I need help with this, pls put step by step
1 answer:
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Answer:
Option (1) is the correct option.
Step-by-step explanation:
From the given frequency table,
Option (1).
Tossing an even number is more likely than tossing an odd number.
Frequencies of tossing even numbers 2, 4, 6 = 10, 10, 9
Frequencies of tossing odd numbers 1, 3, 5 = 8, 6, 7
Which shows frequencies of tossing even numbers are more.
Therefore, Option (1) is correct.
Option (2)
The number 2 will be the next number tossed.
Since it is unpredictable, therefore, this option is incorrect.
Option (3)
Number 4 is half as likely to be tossed as the number 3.
Frequency of tossing number 3 = 6
Frequency of tossing 4 = 10
Frequency of tossing 3 is not the half of tossing 4.
Therefore, Option (3) is incorrect.
Option (4)
Probability of tossing the number 2 =
=
=
=
Therefore, option (4) is incorrect.
So for this, we will be using synthetic division. To set it up, have the equation so that the divisor is -10 (since that is the solution of k + 10 = 0) and the dividend are the coefficients. Our equation will look as such:
<em>(Note that synthetic division can only be used when the divisor is a 1st degree binomial)</em>
- -10 | 1 + 2 - 82 - 28
- ---------------------------
Now firstly, drop the 1:
- -10 | 1 + 2 - 82 - 28
- ↓
- -------------------------
- 1
Next, you are going to multiply -10 and 1, and then combine the product with 2.
- -10 | 1 + 2 - 82 - 28
- ↓ - 10
- -------------------------
- 1 - 8
Next, multiply -10 and -8, then combine the product with -82:
- -10 | 1 + 2 - 82 - 28
- ↓ -10 + 80
- -------------------------
- 1 - 8 - 2
Next, multiply -10 and -2, then combine the product with -28:
- -10 | 1 + 2 - 82 - 28
- ↓ -10 + 80 + 20
- -------------------------
- 1 - 8 - 2 - 8
Now, since we know that the degree of the dividend is 3, this means that the degree of the quotient is 2. Using this, the first 3 terms are k^2, k, and the constant, or in this case k² - 8k - 2. Now what about the last coefficient -8? Well this is our remainder, and will be written as -8/(k + 10).
<u>Putting it together, the quotient is </u>