can buy is 10.
Learn more about inequality:
brainly.com/question/17578702
brainly.com/question/25275758
brainly.com/question/14361489
brainly.com/question/1462764
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