Sum/difference:
Let

This means that

Now, assume that
is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that
was rational, which proves that the sum/difference of the two given terms was irrational
Multiplication/division:
The logic is actually the same: if we multiply the two terms we get

if again we assume x to be rational, we have

But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.
X^2 + y^2 - 2x + 8y - 47 = 0
x^2 + y^2 - 2x + 8y = 47
(x^2 - 2x) + (y^2 + 8y) = 47
(x^2 - 2(1)x) + (y^2 + 2(4)y) = 47
(x^2 - 2(1)x + 1^2) + (y^2 + 2(4)y + 4^2) = 47 + 1^2 + 4^2
(x - 1)^2 + (y + 4)^2 = 64 = 8^2
r=8
Marked(10)/total = 3/20 (from sample)
total/10 = 20/3 (inverting the above proportion)
total = 10•20/3 = 200/3 ≈ 67
Answer:
50
Step-by-step explanation:
Angle 1 is 110.
Angle 3 is 2x plus 10.
Angle 1 and 3 are vertically opposite angles.
And vertically opposite angles r equal.
Which means, angle 1=angle 3,and angle 2=angke 4.
Here we only Need angle 2 and 3.
Angke 2= angle 3.
Which is 2x plus 10=110.
Therefore 2x=110-10=100
Therefore x = 100÷2=50
There u have it ma'am.
Following are the solution parts for the given question:
For question A:
In the given question, we calculate
of the confidence interval for the mean weight of shipped homemade candies that can be calculated as follows:

Using the t table we calculate
When
of the confidence interval:
So
confidence interval for the mean weight of shipped homemade candies is between
.
For question B:

Here we need to calculate
confidence interval for the true proportion of all college students who own a car which can be calculated as

Using the Z-table we found
therefore
the confidence interval for the genuine proportion of college students who possess a car is
So
the confidence interval for the genuine proportion of college students who possess a car is between 
For question C:
- In question A, We are
certain that the weight of supplied homemade candies is between 392.47 grams and 427.53 grams. -
In question B, We are
positive that the true percentage of college students who possess a car is between 0.28 and 0.34.
Learn more about confidence intervals:
brainly.in/question/16329412