Answer:
The 98% confidence interval for the mean number of hours of study time per week for all students is (20.9, 25.1).
Step-by-step explanation:
Confidence interval:
Sample mean plus/minus the margin of error.
In this question:
Mean of 23.
Margin of error 2.1.
Then
23 - 2.1 = 20.9
23 + 2.1 = 25.1
The 98% confidence interval for the mean number of hours of study time per week for all students is (20.9, 25.1).
An integer may be a multiple of 3.
An integer may be 1 greater than a multiple of 3.
An integer may be 2 greater than a multiple of 3.
It is redundant to say an integer is 3 greater than a multiple of 3 (that's just a multiple of 3, we've got it covered). Same for 4, 5, 6, 7...
Let's consider a number which is a multiple of 3. Clearly, we can write 3+3+3+3+... until we reach the number. It can be written as only 3's.
Let's consider a number which is 2 greater than a multiple of 3. If we subtract 5 from that number, it'll be a multiple of 3. That means we can write the number as 5+3+3+3+3+... Of course, the number must be at least 8.
Let's consider a number which is 1 greater than a multiple of 3. If we subtract 5 from that number, it'll be 2 greater than a multiple of 3. If we subtract another 5, it'll be a multiple of 3. That means we can write the number as 5+5+3+3+3+3+... Of course, the number must be at least 13.
That's it. We considered all the numbers. We forgot 9, 10, 11, and 12, but these are easy peasy.
Beautiful question.
the sequence of 5 numbers for the given rule and inital number is:
{1, -1, - 7, -25, -79}
<h3>How to find the first 5 numbers in the given sequence?</h3>
A sequence is a list of numbers in order, such that some rule is met.
in this case, the rule is:
"Each number is 4 less than 3 times the previous number".
And we are told to start with the number 1, so the second number will be:
n₂ = 3*(1) - 4 = -1
The third number will be:
n₃ = 3*(-1) - 4 = -3 - 4 = -7
The fourth number will be:
n₄ = 3*(-7) - 4 = -21 - 4 = -25
The fifth number will be:
n₅ = 3*(-25) - 4 = -79
Then the sequence of 5 numbers for the given rule and inital number is:
{1, -1, - 7, -25, -79}
If you want to learn more about sequences:
brainly.com/question/6561461
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Answer:
x = 11.5, y = -5.5.
As an ordered pair this is (11.5, -5.5).
Step-by-step explanation:
2x+4y=1 Multiply this by 3:
3x+5y=7 Multiply this by -2.
6x + 12y = 3
-6x - 10y = -14 Adding these 2 equations:
0 + 2y = -11.
y = -11/2
y = -5.5.
Now plug this into the first equation:
2x + 4(-5.5) = 1
2x = 1 + 22
x = 23/2
x = 11.5.